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Performance Analysis of Spectrum Sensing Algorithm using Multiple Antenna in Cognitive Radio

Komal R. Pawar  and Dr.Tanuja S. Dhope

Abstract: There is a rapid growth and development of new wireless devices and applications; therefore there is increase in demand for wireless radio spectrum. Cognitive radio is used to solve spectrum scarcity and meet the ever increasing demand of spectrum using dynamic spectrum access. In context to cognitive radio, spectrum sensing is found to be a crucial task. In this paper, we have evaluated the energy detection technique for spectrum sensing using time domain and frequency domain- periodogram method. For performance comparison parameters like the probability of detection, probability of miss detection and probability of false alarm for change in values of signal to noise ratio, sample count are taken into consideration. Multiple antenna techniques help to reduce multipath and shadowing effects of wireless channels and also provide better bit error rates.

Keywords—spectrum sensing, energy detection, multiple antenna.

1 Introduction

As number of users, data rates, wireless devices and its applications are growing rapidly, there is demand for large amount of radio spectrum[1].Spectrum is a limited resource, therefore it is difficult to efficiently utilize the whole Spectrum[2]. The static frequency allocation scheme is found to be not effectively utilized and since spectrum is limited source, new spectrum allocations are difficult. Cognitive radio (CR) technology was introduced which uses dynamic frequency allocation scheme and solves the problem of spectrum scarcity [3]. In CR, the spectrum is checked continuously which is used by licensed user and if found to be idle then it is given to the unlicensed user. Energy detection, Matched filter detection, and Cyclostationary detection are some of spectrum sensing technique [2][4]. Amongst these, the energy detection is a semi-blind detection method used for detection of an unknown signal in additive noise [5]. It is advantageous over the rest of methods as it does not require any prior information of primary received signal and also it has low complexity [6]. Matched filter requires accurate synchronization and prior information of the signal. The cyclostationary method requires knowledge of cyclic frequencies of primary user. It is less prone to noise uncertainty and provides better detection at low SNR regimes and it requires less signal samples [6][7]. In wireless channels fading, shadowing makes spectrum sensing is difficult task.

The Neyman-Pearson criteria states that the spectrum sensing is binary hypothesis sensing problem. Such as given below,

                                               Y(n)= w(n)   : H0                                  (1)

                                  Y(n)= x(n) +y(n) : H1         (2)           

where x(n)=h_s(n), h is the channel gain, w(n) is noise sample with mean zero and variance 2σ_w^2. H0 = Absence of user,    H1= Presence of user.

   Multiple antenna technique is currently used for effective communication and reliable signal transmission. Two-stage sensing method provides efficient utilization of multiple antennas with respect to sensing time and hardware [8]. The performance evaluation of ED using Rayleigh fading channels and unknown deterministic signal is proposed in [9] [10]. Multiple antenna OFDM scheme along with square law combining technique for energy detection provides better performance than single antenna at low signal to noise ratio [10]. Overall the multiple antenna method increases spectrum efficiency and improves system performance. Table 1 reflects the comparison of various spectrum sensing techniques.

Table 1 Comparison of Spectrum Sensing Techniques

Types Matched filter detection Cyclostationary detection Energy detection

Pros It requires less signal  samples It is more robust to noise variations.

    Easy to implement


Requires accurate data of primary signal Cyclostationary features needs to be associated with primary signal High false alarm due to noise uncertainty


Komal R. Pawar

Department of Electronics & Telecommunication Engineering, GHRCEM,Maharashtra,Pune , e-mail: [email protected]

Dr.Tanuja S. Dhope

Faculty of Electronics & Telecommunication Engineering, GHRCEM, Maharashtra, Pune, e-mail:[email protected]

2 Energy Detection

One of the most generic and common method for spectrum sensing is energy detection [11]. Energy detection method measures energy of received signal over specific time interval. Energy detection can be implemented in both time domain and frequency domain. The energy detection in frequency domain requires FFT computations. Energy detector simply requires band pass filter BPF, ADC, square law device and integrator.

Initially the primary signal is band limited using band pass filter. The signal is then squared and integrated over some time period T. The output is compared with threshold to determine whether primary signal is present[12]. X(n) is the input primary signal applied to the energy detector.

The test static can be represented as,


                         €_time=∑_(n=1)^N'▒'〖'|X(n)|'〗'^2                       (3)

                                          Fig.1. Energy detection

Test static is compared with threshold ( ) to detect whether the signal is present or not.

                           λ'⋚'€_time.                                                                      (4)

Various fading channels are applied to energy detector. While considering performance of system the detection probability and false alarm probability plays a vital role. The formulae for both can be obtained as below[12]:

The probability of false alarm '〖' P'〗'_fa is given by below equation

                  '〖' P'〗'_fa=P{Y>λ/H0}= Q_m (√2y,√λ)                                  (5)   

The probability of detection P_d is given by below equation


                       P_d=P{Y>λ/H1}=(Γ(n,λ⁄2))/(Γ(n))                                          (6)    


This is a discrete fourier transform based method which is used for spectral estimation. The power spectral density is projected through the signal itself.  Power spectral density of the primary input signal is achieved by calculating the fast fourier transform of the samples & later taking the magnitude square of that signal. In periodogram method we consider finite word sequence for estimation of parameters. This technique is similar to multiplying the signal with rectangular window in time domain [12]. Due to sudden change in the signals, undesirable side lobes in frequency response cause spectral leakage. The word periodogram is used to determine the hidden periodicities in time series.  FFT is used instead of DFT for simulations.

                                         Fig.2. Energy detection with Periodogram

                    X(k)=∑_(n=1)^N'▒'〖'X(n)e'〗'^(-j2π(k-1)(n-1)/N)                          (7)

      Where 1≤k≤N                           

Where X(n) is the discrete received signal, N = FFT size. Then we apply X(k) to an energy detector as follows:

                €_periodogram=1/N ∑_(k=1)^N'▒'〖'|X(k)|'〗'^2                        (8)

As seen in this equation, we sum N components of the output of square law device where X(k) is applied to, hence the variance of the statistics fluctuates with respect to FFT size. In order to mitigate this fluctuation, we divide the statistics with FFT number in order to hold the variance constant.

B.Welch’s Periodogram

It is the modified form of periodogram which divides the data sequence into segments along with windowing technique. The hamming window method is used to calculate periodogram for every segment. In this method these data segments can be either overlapping or non overlapping[13]. At beginning the input data sequence is down-converted and low pass filtered. Later the data sequence is partitioned into M non-overlapping or overlapping segments. These segments are processed using FFT. After FFT, the samples are sent to the square-law device. Then L samples are taken from these M segments, followed by a summation of the L samples. Finally, the output values are compared with threshold and corresponding decision regarding presence of signal is done.

                               Fig.3. Energy Detection using Welch’s Periodogram

In Welch periodogram, M segments are applied to fast fourier transform and then L samples are taken from these segments.

w(n)=[w_1 (p) w_2 (p)… w_M (p)]                                                                  (9)

w_1 (γ)=∑_(p=1)^N'▒'〖'w_1 (p) e^(-j2π(γ-1)(p-1)/N) '〗'                                                        (10)

The Welch periodogram is given by:

€_welch=∑_(γ=1)^L'▒'∑_(l=1)^M'▒'1/N'⃒'w_1 (γ) '⃒'^2                                                                 (11)

3 Multiple Antennas

In wireless communication, multiple antenna technique has been a boon to the communication world. As the name suggest there are multiple antennas at transmitter and receiver side which provide better performance in terms of channel capacity and higher data rates as compared to single antennas. The multiple antennas are usually classified into following three types: SIMO, MISO and MIMO. Multiple antennas in context to MIMO provide improved BER, it increases the folded channel capacity, lowers the sensitivity to fading[14]. The MIMO communication system supports greater throughput by exploring the multiple properties of channel. In MIMO the multiple channel data traffic are applied through the antennas. It uses signal processing techniques to obtain information of waveform and corresponding data stream. Incorporation of MIMO significantly improves the data transmission rate thereby enhancing performance of system.

A general block diagram for multi input multi output model is shown in fig.4. The wireless communication system have N_T transmit antennas and N_Rreceive antennas. The expression for MIMO channel model is given through its input output relationship as follows,

                                          Y=HX+N                                                            (12)

Where H is the channel matrix whose elements are independent. X is primary signal and N is the noise.

  Fig. 4 MIMO system model.

Channel matrix is given by,

                                   H=('█'(h_(11   ) h_12  '⋯'h_(1N_T )@'⋮'           '⋮'            '⋮'@h_(N_R 1)  h_(N_R 2)'⋯'h_(N_R N_T ) ))


Higher data rates

Low interference

Performance  analysis of Spectrum Sensing Algorithm Using Multiple Antenna in Cognitive Radio

4 Simulation Results

In this section, we illustrate numerical results to evaluate the performance of energy detector. The simulation results show energy detection in time domain using BPSK modulation under AWGN and Rayleigh channel. The simulation study shows comparison of Probability of detection (P_d), probability of miss detection (P_md), and probability of false alarm ('〖' P'〗'_fa) with respect to SNR. Here symbol length N, is assumed to be 100.

Fig. 5 shows the Probability of miss detection versus SNR for varying probability of false alarm. We have considered two values of '〖' P'〗'_fa i.e. when '〖' P'〗'_fa=0.5 and 0.8.

Fig. 5 P_md Vs SNR for varying '〖' P'〗'_fa

Similarly fig. 6 shows probability of detection Vs SNR for varying probability of false alarm. To achieve better detection for energy detector, the detection probability will be high, probability of miss-detection will be low having low Probability of false alarm.

Fig. 6 P_d Vs SNR for varying '〖' P'〗'_fa

Fig. 7 illustrates the Probability of miss detection versus probability of false alarm. The SNR has fixed value i.e. here they are fixed at SNR=1.25db, and SNR=1.09 db, M is no of segments M=10.

                                                    Fig.7  P_md Vs '〖' P'〗'_fa for fixed SNR     

Fig. 8 show the Probability of detection versus probability of false alarm at fixed SNR. Similar values are used for simulation. SNR=1.25db, SNR=1.09 db, M=10.


                                               Fig. 8  P_d  Vs '〖' P'〗'_fa for fixed SNR

From fig. 9 we observe that 4 antennas are present and amongst them, one antenna is chosen for communication purpose. The simulation is carried out with 2-PSK for detection probability versus false alarm probability. Here SNR=2.0 and N=20.

Antenna channel Gains are

0.814724   0.905792   0.126987   0.913376

The antenna with the maximum channel gain is chosen. The detection probability of this antenna is plotted separetely for observation purpose in figure 10.

                      Fig. 9 Multiple antenna selection combining

                  Fig. 10 Multiple antenna selection combining with max gain

             Selecting Max gain Antenna-04 with gain = 0.913376.



 Cognitive radio is emerging as the need for today’s generation where efficient spectrum utilization and quality of service are in demand. In this paper, the performance of spectrum sensing for Cognitive Radios using energy detection under AWGN is analyzed. The detection is carried out in time domain with multiple antennas. Multiple antennas are used to overcome the noise uncertainty. Simulation results demonstrate considerable detection performance gain.



    I hereby acknowledge my advisor Prof. Tanuja S. Dhope for guiding me in right direction and also provide sincere gratitude to G.H.R.C.E.M, PUNE for providing framework to accomplish our work.


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