Essay: Automatic Modulation Recognition (AMR)

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CHAPTER 1
INTRODUCTION
Automatic Modulation Recognition (AMR) plays an important role in signal surveillance, frequency spectrum and radio monitoring. Monitoring and control of radio communication is important for both the civilian and military domain. For the civilian authorities this includes signal confirmation, interference confirmation and spectrum management. In connection with the requirement for faster and more reliable communication, the digital processing methods and digital communications are mainly used. Together with the rapid growth of cellular technologies, Personal Communication Services (PCS) and Wireless Local Area Network (WLAN) services in the last decade, a number of different wireless communication standards were proposed and employed. To realize a seamless intercommunication between these different systems, a multiband, multimode smart radio system, such as software radio, is becoming the focus of commercial and research interests.
The role of modulation recognition is to determine the modulation type and associated parameters from a received signal. Automatic Modulation Recognition (AMR) plays an important part in future 4G software radios. The general idea behind the Software Defined Radio (SDR) architecture is to perform considerable amount of signal processing in software instead of it being defined in hardware. This would enable the radio to adapt to changing environment and user requirement by simply updating the software. A receiver incorporating AMR can handle this in real time. Automatic recognition of digital communication signals is used nowadays in various applications such as electronic warfare, surveillance, and threat analysis and spectrum management.
1.1 DIGITAL COMMUNICATION SYSTEM
A typical digital communication system is presented in Fig.1.1. It describes how a communications signal is transmitted from an information source, a transmitter, through a channel, finally to the receiver. Communication basically means transmission of binary sequences {bi}. Such sequences are encoded prior to transmission to make the digital signal more robust to noise, interference and other channel distortions. The resulting signal di(t) is modulated by a sinusoidal carrier and passed through transmission filter to limit the signal bandwidth prior to transmission. The transmitted signal si(t) reaches the receiver end with distortion which may be due to noise or other narrowband signal interferences.
Fig 1.1: Digital Communication System
When a signal travels through a propagation channel, there are noises, distortions, reflections, delays, attenuations and other phenomenon which interfere with the signal of interest. One primary source of interference is thermal noise. Thermal noise is usually modeled using Additive White Gaussian Noise (AWGN). Another phenomenon that can occur in the channel, through which a signal is traveling toward its receiver, is fading. Fading occurs when the amplitude and phase of a signal changes rapidly over short periods of time. It is caused when a signal and a delayed version of itself arrive at the destination at different times. Fading can be caused by
buildings
mountains
weather ; and
the transmitter being in relative motion with the receiver, thus resulting in Doppler shifts.
At the receiver end of a successful communication system, the digital demodulator processes the channel corrupted transmitted waveform and reduces the waveform to a sequence of numbers that represents estimates of the transmitted data symbols. This sequence of numbers is passed through the channel decoder, which attempts to reconstruct the information sequence bi(t) that was originally sent.
1.1.1 Digital Modulation Techniques
Almost all modern communication systems use digital modulation techniques as they offer numerous advantages over analog systems. Digital modulation techniques offer greater noise immunity to channel distortions, easier multiplexing of various forms of information and greater security. Ideally, a desirable modulation scheme provides low bit error rates at low received signal to noise ratio, good performance in multipath and fading conditions, and is easy and cost effective to implement. Existing modulation schemes do not simultaneously satisfy the entire requirement. Some are better in bit error rate performance, while others offer better bandwidth efficiency. Hence trade-offs need to be made while selecting digital modulation schemes.
Digital modulation Techniques are classified as constant envelope and non-constant envelope. Under constant envelope class, there are three subclasses: FSK, PSK, and CPM. Under non-constant envelope class, the subclasses are: ASK QAM, and other non-constant envelope modulations (Proakis, 1995). Among the listed schemes, ASK, PSK, and FSK are basic modulations, and MSK, GMSK, CPM and QAM, etc. are advanced schemes. The generic non-constant envelope schemes, such as ASK and QAM, are generally not suitable for systems with nonlinear power amplifiers. However QAM, with a large signal constellation, can achieve extremely high bandwidth efficiency. M-ary QAM has many practical applications which require higher data rates like ADSL, modems, digital CATV applications, HDTV systems.
The PSK schemes have constant envelope but discontinuous phase transitions from symbol to symbol. M-ary PSK schemes are used in quasi-optical wireless array applications, compressed image communication in mobile fading channel, space applications, Tracking and Data Relay Satellite System (TDRSS), telemetry with high performance wireless MEMS strain-sensing applications, communication systems like TDMA and land mobile satellite communication links. M-ary FSK modulation is not particularly spectral efficient, but offers advantage such as immunity to amplitude noise, bit rate higher than baud rate and constant transmitter power. M-ary FSK modulation is widely applied in power limited systems such as deep space probes, satellites and space telemetry where link capacity may be enhanced at the cost of required transmission bandwidth.
1.2 AUTOMATIC MODULATION CLASSIFICATION (AMC)
Automatic Modulation Classification (AMC) or Recognition (AMR) is the process of deciding, based on observations of the received signal, what modulation is being used at the transmitter. It has long been an important component of noncooperative communications in which a listener desires to intercept an unknown signal from an adversary. It is also becoming increasingly important in cooperative communications, with the advent of the software-defined autonomous radio. Such a radio must configure itself based on the incoming signal and identify the signal class.
Radio monitoring of multiple standards certainly needs the identification of modulation technique for accurate reception of the signal. Integration of the receivers for software based radio would require the identification of multiple modulations at the receiving end. Meaning thereby, an intelligent algorithm identifying the modulation must be running at the receiver end. AMR is the key technology that helps for dynamically changing the function of radio and reacting to the changes in the intercepted signal. Blind Modulation Recognition techniques can be used with an intelligent receiver yielding an increase in transmission efficiency by reducing overhead as it does not use any explicit signaling to indicate modulation signal. The blind modulation detector has to determine the type of modulation used within the information conveyed by the least possible number of received samples. Automatic Modulation Classification is an intermediate step between signal detection and demodulation.
1.3 SOFTWARE DEFINED RADIO (SDR)
With the rapid growth of radio communication technologies, a concept of SDR has been introduced to integrate wireless applications working over any air interface and protocol. In order to realize the adaptive receiver, it is required to identify the digital modulation type of a signal.
A Software-Defined Radio consists of a programmable communication system where functional changes can be made by merely updating software. An SDR system is a radio communication system which can tune to any frequency band and receive any modulation across a large frequency spectrum by means of a programmable hardware which is controlled by software. The hardware of SDR typically consists of a Superheterodyne RF front end which converts RF signals from (and to) IF signals.
1.4 RELATION BETWEEN AMC AND SDR
The relation between AMC and SDR is presented in Fig. 1.2. The RF front end amplifies the signal from the antenna and performs filtering if required. Signal is downconverted to Intermediate Frequency (IF) range and digitized using Analog to Digital (A/D) convertor. Software processing is done through Digital Signal Processor (DSP) or General Purpose Processor (GPP) of which AMC is a major part.
Fig 1.2: Relation between AMC and SDR
The software processing may also include estimation of parameters such as carrier frequency, symbol rate, SNR etc. Suitable features are extracted from the received signals which are used to classify modulated signals. The estimated parameters may be required for demodulation process.
1.5 MOTIVATION TO RESEARCH
Wireless systems are gravitating towards minimal radio hardware designs using flexible architecture software radio. This will greatly simplify the design of a radio system since typical hardware radio components are replaced by software designs. For example, a hardware implementation of a Frequency Modulation (FM) receiver typically uses an integrated circuit to perform signal demodulation. Conversion of this receiver to some other modulation scheme e.g. Amplitude Modulation (AM), requires a physical change to the circuit, which can be difficult or even impossible. Two separate receivers, one AM and other FM are therefore required. The alternative is to convert the hardware demodulation functions to software realizations. Conversion of this software receiver to other modulation schemes is greatly simplified because a change in the software algorithm is all that is required.
Classifying signal types is of high interest in various application areas such as imaging, communication control target recognition and SDR. Hence, the digital modulation recognizers have critical importance. SDR can provide the standard communication platforms which enables non-restrictive wireless roaming across numerous radio technologies such as TDMA, CDMA and GSM.
1.6 PROBLEM STATEMENT AND FOCUS AREA
Automatic Modulation Recognition (AMR) is a procedure performed at the receiver based on the received signal before demodulation when the modulation format is not known to the receiver. The ability to automatically select the correct modulation scheme used in an unknown received signal is a major advantage in a wireless network. Without any knowledge of the transmitted data and many unknown parameters at the receiver, blind identification is a difficult task. Classification process is even more challenging in real world scenarios particularly with multipath fading, frequency selective, and time varying channels.
A significant body of work exists in this area, however most of it deals with small number of symbol states M, relatively clean channel characteristics, or require large amount of data. Maximum classification algorithms developed work only in the presence of AWGN. There are few algorithms that work under conditions of both AWGN and fading environment, still the number of class problems and the lower limit of SNR varies for all. Most of the existing algorithms assume prior knowledge of some parameter such as carrier frequency symbol rate etc. Algorithms which are completely blind in nature need to be developed.
This research first investigated selection of well defined features which are robust to channel variations. A classification procedure was then designed which was applied under realistic channel conditions such as low SNR and multipath fading effect. Carrier Frequency Estimation (CFE) was done using cyclostationary analysis. The objective of the research was to develop, an Automatic and Blind recognition system adaptive to SDR, which can discriminate the digitally modulated signals at the receiver end at low SNR. Ten modulated signals 2ASK, 4ASK, 2PSK, 4PSK, 2FSK, 4FSK, 16QAM, 64QAM, 256QAM, and GMSK were generated and tested for classification.
1.7 APPROACH TO AMC: BRIEF OVERVIEW
The generic pattern classification approach at the receiver end is presented in Fig. 1.3. It consists of mainly three steps:
Signal Preprocessing
Feature extraction and
Classification.
Fig 1.3: Generic Classification Approach
1.7.1 Communication Signal Preprocessing
During the transportation of radio signal in the channel, it gets distorted by noise, fading and large amplitude peaks. The receiver down converts the signal to lower Intermediate Frequency (IF) to adapt to the principle of SDR and IQ decomposes the signal. Once decomposed any form of processing can be done on the signal. Crucial component for implementing a successful AMC is the preprocessor. The main preprocessing requirement for modulation classification is to obtain a signal representation that will reduce degradations. The issues typically addressed at the preprocessor stage are filtering and denoising of signal, estimation of some of the main signal parameters like carrier frequency, bandwidth, and symbol rate or signal to noise ratio. Interference from unwanted signals may disturb the reception of the target signal. Multipath transmission channels will result in fading and introduce propagation degradations in the signal.
The preprocessing task carried out in the present work was signal denoising using wavelet decomposition, carrier frequency estimation and signal equalization. The carrier frequency estimator is based on the phases of the autocorrelation functions of the received signal. A blind carrier frequency estimation algorithm has been developed. The algorithm was tested on generated modulated signals under varying SNR conditions. Equalization of higher order signals was done using Constant Modulus Algorithm (CMA) which belongs to the category of blind Equalization techniques.
1.7.2 Feature Extraction
Features of modulated signals are broadly classified into two categories:
Time domain features: are instantaneous amplitude, frequency, phase and zero crossing time sequence. Standard deviation of instantaneous amplitude, phase and frequency, kurtosis of instantaneous amplitude and frequency, and spectrum symmetry are some of the time domain features used to classify modulated signals.
Frequency domain features: Transform based features are Fast Fourier Transform (FFT) based and Wavelet Transform (WT) based. FFT is used for stationary spectrum and WT for non stationary spectrum. Higher Order Statistical (HOS) parameters such as higher order moments and cumulants are also used as features. Radio signals have the characteristic of being cyclostationary, i.e., the covariance and spectrum varies periodically with time. Whereas some of the feature extraction methods proposed in the literature assume full a priori knowledge about the communication signal i.e. frequency bandwidth symbol rate synchronization etc. while in others, features can be extracted with little or no a priori knowledge.
Time domain features and frequency domain features are presented in Fig. 1.4.
Fig 1.4: Classification of Features of Modulated Signals
In the present work, instantaneous features such as amplitude, frequency and phase were first derived. Stochastic features were calculated based on instantaneous features. Combination of Stochastic features and higher order statistical parameters such as moments and cumulants were used to classify modulated signals. Seven key features used to classify modulated signals are:
Feature vector 1 is the Maximum Value of Power Spectral Density (PSD) of Normalized-Centered Instantaneous Amplitude. It represents the variations in amplitude, which makes this feature useful to discriminate between amplitude and non-amplitude modulations.
Feature vector 2 is the standard deviation of the absolute value of the normalized- centered instantaneous amplitude of a signal segment (). This feature was used to distinguish 2ASK from 4ASK and to classify GMSK signal.
Feature vector 3 is the standard deviation of the centered non-linear component of the absolute instantaneous phase (. This feature provides a clear distinction between 2PSK and 4PSK signal. It value is smaller for modulation class 2PSK/M-QAM and large for M-FSK/ 4PSK.
Feature vector 4 is the standard deviation of the centered non-linear component of the direct (not absolute) instantaneous phase (. The value of this feature reduces to zero for M-ASK and nonzero for others.
Feature vector 5 is the standard deviation of the absolute value of the normalized- centered instantaneous frequency of a signal segment (This is the only feature which distinguishes 2FSK from 4FSK signal.
Feature vector 6 is Eight Order moment (E S,8,4). This feature classifies 16QAM and 64 QAM in one category and 256 QAM in another category.
Feature vector 7 is Eight order cumulant (C S, 8,4) was used to separate 16QAM and 64QAM signal. These features were found to have robust and unique property as the variation in their values in presence of noise and fading was small.
1.7.3 Modulation Classification Techniques
Different ways of categorizing classifiers are into statistical, decision theoretic, fuzzy, or neural network based approach. It cannot be stated that a single classifier is superior to other for all types of problems. Due to its simplicity and good classification abilities, the decision theoretic approach has been popular for modulation classification. Recently, fuzzy logic-based modulation classifiers have also been proposed. Artificial Neural Network (ANN) is a well known mathematical model based on Biological neural network. Decision tree classifier based on threshold values and pattern recognition based neural network classifier has been developed for similar set of conditions and their performances were compared.
1.8 ORGANIZATION OF THESIS
The remainder of this thesis is organized as follows:
Chapter 2 provides overview of work done in the area so far. Year wise survey of developmental attempts is given. Significant contribution and their results are discussed. An elaborate survey is done on feature based techniques used to develop the classifier under various channel conditions. Topic wise literature is shown to get the in depth idea about approach taken by different researchers.
Chapter 3 addresses various digital modulation techniques and their generation. Each modulation type is reviewed and their key properties are derived to show their importance in the modulation classification. The transmission filter effects and mathematical formulation of channel effects such as AWGN and multipath (Rayleigh) fading adopted are discussed. Preprocessing and carrier frequency estimation algorithm are discussed.
Chapter 4 discusses the various features extracted to construct a classifier. Combination of spectral and higher order statistical features is used to construct the classifier. Decision tree based classifier and Neural network based classifier has been developed based on above features and their performances compared.
Chapter 5 illustrates various intermediate and final classifier results. Confusion matrix for all signals was obtained for SNR varying from 20 dB to -5dB under three varying channel effects. Percentage of correct classification was evaluated based on confusion matrix, for different SNR for both Decision Tree and Neural Network based classifier.
Chapter 6 summarises the main outcomes of the work based on performance of different methods. This chapter also discusses potential future directions and Scope for future research in this field.
CHAPTER 2
REVIEW OF LITERATURE
Modulation recognition has been an area of ongoing research for over two decades. As a result, there are numerous methods that have been developed to estimate the modulation scheme of an unknown signal. Each method makes a set of assumptions in order to make a classification, and generally only operates reliably under the limited scenario for which it is designed. The design of a modulation classifier essentially involves two steps: signal preprocessing and proper selection of the classification algorithm. Automatic modulation recognition is an intermediate step between signal detection and demodulation, and plays a key role in various civilian and military applications. Though the earliest work in this area was about three decades ago (Weaver et al., 1969) however, it was not until late 1980’s when more researchers paid their attention to the AMR of communication signals.
There are two approaches to the modulation classification problem.
Likelihood-Based (LB) approach or Decision-theoretic approach.
Feature Based (FB) approach or Statistical pattern recognition.
2.1 LIKELIHOOD BASED APPROACH
The Likelihood Based (LB) approach is based on likelihood ratio, which is to identify the modulation type of a signal through the maximum likelihood ratio of selecting signals and known signals. Within the LB framework, AMC is a multiple composite hypothesis-testing problem. The idea behind the LB-AMC is that the Probability Density Function (PDF) of the observed waveform, conditioned on the embedded modulated signal, contains all information for classification. Depending on the model chosen for the unknown quantities, three LB-AMC techniques are proposed in the literature: Average Likelihood Ratio Test (ALRT), Generalized Likelihood Ratio Test (GLRT) and Hybrid Likelihood Ratio Test (HLRT), Quasi ALRT and Quasi HLRT.
Generative algorithms perform the classification based on probabilistic models that are typically constructed by estimating probability distributions for each class separately. Examples are Naive Bayes (Tan et al., 2006), hidden Markov models obtained with maximum likelihood estimation (Bremaud, 2010) and methods that use likelihood ratio tests such as the ALRT (Su et al., 2008), GLRT (Xu et al., 2011) and HLRT (Polydoros, 2000). Dobre et al. (2006) investigated classification of linear digital modulations in slowly varying flat fading channels. With unknown channel amplitude, phase and noise power at the receive-side, HLRT and Quasi HLRT (QHLRT) based classifiers were developed. The classifiers performance versus computational complexity was discussed. It was shown that the QHLRT algorithm provides a low computational complexity solution, yet yielding performance close to the HLRT algorithm.
Quinghua and Karasawa (2008) considered modulation classification for (QAM) formats. The received signal was assumed to be unsynchronized in both time and frequency, since in practice the receiver has little prior knowledge about the transmitted signal. To tackle this problem, a classifier was proposed based on a combination of blind time synchronization, differential processing, and Maximum Likelihood (ML) detection. A computationally efficient scheme was then developed. Numerical results justified the approach. Su et al. (2008) described a likelihood test based modulation classification method for identifying the modulation scheme of a Software-Defined Radio (SDR) in real-time without pilot symbols between transmitters and receivers. The work converted an unknown signal symbol to an address of the Look-Up Table (LUT), loaded the pre-calculated values of the test functions for the likelihood ratio test, and produced the estimated modulation scheme in real-time. The statistical performance of the LUT based classifier was studied. Simulation results were presented to confirm the theoretical analysis.
Hamid et al. (2009) explored Likelihood-based algorithms for linear digital modulation classification. HLRT and QHLRT based algorithms were examined, with signal amplitude, phase, and noise power as unknown parameters. The algorithm complexity was first investigated, and findings showed that the HLRT suffers from very high complexity, whereas the QHLRT provided a reasonable solution. Classification of BPSK and QPSK signals was presented as a case study. Method-of-Moments (MoM) estimates of the unknown parameters were investigated and used to develop the QHLRT-based algorithm.
A single-sensor setting and a multi-sensor setting that uses a distributed decision fusion approach was analyzed. For a modulation classi’cation system using a single sensor, it was claimed that HLRT achieves asymptotically vanishing probability of error (Pe) whereas the same result cannot be proven for ALRT. In a multi-sensor setting using soft decision fusion, conditions were derived under which Pe vanished asymptotically. Furthermore, the asymptotic analysis of the fusion rule that assumed independent sensor decisions was carried out (Ozdemir et al., 2012).
Xiaoyan and Xiyuan (2012) proposed a new likelihood based method for classifying phase modulated signals in Additive White Gaussian Noise. Their method introduced the new Markov chain Monte Carlo algorithm called additive metropolice algorithm to directly generate the samples of the target posteriori distribution and implement the multidimensional integrals of likelihood functions. Simulation result justified that the method had high accuracy and robustness to phase and frequency offset.
An algorithm for the classification of QAM signal in the presence of Gaussian noise was proposed. The additive noise was modeled by Gaussian mixture distribution. A log likelihood algorithm was used to classifying the signal on the basis of decision ‘theoretic approach and developed a schematic structure of classifier for M-ary QAM signals. The performance was evaluated in terms of probability of successful classification. The performance of the classifier was based on the amplitude density function of received signal. The probability of correct classification was obtained for different sample size of 100, 300, 500 and 700. More than 90% result was achieved for sample size 700 at -2 dB SNR (Bishnoi et al., 2013).
Kebrya and Kim (2013) investigated Likelihood-based algorithms for the classification of linear digital modulations systematically for a multiple receive antennas configuration. Existing Modulation Classification (MC) algorithms were first extended to the case of multiple receive antennas and then a critical problem was identified. To address the performance degradation issue, they proposed a new MC algorithm by optimally combining the Log Likelihood Functions (LLFs). It was demonstrated that the probability of correct classification of the new algorithm approached the theoretical bounds and a substantial performance improvement was achieved compared to the existing MC algorithm.
LB method is based on the statistical character of analyzed signals, resulting in optimum classifier. The optimal solution however suffers from computational complexity. On the other hand, an FB algorithm employs one or several features extracted from the received signal to make decisions. These employed features are generally chosen in an ad-hoc way. Even though the FB methods may not be optimal, they are generally simple to implement, with near-optimal performance, when designed properly.
2.2 FEATURE BASED APPROACH
Since the main differences between the approaches proposed by the referred authors are the features they used, the main part of the survey consists in presenting these features and the corresponding results. There is a large variation in the literature about the features used for modulation classification. The features can be divided into two main groups
Time domain features; and
Frequency domain features.
The statistical pattern recognition or FB approach is divided into two parts. The first is a feature extraction part and its role is to extract the predefined feature from the received data. The second is a pattern recognition part, whose function is to classify the modulation type of a signal from the extracted features. The design of a FB algorithm first needs some features for data representation and then decision making. Once the modulation format is correctly identified, other operations, such as signal demodulation and information extraction, can be subsequently performed.
Examples of features are the variance of the zero-crossing interval (Hsue and Soliman, 1989), the variance of the centered normalized signal amplitude, the correlation between the in-phase and quadrature signal components, phase and frequency, the variance of the magnitude of the signal Wavelet Transform (WT) after peak removal, the phase PDF and its statistical moments and cumulants.
Some of the earlier work on feature based classification has been reviewed. Nagy (1996) presented a unified view on modulation classification. The work described fundamental principle types of features used for classification and algorithm structure. Several schemes to classify ??S??2, ??S??4, PSK2, PSK4, FS??2 and FS??4 signals were proposed. Combination of time and frequency domain features was used to develop classifier for both analog and digital modulation techniques (Azzouz and Nandi, 1996). Extensive survey has been presented for both analog and digital classification. The two general classes of automatic modulation identification algorithms were discussed in detail, which rely on the likelihood function and features of the received signal, respectively. The contributions of numerous articles were summarized in compact forms (Dobre et al., 2007).
An overview of Feature-Based (FB) methods developed for Automatic classification of digital modulations has been presented. Only the most well-known features and classifiers were considered, categorized, and defined. The features included Instantaneous Time Domain (ITD) parameters, Fourier Transform (FT), Wavelet Transform (WT), Higher Order Moments (HOM) to name a few. The classifiers discussed were Artificial Neural Networks (ANN), Support Vector Machines (SVMs) and Decision Tree (DT). The advantages and disadvantages of each technique in classifying a certain modulation scheme were also presented (Hazza et al., 2013).
2.2.1 Time Domain Features
To extract the information contained in instantaneous amplitude, phase and frequency of the signal, different methods were applied by researchers.
Hue and Soliman (1990) employed various differences between signal classes for identification of modulated schemes. The variance of the zero-crossing interval was used as a feature to distinguish FSK from PSK and the unmodulated waveform. They observed that zero-crossing interval is a staircase function for FSK signals, whereas a constant for unmodulated waveform and PSK signals. From the simulation results, it was claimed that successful modulation classification was achievable for SNR>15 dB.
In the proposed method the counts of signals falling into different parts of the signal plane were used to identify the digital modulation types. These methods were either computationally intensive or required a high Carrier-to-Noise Ratio (CNR) (Huo and Donoho, 1998). Wong and Nandi (2001) developed a classifier to discriminate FSK and ASK signals. FSK signals are characterized by constant instantaneous amplitude, whereas ASK signals have amplitude fluctuations, and PSK signals have information in the phase. The maximum of the Discrete Fourier Transform (DFT) of centered normalized instantaneous amplitude was used as a feature to distinguish between FSK and ASK/ PSK classes. A Multi Layer Perceptron (MLP) recognizer was implemented for recognizing ten different modulation types. Simulations achieved 98% success rate at 0 dB SNR.
A new algorithm termed as Histogram-Count Modulation Identification was proposed. In the algorithm, the modulating parameters were considered as the identification parameters for fourteen digital modulation techniques (Rashid et al., 2003). An AMR algorithm that is able to discriminate between analog communication signals and digital communication signals was developed. The proposed algorithm was able to recognize the concrete modulation type if the input is an analog communication signal and to estimate the number of modulation levels and the frequency deviation if the input is an exponentially modulated digital communication signal. For linearly modulated digital communication signals, the proposed algorithm classified them into one of several nonoverlapping sets of modulation types. In addition, in M-ary FSK (MFSK) signal classification, two classifiers were developed. These two classifiers were capable of providing good estimate of the frequency deviation of a received MFSK signal. A blind carrier frequency estimation algorithm and a blind symbol rate estimation algorithm were developed (Yu et al., 2004).
A general digital modulation recognition method was proposed for common M-ary digital modulations. A coarse recognition was executed, and different algorithms were used to estimate the order of modulation. The estimation method of the number of spectrum peaks was modified and a novel recognition algorithm of modulation order of MASK and MQAM was presented. Simulations results proved that the recognition rate of recognition structure and algorithm reached 92% for MFSK, MPSK and MASK when the SNR was above 6 dB. For MQAM, a higher SNR was required. The simulations considered only AWGN channel (Youyong et al., 2008).
A new recognition algorithm to the symbol shaped signals was presented, in which eight digital modulation types were classified. The computer simulation results showed that, the algorithm had a good recognition performance for the shaped signals, further more it had a better recognition performance than the methods without consideration of the symbol shape (Fu-qing et al., 2008). Vito (2010) presented a prototype of an automatic digital modulation classifier based on Real-Time Spectrum Analyzer (RTSA) architecture. The modulation classifier was suitable for efficient spectrum monitoring to identify the signals present in a certain frequency band, without the need of knowing any parameter about them. The realized prototype was able to recognize classical single-carrier modulations such as MPSK, MFSK, MASK MQAM and OFDM modulations such as the discrete multitone.
Popoola and Olst (2011) divided their research work methodology into two stages. The first stage involved the development of Automatic Modulation Recognition (AMR) or AMC using an Artificial Neural Network (ANN). The second stage involved the development of the Cognitive Radio Engine (CRE), which has the developed AMR as its core component. The overall numerical results obtained from the developed CRE’s evaluation showed that the developed CRE could reliably and accurately detect all the modulation schemes considered, without bias towards a particular Signal-to-Noise Ratio (SNR) value, as well as any modulation scheme.
Aslam et al. (2012) explored the use of Genetic Programming (GP) in combination with K-Nearest Neighbor (KNN) for AMC. KNN was used to evaluate fitness of GP individuals during the training phase. Additionally, in the testing phase, they used KNN for deducing the classification performance of the best individual produced by GP. Four modulation types were considered: BPSK, QPSK, QAM16 and QAM64. Cumulants were used as input features for GP.
2.2.2 Frequency Domain Features
2.2.2.1 Cyclostationary Spectrum
Radio signals have the characteristics of being cyclostationary i.e. the covariance and the spectrum varies periodically with time. Gardner and Spooner (1994) claimed that the signals with the same power spectral density but with different modulations may have distinct cyclic spectrum. Spectral correlation function was used for classification of different modulation types and extraction of different signal parameters.
Mobasseri (2000) used pattern recognition approach and constellation obtained from received signal to estimate digital modulation type by applying fuzzy-c cluster analysis. The scheme worked well for low order constellations such as QPSK, 8-PSK and 16-PSK. The algorithm was able to correctly recognize two similar modulations (8-PSK vs. V.29 fallback) with 93% accuracy at SNR 0 dB. 93% and 95% accuracy was achieved for 3 dB and 5 dB respectively. Perfect synchronization was assumed. However, no results were provided for signal propagation over real world propagation channels.
Baarriji et al. (2006) designed an automatic modulation recognition model using linear approximation features for real-time classification of digitally modulated signals without any prior knowledge of signal parameters. Basic FSK, PSK, ASK, QAM, and Gaussian Minimum Shift Keying (GMSK) modulation types were detected and the order identified in a hierarchical fashion. Their simulations claimed 99.9% recognition rates for SNR levels as low as 5 dB. However, only AWGN distortion was considered in their work.
Gulati and Bhattacharji (2006) proposed modified Automatic Blind Modulation Recognition (ABMR) algorithm for recognizing different rectangular QAM signals. The proposed method was robust to preprocessing errors like error in estimation of carrier frequency, synchronization and extraction of constellation from real band-pass signals. The performance of the proposed algorithm was evaluated in both noisy and faded channel through computer simulation.
Hu (2008) presented survey of signal detection and classification for cognitive radios combining the spectral correlation analysis and Support Vector Machine (SVM). Several spectral coherence characteristic parameters, which were insensitive with modulation types and insensitive with SNR variation, were chosen as features for classification. Overall correct classification was above 92.83% for an SNR of 4 dB and 97.32% for 8 dB SNR.
A modulation classifier for a 9-class problem consisting of both analog and digital modulations was developed. The authors considered the ten class modulation formats. Combination of spectral features and the cyclic frequency as features of interest was used for modulation classification (Dobre et al., 2010). Malady and Beex (2010) studied the performance of a cyclostationarity feature based Automatic Modulation Classifier (AMC) by the novel usage of a robust estimate of second order first conjugate cyclostationarity. It was proved that the distribution of the test statistic at a cycle frequency had larger mean and smaller variance when it was based on a robust estimate of the second order first conjugate Cyclic Temporal Moment Function (CTMF) – than when a classical estimate of the second order first conjugate CTMF was used. The improvements were a 4 dB reduction in SNR requirements, a lower false alarm rate, and reduced sensitivity to receiver bandwidth.
A robust AMC method for the classification of FSK, PSK, OQPSK, QAM, and amplitude-phase shift keying modulations in presence of HF noise using feature-based methods was presented. The proposed AMC method used decision-tree approach with pre-computed thresholds for signal classification. In addition, it was able to classify type and order of modulation in both Gaussian and non-Gaussian environments. Average Pcc improved for SNR equal to and greater than 10 dB (Alharbi et al., 2012).
2.2.2.2 Wavelet Transform
The transform of a signal is just another form of representing the signal. It does not change the information content present in the signal. The Wavelet Transform provides a time-frequency representation of the signal. It was developed to overcome the short coming of the Short Time Fourier Transform (STFT), which can also be used to analyze non-stationary signals. While STFT gives a constant resolution at all frequencies, the Wavelet Transform uses multi-resolution technique by which different frequencies are analyzed with different resolutions. A number of researchers have applied Wavelet Transform to modulated signals. Wavelet coefficients are extracted as features for classification. The Haar, Daubechies, Symlets and Coiflets are compactly supported orthogonal wavelets. These wavelets along with Meyer wavelets are capable of perfect reconstruction. The Meyer, Morlet and Mexican Hat wavelets are symmetric in shape. The wavelets are chosen based on their shape and their ability to analyze the signal in a particular application.
Lin and Kuo (1994) applied Morlet wavelet to detect the phase changes, and used the likelihood function based on the total number of detected phase changes as a feature to classify MPSK signal. Haar wavelet was used to compute the wavelet transform and considered a 6-class problem consisting of M-ary PSK and M-ary FSK. They obtained an average success rate of 98% at an SNR of 15 dB for data length of 100 symbols.
The time-frequency analysis i.e. Wavelet Transform (WT) was applied for nonstationary signals. It was reported that the wavelet approach approximated both the signal envelop and frequency content. This motivated the authors to effectively utilize the WT approach for estimating the pattern. Simulation results on both synthetic and ‘real world’ short-wave signals proved that their approach was robust against noise up to a signal-to-noise ratio (SNR) of approximately 10 dB. A success rate greater than 94 % was obtained (Ketterer et al., 1999). Hong and Ho (1999) applied wavelet transform to distinguish QAM, PSK, and FSK signals. The approach was to use WT to extract transient characteristics. The relevant statistics for optimum threshold selection was derived under condition that input noise was AWGN. The percentage of correct identification was about 97% when SNR was greater than 5 dB.
A new noise-robust modulation identification method for the adaptive receiver based on software defined radio was developed. The proposed method distinguished M-ary FSK from M-ary PSK by using the characteristics obtained from the wavelet coefficients of each modulated signal. Signals were analyzed for SNR limit of 8 dB. Average classification result for M-ary PSK was 99.1% for 8 dB SNR (Jin et al., 2004).
Binary PSK/CPFSK and MSK identification was investigated. The complex Shannon wavelet was applied to identify binary modulation signals under constant envelope scheme and it failed to identify the nonconstant envelop modulation schemes. The proposed method worked reliably in SNR values greater than 9 dB (>95% average result) and its performance did not depend either on the number of symbols or phase/frequency change instants of used modulation signals (Pavlik, 2005). An algorithm for modulation recognition of received signals in the presence of AWGN with the use of the wavelet transform was developed. The decision was made based on the extraction of some special features of the Continuous Wavelet Transform of the received signal. After extended simulation the algorithm proved to be practically inerrable for 12 dB SNR and achieved low rates of false detection for 10 dB SNR (Maliatsos et al., 2006).
Automatic modulation identification algorithm has been developed to classify QPSK and GMSK signals with AWGN channel. This algorithm failed to identify when SNR was less than 12 dB (Prakasam and Madheswaran, 2007). A generalized modulation identification scheme was developed and presented. With the help of this scheme, the automatic modulation classification and recognition of wireless communication signals with a priori unknown parameters was possible. The special features of the procedure were the possibility to adapt it dynamically to nearly all modulation types, and the capability to identify. The developed scheme based on wavelet transform and statistical parameters was used to identify M-ary PSK, M-ary QAM, GMSK, and M-ary FSK modulations. Correct modulation identification was possible to a lower bound of 5 dB. The identification percentage was analyzed based on the confusion matrix. When SNR was above 5 dB, the probability of detection of the proposed system was above 96% (Prakasan and Madheshwaran, 2008).
The performance of the classifier for eight digitally modulated signals using 4 WT key features (i.e., 4 level scale) was evaluated and compared with that of decision tree classifier to adapt the modulation classification module in software radio. Results indicated an overall success rate of 95% at the SNR of 10 dB in presence of AWGN channel (Cheol-Sun et al., 2008).
Discrete Wavelet Transform (DWT) and adaptive wavelet entropy were used in feature extraction stages of these intelligent systems. A new Discrete Wavelet Neural Network (DWNN) and Discrete Wavelet Adaptive Network Based Fuzzy Inference System (DWANFIS) methods were offered for Automatic Digital Modulation Recognition (ADMR) and the performance comparison between these new DWNN and DWANFIS intelligent systems were performed. The digital modulation types used in this study are ASK2, ASK4, ASK8, FSK2, FSK4, FSK8, PSK2, PSK4 and PSK8. Mean correct recognition rates of 96.51% and 90.24% were obtained by using DWNN and DWANFIS intelligent systems, respectively (Avci and Avci, 2008).
A digital modulation classification method based on Discrete Wavelet Transform (DWT) and artificial neural networks (ANN) was presented to distinguish digital modulation, like QAM, PSK, and FSK signals. High recognition rates of about 97% were obtained (Faek, 2010). The proposed algorithm was verified using Higher-order statistical moments (HOM) of Continuous Wavelet Transform (CWT) as a features set. A multilayer feed-forward neural network trained with resilient back propagation learning algorithm was proposed as a classifier. The purpose was to discriminate among different M-ary shift keying modulation schemes and the modulation order without any priori signal information. The recognition probability of M-ASK, M-PSK, M-QAM, M-FSK, and MSK was higher than 99% when SNR was 4 dB. M-PSK signals classification percentage was higher than 99% when SNR was not lower than 4 dB (considering 100 symbols) (Hassan et al., 2010).
A novel method for recognition of modulation signals by wavelet transform and neural network theory was introduced. In this algorithm, instantaneous feature parameters of received signals were extracted using wavelet transform. Error Back Propagation Neural Network (EBPNN) with supervised training was used to design the classifier. The singular values obtained were used as feature vector to design the classifier. The identification in category for FSK and PSK was simulated respectively, and the simulation results proved the approach proposed was efficient (Hou and Feng, 2011).
2.2.2.3 Statistical Features
Some feature based classifiers are based on higher order statistics such as higher order moments and cumulants. Advantages of higher order statistics include the ability to identify non-gaussian processes and non-minimun phase systems, to detect and characterize signal non-linear properties. Moments and cumulants are statistical features used to identify distinguishing characteristics of data. These statistical features have specifically been used in the field of signal processing to help identify the modulation type of a noisy signal. Moments and cumulants are used as they are peculiarly resilient to noise effects. Other statistical features are distributions such as PDF or parameters describing the distribution. These parameters are mean, standard deviation (variance) etc.
Liedtke (1984) described a computer simulation of an automatic classification procedure for digitally modulated communication signals with known parameters. This work focused on binary ASK, binary FSK, and the three types of PSK (i.e., two, four, and eight). However, the classification procedure was conducted on a Burroughs B5500 computer, which of course was not as fast as the vast majority of today’s computers. A classification method for the BPSK, QPSK, BFSK, QFSK signals was proposed based on the autoregressive modeling. Instantaneous carrier frequency and BW of the intercepted signal was obtained from the poles of the autoregressive polynomial for each analysis frame of the intercepted signal. The following feature vectors were derived: Mean of the instantaneous frequency and standard deviation of the instantaneous frequency. It was claimed that success rate is greater about 99% at a SNR of 15 dB (Assaleh et al., 1992).
Tiara and Murakami (1999) proposed to classify analog frequency and amplitude modulation types using first and second order moments. However, their proposed automatic classification program was primarily used to first distinguish between analog and digital signals. Their classification was an attempt to classify the analog case, while the digital case was not classified.
A classification method for baseband digitally modulated signals was proposed based on the feature extraction and fuzzy classification method. Carrier frequency was the only parameter assumed to be known a priori. Basic features used in the classification problem were Kurtosis of the envelope of the signal (Lopatka and Pepdisz, 2000).
A modulation classification algorithm using fourth-order cumulants as the features of interest in a hierarchical structure was developed. One sample per symbol interval and perfect channel equalization was assumed. They considered several 2-class problems, a 4-class problem {BPSK, PAM-4, QAM (4, 4), PSK-8} and a 8-class problem {BPSK, PAM-4, PSK-4, PSK-8, V32, V29, V29c, QAM (4,4)}. They also briefly discussed the effects of various channel imperfections on the classifier performance. They achieved 93% average identification for lower bound SNR of 0 dB (Swami and Sadler, 2000).
A classification method based on elementary fourth-order cumulants was proposed. It was assumed that the carrier phase offset, symbol timing offset and the pulse shape are known. The performance of the proposed classifier was analyzed in the case of small phase offset, small frequency offset, and residual channel effect, small symbol timing offset, self-interference, co-channel interference and impulsive nongaussian noise (Ananthram and Sadler, 2000). Spooner (2001) used sixth-order cyclic cumulants for modulation classification. Three 2-class problems, two 3-class problems and two 4-class problems were considered. A root-raised cosine pulse shape with a roll-off factor 0.35, 10 samples per symbol interval and a priori knowledge of the pulse shape coefficients. An average success rate of 90%, at an SNR of 9 dB for data length of 3000 symbols was obtained.
Automatic modulation Recognition of digital modulated signals was proposed based on the feature extraction and Artificial Neural Network approach. Statistical features were used as a feature set and a Multi Layer Perception (MLP) was used as a classification method. ASK2, ASK4, BPSK, QPSK, FSK2, FSK4, QAM16, and QAM64 were used to evaluate the performance of the proposed classifier (Wong and Nandi, 2001).
The major problems, approaches and some algorithms to recognize automatically the type of the modulated signals were discussed. Algorithms to estimate some important features of the modulated signals, such as the wave carrier frequency were discussed and simulated. Modulations were distinguished using various selected features for 12 dB SNR (Guen and Mansour, 2002). A classification method, based on the relationships between the second and higher moments of received signal and noise power, was proposed. The proposed classifier used mixed moments of different orders of the intercepted signal as a feature set (Dai, 2002).
Information extracted from the instantaneous amplitude and phase of the received signal was exploited for linear modulation recognition. The statistic was compared against a threshold for decision making at a tree node, as part of the binary decision tree classifier. The phase PDF and its statistical moments were investigated for PSK signal recognition (Lichun, 2002). The performance of fourth, sixth and eighth order cyclic cumulants for modulation classification for several 2- class problems was developed. They assumed a priori knowledge of carrier frequency as well as pulse shape coefficients. They considered three 2-class problems: {QAM-16, QPSK}, {ASK-4, ASK-8} and {QAM-16, QAM-64}. For the {QAM-16, QPSK} 2-class problem, they obtained an average success rate of 99% at an SNR of 5 dB for data length of 3000 symbols (Dobre et al., 2003).
An algorithm based on higher-order cyclic cumulants for the modulation classification of QAM signals in the presence of carrier phase and carrier frequency offsets was developed. The use of feature vectors consisting of fourth-, sixth and eighth-order cyclic cumulants was proposed. A priori knowledge of the pulse shape coefficients was assumed. For a 2-class problem consisting of {QAM-4, QAM-16} constellations, an average success rate of 96% was obtained at an SNR of 7 dB for data length of 900 symbols (Dobre et al., 2004).
Fourth and second order moments of the received QPSK and 16QAM signals were used as features for identification. 95% correct classification was obtained for 5 dB SNR i.e. only in presence of AWGN channel (Martret and Boiteau, 2005). A new pattern recognition approach for automatic modulation recognition of MPSK (2, 4, and 8) signals in broad-band Gaussian noise was used. The method was based on constellation rotation of the received symbols, and 4th order cumulant of a 1D distribution of the signal’s in-phase component. Correct classification was obtained for all considered signals when SNR was above 8 dB. Allowing probability of error to be Pe = 0.05, classification was assured when SNR was 0 dB for BPSK and SNR was 4 dB for QPSK and 8PSK (Pedzisz and Mansour, 2005).
A feature-based modulation classification algorithm was developed using fourth- and eighth order cumulants as the features of interest for M-QAM, M-PSK, M-ASK classification in a Line Of Sight (LOS) channel using a hierarchical structure. They considered one sample per symbol interval, rectangular pulse shape and perfect carrier frequency synchronization. They considered several 2-class problems, two 3-class problems and one 5-class problem (Liu and Xu, 2006).
A modulation classification scheme for MPSK signals was proposed. Frequency and timing synchronization was achieved before fourth-order-cumulant based modulation classification algorithm was carried out. The recognition range included BPSK, QPSK, 8PSK and pi/4 DQPSK (Shen et al., 2006).
The method introduced modulation classification for digitally modulated signals in the presence of AWGN. This method does not need any prior knowledge of the signals, such as SNR, symbol rate and carrier frequency. Four kinds of features were extracted to achieve a tree-based classification approach, and three Radial Basis Function (RBF) neural networks were employed in the classifier. Monte-Carlo experiment was done to test the performance of the classifier. For the signal of each modulation type, 1000 samples were generated under each SNR (0 dB to 20 dB), the step size was 5 dB, in which 500 samples were used for training, and the other 500 samples for testing. The simulation results indicated that the correct recognition rate was larger than 92.6′ when SNR was above 10 dB (Hou et al., 2006).
A classification algorithm using the cumulants of the differentially processed signal was used as the features of interest in order to perform modulation classification in the presence of frequency offsets. A 10-class problem was considered, consisting of the following constellations: {BPSK, PSK-8, PSK-16, PAM-4, QAM-8, QAM-16, QAM-32, QAM-64, QPSK and OQPSK}. They considered 2 samples per symbol interval, rectangular pulse shape and a LOS channel. They obtained an average success rate of 90% at an SNR of 10 dB (Mirarab and Sobhani, 2007).
Feature extraction method using HOS analysis combined with difference to the Nth Power manipulation has been examined in application for Automatic Modulation Recognition (AMR) to perform scheme recognition of three digital modulation signals, i.e. QPSK-16QAM-64QAM in the AWGN transmission channel. They obtained accuracy rate of AMR using the method of simple decision obtained 90% for SNR above 10 dB in its classifier, while using the method of voted decision was 96% (Wijanto et al., 2009).
Eight order cyclic cumulant was proposed as feature of interest to perform modulation classification in flat fading environment. A perfect carrier synchronization and prior knowledge of pulse shape coefficients was assumed. The proposed algorithm gave an average success rate of 81% at an SNR of 10 dB (Dobre et al., 2009).
A PSK modulation scheme recognition technique for use in a software radio system was proposed. The technique was capable of determining the modulation scheme of a signal in the case when the digital modulation scheme class is not known a priori but PSK scheme (Islam et al., 2009). Features which do not require prior knowledge of the signal parameters, such as number of peaks in envelop, histogram location of these peaks, higher order moments were considered for classification. Two classification techniques decision tree based and Bayesian based classification based were compared. Both of the proposed recognition systems are able to discriminate ASK2, ASK4, ASK8, PSK4, PSK8, QAM8, FSK2, FSK4, FSK8, CW and Noise at SNR above 15 dB with a success rate 100% (Erdem, 2009).
A combination of higher order moments of the received signal as well as the moments of the differentially processed signal were used as the features of interest to perform modulation classification in the presence of frequency offsets. A 10-class problem was considered for classification. An average success rate of 91% was obtained at an SNR of 10 dB for data length of 1000 symbols (Chaithanya and Reddy, 2010).
2.3 CLASSIFIERS IN PRESENCE OF FADING ENVIRONMENT
When a signal travels through a propagation channel, there are noises, distortions, reflections, delays, attenuations and other phenomenon which interfere with the signal of interest. One primary source of interference is thermal noise, caused by thermal agitation of electrons, which is present in all electronic devices and is a function of temperature. Thermal noise is usually modeled using Additive White Gaussian Noise. Other types of noise include intermodulation noise, cross-talk, and impulse noise etc.
Another phenomenon that can occur in the channel, through which a signal is traveling toward its receiver, is fading. Fading occurs when the amplitude and phase of a signal changes rapidly over short periods of time or travel distances. Multipath phenomena results in a received signal that significantly differs in amplitude and phase, from that sent. Fading can also be caused by the transmitter being in relative motion with the receiver, and the resulting Doppler shifts. In digital communication, equalizers are designed to compensate the channel distortions.
Modulation classification of modulated signals was analyzed in unknown dispersive channels (Paris et al., 1997). This method provided a tutorial introduction to the Constant Modulus (CM) criterion for blind Fractionally Spaced Equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the Constant Modulus Algorithm (CMA) (Johnson et al., 1998). The symbols of a QAM constellation were classified into several subsets, where the symbols in each subset have the same magnitude. It was stated that the number of subsets increased with the QAM constellation size. For each possible modulation type, the joint PDF of the magnitudes in different sets was derived. Then the ML criterion was employed to accomplish modulation classification. The symbol rate, noise power was known. The channel effect considered was only via additive Gaussian noise (Tiara and Murakami, 1999).
A neural network based classification scheme was proposed for classification of modulation types in presence of noise and fading. A hierarchical modulation approach was selected. Back propagation neural network units were adopted to cope with propagation environments that constantly change, as in case of real world communication. Overall classification performance was 99% at 20 dB down to 90% at 8 dB for rural area propagation where as overall performance was 82% at 20 dB and 68% at 11 dB for highly distorted channels (Hatzichristos, 2001).
Fading channel modeling and trained equalization techniques have been discussed. It included channel estimation and timing synchronization. It emphasized on need of equalization in case of GSM systems (Pathak, 2002). A single signal in AWGN, with the parameters perfectly known, and a rectangular pulse shape were assumed. In addition to ASK, PSK, QAM and FSK, the identification of other modulations such as MSK was examined (Venalainen et al., 2002).
A neural network for automatic recognition of two types of digital passband modulations was developed. A feed-forward network with six hidden neurons was trained to recognize BPSK and minimum shift keying signals. The performance of the classifier was tested in the presence of additive white Gaussian noise between SNR levels of 10 dB to 12dB, showing a 95% to 99% correct recognition rate. However the simulations for SNR levels outside of this range were not reported (Kalinin and Kavalov, 2002).
A signal modulation classifier design was presented using artificial neural networks. The authors analyzed system-level issues including carrier synchronization, bandwidth estimation, and modulation classification. Analysis of the feature space used in the neural network was also done. The classification statistics were over 80% success rates in the presence of noise (Bin Le et al., 2006). Ebrahimzadeh and Seyedin (2006) proposed a novel Automatic Digital Modulation Types Identifier (ADMTI) in dispersive environment. In the ADMTI’s structure, undesired effects of channel were mitigated by an equalizer. Higher order cumulants and moments (up to eighth) were used as features and classification was performed by a multiclass SVM-based classifier. Simulation results showed that ADMTI was able to identify different types of modulations (e.g. QAM64, V.29 and ASK8) with high accuracy even at low SNRs.
Biswas (2006) analyzed performance of different M-ary modulation schemes over wireless fading channel. Effect of AWGN noise on the performance of various modulated signals was analyzed. Ebrahimzadeh and Ardeshir (2007) used a multiclass classifier based on support vector machines to determine the types of the received signals. Simulation results claimed that the proposed method had a high success rate for recognition of different digital signal types, even at low signal to noise ratio.
In this correspondence, higher-order Cyclic Cumulants (CCs) were explored to discriminate linear digital modulations in flat fading channels. Single- and multi-antenna CC-based classifiers were investigated (Dobre et al., 2009). The method was applied to signals with FSK, BPSK, MSK, QAM-16 and QPSK modulations. The spectrogram analysis was used for the modulation type recognition. This classification method was examined on signals corrupted by Gaussian noise, phase noise and on signals after their transmission through multipath Rayleigh fading channel (Kubankova, 2009). The developed technique identified a variety of digital signal types. Tests and simulations using an additive white Gaussian noise with Rayleigh fading channel proved that the classifier has a success rate of 96.16% for signals with SNR equal to 5 dB (Khurshid et al., 2007).
A hierarchical cyclostationary-based classifier was proposed to reliably identify the signal type of a wide range of unknown signals. The proposed system assumed no a priori knowledge of critical signal statistics such as carrier frequency, carrier phase, or symbol rate. The system was designed with a multistage approach to minimize the number of samples required to make a classification decision while simultaneously ensuring the greatest reliability in the current and previous stages. The system performance was demonstrated in a variety of multipath fading channels, where several multi antenna-based combining schemes were implemented to exploit spatial diversity. The resulting modulation classification system was capable of reliably determining the modulation scheme of received signals in moderate channel conditions. With the addition of multiple receive antennas, the performance of the classifier increased even further. In multipath and fast fading channels, the final modulation discrimination capability of the classifier became unreliable (Erdem, 2007).
A novel blind equalization method was proposed for multipath Rician fading channels. In the proposed method, based on blindly estimated characteristics of Rician fading channel, a realizable DFE was designed to minimize the Mean Square Error (MSE) from the frequency domain perspective. DFE’s filters were implemented in an adaptive structure to enable dealing with rapid time-varying channels (Moazzen et al., 2009).
Babu and Kumar (2010) applied the developed method FSK, BPSK, MSK, QAM-16 and QPSK modulations. It was a method of adaptive multi-modulus equalization for an equalizer. A cost from a cost function was calculated according to a Constant Modulus Algorithm (CMA). Faek (2010) performed feature extraction via the DWT detail coefficients of the digital signals using (db4) mother wavelet, because of the usefulness of wavelet in signal de-noising. The extracted features were presented to an ANN for pattern recognition. The performance of the classification scheme was investigated. Recognition rates obtained were 97%. Proposed method for AMR for cognitive receivers used constellation shape based identification to distinguish BPSK, QPSK, OQPSK, 8-PSK under varying SNR and data rate conditions (Sophia et al., 2012).
2.4 RELATED WORK ON CARRIER FREQUENCY OFFSET ESTIMATION
There are different methods that use envelope information to extract features for classification of digitally modulated signals. However, most of these methods require some of the signal parameters such as carrier frequency, pulse shape, time of arrival, symbol rate, signal to noise ratio, to be known or to be extracted. In digital modulation recognition, in general, there is no priori information on the center frequencies of the signals. Even if the center frequency is known nominally, by the published standards or by intelligence, carrier frequency offset estimation should be performed to compensate the local oscillator drifts and Doppler shifts induced by the relative motion of mobile systems and channel effects. Channel estimation and synchronization can be made by the usage of set of known data symbols. However, data-aided or timing-aided techniques reduce the effective transmission rate and may not be feasible in many applications.
A prototype blind retrain procedure was developed to demonstrate the feasibility of the techniques for high-speed multipoint modems (Jablon, 1992). The relationship between the cyclic estimators and the Non Linear Least Square (NLLS) estimators was studied. The problems with Cyclic Cumulants Based (CCB) estimators and NLLS estimators were as follows. First, the workable frequency range of an estimator was proportional to the sampling rate and inverse-proportional to the value of K. For some modulation types, the minimum value of K was very large (e.g., K=16 for PSK16). Secondly, for a fixed data record size, a larger K also meant the variances of the estimated statistics were higher, resulting in a worse performance (Giannakis and Zhou, 1995).
Two open-loop algorithms were developed for estimating jointly, frequency offset and symbol timing of a linearly modulated waveform transmitted through a frequency-flat fading channel. The methods exploited the received signal’s second-order cyclostationarity (Gini and Giannakis, 1998). The carrier frequency was estimated by averaging the instantaneous frequency of the received signal. The implied pulse-shaping function was rectangular in time domain and only limited to one symbol duration (Assaleh et al., 2000).
Decision feedback carrier recovery loops for coherent demodulation of the 16 QAM signal format were discussed. Two types of decision-directed phase detector referred as basic or original Phase Detector (PD) and Phase-Frequency Detector (PFD) were used in order to extend the acquisition range of the loop (Mouaki and Gagnon, 2000).
A polarity decision carrier recovery algorithm was proposed that was useful for carrier acquisition in high order-QAM. The Phase Detector (PD) output and its variance characteristics were mathematically derived and the simulation results were presented (Kim and Choi, 2001). The problem of blind Carrier Frequency-Offset (CFO) estimation in QAM, PSK, and PAM communications systems was discussed. The performance of a standard CFO estimate, which consisted of first raising the received signal to the Mth power, and then the Nonlinear Least Squares (NLLS) estimation approach, was applied (Ciblat and Ghogho, 2006).
Two classifiers were developed. These two classifiers were capable of providing good estimate of the frequency deviation of a received MFSK signal. A blind carrier frequency estimation algorithm and a blind symbol rate estimation algorithm was also developed (Yu, 2006). A feature based hierarchical modulation classification method was developed to discriminate various modulation formats in presence of Rayleigh fading multipath and timing and carrier frequency offset. Both cumulants and moments were used as features to discriminate modulation formats. Performance of the proposed classification method is evaluated under Rayleigh fading flat as well as multipath environment. With the proposed approach, the values of average percentage of correct classification were 68.98%, 88.93% and 98.20% for 5 dB, 10 dB, and 15 dB respectively (Karthik, 2011).
A joint blind equalization and carrier-phase recovery solution was developed. Proposed method was compared to adaptive methods through computer simulations for higher-order QAM signaling on symbol and fractionally spaced channel (Abrar and Nandi, 2010). In a typical CR scenario, training sequence or channel knowledge is not available, and hence blind equalizers are widely used. Novel CR receivers were proposed where the performance of the AMC was also considered while adapting the parameters of the blind equalizer (Ramkumar et al., 2011).
After scanning the literature to answer the question ‘which AMC technique is the best in terms of performance under realistic conditions’? it turned out that performance comparison of published classifiers is not straightforward. There are a number of reasons for this. First, performance of different classifiers cannot be compared, unless the modulation schemes are the same. It was observed from literature that the modulated signals vary from work to work. Second, most of the classifiers are designed to handle specific unknown parameters. So, one cannot really compare their performance, unless the uncertainties the classifiers taken into account are the same. Some classifiers are only developed in the presence of AWGN without taking into account real time multipath conditions. Some classifiers assume prior knowledge of parameters such as carrier frequency, symbol rate etc. Few classifiers have been developed which are completely blind in nature.
Major contributions in the area of Automatic Modulation classification have been compared and summarized in Table 2.1
It is apparent from above survey that, few works address the problem of modulation classification in AWGN and multipath scenarios for a large class of modulation schemes without any prior knowledge of incoming signals. One or more parameters are generally assumed to be known. Effect of multipath fading has been taken into consideration by few researchers. This motivated our search to develop a modulation classification algorithm for a large class of constellations in noisy and fading environment for low SNR.
CHAPTER 3
CHANNEL MODELING AND PREPROCESSING
In AMR, the classifier performance is based on radio signal segments. Most commonly, classifiers have been trained and tested on synthetically generated signals in a simple Additive White Gaussian Noise (AWGN) channel model. A measure of quality has been the SNR level at which the classifier breaks down. Very few works have taken account of channel distortions models in addition to AWGN. Most practical applications have limited bandwidth and therefore some form of pulse shaping need to be applied to the signal to reduce its bandwidth before transmission.
The complete work is divided into three major sections. First section consists of generation of modulated signal. Second section deals with two types of channel modeling. AWGN Channel and Multipath Rayleigh fading channel were simulated to obtain a more realistic picture of the classifier performance. The third section discusses preprocessing tasks carried out on the received signals. The preprocessing tasks applied on the signals were denoising, estimation of carrier frequency and signal equalization.
3.1 METHODOLOGY ADOPTED
The complete flow of work is illustrated in Fig. 3.1. The objective was to develop a classifier at the receiver end that could classify unknown modulated signals. The work was divided in three main sections.
Transmission end processing
Channel modeling
Receiver end processing
Fig 3.1: Algorithm for Modulation Classification
3.1.1 Transmission End Processing
Test signals 2ASK, 4ASK, 2PSK, 4PSK, 2FSK, 4FSK, 16QAM, 64QAM, 256QAM and GMSK were generated by modulating a carrier using random binary sequence as message signal. Raised cosine filter was used as transmission filter to band limit the signal.
3.1.1.1 Digital Modulation
Complex Envelope: The spectral redundancy of the received real band-pass signal can be reduced by using analytic representation also called pre-envelope. An analytic signal can be obtained by using a Hilbert transformer. The sampling frequency can be reduced to exactly the band-width of the received signal by downconverting the analytic signal. This representation is called complex envelope. The nature of the modulated signals leads to high sampling rates and an excessive amount of memory is required when the received signal is stored (Rosti, 1998). There are ways to lower the sampling rate and reduce the amount of memory needed. This can be achieved by using signal representations different from the directly sampled form.
If r(t) is real bandpass signal, z(t) analytical signal, then complex envelope c(t) is obtained from the analytic signal z(t) as follows
‘ (3.1)
where, … (3.2)
– ‘ (3.3)
where, is Hilbert transform of
The complex envelope c(t) is the frequency shifted version of the analytic signal z(t) as given in Eq. 3.1.
The real and imaginary parts of are called the in-phase (I) and quadrature (Q) component, respectively. The instantaneous amplitude, instantaneous phase (t), and instantaneous frequency f(t) can be easily obtained from the analytic and complex envelope representations. The instantaneous amplitude is expressed in Eq.3.4
‘ (3.4)
The instantaneous amplitude can be similarly extracted from the sampled signal r(i), where i is the time index. The normalized centered instantaneous amplitude sequence can be obtained from the instantaneous amplitude sequence as follows
‘ (3.5)
where,
=sample mean of ‘ (3.6)
and Ns is the number of samples in a segment. Normalization by ma is used to compensate the channel gain.
The instantaneous phase of the signal is expressed as
‘ (3.7)
The derivative of the instantaneous phase is the angular frequency w(t). The instantaneous frequency of the modulated signal is expressed in Eq. 3.8.
‘ (3.8)
where,
A general analytic representation of digital modulated signals is given by Eq. 3.9
‘ (3.9)
where,
= amplitude and = frequency of the carrier
s[m] = the discrete symbol sequence
s[m] comprises of an alphabet distinctive for the modulation type.
The elements of the alphabet are complex-valued points in the signal space. The waveform is a real-valued signal pulse whose shape influences the spectrum of the modulated signal. The pulse shape reduces the large band-width caused by the discontinuities in the symbol sequence. In order to avoid Inter-Symbol Interference (ISI), it is often required that = 1 and = 0 for n = ??1, ??2 . . . Such shapes are, e.g., sinc and raised cosine pulses.
Amplitude Shift Keying (ASK): Amplitude Shift Keying is the simplest digital modulation scheme. The alphabet consists of M = 2b points in the real line of the signal space where each point represents a sequence of b bits. Therefore the symbols are represented by different amplitude levels of the modulated signal. The analytic ASK modulated signal can be expressed using
s[m] = (2n + 1 – M) d in Eq. (3.9)
where,
n ?? [0,M ‘ 1] = nth symbol and
2d = distance between adjacent signal amplitudes.
The instantaneous amplitude of the ASK modulated signal can be expressed as
‘ (3.10)
where,
‘ (3.11)
i.e., the absolute value of the symbol function s(t) with different amplitude levels scaled by .
The instantaneous phase is obtained as follows
‘ (3.12)
where, u(t) is the unit step function.
The instantaneous frequency may be expressed as
‘ (3.13)
The impulses in the instantaneous frequency occur at symbol transitions. The generated 2ASK modulated signal is presented in Fig. 3.2. 2ASK modulated signal and 2ASK signal with AWGN is presented in Fig. 3.2(a) and Fig. 3.2(b) respectively. Faded 2ASK signal is presented in Fig. 3.2(c). Noisy and faded 2ASK signal is presented in Fig. 3.2(d).
Fig 3.2: 2ASK Modulated Signal
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of 2ASK modulated signal is illustrated in Fig. 3.3(a), Fig. 3.3(b) and Fig. 3.3(c) respectively.
Fig 3.3: Instantaneous Features of 2ASK Signal
The generated 4ASK modulated signal is presented in Fig. 3.4. 4ASK modulated signal and 4ASK signal with AWGN is presented in Fig. 3.4(a) and Fig. 3.4(b) respectively. Faded 4ASK signal is presented in Fig. 3.4(c). Noisy and faded 4ASK signal is presented in Fig. 3.4(d).
Fig 3.4: 4ASK Modulated Signal
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of 4ASK modulated signal is illustrated in Fig. 3.5(a), Fig. 3.5(b) and Fig. 3.5(c) respectively.
Fig 3.5: Instantaneous Features of 4ASK Signal
Phase Shift Keying (PSK): Phase Shift Keying is obtained by defining a unique phase state of the carrier for every symbol as follows
‘ (3.14)
where symbols do not have any effect in the instantaneous amplitude. The analytic PSK modulated signal may be expressed as
‘ (3.15)
2PSK and 4PSK are commonly called Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK), respectively. Larger constellations are too dense and therefore not robust to noise. There is still some contribution of) the envelope but due to the properties of g(t) its sum will be approximately unity. The instantaneous amplitude is given by
‘ (3.16)
The instantaneous phase depends on the summation term m in Eq. 3.15. Therefore the expression for the instantaneous phase is
‘ (3.17)
where, the unit step functions pick up the correct phase term in every time instant. The phase of the modulated signal consists of the phase states caused by the symbol sequence. The instantaneous frequency is obtained by
‘ (3.18)
The impulses in the instantaneous frequency occur at symbol transitions.
The generated 2PSK modulated signal is presented in Fig. 3.6.
Fig 3.6: 2PSK Modulated Signal
2PSK modulated signal and 2PSK signal with AWGN is presented in Fig. 3.6(a) and Fig. 3.6(b) respectively. Faded 2PSK signal is presented in Fig. 3.6(c). Noisy and faded 2ASK signal is presented in Fig. 3.6(d).
Fig 3.7: Instantaneous Features of 2PSK Signal
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of 2PSK modulated signal is illustrated in Fig. 3.7(a), Fig. 3.7(b) and Fig. 3.7(c) respectively.
Quadrature Amplitude Modulation (QAM): Quadrature Amplitude Modulation is a combination of ASK and PSK. The symbols are separated by both amplitude and phase differences. QAM is mostly used in wired channels, e.g. cables, due to the larger number of the symbols and weaker tolerance for noise. Constellations are often chosen to be powers of 2 up to order of 256.
The symbols may be represented as complex numbers Re{s[m]} +jIm{s[m]}, where Re{??} denotes the real component and Im{??} denotes the imaginary component. The symbols in polar coordinates are expressed as follows
‘ (3.19)
where and ‘ (3.20)
The analytic QAM signal is now given by
‘ (3.21)
where, and are the only terms affecting on the envelope and
A[m] ‘ 0, so the absolute value can be omitted. The instantaneous amplitude may be expressed as
… (3.22)
Again, because ‘ 0, it does not have any effect on the instantaneous phase. The instantaneous phase is obtained by
‘ (3.23)
Due to discontinuities in the instantaneous phase the expression for the instantaneous frequency may be written as
‘ (3.24)
The generated 16QAM modulated signal is presented in Fig. 3.8.
Fig 3.8: 16QAM Modulated Signal
16QAM modulated signal and 16QAM signal with AWGN is presented in Fig. 3.8(a) and Fig. 3.8(b) respectively. Faded 16QAM signal is presented in Fig. 3.8(c). Noisy and faded 16QAM signal is presented in Fig. 3.8(d).
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of 16QAM modulated signal is illustrated in Fig. 3.9(a), Fig. 3.9(b) and Fig. 3.9(c) respectively.
Fig 3.9: Instantaneous Features of 16QAM Signal
Frequency Shift Keying (FSK): Frequency Shift Keying differs from the digital modulation schemes described so far due to the fact that it cannot be represented by Eq. 3.9. The FSK modulated signal comprises of pulses having different frequencies depending on the symbol. Usual choices for the number of the different frequencies are 2, 4 and 8. The phase of the FSK signal can be continuous or discontinuous depending on the duration of the pulses. If there are an integer number of periods in every pulse, the phase of the signal will be continuous. The analytic FSK modulated signal may be expressed as follows
‘ (3.25)
where,
‘ (3.26)
is the frequency difference of two adjacent pulses. The signal is called Continuous-Phase FSK (CPFSK) if the pulse shape is a square and The envelope of the FSK signal will be constant
‘ (3.27)
The generated 2FSK modulated signal is presented in Fig. 3.10.
Fig 3.10: 2FSK Modulated Signal
2FSK modulated signal and 2FSK signal with AWGN is presented in Fig. 3.10(a) and Fig. 3.10(b) respectively. Faded 2FSK signal is presented in Fig. 3.10(c). Noisy and faded 2FSK signal is presented in Fig. 3.10(d).
Fig 3.11: Instantaneous Features of 2FSK Signal
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of 2FSK modulated signal are illustrated in Fig. 3.11(a), Fig. 3.11(b) and Fig.3.11(c) respectively.
The band-width of the FSK signals may be reduced by choosing which is called Minimum Shift Keying (MSK) and by choosingas low-pass filter with Gaussian shape Gaussian MSK (GMSK) signal is achieved, which is used in global system for mobiles (GSM).
The instantaneous phase is given by
‘ (3.28)
where, the value of the integral depends only on the pulse shape. The instantaneous frequency varies with respect to the symbol values and is given as
‘ (3.29)
Gaussian Minimum Shift Keying (GMSK): Gaussian Minimum Shift Keying??is a Continuous-Phase??Frequency-Shift Keying??modulation scheme. It is similar to standard Minimum-Shift Keying (MSK), where the digital data stream is first shaped with a??Gaussian filter??before being applied to a frequency modulator. There are no phase discontinuities as the frequency changes occur at the carrier zero crossing points. GMSK modulation is widely used in GSM cellular technology. The generated GMSK modulated signal is presented in Fig. 3.12.
Fig 3.12 (a): GMSK Modulated Signal Fig 3.12(b): Noisy GMSK Signal
GMSK modulated signal and GMSK signal with AWGN is presented in Fig. 3.12(a) and Fig. 3.12(b) respectively.
Fig 3.13: Instantaneous Features of GMSK Signal
Instantaneous features were derived from faded and noisy modulated signal. Instantaneous amplitude, instantaneous phase and instantaneous frequency of GMSK modulated signal is illustrated in Fig. 3.13(a), Fig. 3.13(b) and Fig. 3.13(c) respectively.
3.1.2 Transmission or pulse shaping filters
Most digital communication signals, especially wireless ones have limited bandwidth available to allow for simultaneous transmission of several messages. As a result the modulated signal is passed through a transmission filter prior to transmission. In addition transmission channel are usually band limited, which leads to Inter Symbol Interference (ISI). In the transmitted signal, it is important that transmission filter be so designed so that the ISI does not increase further. Raised cosine filters are designed so that the ISI introduced by the filter band limited structure is equal to zero at correct sample points.
A raised Cosine Filter belongs to the class of filters which satisfy the Nyquisit Criteria. The transfer function of raised cosine filter is given by
x(t) = ‘ (3 .30)
X(f) = T ‘ (3.31)
=
=
where, T is the symbol period and
is called roll off factor .
The roll off factor determines the excess bandwidth of the filter. A roll off factor of 0.5 implies that the bandwidth of the filter is 1.5 times the input sampling frequency. As the value of roll off factor increases the bandwidth also increases. Upsampling factor represents the number of samples per symbol in the filtered output signal.
3.2 TRANSMISSION CHANNEL MODELING
Radio communication channels introduce noise, fading, interference, and other distortions into the signals that they transmit. The implementation of realistic transmission channel is essential for the performance evaluation of any signal classification method. Such a specification is essential as the transmission channel can severely affect transmitted signal either by increasing ISI or by lowering effective SNR level. This section describes the channel features of Additive White Gaussian Noise (AWGN) and Rayleigh fading model.
3.2.1 AWGN channel
The noise analysis of communication systems is often based on an idealized noise process called Additive White Gaussian Noise (AWGN). In this type of channel, the noise distorting the signal is a wide sense stationary random process that is independent of frequency. Channel noise is introduced anywhere between the transmitter output and the receiver input. Modulation schemes are chosen or designed according to channel characteristic in order to optimize their performance. AWGN channel is a universal channel model for analyzing modulation schemes.
The received signal is thus represented as
‘ (3.32)
where, is the received signal,
is the transmitted signal; and
n(t) is the additive white Gaussian noise.
AWGN is defined in terms of its power spectral density which is given as
‘ (3.33)
where is a constant and the factor 1/2 has been included to indicated that half the power is associated with positive frequencies and half with negative frequencies.
The autocorrelation function and the power spectral density of white noise are presented in Fig. 3.14 and Fig. 3.15 respectively.
Fig 3.14: Autocorrelation Function of AWGN Fig 3.15: PSD of AWGN
3.2.2 Multipath Rayleigh Fading Channel
In wireless communications, signal fading is caused by multi-path effect. Multi-path effect means that a signal transmitted from a transmitter may have multiple copies traversing different paths to reach a receiver. Thus, at the receiver, the received signal should be the sum of all these multi-path signals. Because the paths traversed by these signals are different, these signals interact with each other. If signals are in phase, they would intensify the resultant signal otherwise, the resultant signal is weakened due to out of phase. This phenomenon is called channel fading. In general, there are two criteria to measure channel fading, including
Doppler spread
Delay spread.
Doppler Spread: Due to Doppler effect, if a transmitter is moving away from a receiver, the frequency of the received signal is lower than the one sent out from the transmitter. In wireless communications, there are many factors that can cause relative movement between a transmitter and a receiver. The lengths of signal path are often different, which correspond to different movement speeds of transmitter signals, and in turn different frequency shifts on the signal paths. As a result, a frequency spread is caused in the signal spectrum.
Delay Spread: The different signal paths between a transmitter and a receiver correspond to different transmission times. For an identical signal pulse from the transmitter, multiple copies of signals are received at the receiver at different moments. The direct effect of these non simultaneous arrivals of signal causes the spread of the original signal in time domain. This spread is called delay spread. The delay spread puts a constraint on the maximum transmission capacity on the wireless channel. Specifically, if the period of baseband data pulse is larger than that of delay spread, ISI will be generated at the receiver. That is, the data signals on two neighboring pulse periods are received at the same time, which causes the receiver not to be able to distinguish them. Rayleigh fading channels are useful models of real-world phenomena in wireless communications.
Rayleigh fading is a statistical model for the effect of propagation??environment on a radio??signal, such as that used by??wireless??devices. Rayleigh fading models assume that the magnitude of a signal that has passed through such a??transmission medium??(also called a??communication channel) will vary randomly, or??fade, according to a??Rayleigh Distribution-the radial component of the sum of two uncorrelated??Gaussian??random variables.
The direct and major reflected paths between a stationary radio transmitter and a moving receiver are illustrated in Fig. 3.16.
Fig 3.16: Direct and Major Reflected Paths between Transmitter and Receiver
The major paths result in the arrival of delayed versions of the signal at the receiver. In addition, the radio signal undergoes scattering on a local scale for each major path. Such local scattering is typically characterized by a large number of reflections by objects near the mobile. These irresolvable components combine at the receiver and give rise to the fading. Due to this phenomenon, each major path behaves as a discrete fading path. Rayleigh fading distribution is used in wireless mobile communication to describe the statistical time varying nature of flat fading signal i.e. a signal that has all ray paths attenuated uniformly. This means that there is no line of sight path between the transmitter and the receiver might be in relative motion, therefore time spread and Doppler shift may also be considered. The relative motion between the transmitter and receiver causes Doppler shifts which are taken into consideration. The discrete expression of received signal in Rayleigh fading environment is given by
‘ (3.34)
where, is a Rayleigh random variable.
is the signal sequence, and
is the noise
In wireless applications, such as standard Global System for Mobile Communication systems (GSM) prefer to specify Doppler shifts in terms of the speed of the mobile. If the mobile moves at speed v making an angle of ?? with the direction of wave motion, then the Doppler shift is
fd = (vf/c)cos ‘?? (3.35)
where, f is the transmission carrier frequency an c is the speed of light.
The Doppler frequency represents the maximum Doppler shift arising from motion of the mobile. Local scattering typically comes from many angles around the mobile. This scenario causes a range of Doppler shifts, known as the Doppler spectrum. The type of Doppler spectrum specified is Jakes spectrum. The Jakes Doppler power spectrum model is based on the Clarke-Gilbert model. The Clarke-Gilbert model is also called the classical model which assumes fixed transmitter and moving omnidirectional receiver. The Jakes Doppler power spectrum applies to a mobile receiver.
The normalized Jakes Doppler power spectrum is given analytically by:
=1/[(] ‘ (3.36)
where, is the maximum Doppler frequency.
Modeling of Multipath Rayleigh Fading Channel: The multipath fading channel is modeled as a linear Finite Impulse-Response (FIR) filter. Let { denote the set of samples at the input to the channel. Then the samples at the output of the channel are related to {through:
‘ (3.37)
where is the set of tap weights given by:
‘ (3.38)
In the equations above:
is the input sample period to the channel.
, where, is the set of path delays. K is the total number of paths in the multipath fading channel.
, where, , is the set of complex path gains of the multipath fading channel. These path gains are uncorrelated with each other.
and are chosen so that is small when n < or >
All modulated signals were subjected to Rayleigh fading where Doppler shift was varied to simulate three fading conditions low fading, medium fading and severe fading. Generation of GMSK signal in the presence of AWGN and Multipath Rayleigh fading channel effect is presented in Fig. 3.17.
Fig 3.17: Simulink model for GMSK Signal in Presence of AWGN and Rayleigh Fading Channel
The simulation set up for channel modeling is presented in Table 3.1.
Table 3.1 Simulation Set up for Channel Modeling
The multipath components of received GMSK signal is presented in Fig 3.18. The components were obtained at the output of fading channel for Doppler shift (fd ) of 4Hz. Since Doppler shift is small, number of multipath components is two, one direct and other after reflection. The signal was then applied to noisy channel for 3 dB SNR value.
Fig 3.18: Multipath Components for Low Fading (fd = 4Hz)
The multipath components for Doppler shift of 100Hz are presented in Fig. 3.19. It was observed that number of components and reflections increased because of increased Doppler shift. Fading results in increase of scattering of constellation plots. The effect of which has been reduced through equalization in preprocessing stage.
Fig 3.19: Multipath Components for Severe Fading (fd = 100 Hz)
3.3 PREPROCESSING
A crucial component for implementing the successful AMC is the preprocessor. The pre-processor’s work is to increase the performance of the classifier. The pre-processor removes disturbances from the signal thus increasing the SNR. Filtering, down converting, and equalizing the received signal are also done in the preprocessing stage. In present work the preprocessing tasks carried were denoising using wavelet decomposition, equalization and carrier frequency estimation.
3.3.1 De-noising
De-noising methods based on wavelet decomposition is one of the most significant applications of wavelets. In de-noising, wavelet decomposition is done since noise signals are included in high frequency details. Decomposed wavelet coefficients were processed using threshold setting. Finally, wavelet reconstruction of the signal was performed to reduce the noise in the signal. The de-noising procedure is as follows
Load noisy and Doppler shifted signal.
Perform Wavelet decomposition & calculate wavelet coefficients.
Estimate the noise standard deviation from the detail coefficients.
Select global threshold for signal de-noising.
Denoise the signal using the above threshold with soft thresholding.
3.3.2 Equalization
In data communication, digital signals are transmitted by the sender through an analog channel to the receiver. No ideal analog media such as telephone cables and radio channels typically distort the transmitted signal. In radio wave propagation, a certain degree of randomness exists due to factors such as atmospheric conditions, temperature other transmissions and Doppler shift (relative motion between transmitter and receiver). Time-dispersive channels can cause Inter Symbol Interference (ISI). For example, in a multipath scattering environment, the receiver sees delayed versions of a symbol transmission, which can interfere with other symbol transmissions. An equalizer attempts to mitigate ISI and thus improve the receiver’s performance.
Equalization Techniques: Linear equalizers, a class that is further divided into these categories:
Symbol-spaced equalizers (SSEs)
Fractionally Spaced Equalizers (FSEs)
Decision-Feedback Equalizers (DFEs)
Linear and decision-feedback equalizers are adaptive equalizers that use an adaptive algorithm when operating. Some adaptive algorithms are
Least Mean Square (LMS)
Recursive Least Squares (RLS)
Constant Modulus Algorithm (CMA)
One of the earliest and most successful applications of adaptive filters is adaptive channel equalization in digital communication systems. Using the standard LMS algorithm, an adaptive equalizer is a Finite-Impulse-Response (FIR) filter whose desired reference signal is a known training sequence sent by the transmitter over the unknown channel. The reliance of an adaptive channel equalizer on a training sequence requires that the transmitter cooperates by (often periodically) resending the training sequence, lowering the effective data rate of the communication link.
In many high-data-rate band limited digital communication systems, the transmission of a training sequence is either impractical or very costly in terms of data throughput. Conventional LMS and RLS adaptive filters depending on the use of training sequences cannot be used. For this reason, blind adaptive channel equalization algorithms that do not rely on training signals have been developed. CMA belongs to category of blind adaptive equalization technique.
Constant Modulus Algorithm (CMA): Constant modulus algorithm belongs to the class of blind adaptive equalization technique. Blind channel equalization is also known as a self-recovering equalization. The objective of blind equalization is to recover the unknown input sequence to the unknown channel based solely on the probabilistic and statistical properties of the input sequence. The receiver can synchronize to the received signal and to adjust the equalizer without the training sequence. The term blind is used in this equalizer because it performs the equalization on the data without a reference signal. Instead, the blind equalizer relies on knowledge of the signal structure and its statistic to perform the equalization. The objective of blind equalization is to recover the unknown input sequence to the unknown channel based solely on the probabilistic and statistical properties of the input sequence. The receiver can synchronize to the received signal and to adjust the equalizer without the training sequence.
Constant Modulus Algorithm ‘Fractionally Spaced Equalizer (CMA-FSE) technique has been used to undo the channel effect without the knowledge of channel itself. The constant modulus algorithm is a stochastic gradient algorithm designed to force the equalizer weights to keep constant envelope of received signal. However it was seen that CMA performance was better for M-ary PSK and QAM. The CMA algorithm defines a cost function to estimate channel noise in a received signal. The higher the output (cost) of the cost functions, the larger the channel noise in the received signal. The equalizer first calculates an equalized signal by adding the products of the received signal and the tap weights. After obtaining the equalized signal, the cost function calculates the cost of the equalized signal. The cost indicates the noise level of the received signal, and this cost is used to adjust the tap weights of the equalizer. The equalizer then calculates a new equalized signal using the updated tap weights, and obtains a new cost from the new equalized signal. The cost of the function is expected to be reduced by repeating the above processes. The lower the cost, the lower the noise in the received signal (Hatzichristos, 2001).
CMA cost function is given by
‘ (3.39)
where, s(n) is the signal to equalize and
is positive real constant determined by the pattern of constellation diagram.
The cost function J(n) is minimized iteratively using gradient based algorithm with update equation (Haykins, 1996) .
)-??J (n) ‘ (3.40)
where h = tap weight vector and
?? = is the step size parameter.
The Constant Modulus Algorithm with Fractionally Spaced Equalizer belongs to category of blind equalization technique, designed to undo channel effect without any knowledge of channel itself. In any standard CMA equalization system the coefficient taps are baud spaced. The implementation of fractional spaced equalizer using constant modulus combines advantage of both concepts. In present work the CMA-FSE algorithm was tested on 2PSK, 4PSK, 16QAM, 64QAM and 256QAM. SNR was set to 30 dB (Hatzichristos 2001). Simulation results proved that this method almost cancels the channel effect in 2PSK, 4PSK, and 16QAM as illustrated in Fig. 3.20, Fig. 3.21 and Fig. 3.22 respectively. Ideal constellation and scatter plot before and after equalization is illustrated in Fig. 3.20. Black star is ideal constellation plot of 2PSK signal. Blue cross presents scattered plot due to fading and channel distortion, and green dots represent clustered signal.
Fig 3.20 Constellation Plot for 2PSK Signal
Scatter plot of 4PSK signal before and after equalization, as well as the signal constellation for 4PSK modulation is presented in Fig. 3.21. It is observed from the plot that the points of the equalized signal are clustered more closely around the points of the signal constellation. This plot is obtained when finally equalizer weights have converged.
Fig 3.21 Constellation Plot for 4PSK
The signal before equalization deviates noticeably from ideal 16-QAM signal constellation. After convergence the equalizer’s weights work well on the received signal. As a result, the equalized signal looks far more like a 16-QAM signal constellation than the received signal does. The equalized signal in its steady state is presented in Fig. 3.22. On comparing scatter plots of 2PSK and 4PSK with scatter plot of 16QAM it is observed that deviation was more from ideal constellation plot.
Fig 3.22 Constellation plot for 16QAM
Ideal, received signal after channel distortion and equalized 64QAM signal is presented in Fig. 3.23. It is observed that received signal has more deviation from ideal constellation. As the equalized signal is clustered more closely around points of signal constellation, 64QAM signal is still recoverable after distortion.
Fig. 3.23 Constellation Plot for 64QAM
The constellation and scatter plot of 256QAM is presented in Fig. 3.24. The scatter plot is far more deviated as compared to 16QAM and 64QAM signal. As compared to 64QAM signal, 256QAM signal after equalization is not completely recoverable which affect classification results.
Fig 3.24 Constellation plot for 256QAM
3.3.3 Carrier Frequency Offset Estimation
Software Defined Radio (SDR) is foundation for wireless devices. To realize SDR systems parameters like carrier frequency, symbol rate, and modulation scheme should be reconfigured by adaptive receiver. In a conventional communications system, the receiver works cooperatively with the transmitter. The conventional type of receiver has a priori knowledge of the modulation format of the transmitted signal. The AMR problems are blind in nature. That is, the signals captured by an AMR receiver have no prior knowledge. In cooperative communications systems, Data-Aided (DA) methods (Kuo and Fitz, 1997; Mengali and Morelli, 2000) are often employed to estimate the carrier frequency, where a known training or pilot symbol sequence is periodically transmitted in addition to the effective information-bearing data. The training sequence does simplify the estimation of carrier frequency. However, it reduces the effective transmission rate.
In AMR, in general, there is no prior information on the center frequencies of the signals. Even if the center frequency is known nominally, by the published standards or by intelligence, carrier frequency offset estimation should be performed to compensate the local oscillator drifts and Doppler shifts induced by the relative motion of mobile systems and channel effects. Since a known training symbol sequence is unavailable hence estimation of signal parameters is required in AMR.
It is noted that only some AMR related publications have been concerned with the estimation of carrier frequency. Hsue and Soliman (1990) took the reciprocal of the average zero-crossing interval as the estimate of the carrier frequency. Assaleh et al. (1992) estimated the carrier frequency by averaging the instantaneous frequency of the received signal. The implied pulse-shaping function was rectangular in time domain and only limited to one symbol duration in these schemes. When a nonrectangular pulse shaping function is employed in the transmitted signal, the performance of these schemes may degrade greatly. The carrier frequency estimation can also benefit from a certain kind of precoders in the transmitter (Serpedin et al., 2000) or the known pulse-shaping function (Gini and Giannakis, 1998; Ghogho et al. 1999). It should be noted that such schemes are not feasible to non-cooperative applications although they are claimed to be blind.
Some Non-Data-Aided (NDA) methods have been developed to overcome the problems with DA methods. A widely applied NDA method is the Conjugate Cyclic Correlation based (CCB) approach (Ciblat et al., 2002). The CCB estimators assume that the transmitted symbols be noncircularly distributed. Based on the observation that the unique nonzero conjugate cycle frequency of the received signal is twice of the carrier frequency, the CCB estimators retrieve the carrier frequency by searching the peak of the Discrete Fourier Transform (DFT) of the conjugate time-varying correlations. If the transmitted symbols are circularly distributed, cyclic moments should be used (Giannakis and Zhou, 1995). The Nonlinear Least Square (NLLS) estimators are also popular in carrier frequency estimation. They studied the relationship between the cyclic estimators and the NLLS estimators.
A blind carrier frequency estimation algorithm has been developed. The carrier frequency estimator is based on the phases of the autocorrelation functions of the received signal (Sun and Feng, 2010). Algorithm is tested for various carrier frequencies of the generated modulated signals under varying SNR conditions.
The term ‘Cyclostationary’ is mainly used for a special class of non-stationary random signals which exhibit periodicity in their statistics. Cyclostationary spectral analysis gives more information about the signal, compared to the conventional spectral analysis. Therefore, the cyclostationary characteristics of the digitally modulated signals are investigated. This method is based on the ideological of spectrum peak searching. The carrier frequency estimator is based on the phases of the autocorrelation functions of the received signal. Unlike the cyclic correlation based estimators, it does not require the transmitted symbols being noncircularly distributed. The time-varying correlation function of s(t) input signal is defined as
s*() ‘ (3.41)
Carrier frequency estimation was done for modulated signals. Carrier frequency offset was calculated and compensated. Algorithm was tested for varying carrier frequencies. Simulink Model for carrier frequency estimation of GMSK signal is presented in Fig. 3.25. The effect of varying Doppler shift, path delay and varying SNR was observed on carrier frequency estimation.
Fig. 3.25: Simulink Model for Carrier Frequency Estimation of GMSK Signal
Results showed that correct estimation of carrier frequency was achieved for low SNR. However in the presence of Rayleigh fading specially with the increase in Doppler’s shift accuracy of CFE dropped even for relatively high SNR. Correct carrier frequency estimation was achieved for SNR -3 dB and even -5 dB when band limiting filter was used prior to transmission of signal in the channel.
CHAPTER 4
METHODS OF FEATURE EXTRACTION AND CLASSIFICATION
Feature extraction and classification algorithm stages are the main parts of a modulation recognition system. Performance of the modulation recognition system mainly depends on the prior knowledge of some of the signal parameters, selection of the key features and classification algorithm. Different types of digital signal have different characteristics. Finding proper features for the recognition of digital signals, particularly in case of higher order and/or nonsquare kinds of digital signal are a serious problem. The key features for modulation classification in pattern recognition approach must be selected. These features should have robust properties which are sensitive with modulation types and insensitive with SNR variation. The feature extraction part reduces the dimensionality of the measurement by extracting the distinctive features. It should be simple and fast to calculate. There are several ways to make the decision, based on the obtained features such as decision functions, distance functions, and neural networks.
Feature extraction techniques are based on spectral analysis, instantaneous attributes (amplitude, phase and frequency), wavelet transform, higher order statistical moments and cumulants and shape matching of signal constellations. Various features used to distinguish the digitally modulated signals are described. Feature based classification techniques are then discussed. In the present work stochastic and higher order statistical features were derived. Seven key features have been used to develop the classifier. Two types of classifiers were developed based on derived features and their performances were compared.
4.1 FEATURE EXTRACTION
In AMR, feature extraction is essential, as classification is based on signal segments consisting of thousands of samples. In pattern recognition it is necessary to reduce the dimensionality of the data before presenting it to the classifier. This dimensionality reduction is called feature extraction and consists of finding a smaller set of characteristics that helps the classifier to generalize between examples of the same class and to discriminate between examples of different classes Features can be put into two broad categories
Instantaneous Time domain features
Frequency domain features
4.1.1 Instantaneous Time Domain Features
Instantaneous features are related to the instantaneous amplitude, phase, and frequency as discussed and derived in chapter 3. These features represent all variations in the received modulated signal. The general form of received modulated signal is given by
r(t) =Re ‘ (4.1)
where C(t) is the complex envelop of modulated signal,
n(t) is AWGN,
fc is the carrier frequency ,
is the Rayleigh channel amplitude,
is the phase offset,
is the carrier frequency offset and
Re{.} denotes the real part.
Modulation is characterized by varying the following parameters: carrier frequency, phase, or amplitude. The instantaneous variation of these parameters is often exploited for the purpose of modulation classification. If denotes Hilbert transform of signal r(t) defined in Eq. 4.1 the mathematical formulas for the instantaneous amplitude , phase (t) and frequency f(t) are
‘ (4.2)
(t)=arg ‘ (4.3)
‘ (4.4)
The received signal, which is sampled at sampling rate fs Hz, is expressed in complex form by applying Hilbert transform. The complex data sequence is divided into several nonoverlapping segments, where each segment contains Ns samples. For each segment, the instantaneous amplitudes and instantaneous phases are then extracted, where the index i represents that and are the ith complex sample. A simple scheme is employed to unwrap the instantaneous phases, resulting in an unwrapped phase sequence}. The nonlinear phases} are then obtained by removing the linear phase owing to carrier frequency from the unwrapped phases. The instantaneous frequency 1} is also derived by differentiating the sequence of.
‘ (4.5)
There are various features which are based on instantaneous amplitude, phase and frequency. Some of the instantaneous time domain features are discussed below
The standard deviation of the absolute value of the normalized- centered instantaneous amplitude of a signal segment
‘ (4.6) where, = value of normalized-centered instantaneous at time,
t = (i=1, 2,’. .Ns)
where, fs = sampling rate
= the number of samples per signal segment.
and
= sample mean of a (i) =
The standard deviation of the absolute value of the normalized-centered instantaneous amplitude in the non-weak segment of a signal is given by
‘ (4.7)
where, = threshold value for of the non weak is signal and below which the estimation of the instantaneous phase is very noise sensitive.
L = length of non weak values.
The standard deviation of the centered non-linear component of the direct (not absolute) instantaneous phase in non-weak segment is given as
‘ (4.8)
where,
the non linear phase =(i) ‘0
0 =
The standard deviation of the centered non-linear component of the absolute instantaneous phase in a non-weak segment
‘ (4 .9)
The standard deviation of the absolute value of the normalized- centered instantaneous frequency of a signal segment
‘ (4.10)
where, normalized- centered instantaneous frequency sequence
= symbol rate of digital sequence
The standard deviation of the absolute value of the normalized- centered instantaneous frequency of a non-weak segment
‘ (4.11)
where L is the number of non-weak samples in the segment.
The kurtosis (fourth order moment) of the normalized instantaneous amplitude and frequency
‘ (4.12)
‘ (4.13)
Spectrum symmetry measured by the ratio S given by
where,
‘ (4.14)
‘ (4.15)
where, is received complex signal.
The instantaneous features standard deviation of absolute amplitude (??aa) and standard deviation of instantaneous amplitude (??a) capture the variation of modulated signal amplitude. Hence, they are used for determining ASK order (Yuan et al., 2004) and to distinguish ASK signals from PSK signals. The instantaneous features related to phase variation are very useful in finding PSK modulation order (Youyong et al., 2008) to distinguish MFSK/2PSK from 4PSK/MQAM modulations and to separate MASK from MPSK/MQAM. Features standard deviation of absolute frequency (??af) and standard deviation of normalized frequency (??nf) can be used to find the order of FSK modulation, and to separate PSK signals from FSK signals (Vito et al., 2010).
Feature such as kurtosis of instantaneous amplitude (was used with DT classifier to separate AM from 2ASK/4ASK, and kurtosis of instantaneous frequency () to separate FM from 2FSK/4FSK (Nandi and Azzouz, 1997). Further was used to separate FSK/PSK from ASK/QAM and to separate FSK from PSK (Youyong et al., 2008).
4.1.2 Frequency Domain Features
In frequency domain basically the power spectrum (energy distribution as a function of frequency) is analyzed. Dependent on the characteristics of signals following parameters are used as features.
Stationary Spectrum: Estimating the power distribution directly from the FFT gives a very erratic function. To reduce the variance of the spectrum averaging is needed. The maximum value of Power Spectral Density (PSD) of normalized-centered instantaneous amplitude.
‘ (4.16)
represents the variations in amplitude which make this feature useful to discriminate between amplitude and non amplitude modulations in both analog and digital modulations. This feature can express the character of signal’s envelope and was added to differentiate between the modulation schemes that carry amplitude modulation and those that do not. This feature was used to discriminate between MQAM/MASK and FSK/PSK modulations (Cheol-Sun, 2008).
Cyclostationary Spectrum: Radio signals and most manmade signals have the characteristics of being cyclostationary i.e. the covariance and the spectrum varies periodically with time. A random signal is considered cyclostationary if it’s HOMs are periodic. The cyclostationarity of modulated signal is due to the periodical repetition invoked by the symbol rate. This feature does not need a prior knowledge of Carrier Frequency Offset (CFO), Carrier Phase Offset (CPO) (Rosti, 1998).
A continuous-time second-order random process {X(t); t'(”,’)} is defined to be Cyclostationary in the wide-sense, or of second order, with cycle period T if and only if its mean and autocorrelation exhibit the periodicity
‘ (4.17)
If the symmetric delay product ?? = t1 ‘ t2.
Then the autocorrelation function in Eq. 4.17 can be rewritten as
‘ (4.18)
Since the autocorrelation function is periodic it can be expanded to its Fourier series representation,
‘ (4.19)
where,
‘ (4.20)
and ?? is the cyclic frequency.is called Cyclic Autocorrelation Function (CAF) which is function of two variables ?? and ??.
For a process that exhibits a single periodicity, the range of ?? is the set of integers multiples, i.e. harmonics of the fundamental frequency. For ?? =0 the Fourier series coefficient is equal to the time averaged probabilistic autocorrelation function defined for a Wide Sense Stationary (WSS) process (Gardner and Spooner, 1994). Thus a process X(t) is cyclostationary of second order if and only if for any . If the autocorrelation of a process X(t) is not periodic, it cannot be expanded to a Fourier series.
In that case can be defined as
‘ (4.21)
where, is the time averaging operation defined as
‘ (4.22)
If is nonzero for some , the process is called polycyclostationary (or multiply cyclostationary or almost cyclostationary).
4.1.3 Wavelet Transform
There exist MC methods that have been using non- stationary spectral estimates as features. Wavelets are one of the examples. Different modulation schemes have the characteristic of different transients in amplitude, frequency or phase. The Wavelet Transform (WT) is one of the tool for analyzing non-stationary signals, which include digital communication signals. The WT magnitude of communication signals vary with modulation types. The WT has capability to extract transient information which can be exploited for modulation classification. WT contains transients in amplitude, frequency or phase and is quite suitable at extracting transient information.
It was developed to overcome the short coming of the Short Time Fourier Transform (STFT), which can also be used to analyze non-stationary signals. While STFT gives a constant resolution at all frequencies, the Wavelet Transform uses multi-resolution technique by which different frequencies are analyzed with different resolutions. Another attractive feature of WT is that it can be computed using fast algorithm (e.g., Fast WT) and hence allowing identification of modulation types in real time. Wavelet transform is another common technique used for features extraction as it has the advantage of being able to reduce effect of noise (Maliatsos et al., 2007).
4.1.3.1 Continuous Wavelet Transform (CWT)
The wavelet transform decomposes the signal in terms of a fundamental waveform, called mother wavelet. This analysis reveals both time and frequency domain information for variable resolutions. The main advantage is the ability to analyze a localized area of a larger signal, revealing signal aspects (trends, discontinuities etc) that could not be noticed otherwise (e.g. with a Fourier transform). A wavelet is a properly chosen, zero-mean waveform of finite duration (Hamid, 2007). Different modulation schemes have different transients, and the differences can be exploited by CWT for modulation classification. The wavelet transform decomposes a signal from time- domain to time-scale or wavelet domain.
The continuous wavelet transform of a signal s(t) is defined as
‘ (4.23)
where, a = scale ,
translation and
the superscript * denotes complex conjugate.
The function ??(t) is the mother wavelet and ?? a,r (t) comes from time scaling and the translation of the mother wavelet. The window size of the wavelet transforms decreases as the analyzing frequency increases. As a result, a small scale baby wavelet has short duration and rich high frequency content and thus can locate and represent the transients well. This makes the wavelet transform ideal for transient analysis and detection.
For the digital implementation the integral in Eq. 4.23 is replaced by summation. By setting sampling time and restricting the scale to be an even integer.
‘ (4.24)
The Haar CWT of PSK signal at n=iT, the instant where the phase change occurs
‘ (4.25)
‘ (4.26)
CWT has different values wherever a phase change occurs. If a is chosen to be a small value is chosen (a narrow baby wavelet), there will be peaks at times where phase change occurs.
The CWT Haar magnitude of FSK signal is
‘ ‘ (4.27)
Analogous to PSK, peaks occur when the symbol changes in non continuous phase FSK As the frequency is a variable, the CWT magnitudes resembles a multi-step function with a number of level equal to the number of modulation frequencies. M-ary FSK can be identified by determining the number of DC levels.
The CWT Haar magnitudes of 16QAM signals is
‘ (4.28)
The CWT Haar magnitude of PSK signal is a constant, while the CWT Haar magnitude of FSK signal is a multistep function since the frequency is a variable. The FSK can be distinguished by computing the variance of CWT magnitude after removing the peaks by median filtering. Standard deviation, variance of wavelet transform coefficients can be used as features to classify modulated signals.
4.1.3.2 Discrete Wavelet Transform (DWT)
Feature extraction is the key to pattern recognition. Two available sources of information involved with time and frequency domains are inherent in communication signals. When the signal includes important structures that belong to different scales, it is often helpful to decompose the signal into a set of ‘detail components’ of various sizes. The WT decomposition process is used to find wavelet coefficients. It can be iterated with successive approximations being decomposed in turn, so that one signal is broken down into many lower-resolution components as shown in Fig. 4.1. This is called the Wavelet Decomposition Tree (WDT). Approximation and detail coefficients are derived at different levels which are used as features. Several families of wavelets are Haar, Daubechies, Biorthogonal, Coiflets, Symlets, Morlets, Mexican Hat and Meyer.
Fig 4.1: Approximation and Detail Coefficients
Discrete Wavelet Transform (DWT) analyzes signals at different frequency bands with different resolutions by decomposing a signal into coarse approximation and detail information, so it is widely used in pattern recognition and classification. DWT employs two sets of function, known as the scaling functions and wavelet functions, which can be viewed as low-pass and high- pass filters, approximation coefficients and detail coefficients.
The DWT procedure is given as follows: From the scaling coefficient c0(k), the wavelet coefficient d1(k) is computed by Eq. 4.29 and c1(k) by Eq. 4.30. The Wavelet Transform Coefficients (WTCs) of a given function f(t) at the jth level and kth point are computed as
‘ (4.29)
The wavelet coefficient is obtained by convolving the sequence with high pass filter, and then decimating by a factor of two. The scaling function coefficient at the jth level and kth point becomes
‘ (4.30)
where, is a wavelet low pass filter .
Eq. 4.29 and Eq. 4.30 are applied recursively to compute d2(k) and c2(k) from c1(k), and so forth. This process is called the analysis or decomposition part of the DWT as presented in Fig. 4.2. In this Figure, the results of the DWT are the scaling coefficients c2(k) and wavelet coefficients d1(k) and d2(k). Further, both the scaling and wavelet coefficients are referred to wavelet transform coefficients. The different resolution for each level is related to the number of WTCs. For level j the number of WTCs equal 2j. As the number of WTCs decreases, the time resolution is reduced and each scaling space contains gradually less information. The differences in information between the scaling spaces at level j and level j-1 is contained in the wavelet space at level j. The bandwidth of the frequency band at level j is half that of the frequency band at level j-1.
Fig 4.2: Decomposition of Signal using DWT
The approximation coefficients are the high-scale, low-frequency components of the signal, while the detail coefficients are the low-scale, high frequency components. The DWT, or filtering, process can be repeated until only one approximation coefficient is found, the next lower frequency region, and so on. The DWT based features have been proposed with ANNs (Prakasam and Madheswaran, 2008) and SVMs (Cheol-sun et al., 2008) for the classification of different digital modulation schemes including FSK, PSK and QAM modulations.
4.1.4 Higher Order Statistical (HOS) Features
Wavelet transform is not computationally intensive but can classify the modulation scheme of an unknown signal very well. However it cannot classify modulation order accurately for all modulation schemes. Higher order statistical parameters such as Moments and cumulants are used to classify higher order signals. Moments and cumulants are statistical features used to help identify distinguishing characteristics of data (Dobre et al., 2003). These statistical features have specifically been used in the field of signal processing to help identify the modulation type of a noisy signal. Moments and cumulants are peculiarly resilient to noise effects (Young, 2008).
Higher Order Statistics (HOS) are divided into Higher order Moments (HOMs) and Higher Order Cumulants(HOCs), which are widely used in classification of various ASK, PSK, and QAM signals . These features have three main advantages: i) reflect the higher order statistical characteristics of signal ii) eliminate the effect of noise and iii) have robustness to phase rotation. The HOCs features have been used in a number of published works with both Decision Tree (DT) and Pattern Recognition (PR) classifiers (Han et al., 2004).
4.1.4.1 Moments
Probability distribution moments are a generalization of the concept of the expected value, and are used to define the characteristics of a probability density function. The kth moment of a random variable is given by
‘ (4.31)
where ?? is the mean of the random variable .The definition for the kth moment for a finite length discrete is given by
‘ (4.32)
where N is the data length and signals are assumed to be zero mean .
The auto-moment of the random variable may be defined as
‘ (4.33)
where, p and q represent the number of non conjugated terms and number of the congugated terms respectively and p+q is called the moment order. For example, for p=2 and q=0 Eq. 4.33 becomes
‘ (4.34)
which is the second moment or the variance of random variable.
In similar way expressions for, were derived. The normalized moments are called skewness and kurtosis respectively. Skewness is the measure of symmetry of PDF, where as kurtosis is the degree of peakedness (density of peaks) of the Probability Density Function (PDF). Second or higher order moments describe the shape of the PDF of the distribution and the sequence of moments is analogous to the components of Fourier sequence. Using the definition of auto moments, the expressions for moments of order 2, 4, 6 and 8 may be derived as shown in Table 4.1.
Table 4.1: Statistical Moments of the form ai+jbi
4.1.4.2 Cumulants
Consider a scalar zero mean random variable s with characteristic function:
‘ (4.35)
Expanding the logarithm of the characteristic function as a Taylor series,
‘ (4.36)
where the constant are called the cumulants. The first three cumulants are identical to first three moments.
‘ (4.37)
The symbolism for the order cumulant is similar to that of the order moment. More specifically
‘ (4.38)
4.1.4.3 Relation between Cumulants and Moments
The nth order cumulant is a function of the moments of orders up to (and including) n. Moments may be expressed in terms of cumulants as
‘ (4.39)
where, the summation index is overall partitions for the set of indexes (1,.., n)’and q is the number of elements in a given partition .Cumulants may also be derived in terms of moments. The nth order cumulant of a discrete signal s(n) is given by
‘ (4.40)
where, the summation is being performed for all partitions for the set of indexes (1,’n).
The relation between cumulants and Moments is presented in Table 4.2.
Table 4.2: Relation between Moments and Cumulants
4.2 FEATURE BASED CLASSIFICATION
A natural step after feature extraction is making decision to identify the type of intercepted signal. In FB methods, decision-making can be achieved by two methods. The first is the Decision Tree (DT) method (Yuan et al., 2004; Maliatos et al., 2007; Fu-king et al., 2008), while the second method is based on using Pattern Recognition (PR) such as ANNs (Azzouz and Nandi, 1998; Prakasan and Madheshwaran, 2008) or combinations of more than one Artificial Intelligence (AI) technique to optimize the solution. The main objective of using PR techniques is to enhance the classification rate at low SNR.
4.2.1 Wavelet Transform based DT Classifier (Technique 1)
Different modulation schemes have the characteristic of different transients in amplitude, frequency or phase. The Wavelet Transform (WT) is a powerful tool for analyzing non-stationary signals, which include digital communication signals, and the WT magnitude of communication signals vary with modulation types. The WT has capability to extract transient information which can be exploited for modulation classification.
Wavelet Transform was used to derive statistical parameters to identify M-ary PSK, M-ary QAM and M-ary FSK modulations. Statistical parameters were calculated and compared against certain threshold values to detect the modulation type. In ideal case, the Haar WT magnitude of a PSK signal is a constant and that of a FSK signal is a multistep function. Hence the variance of of an input signal was used as a feature to classify the two signals. Compared to PSK and FSK signals, one distinction in QAM signal is that it does not have constant amplitude. The of a QAM signal is a multi-step function similar to that of a FSK signal because of the change in amplitude as symbol changes.
The modulation identification scheme used is presented in Fig. 4.3. Histogram peak count technique was used to distinguish the modulated signals for varying SNR’s. Based on the peaks, signals were put into class A and class B.
Fig 4.3: Identification Algorithm
Since the transient characteristics of M-ary QAM and M-ary PSK signal are constant, it will have single peak in its histogram but the M-ary FSK signals have more than single peak because these signals have multistep frequency component. Verification of signals was also done by finding the transient values by applying 1D wavelet transform to various modulated signals using Haar wavelet.
Table 4.3: Class Distinction of Modulated Signals
Signals falling in class A and class B are presented in Table 4.3. Further classification of signals belonging to class A was done based on comparison of statistical values with threshold values. Classification algorithm using mean (th1) and variance (thp1, thp2, thq1, thq2) as calculated using wavelet transform is presented in Fig. 4.4.
Fig 4.4: Classification of Class A Type Signals
The simulated results using wavelet transform technique and statistical parameter measurement was obtained. It was observed that high percentage of correct modulation identification was possible for SNR up to 5 dB. However when higher order QAM signals were added and fading channel effect was considered, percentage of correct classification dropped. The fall in identification rate is due to the fading effect. Higher order QAM signals are majorly affected by channel distortion hence misclassification rate increases. This in turn affects the overall correct classification rate.
4.2.2 Wavelet Transform based DT Classifier (Technique 2)
In this approach the identifier consists of two branches as presented in Fig. 4.5. One branch is without amplitude normalization and the other is with amplitude normalization.
Fig 4.5: Algorithm for Feature Extraction using Wavelet Transform
The identifier first finds the wavelet transform of an input signal. After removing the peaks by a median filter, the identifier computes the variance of the median filter outputs. V1 is the variance obtained without normalization and V2 is variance with normalization. Better results were expected as peak removal was done by median filter.
Features of ASK, PSK, FSK and QAM signals were compared. Compared to PSK and FSK signals, one distinction in QAM signal is that it does not have constant amplitude. The continuous wavelet transform of the normalized signal was taken into consideration. Knowing that the amplitude of the normalized signal is constant and, it was observed that the signal normalization would only affect the wavelet transform of nonconstant envelope modulations (i.e., ASK and QAM), and would not affect wavelet transform of constant envelope ones (i.e., FSK and PSK). There should be distinct peaks in the wavelet transform of the signal and that of the normalized one resulting from phase changes at the times where the HAAR wavelet covers a symbol change.
The of a QAM signal is a multi-step function similar to that of a FSK signal because of the change in amplitude as symbol changes. On the other hand, if QAM signal is normalized, it will behave like a PSK signal and its will be a constant. Amplitude normalization has little effect on the of PSK and FSK signals since both of them have constant amplitude. Hence QAM, PSK and FSK signals could be distinguished by computing the variances of with and without applying amplitude normalization. The length of the median filter was 20. The scale of the Haar wavelet was 4. Signals were analyzed for SNR varying from 0 dB to 25 dB.
Simulations proved that the percentage of correct identification was higher, when SNR was not lower than 5 dB. In this approach also, misclassification was high for SNR less than 5 dB and degraded further in presence of fading. Further this approach limited the identification of higher order modulated signals.
4.2.3 Stochastic and HOS based Classifier
Modulated signals such as 2ASK 4ASK, 2PSK, 4PSK, 2FSK, 4FSK, 16QAM, 64QAM, 256QAM and GMSK were generated. AWGN channel noise and multipath Rayleigh fading was added to simulate channel condition. Instantaneous features such as amplitude, frequency and phase for set of signal were first derived for all set of signals as discussed in chapter 3. Seven features were derived from the received signal as listed in Table 4.4.
Table 4.4: List of Feature Vectors for Classification
The features to be used for AMR must be selected so that they are sensitive to the modulation types of interest. The classifier operates on extracted features and makes a decision about the modulation type. Several pattern matching techniques exist as linear classifiers, tree classifiers neural network based classifiers, hypothesis testing based classifiers and adhoc based classifiers.
4.2.3.1 Decision Tree Classifier
Decision tree methods are one of the basic classification procedures in which decision at each stage is made according to predefined threshold values. In these methods predefined threshold values are the main parameters affecting the performance of the classifier. Therefore, threshold values of the selected features must be chosen carefully in order to reduce the probability of wrong decision. Moreover, sequence order of the features and the threshold values should be updated to recognize a modulation type.
For decision theoretic classification approaches, modulation formats are determined by traversing a decision tree where the features are tested against thresholds at the tree nodes until reaching an end-node, which indicates a format. A decision tree requires few resources and executes very quickly. It is therefore suitable for online classification and for implementation in resource-limited systems. Due to its simplicity and good classification abilities, the decision theoretic approach has been popular for modulation classification (Iverson et al., 2006). The main advantage of using DT algorithms is the simplicity of implementation (Vito and Rapuano, 2009). In addition, DT methods can be promoted to accommodate more modulations by adding additional decision branches.
Seven key features were used as input to decision tree classifier to distinctly classify the set of modulated signals. Decision Tree classifier based on threshold values of feature vectors is presented in Fig. 4.6. Feature vector 1 categorizes MFSK, MPSK, and GMSK below a threshold value of 0.3 and MASK and MQAM above it. Feature vector 4 ( divides MFSK and GMSK below a threshold value of 1 and MPSK above the value. Feature vector 2 () separates GMSK and MFSK below and above a threshold value of 0.25. Feature vector 3 ( classifies 2PSK and 4PSK below and above the threshold value of 0.6.
Fig 4.6: Decision Tree Classifier Based on Combination of Features
Feature vector 2 () classifies 2ASK and 4ASK signals below and above a threshold value of 0.25. Feature vector 5 ( distinguishes 2FSK below the threshold value of 0.25 and 4FSK signal above it. Feature vector 6 (Eight Order moment E S,8,4) classifies 16QAM and 64 QAM in one category below a threshold value of 4 and 256 QAM in another category. Feature vector 7 (Eight order cumulant C S,8,4) was used to separate 16QAM and 64QAM signal below and above a threshold value of 20. Hence seven key features completely classify ten modulated signals.
4.2.3.2 Artificial Neural Network based Classifier
ANNs have proven to give good classification results and especially in noisy conditions, offer better performance than decision trees (Khurshid et al., 2007; Faek 2010) proposed recognition scheme using ANN method. ANN is a well known mathematical model based on Biological neural network.ANN is good in finding the desired pattern of the data. It also establishes the relationship between the input and output. ANN can easily work in complex environment where other computations fail. ANN is good in non linear mapping of the signal, as well as self adaptability. Thus ANN is employed for recognizing different M-ary modulations (Bhavna et al., 2012).
ANNs can adapt and learn to work with complicated signals. In view of learning algorithms, the ANNs can be categorized into supervised or unsupervised networks. In the supervised ANNs, one part of the data set is used for learning and the other part is used for testing. On the other hand, the unsupervised ANNs cluster the input data and train themselves. The first technique gives results that are more accurate. However, it needs a large number of data compared to the unsupervised techniques. Most of the ANNs that have been tested in AMC field use the supervised learning techniques including Multi-Layer Perceptrons (MLP) and Radial Basis Function (RBF). The MLP is attractive for the designers because it needs small memory.
Multilayer Perceptron (MLP): Several types of ANNs exist but the most common one used for AMR is the Multi-Layered Perceptron. Before looking at that, it is useful to look at its basis constituent, namely the Perceptron. The Perceptron consists of the weights, the summation processor and the adjustable threshold as presented in Fig. 4.7.
Fig. 4.7: A Perceptron
A Perceptron models a neuron by receiving weighted input and returning an all-or-nothing output depending on whether the weighted sum of input is less or greater than an adjustable threshold. The input and the weights can be positive or negative real values. If the sum of the weighted input is greater than the threshold, the Perceptron is said to fire and output a 1. If the sum is below or equal to the threshold, the output is 0. The Perceptron’s ability to learn is a matter of modifying the values of the weights and threshold.
A Perceptron can only be used in linearly separable, 2-class classification problems. This is a major limitation, as can be illustrated by looking at the Exclusive-OR (XOR) problem. A XOR gate is supposed to output 0 if the two input are the same or output a 1 if the two input are different. The Perceptron cannot solve this somewhat
Fig 4.8: X-OR Truth Table and Graphical Representation of Solution.
simple problem because the output classes are not linearly separable as presented in Fig. 4.8. The limitations of the Perceptron led to the development of the Multi-Layered Perceptron with the popular back-propagation learning algorithm.
A Multi-Layered Perceptron (MLP) is able to handle more complex and non-linear classification problems. An example of an MLP is illustrated in Fig. 4.9. It consists of one input layer, one or more hidden layer and one output layer of computational nodes (Perceptron). Each node in a layer is connected to all nodes in the layer immediately behind and in front, but there are no connections between the nodes within a layer. The input signal is propagated through the network in a forward direction on a layer-by-layer basis. In an AMR task, the number of input nodes typically corresponds to the number of features that are extracted from the signal.
Fig 4.9: An Example of 4 Input 3 Output MLP, 1 Hidden Layer with 4 Nodes Each
Similarly, the number of output nodes corresponds to the number of modulation schemes. When classifying a modulation scheme all the output should ideally be zero except the output that represents the classified modulation scheme, which should be one. The hidden layers are not part of the input or output of the MLP. Their purpose is basically to enable the MLP to learn more complex classification problems through internal mappings.
The number of hidden layer and nodes is somewhat arbitrary. Too few may prevent the MLP from classifying and too many may cause an unnecessarily long training time and over-fitting. Over-fitting occurs when the MLP is trained too long so that the decisions boundaries get too close to the training examples. The MLP will consequently be very good for classifying the training examples, but will be very poor for classifying unseen and slightly different test examples.
CHAPTER 5
RESULTS AND DISCUSSION
Automatic digital modulation classification adaptive to SDR, in multipath fading environments as well as additive white Gaussian noise is the core of the thesis. The general idea behind the SDR architecture is to perform signal processing in software instead of being defined in hardware. This enables the radio to get adapted to change in environment and user requirements by simply updating the software or by using adaptable software systems. In such scenarios, a broadcaster could change the appropriate modulation scheme according to the capacity of the channel. Since a single SDR system robustly handles multiple modulations, AMR is an important issue for such system. Meaning thereby, an intelligent algorithm identifying the modulation must be running at the receiver side.
The main objective of work was to develop a generalized algorithm at the receiving end to identify simultaneously the various digital modulation types under varying Signal to Noise Ratio (SNR) and channel conditions. The MATLAB and Simulink models generated ten modulated signals, modeled propagation through noisy channels, and sent these signals through a classification scheme that attempted to identify and classify these modulation types correctly. Results demonstrate the robustness of the hybrid features, to various levels of noise and fading. The simulation and results obtained for the performance of the designed modulation classification system are discussed. The system was evaluated under varying channel conditions, without a priori knowledge of critical signal parameters. The progress of work was as follows.
Performance analysis of Wavelet transform based classifier without preprocessing.
Performance analysis of Wavelet transform based classifier with preprocessing.
Performance analysis of Stochastic and HOS hybrid feature based DT classifier.
Performance analysis of stochastic and HOS hybrid feature based ANN classifier.
Comparison of performance of DT and ANN classifiers for lower bound SNR of -5 dB.
The commonly used performance evaluation metric for classifier is percentage of correct classification given by Confusion matrix. A Confusion Matrix??is a specific table layout that allows visualization of the performance of an algorithm. Each column of the matrix represents the instances in a predicted class, while each row represents the instances in an actual class.??The system performance is measured by its Probability of correct classification (Pcc), defined as the percentage of the total number of modulation classifications made that were accurate.
5.1 WAVELET TRANSFORM BASED CLASSIFIER (TECHNIQUE 1)
The developed algorithm was verified for 2FSK, 4FSK, 2PSK, 4PSK, 16QAM and GMSK modulation schemes. Wavelet transform was applied to extract the transient characteristics of the received signal. After extracting the transient characteristics, the coefficients were extracted to generate the histogram peak. A noisy 2PSK signal is presented in Fig. 5.1.
Fig 5.1: 2PSK Signal
The histogram plot and histogram peak of 2PSK is presented in Fig. 5.2 and Fig. 5.3 respectively. Since M-ary PSK signal has constant transient characteristics, a single peak is obtained in its histogram as presented in Fig. 5.3.
Fig 5.2: Histogram Plot of 2PSK Signal
Fig 5.3: Histogram Peak for 2PSK Signal
2FSK signal and its histogram plot are presented in Fig. 5.4 and Fig. 5.5 respectively. Multiple peaks are obtained as the signal has multistep frequency component which distinguishes the two signals as presented in Fig. 5.6.
Fig 5.4: 2FSK signal
Fig 5.5: Histogram Plot of 2FSK Signal
Fig 5.6: Histogram Peak of 2FSK Signal
Mean and Variance are used as features to distinguish the modulated signals. Performance of classifier is evaluated by the percentage of correct classification. Probability of correct classification (Pcc) is presented in Table 5.1.
Table 5.1: Probability of Correct Classification (Pcc %) at Different SNR
Technique 1
Following observations are made from Table 5.1:
Signals are 100% correctly classified upto 10 dB.
For 5 dB SNR signal classification is >= 98% where 4FSK signal is 100% correctly identified even at 5 dB SNR.
The identification rate for 2PSK and 4FSK is 92% at 0 dB SNR.
95% results are achieved for 4PSK and 16QAM. However the % classification results obtained are only in presence of AWGN.
Average performance of the classifier at 5 dB and 0 dB is 98.83% and 93.3% respectively.
5.2 WAVELET TRANSFORM BASED CLASSIFIER (TECHNIQUE 2)
In this technique, Wavelet transform was used to derive the feature after preprocessing. The continuous wavelet transform of the normalized signal was taken into consideration. The Intermediate Frequency (IF) considered is 1000Hz. The length of the median filter was 20. The scale of the Haar wavelet was 4. Signals were analyzed for SNR varying from 0 dB to 20 dB. Variance was selected as feature to distinguish the signals.
The signals were analyzed with and without amplitude normalization. Simulated results illustrate that there are distinct peaks in the wavelet transform of the signal and that of the normalized one, resulting from phase changes at the times where the Haar wavelet covers a symbol change. Signal normalization will only affect the wavelet transform of nonconstant envelope modulations (i.e. ASK and QAM), and will not affect wavelet transform of constant envelope ones (i.e. FSK and PSK).
2FSK Signal and 2FSK signal with AWGN is presented in Fig. 5.7(a) and Fig. 5.7(b) respectively. Amplitude normalization has little effect on the of FSK signals as it has constant amplitude.
Fig 5.7: (a) 2FSK Signal (b) 2FSK Signal with AWGN
The Haar Wavelet transformed 2FSK signal is presented in Fig. 5.8. 2FSK signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.8(a) and Fig. 5.8(b) respectively. 2FSK noisy signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.8(c) and Fig. 5.8(d). Amplitude normalization does not affect FSK signal since it is constant amplitude modulation. Hence of amplitude normalized FSK signal will remain the same. FSK signal is multistep function before and after normalization hence it variance without amplitude normalization and with normalization will be greater than zero.
Fig 5.8: Wavelet Transformed 2FSK Signal
2PSK signal and 2PSK signal with AWGN noise is presented in Fig. 5.9(a) and Fig. 5.9(b).
Fig 5.9: (a) 2PSK Signal (b) 2PSK Signal with AWGN
The Haar Wavelet transformed 2PSK signal is presented in Fig. 5.10. 2PSK signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.10(a) and Fig. 5.10(b) respectively. 2PSK noisy signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.10(c) and Fig. 5.10(d). Amplitude normalization does not affect PSK type signal because it does not contain amplitude variation. Ignoring the peaks the of PSK signal is a constant. The variance of a constant is zero. This feature distinguishes PSK signal from QAM and FSK signals.
Fig 5.10: Wavelet Transformed 2PSK Signal
The generated 16QAM signal is presented in Fig. 5.11. 16QAM signal without noise and 16QAM signal with AWGN are presented in Fig. 5.11(a) and Fig. 5.11(b).
Fig 5.11: (a) 16QAM Signal (b) 16QAM Signal with AWGN
The Haar Wavelet transformed 16QAM signal is presented in Fig. 5.12. 16QAM signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.12(a) and Fig. 5.12(b) respectively.
Fig 5.12: Wavelet Transformed 16QAM Signal
The of a QAM signal is a multi-step function similar to that of a FSK signal because of the change in amplitude as symbol changes. On the other hand, if QAM signal is normalized, it will behave like a PSK signal and its will be constant. The amplitude variations disappear after amplitude normalization. A QAM signal with amplitude normalization will have a constant with peaks due to phase change. Noisy 16QAM signal without amplitude normalization and with amplitude normalization is presented in Fig. 5.12(c) and Fig. 5.12(d). For QAM signal since without amplitude normalization is multistep function, its variance will be greater than zero and since it is constant after amplitude normalization the variance will be less than zero. This feature separates it from PSK and FSK. QAM, PSK and FSK signals were distinguished by computing the variances of with and without applying amplitude normalization.
The Probability of correct classification is presented in Table 5.2.
Table 5.2 Probability of Correct Classification (Pcc %) at Different SNR
(Technique 2)
As compared to Table 5.1 it is observed that improved results are obtained because of preprocessing done by median filter. Following observations are made from Table 5.2:
Signals are 100% correctly classified beyond 10 dB.
The average classification rate at 5 dB SNR is 98.5% where 4FSK signal is 100 % correctly classified. 2FSK and 4PSK are 99% correctly classified. 4ASK, 2PSK and 16QAM are 98% correctly classified.
The average classification rate for the seven signals at 5 dB and 0 dB is 98.5% and 94.3% respectively.
5.3 STOCHASTIC AND HOS BASED CLASSIFIER
The test signals were considered to be zero mean. This proves to be true in all the signal generation tests run. The zero mean assumption was utilized because this greatly facilitates the mathematical equations associated with calculating higher order statistics. A total of 10,000 samples per modulation scheme were created and stored. Each signal modulation type was tested 100 times in the classification algorithm to derive statistics for the results. Finally, each signal modulation type was sent through two different channels including AWGN and Rayleigh fading. Signals were tested in various levels of noise from no noise (SNR =’) to extremely noisy conditions (SNR= -5 dB) for three types of fading channels.
Seven feature vectors used for classification of modulated signals are listed in Table 5.3. The features are instantaneous parameters of modulated signal and higher order moments and cumulants.
Table 5.3: Feature Vectors for Classification
These features were found to have robust and unique property as the variation in their values in presence of noise and fading was small. Robustness of selected features was first investigated in presence of Additive White Gaussian Noise. Five features based on instantaneous amplitude, phase and frequency were derived for varying SNR.
Feature vector 1 is the Maximum Value of Power Spectral Density (PSD) of Normalized-Centered Instantaneous Amplitude. Plot of values obtained for Feature vector 1 using Eq. 4.16 for ten modulated signals are presented in Fig. 5.13.
Fig 5.13: Feature Vector 1 ()
It represents the variations in amplitude, which makes this feature useful to discriminate between amplitude and non-amplitude modulations. This feature was used to discriminate between constant envelope signals FSK and non constant envelope signals ASK.
Following observations are made from Fig. 5.13
For FSK/GMSK, since there is no amplitude variation the value of this feature is small and approaches zero for GMSK signal.
categorizes M-QAM/M-ASK in one group above a threshold value of 0.3 and M-PSK/M-FSK/GMSK in another group below that threshold value.
The value of lies in the range of 0.6 to 0.8 for M-QAM signals. Since 16QAM, 64QAM and 256QAM signals are clustered hence this feature cannot be used to classify these signals.
2PSK, 4PSK, 2FSK and 4FSK signals all lie in the same range of 0.3. Since all the four signals overlap they cannot be classified using this feature.
Feature vector 2 is the standard deviation of the absolute value of the normalized- centered instantaneous amplitude of a signal segment (). The plot of feature vector 2 for values calculated using Eq. 4.6 is presented in Fig. 5.14.
Fig 5.14: Feature Vector 2 ()
This feature is used to distinguish 2ASK from 4ASK and to classify GMSK signal.
4ASK signal falls above threshold value of 0.35 and 2ASK below the threshold level.
It is observed from Fig. 5.14 that easily separates GMSK signal.
The separation between 2ASK and 4ASK is less below 0 dB, which improves for SNR > 5 dB.
2FSK, 4FSK, 2PSK and 4PSK signals overlap within a small range of 0.25 and 0.28. Hence this feature cannot distinguish these four signals.
It is observed that higher order QAM signals all overlap for a very low value (almost zero).
Feature vector 3 is the standard deviation of the centered non-linear component of the absolute instantaneous phase (. The calculated values obtained using Eq. 4.9 is presented in Fig. 5.15. This feature provides a clear distinction between 2PSK and 4PSK signal.
Fig 5.15: Feature Vector 3 ()
The value of this feature is smaller for modulation class 2PSK/M-FSK and large for M-QAM/ 4PSK.
serves to check if the received signal contains indirect phase information or not.
This feature proves to be very good selection in distinguishing 2PSK and 4PSK signals for SNR as low as -5 dB. This gives high percentage of correct classification for such low value of SNR.
M-QAM signals closely lie in the range of 0.8 to 0.9. This feature therefore cannot be used to classify order of M-QAM signals.
2FSK and 4FSK overlap at a value of 0.45. cannot separate these two signals.
Feature vector 4 is the standard deviation of the centered non-linear component of the direct (not absolute) instantaneous phase (. The value of this feature obtained by using Equation 4.8 reduces to zero for M-ASK and nonzero for others as presented in Fig. 5.16.
Fig 5.16: Feature Vector 4 ()
Feature vector 5 is the standard deviation of the absolute value of the normalized- centered instantaneous frequency of a signal segment. Plot of values obtained for feature vector 5 using Eq. 4.10 is presented in Fig. 5.17.
Fig 5.17: Feature Vector 5 ()
This is the only feature which distinguishes 2FSK from 4FSK signal.
The selected threshold value is able to separate the two signals but clear separation between the two signals is obtained for SNR > 0 dB as indicated by Fig. 5.17.
M-QAM signals could not be classified using this feature as they are closely spaced.
Feature Vector 6 : (E S,8,4 ) Eighth Order moment was used to separate higher order QAM signals. For zero mean discrete signal sequence of the form , E S,8,4
is moment of order eight. Its value is computed using Eq. 5.1.
(5.1)
This feature categorizes 16QAM, 64QAM in one class below the threshold value of 4 and 256QAM in another class above this threshold value.
Feature vector 7 : (C S,8,4) Eighth order cumulant classifies 16QAM and 64QAM signal below and above a threshold value of 20. It is calculated using Eq. 5.2
+ (5.2)
where
‘ (5.3)
‘ (5.4)
‘ (5.5)
‘ (5.6)
‘ (5.7)
‘ (5.8)
It is observed from Fig. 5.13 to Fig. 5.17 that these features can be used to classify modulated signals clearly up to 5 dB and also for some signals for SNR as low as -5 dB. Since Features 1 to 5 could not separate higher M-QAM signals, Feature vector 6 and Feature vector 7 were used to classify 16QAM, 64QAM and 256QAM.
Calculated values of selected moments and cumulants using Eq. 5.1 to Eq. 5.8 are presented in Table 5.4.
Table 5.4: Values of Selected Moments and Cumulants
Following points are observed from Table 5.4
The values are too close to each other to distinctly classify all signals.
Moment E s,2,2 has similar value of 0 for 4PSK, 16QAM, 64QAM and 256QAM. Hence this feature could not be used to classify order of M-QAM signals. Its value is same for GMSK and 2PSK. It has a constant value of 0.5 for 2ASK, 4ASK and 2FSK.
Moment Es,4,4 has a constant value of – 0.6 for all M-QAM signals. Hence this feature value cannot be used to separate M-QAM signals.
Moment Es,4,3 again puts all QAM signals in one category.
Moment Es,4,2 can be used to separate 16QAM signal from 64QAM and 256QAM as its value is 0 for 16QAM and 1.3 for 64QAM and 256QAM.
Moment Es,8,6 can also not be used to distinguish order of M-QAM signals as they are all having similar value of around -2.
Moment Es,8,4 is used to put M-QAM signals in two categories. 16QAM and 64QAM in one group and 256QAM in another group.
Cumulant Cs,8,4 is used to separate 16QAM and 64QAM.
It is observed from Table 5.4 that other signals can also be classified using combination of moments and cumulants but the computational complexity and simulation time of algorithm increases.
5.3.1 Performance of DT Classifier
Random Binary signal was generated for each modulation type. Three types of channel conditions were considered. Signals were simulated for 26 values of SNR (-5 dB to 20 dB) for each channel type. Confusion matrix was obtained for 100 trials of each SNR. Performances of the decision tree method system at SNR of -5 dB, -3 dB, 0 dB, 3 dB, 5 dB, 10 dB, 15 dB and 20 dB were obtained in the form of confusion matrix. Confusion matrix is a matrix providing information about the output of the recognition system for the given modulation type. Confusion matrix obtained for -5 dB SNR under no fading condition is presented in Table 5.5.
Table 5.5: Confusion Matrix of DT Classifier
(SNR= -5 dB) each SNR 100 trials
Following points are observed from Table 5.5
It is observed that of 100 trials, 2ASK signal is correctly classified for 90 trials and misclassified for 10 trials as 4ASK signal.
2PSK and 4PSK signals are 100% correctly classified.
2FSK modulated signal is correctly identified for 91 times and misclassified as 4FSK five times and as GMSK four times.
GMSK signal is correctly identified for 92 trials and misclassified for 8 trials.
Pcc for 64QAM and 256QAM is 82 % and 80 % respectively.
The above results are obtained for very noisy channel for lower bound SNR of -5 dB. Results are expected to improve as SNR increases.
Confusion Matrices for SNR -3 dB, 0 dB, 3 dB, 5 dB, 10 dB, 15 dB and 20 dB are shown in Appendix A.
Based on the confusion matrices obtained for different SNR, percentage identification results (Pcc %) are presented under no fading condition i.e. only in presence of AWGN channel in Table 5.6.
Table 5.6: Probability of Correct Classification (Pcc %) for Decision Tree Classifier
(No Fading, each SNR 100 trials)
Following observations are made:
Signals are 100 % correctly classified up to 10 dB. High percentage of results is obtained for SNR up to 0 dB. More than 91% of correct classification results are achieved for all signals except 256QAM.
16QAM signal is 100% correctly identified upto SNR = 3 dB.
The identification results obtained for all signals is more than 92% except 64QAM and 256QAM for SNR = -3 dB.
Robustness of selected combination features was investigated next by studying their behavior by passing modulated signals through Rayleigh fading channel. The channels considered were low fading channel (Doppler shift = 5Hz) medium fading channel (Doppler shift = 40Hz) and severe fading channel (100Hz).
Percentage of correct classification for low fading channel is illustrated in Table 5.7.
Table 5.7: Probability of Correct Classification (Pcc %) for Decision Tree Classifier
(Low Fading, Each SNR 100 trials)
Following points are indicated by Table 5.7:
All signals are 100% correctly identified for 10, 15 and 20 dB SNR similar to the case when no fading was applied. This is because under low fading channel conditions channel distortion introduced was low and preprocessing improved the signal strength.
An improvement of upto 4% is observed in almost all signals when there was 2dB improvement in SNR from 3 dB to 5 dB.
The difference in identification results for SNR values of 3 dB and 0 dB is very small.
Almost all signals are at least 92% correctly identified for low SNR value of 0 dB except 64QAM and 256QAM signals.
Similarly Probability of correct classification for medium fading is presented in Table 5.8.
Table 5.8: Probability of Correct Classification (Pcc %) for Decision Tree Classifier
(Medium fading, each SNR 100 trials)
Following inferences are made from Table 5.8:
2FSK, 4FSK, 2PSK and 4PSK signals are 100% correctly identified beyond 10 dB SNR due to increased channel distortion.
2PSK and 4PSK are 100% correctly identified even under conditions of increased fading for low SNR value of -5 dB.
64QAM signals and 256QAM signals have lowest identification results of 70% for SNR= -5 dB under medium fading conditions.
Percentage of correct identification results for DT classifier under severe fading conditions is presented Table 5.9.
Table 5.9: Probability of Correct Classification (Pcc %) for Decision Tree Classifier
(Severe Fading, each SNR 100 trials)
Following points are inferred from Table 5.9:
All signals are 100% correctly identified for SNR value of 20 dB.
Seven signals 2ASK. 4ASK, 2FSK, 4FSK, 2PSK, 4PSK and GMSK signals are 100% correctly identified for 15 dB SNR value.
Four signals 2ASK, 2FSK, 4FSK and 16QAM are obtained with >= 90% correct identification for 5 dB SNR.
As it is observed that fading greatly affects the results, hence percentage classification obtained only in presence of AWGN and in presence of severe fading show significant variation.
On comparing the percentage identification results obtained through DT classifier in Table 5.6, Table 5.7, and Table 5.8 and Table 5.9 it is inferred that:
The variation in % results obtained for only AWGN channel and for low fading channel is less.
The difference in results increases for medium fading condition.
More than 90% of correct identification of signals is achieved for SNR >= 3 dB both for no fading and low fading conditions.
5.3.2 Performance of ANN Classifier
MLP neural network has been used to develop the classifier. The Neural Network Pattern Recognition Tool was used to select data, create and train a network, and evaluate its performance using mean square error and confusion matrices. A two-layer feed-forward network, with sigmoid hidden and output neurons, was used to classify vectors arbitrarily, given enough neurons in its hidden layer. Samples were classified using Pattern Recognition tool with input and target data.
The network was trained with scaled conjugate gradient backpropagation algorithm. Input and output matrix was prepared. Input layer consisted of seven nodes representing seven features. Output layer had ten nodes each representing one of the ten modulation techniques. 500 samples of each signal were taken constituting 5000 samples for ten modulated signals. Input matrix size was 7×5000. The MLP classifier was tested with 20 neurons for one hidden layer. The size of output matrix was 5000×10 as there were 10 output nodes each representing one of the ten modulation types.
Simulation set up for development of classifier is presented in Table 5.10.
Table 5.10: Simulation Set up for Development of Classifier
The samples are divided randomly in three categories.
Training samples: are presented to the network during training, and the network is adjusted according to its error.
Validation samples: are used to measure network generalization, and to halt training when generalization stops improving. Training automatically stops when generalization stops improving, as indicated by an increase in the mean square error of the validation samples.
Testing samples: are independent measures of network performance during and after training.
Confusion matrix thus obtained was used to evaluate the performance of the ANN based classifier.
Confusion Matrix obtained under simulated conditions of noisy channel (only AWGN) is presented in Table 5.11.
Table 5.11: Confusion Matrix of ANN Classifier (SNR = -5 dB)
(No Fading each SNR 100 trials)
Following points are inferred from Table 5.11:
Improved results are obtained using ANN classifier as compared to DT classifier. This results from the fact that decision tree requires a careful selection of the threshold values, whereas an ANN can sort out the decision boundaries automatically.
For 100 trials 2ASK signal is correctly identified 95 times and misclassified as 4ASK 5 times.
4ASK signal is correctly identified 92 times and misclassified 8 times as 2ASK of 100 trials.
2PSK and 4PSK are 100% correctly classified. Similar performance is achieved by DT classifier for PSK signals.
64QAM signal is correctly identified 88 times and misclassified 12 times as 16QAM. 256 QAM signals are classified correctly for 82 trials and misclassified 10 times as 64QAM and 8 times as 16QAM.
Confusion matrix of modulated signals at different SNR under varying faded channels obtained by using Neural Network is given in Appendix A.
Based on the confusion matrices obtained for different SNR, percentage identification results for different SNR under no fading condition are presented in Table 5.12.
Table 5.12: Probability of Correct Classification (Pcc %) for ANN Classifier
(No Fading, each SNR 100 trials)
Percentage of correct identification improved for all modulated signals.
Percentage identification achieved is > 90% for SNR >= 3 dB.
64 QAM signals is 88 times correctly identified at -5 dB. An improvement of 6% was achieved as compared to DT classifier.
Percentage improvement of 2% is achieved for 256QAM signal.
The identification for GMSK signal is 90% similar to that of DT classifier.
Percentage of correct identification using ANN for AWGN channel and low fading condition is presented in Table 5.13.
Table 5.13: Probability of Correct Classification (Pcc %) for ANN Classifier
(Low Fading, each SNR 100 trials)
Following points are indicated by Table 5.13:
The difference in percentage identification for no fading and low fading conditions is small.
All signals are 100% correctly identified for 10, 15 and 20 dB SNR similar to the case when no fading was applied.
An improvement in classification is observed in 2ASK, 4ASK, 2FSK, 4FSK, 64QAM and 256QAM signals.
Probability of correct classification (Pcc) for medium fading channel is presented in Table 5.14.
Table 5.14: Probability of Correct Classification (Pcc %) for ANN Classifier
(Medium Fading, each SNR 100 trials)
Following inferences are made from Table 5.14:
2ASK, 4ASK, 2PSK 4PSK and GMSK signals are 100% correctly identified for 10 dB SNR.
2PSK and 4PSK are 100% correctly identified even under conditions of increased fading for low SNR value of -5 dB.
64QAM signals and 256QAM signals have lowest identification results of 75% and 71% respectively for SNR = -5 dB under medium fading conditions. ANN classifier shows an improvement of almost 5% as compared to DT classifier for these signals.
Pcc drops in presence of fading but improved results were obtained using ANN classifier. As expected, high percentage of results are obtained for high SNR.
Probability of correct identification (Pcc) for medium fading channel is presented in Table 5.15.
Table 5.15: Probability of Correct Classification (Pcc %) for ANN Classifier
(Severe Fading, each SNR 100 trials)
All signals are 100% correctly identified for SNR value of 20 dB.
Four signals 2ASK. 4ASK, 2PSK and 4PSK are 100% correctly identified for 15 dB SNR value.
Eight signals 2ASK, 4ASK, 2FSK, 4FSK 2PSK, 4PSK and 16QAM are obtained with >= 90% correct identification for 5 dB SNR.
Results obtained only in presence of AWGN and in presence of severe fading have significant variation.
5.3.3 Comparison of DT and ANN based classifier
Based on Percentage identification results, performance comparison of DT and ANN classifier at different SNR’s for ten modulated signals has been evaluated. Probability of correct classification (Pcc) of 2ASK signal obtained through confusion matrix by DT classifier is presented in Fig. 5.18.
Fig 5.18: Pcc of 2ASK Signal using DT Classifier
The SNR range taken is from -5 dB to 20 dB.
It is observed that 2ASK signal is 100% correctly identified for 15 and 20 dB for all channel conditions.
2ASK signal is 100% correctly identified at 10 dB for no fading and low fading conditions.
Probability of correct classification Pcc of 2ASK is > 90% at 5 dB SNR for all types channel conditions.
Pcc of 2ASK is 95% for no fading and 84 % for severe fading at 0 dB SNR.
2ASK signal is 90% correctly classified for no fading condition and 73% for severe fading for -5 dB SNR.
Probability of correct classification (Pcc) of 2ASK signal obtained through confusion matrix by ANN classifier is presented in Fig. 5.19.
Fig 5.19: Pcc of 2ASK Signal using ANN Classifier
Signals are 100% correctly identified at 15 dB and 20 dB.
100% correct identification is obtained at 10 dB for all fading conditions except severe fading.
For similar conditions and using same features ANN classifier performs better at 5 dB, 0 dB and -5 dB, as Pcc improves for different SNR values.
Probability of correct classification (Pcc) of 4ASK signal obtained through confusion matrix by DT classifier is presented in Fig. 5.20.
Fig 5.20: Pcc of 4ASK Signal using DT Classifier
Following points are concluded:
4ASK signal is 100% correctly identified for 15 dB and 20 dB. Results are almost similar for simulation in presence of only AWGN channel and in presence of low fading effect.
Identification rate is more than 87% at 5 dB for all channel conditions
Pcc drops for low SNR mainly when fading effect aggravates.
Similarly Probability of correct classification (Pcc) of 4ASK signal obtained through confusion matrix by ANN classifier is presented in Fig. 5.21.
Fig 5.21: Pcc of 4ASK Signal using ANN Classifier
4ASK signal is 100% correctly classified at 15 dB and 20 dB under all channel conditions.
4ASK signal is 100% correctly classified for all channel conditions at 10 dB SNR except for severe fading.
More than 80% correct identification is achieved at 0 dB SNR.
Comparative charts of 2PSK, 4PSK, 2FSK, 4FSK, GMSK, 16QAM, 64QAM and 256QAM signals are presented in Appendix B.
Percentage identification of DT Classifier is analyzed to evaluate the performance scheme wise at low SNR. The evaluation for -5 dB, -3 dB and 0 dB SNR in presence of AWGN is presented in Table 5.16.
Table 5.16: Performance of DT Classifier
(% Classification, No Fading)
Following observations are made from the above table
The classifier performs best for 2PSK and 4PSK signals even for low SNR.
16QAM signal is correctly identified for correct classification of 94% at -5 dB and 97% for 0 dB.
In the absence of fading high percentage of result i.e. 92% is obtained for GMSK signal for -5 dB SNR.
64QAM and 256QAM have lower identification results as compared to other schemes.
The evaluation for -5 dB, -3 dB and 0 dB in presence of AWGN and low fading condition is presented in Table 5.17.
Table 5.17: Performance of DT Classifier
(% Classification, Low Fading)
Following inferences are made from Table 5.17
2PSK and 4PSK signals are 100% classified.
Percentage Classification of 16QAM is 91% and that of 2FSK, 4FSK is 90%.
The percentage identification results show a decreasing trend in the order of 16QAM, 2FSK, 4FSK, 2ASK, GMSK, 4ASK, 64QAM and 256QAM.
The evaluation of DT Classifier for -5 dB, -3 dB and 0 dB in presence of AWGN and severe fading condition is presented in Table 5.18.
Table 5.18: Performance of DT Classifier
(% Classification, Severe Fading)
Following points are concluded from Table 5.18
The classifier works best for 2PSK and 4PSK signals for severe conditions also.
The percentage classification results of 2ASK and 2FSK are 73% and 71% respectively and for GMSK and 4ASK it is 70%.
Higher order QAM signals 16QAM, 64QAM and 256QAM degrade severely in presence of fading.
Percentage identification of ANN Classifier is analyzed to evaluate the performance scheme wise at low SNR. The evaluation for -5 dB, -3 dB and 0 dB in presence of AWGN is presented in Table 5.19.
Table 5.19: Performance of ANN Classifier
(% Classification, No Fading)
Following points are concluded from Table 5.19
2PSK and 4PSK are 100% correctly identified for low values of SNR.
The performance of ANN classifier is better than DT classifier.
The percentage identification results show a decreasing trend in the order of 16QAM, 2ASK, 2FSK, 4FSK and GMSK signals.
DT classifier gives better results than ANN for GMSK signal.
The evaluation for -5 dB, -3 dB and 0 dB in presence of AWGN and low fading condition is presented in Table 5.20.
Table 5.20: Performance of ANN Classifier
(% Classification, Low Fading)
Following conclusions are drawn from Table 5.20
Both DT and ANN classifier give best performance for 2PSK and 4PSK.
ANN classifier gives improved results for even 64QAM and 256QAM signals which improve the average performance of ANN classifier.
The performance of ANN classifier for -5 dB, -3 dB and 0 dB SNR in presence of AWGN and severe fading condition is presented in Table 5.21.
Table 5.21: Performance of ANN Classifier
(% Classification, Severe Fading)
Following points are highlighted from Table 5.21
The signals are classified in the order 2PSK, 4PSK, 2ASK, 4ASK, 4FSK, 2FSK, GMSK, 16QAM, 64QAM and 256QAM based on identification results.
ANN classifier performs best in severe conditions for higher order QAM signals.
An improvement of about 5.5 % is achieved by ANN classifier at low SNR value of -5 dB.
Average performance of both Decision Tree (DT) classifier and ANN classifier for three types of channel for full class recognition is presented in Table 5.22.
Table 5.22: Average Performance of DT and ANN Classifier
Following observations have been done based on results obtained:
The performance of proposed DT Classifier and ANN classifier is 100% for 2PSK and 4PSK for SNR = -5 dB.
Both classifiers classify 4ASK signal with a rate of 97% at 3 dB SNR.
The percentage identification achieved for GMSK is found to be better in DT classifier. For -5 dB it is 90% for both DT and ANN classifier, DT classifier results in 94% and 97% correct identification whereas ANN gives 92% and 93% results for SNR = -3 dB and 0 dB respectively.
Average performance of both DT and ANN classifiers drop mainly due to higher order QAM signals which are majorly affected by noise and fading and are not recoverable even after equalization. It is 91.1% for DT classifier and 93% for ANN classifier at -5 dB.
The success rate of ANN classifier is better than DT classifier for medium fading and severe fading conditions. The correct classification is 82% for DT and 85 % for ANN for medium fading, 70% for DT 75.5 % for ANN for severe fading at -5 dB SNR respectively.
Fig 5.22: Performance Comparison of DT and ANN Classifier
The performance of two classifiers is presented in Fig. 5.22. It is observed that ANN classifier performs better than DT classifier. However the difference in classification results is less for higher SNR and low fading conditions. The advantage of ANN classifier becomes obvious for low SNR and high fading conditions. The advantage of the neural networks technique as recognizers is that these methods do not require specifying the number of the clusters in data sets before the process. Whereas a decision tree requires a careful selection of the threshold values, an ANN can sort out the decision boundaries automatically. ANN is therefore more adaptable to modulation schemes. The presented classification algorithm is not limited to any special class of modulations. On the other hand, this approach can be extended and modified to recognize other types of modulated communication signals.
The developed Automatic Modulation Recognition (AMR) algorithm could identify the modulation scheme of a transmitted signal with a high probability of success. Finally, using a neural network for classification constitutes a highly flexible method since the network can be retrained easily in order to incorporate new signal types. Automatic recognition of digital signal formats is an important subject for novel communication systems. Such classifiers play an important role in non-cooperative communications, such as intelligent demodulation, radio monitoring, electric surveillance etc.
CHAPTER 6
SUMMARY CONCLUSION AND FUTURE SCOPE
Automatic modulation classification is of major importance in civilian and military applications. The interest in this area has increased in recent years owing to the advances in reconfigurable signal processing systems, especially in software defined radio. A Blind modulation classification deals with identification of modulation formats from received signal without the knowledge of the type of modulation transmitted. Without any knowledge of the transmitted data and many unknown parameters at the receiver, blind identification is a difficult task. Classification process is even more challenging in real world scenarios with multipath fading, frequency selective, and time varying channels.
6.1 Summary and Conclusion
In present work, a blind recognition system based on hybrid features has been developed to discriminate the digitally modulated signals in an AWGN and faded channel. The main motivation behind using Automatic Modulation Recognition (AMR) in present work is based on the inherent potential of AMR in recognition of modulation communication signals without foreknowledge of its feature.
It is essential to focus on the fact that in the developed algorithm the different modulated signals are digitalized in RF or IF stages (the carrier frequency is unknown) with respect to SDR principles. The recognition is done without any priori signal information, and this algorithm shows robustness over fading channels.
Various feature based classification techniques were extensively surveyed to decide upon the selection of robust features for classification. The components used in classifying digital modulation types in multipath fading environments as well as AWGN were discussed. The MATLAB and Simulink models generated the signals, modeled propagation through noisy channels and sent these signals through a classification scheme that attempted to identify and classify these modulation types correctly.
Average classification result for Wavelet Transform based classifier was 93.3 % for 0 dB SNR.
Average classification results improved to 94.5% for the Wavelet Transform based classifier when signal preprocessing was done prior to classification. However, in this technique the number of signals that could be identified was limited.
Hybrid feature based classifier demonstrates the robustness of the higher order statistical features to various levels of noise and fading.
The computational complexity reduces for hybrid feature based classifier.
In present work, a set of features were used for classification such as instantaneous and stochastic parameters for classification of lower order modulation schemes and higher order moments and cumulants for classification of 16QAM, 64QAM and 256QAM.
Classification algorithm is important part of a modulation recognition system. Two techniques were developed for classification:
Decision tree
Pattern recognition based neural network technique.
In the Decision tree classification, threshold values were derived for each modulation type at SNR values ranging from 20 dB to as low as -5 dB.
The developed recognition systems are able to discriminate 2PSK and 4PSK modulated schemes with highest recognition rate of 100% in presence of noise and fading.
The performance of DT classifier is >= 90% for 2ASK, 4ASK, 2FSK, 4FSK, GMSK and 16QAM signals for low SNR of -5 dB in absence of fading.
The success rate is around 99 % (no fading condition) for SNR = 5dB. Overall classification result obtained for SNR = 3dB is more than 97%.
The average performance of classifier 91.1% for DT classifier and 93% for ANN classifier at -5 dB for no fading condition.
The success rate of ANN classifier is better than DT classifier for medium fading and severe fading conditions. The correct classification is 82% for DT and 85% for ANN for medium fading, 70% for DT 75.5% for ANN for severe fading at -5 dB SNR respectively.
Average performance of classifier under medium and severe conditions falls mainly due to misclassification of higher order QAM signals. It is observed that the performance of the ANN classifier is superior to decision tree based method, at low SNR values.
The developed classifier performs best for MPSK signals and degrades for 64QAM and 256QAM signals.
6.2 Future Scope
This work is a small contribution in a large body of research conducted in this area. However, several areas remain open for further research and improvements to the proposed classifier design.
Future work or extensions of this model can include other modulation types for e.g. Orthogonal Frequency Division Multiplexing, Cyclical Shift Keying, and Trellis Coded Modulation.
Further research could be done to evaluate frequency hopped modulated signals.
Extension of the classifier to additional signal types would be of added benefit so as to operate on a larger set of signals. Moreover, identification of the pulse shape of received signals would increase the precision of the classification, and would allow more reliable demodulation of the received signals once after their modulation scheme has been determined.
Furthermore mitigating effects due to transmitter timing errors and phase jitter would increase the reliability of estimates made of lower fidelity systems.
Another area of necessary research includes extending the classification system to consider signals that undergo jamming, and the joint classification of multiple, possibly overlapping signals.
Finally, evaluation of the classifier with actual transmitted waveforms would be of benefit to realize hardware solution of simulated performance.
New classification problems have raised as a result of emerging wireless technologies, such as, single carrier versus multicarrier modulation recognition, classification of signals received from single and multiple transmit antennas etc. These issues imply that AMC in real-world environments continues to be a dynamic research field.

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