Essay: Digital image processing

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  • Digital image processing
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Since different streams in the compressed image have different importance to image quality, more important streams should be transmitted with more protection from errors as compared to less important streams. To achieve this is to transmit different streams with unequal transmit power with more important streams being transmitted with more power and less important streams with lesser power, without violating the total power constraint.
In this UPA method for transmission of different streams in a JPEG compressed image over MIMO systems. The main goal of this method is to transmit different streams from different antennas with unequal power such that overall distortion due to each block in the transmitted image is minimized. The total transmits power over all the antennas are kept constant during each symbols period.
Transmission of progressive images, such as coded through the set partition in hierarchical tree, is often desired, because the restored image quality can be incrementally improved and is always the optimal for a given number of sequentially decoded error free bits.
However, progressive data are sensitive to the channel noise.
A signal bit error may cause the loss of synchronization between the encoder and decoder and, hence, makes the data completely useless. JSCC (joint source channel coding) is most commonly studied joint design problem for image and video communication in the literature, another important joint design problem allocation and optimization for image and video communication.
The main goal for such problems is either to minimize the total distortion with a constraint on maximum “tolerable” distortion. In section we discuss various existing efficient image and video communication. The main goal of all the methods discussed above was either the minimization of energy/power with a constraint on total allowable distortion and the minimization of distortion with a constraint on total energy/power.
These methods showed large amounts of energy/power savings or quality gains as compared to methods that transmitted the images and videos with equal power.
3.2 Digital Images
A digital image is a numeric representation (normally binary) of a two-dimensional image. Depending on whether the image resolution is fixed, it may be of vector or raster type. By itself, the term “digital image” usually refers to raster images or bitmapped images.
Raster images have a finite set of digital values, called picture elements or pixels. The digital image contains a fixed number of rows and columns of pixels. Pixels are the smallest individual element in an image, holding quantized values that represent the brightness of a given color at any specific point. Typically, the pixels are stored in computer memory as a raster image or raster map, a two-dimensional array of small integers. These values are often transmitted or stored in a compressed form.
Raster images can be created by a variety of input devices and techniques, such as digital cameras, scanners, coordinate-measuring machines, seismographic profiling, airborne radar, and more.
They can also be synthesized from arbitrary non-image data, such as mathematical functions or three-dimensional geometric models; the latter being a major sub-area of computer graphics. The field of digital image processing is the study of algorithms for their transformation. Most users come into contact with raster images through digital cameras, which use any of several image file formats.
Some digital cameras give access to almost all the data captured by the camera, using a raw image format. The Universal Photographic Imaging Guidelines (UPDIG) suggests these formats be used when possible since raw files produce the best quality images. These file formats allow the photographer and the processing agent the greatest level of control and accuracy for output. Their use is inhibited by the prevalence of proprietary information (trade secrets) for some camera makers, but there have been initiatives such as Open RAW to influence manufacturers to release these records publicly. An alternative may be Digital Negative (DNG), a proprietary Adobe product described as “the public, archival format for digital camera raw data”. Although this format is not yet universally accepted, support for the product is growing, and increasingly professional archivists and conservationists, working for respectable organizations, variously suggest or recommend DNG for archival purposes.
Vector images resulted from mathematical geometry (vector). In mathematical terms, a vector consists of point that has both direction and length. Often, both raster and vector elements will be combined in one image; for example, in the case of a billboard with text (vector) and photographs (raster). Early Digital fax machines such as the Bart lane cable picture transmission system preceded digital cameras and computers by decades. The first picture to be scanned, stored, and recreated in digital pixels was displayed on the Standards Eastern Automatic Computer (SEAC) at NIST. The advancement of digital imagery continued in the early 1960s, alongside development of the space program and in medical research. Projects at the Jet Propulsion Laboratory, MIT, Bell Labs and the University of Maryland, among others, used digital images to advance satellite imagery, wire photo standards conversion, medical imaging, videophone technology, character recognition, and photo enhancement.
Rapid advances in digital imaging began with the introduction of microprocessors in the early 1970s, alongside progress in related storage and display technologies. The invention of computerized axial tomography (CAT scanning), using x-rays to produce a digital image of a “slice” through a three-dimensional object, was of great importance to medical diagnostics. As well as origination of digital images, digitization of analog images allowed the enhancement and restoration of archaeological artifacts and began to be used in fields as diverse as nuclear medicine, astronomy, law enforcement, defense and industry.
Advances in microprocessor technology paved the way for the development and marketing of charge-coupled devices (CCDs) for use in a wide range of image capture devices and gradually displaced the use of analog film and tape in photography and video graph towards the end of the 20th century. The computing power necessary to process digital image capture also allowed computer-generated digital images to achieve a level of refinement close to photorealism.
3.2.1 Tasks
Digital image processing allows the use of much more complex algorithms, and hence, can offer both more sophisticated performance at simple tasks, and the implementation of methods which would be impossible by analog means.
In particular, digital image processing is the only practical technology for:
Feature extraction
Pattern recognition
Multi-scale signal analysis
Some techniques which are used in digital image processing include:
Linear filtering
Principal components analysis
Independent component analysis
Hidden Markov models
Anisotropic diffusion
Partial differential equations
Self-organizing maps
Neural networks
3.2.2 Applications
Digital camera images generally include specialized digital image processing hardware — either dedicated chips or added circuitry on other chips — to convert the raw data from their image sensor into a color-corrected image in a standard image file format. Images from digital cameras can be further processed to improve their quality or to create desired special effects. This additional processing is typically executed by special software programs that can manipulate the images in a variety of ways.
Film West world (1973) was the first feature film to use digital image processing to pixel late photography to simulate an android’s point of view.
Intelligent transportation systems is digital image processing has wide applications in intelligent transportation systems, such as automatic number plate recognition and traffic sign recognition.
Image Sharpening and Restoration refers here to process images that have been captured from the modern camera to make them a better image or to manipulate those images in way to achieve desired result. It refers to do what Photoshop usually does. This includes Zooming, blurring, sharpening, gray scale to color conversion, detecting edges and vice versa, Image retrieval and Image recognition.
Medical Fields
Gamma Ray Imaging 2.
UV Imaging
X-Ray Imaging
PET Scan
Medical CT
Machine/Robot vision apart from the many challenges that a robot faces today, one of the biggest challenges still is to increase the vision of the robot: making the robot able to see things, identify them, identify the hurdles, etc. Much work has been contributed by this field and a complete other field of computer vision has been introduced to work on it.
Hurdle Detection is one of the common task that has been done through image processing, by identifying different type of objects in the image and then calculating the distance between robot and hurdles.
Color Processing includes processing of colored images and different color spaces that are used. For example RGB color model, Y Cb Cr, HSV. It also involves studying transmission, storage, and encoding of these color images.
Pattern Recognition involves study from image processing and from various other fields that includes machine learning (a branch of artificial intelligence). In pattern recognition, image processing is used for identifying the objects in an image and then machine learning is used to train the system for the change in pattern. Pattern recognition is used in computer aided diagnosis, recognition of handwriting, recognition of images e.t.c.
Video Processing is nothing but just the very fast movement of pictures. The quality of the video depends on the number of frames/pictures per minute and the quality of each frame being used. Video processing involves noise reduction, detail enhancement, motion detection, frame rate conversion, aspect ratio conversion, color space conversion e.t.c.
3.3 Characteristics of Systems
A system is characterized by how it responds to input signals. In general, a system has one or more input signals and one or more output signals. Therefore, one natural characterization of systems is by how many inputs and outputs they have:
SISO (Single Input, Single Output)
SIMO (Single Input, Multiple Outputs)
MISO (Multiple Inputs, Single Output)
MIMO (Multiple Inputs, Multiple Outputs)
It is often useful (or necessary) to break up a system into smaller pieces for analysis. Therefore, we can regard a SIMO system as multiple SISO systems (one for each output), and similarly for a MIMO system. By far, the greatest amount of work in system analysis has been with SISO systems, although many parts inside SISO systems have multiple inputs (such as adders).Signals can be continuous or discrete in time, as well as continuous or discrete in the values they take at any given time:
Signals that are continuous in time and continuous in value are known as analog signals.
Signals that are discrete in time and discrete in value are known as digital signals.
Signals that are discrete in time and continuous in value are called discrete-time signals. While important mathematically, systems that process discrete time signals are difficult to physically realize. Switched capacitor systems, for instance, are often used in integrated circuits. The methods developed for analyzing discrete time signals and systems are usually applied to digital and analog signals and systems.
Signals that are continuous in time and discrete in value are sometimes seen in the timing analysis of logic circuits or PWM amplifiers, but have little to no use in system analysis.
With this categorization of signals, a system can then be characterized as to which type of signals it deals with:
A system that has analog input and analog output is known as an analog system.
A system that has digital input and digital output is known as a digital system.
Systems with analog input and digital output or digital input and analog output are probable. However, it is usually easiest to break these systems up for analysis into their analog and digital parts, as well as the necessary analog to digital or digital to analog converter.
Another way to characterize systems is by whether their output at any given time depends only on the input at that time or perhaps on the input at some time in the past (or in the future!).
Memory less systems do not depend on any past input. In common usage memory less system are also independent of future inputs. An interesting consequence of this is that the impulse response of any memory less system is itself a scaled impulse.
Systems with memory do depend on past input.
Causal systems do not depend on any future input.
Non-causal or anticipatory systems do depend on future input.
It is not possible to physically realize a non-causal system operating in “real time”.
However, from the standpoint of analysis, they are important for two reasons.
First, the ideal system for a given application is often a non-causal system, which although not physically possible can give insight into the design of a derived causal system to accomplish a similar purpose.
Second, there are instances when a system does not operate in “real time” but is rather simulated “off-line” by a computer, such as post-processing an audio or video recording. Further, some non-causal systems can operate in pseudo-real time by introducing lag, if a system depends on input for 1 second in future, it can process in real time with 1 second lag.
Analog systems with memory may be further classified as lumped or distributed. The difference can be explained by considering the meaning of memory in a system. Future output of a system with memory depends on future input and a number of state variables, such as values of the input or output at various times in the past. If the number of state variables necessary to describe future output is finite, the system is lumped; if it is infinite, the system is distributed.
Finally, systems may be characterized by certain properties which facilitate their analysis:
A system is linear if it has the superposition and scaling properties. A system that is not linear is non-linear.
If the output of a system does not depend explicitly on time, the system is said to be time-invariant; otherwise it is time-variant.
A system that will always produce the same output for a given input is said to be deterministic.
A system that will produce different outputs for a given input is said to be stochastic.
There are many methods of analysis developed specifically for linear time-invariant (LTI) deterministic systems. Unfortunately, in the case of analog systems, none of these properties are ever perfectly achieved. Linearity implies that operation of a system can be scaled to arbitrarily large magnitudes, which is not possible. Time-invariance is violated by aging effects that can change the outputs of analog systems over time (usually years or even decades). Thermal noise and other random phenomena ensure that the operation of any analog system will have some degree of stochastic behavior. Despite these limitations, however, it is usually reasonable to assume that deviations from these ideals will be small.
3.3.1 SISO
SISO systems are typically less complex than multiple-input multiple-output (MIMO) systems. Usually, it is also easier to make order of magnitude or trending predictions “on the fly” or “back of the envelope”. MIMO systems have too many interactions for most of us to trace through them quickly, thoroughly, and effectively in our heads.
Frequency domain techniques for analysis and controller design dominate SISO control system theory. Bode plot, Nyquist stability criterion, Nichols plot, and root locus are the usual tools for SISO system analysis. Controllers can be designed through the polynomial design, root locus design methods to name just two of the more popular. Often SISO controllers will be PI, PID, or lead-lag.
Fig. 3(a): Single Input Single Output
3.3.2 SIMO
SIMO (single input, multiple outputs) is an antenna technology for wireless communications in which multiple antennas are used at the destination (receiver). The antennas are combined to minimize errors and optimize data speed. The source (transmitter) has only one antenna. SIMO is one of several forms of smart antenna technology, the others being MIMO (multiple input, multiple output) and MISO (multiple input, single output).
In conventional wireless communications, a single antenna is used at the source, and another single antenna is used at the destination. In some cases, this gives rise to problems with multipath effects. When an electromagnetic field (EM field) is met with obstructions such as hills, canyons, buildings, and utility wires, the wave fronts are scattered, and thus they take many paths to reach the destination. The late arrival of scattered portions of the signal causes problems such as fading, cut-out (cliff effect), and intermittent reception (picket fencing). In digital communications systems such as wireless Internet, it can cause a reduction in data speed and an increase in the number of errors. The use of two or more antennas at the destination can reduce the trouble caused by multipath wave propagation.
SIMO technology has widespread applications in digital television (DTV), wireless local area networks (WLANs), metropolitan area networks (MANs), and mobile communications. An early form of SIMO, known as diversity reception, has been used by military, commercial, amateur, and shortwave radio operators at frequencies below 30 MHz since the First World War.
3.3.3 MISO
MISO (multiple inputs, single output) is an antenna technology for wireless communications in which multiple antennas are used at the source (transmitter). The antennas are combined to minimize errors and optimize data speed. The destination (receiver) has only one antenna. MISO is one of several forms of smart antenna technology, the others being MIMO (multiple inputs, multiple outputs) and SIMO (single input, multiple outputs).
In conventional wireless communications, a single antenna is used at the source, and another single antenna is used at the destination. In some cases, this gives rise to problems with multipath effects. When an electromagnetic field (EM field) is met with obstructions such as hills, canyons, buildings, and utility wires, the wave fronts are scattered, and thus they take many paths to reach the destination. The late arrival of scattered portions of the signal causes problems such as fading, cut-out (cliff effect), and intermittent reception (picket fencing). In digital communications systems such as wireless Internet, it can cause a reduction in data speed and an increase in the number of errors. The use of two or more antennas, along with the transmission of multiple signals (one for each antenna) at the source, can reduce the trouble caused by multipath wave propagation.
MISO technology has widespread applications in digital television (DTV), wireless local area networks (WLANs), metropolitan area networks (MANs), and mobile communications.
3.3.4 MIMO
Understanding of SISO, SIMO, MISO and MIMO In radio , multiple-inputs and multiple-outputs or MIMO (commonly pronounced my-moh or me-moh), is the use of multiple antennas at both the transmitter and receiver to improve communication performance. It is one of several forms of smart antenna technology. MIMO technology has attracted attention in wireless communications, because it offers significant increases in data throughput and link range without additional bandwidth or transmit power. It achieves this by higher spectral efficiency (more bits per second per hertz of bandwidth) and link reliability or diversity (reduced fading). Because of these properties, MIMO is an important part of modern wireless communication standards as IEEE 802.11n (Wi-fi), 3GPP Long Term Evolution, Wi-MAX and HSPA+.
Fig. 3(b): Multiple Input Multiple Outputs
Functions of MIMO
MIMO can be sub-divided into three main categories, preceding, spatial multiplexing or SM, and diversity coding. Proceeding is multi-stream beam forming, in the narrowest definition. In more general terms, it is considered to be all spatial processing that occurs at the transmitter. In (single-layer) beam forming, the same signal is emitted from each of the transmit antennas with appropriate phase (and sometimes gain) weighting such that the signal power is maximized at the receiver input.
The benefits of beam forming are to increase the received signal gain, by making signals emitted from different antennas add up constructively, and to reduce the multipath fading effect. In the absence of scattering, beam forming results in a well defined directional pattern, but in typical cellular conventional beams are not a good analogy. When the receiver has multiple antennas, the transmit beam forming cannot simultaneously maximize the signal level at all of the receive antennas, and proceeding with multiple streams is used. Note that proceeding requires knowledge of channel state information (CSI) at the transmitter.
Spatial multiplexing requires MIMO antenna configuration. In spatial multiplexing, a high rate signal is split into multiple lower rate streams and each stream is transmitted from a different transmit antenna in the same frequency channel. If these signals arrive at the receiver antenna array with sufficiently different spatial signatures, the receiver can separate these streams into (almost) parallel channels. Spatial multiplexing is a very powerful technique for increasing channel capacity at higher signal-to-noise ratios (SNR).
The maximum number of spatial streams is limited by the lesser in the number of antennas at the transmitter or receiver. Spatial multiplexing can be used with or without transmit channel knowledge. Spatial multiplexing can also be used for simultaneous transmission to multiple receivers, known as space-division multiple accesses. By scheduling receivers with different spatial signatures, good reparability can be assured. Diversity Coding techniques are used when there is no channel knowledge at the transmitter.
In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called space-time coding. The signal is emitted from each of the transmit antennas with full or near orthogonal coding. Diversity coding exploits the independent fading in the multiple antenna links to enhance signal diversity. Because there is no channel knowledge, there is no beam forming or array gain from diversity coding. Spatial multiplexing can also be combined with proceeding when the channel is known at the transmitter or combined with diversity coding when decoding reliability is in trade-off.
Fig. 3(c): Forms of MIMO
MIMO communication
Up to now, multi-antenna MIMO (or Single user MIMO) technology has been mainly developed and is implemented in some standards, e.g. [802.11n] products.
SISO /SIMO/MISO are degenerate cases of MIMO
Multiple-input and single-output (MISO) is a degenerate case when the receiver has a single antenna.
Single-input and multiple-output (SIMO) is a degenerate case when the transmitter has a single antenna.
Single-input and single-output (SISO) is a radio system where neither the transmitter non receiver has multiple antenna.
Principal single-user MIMO techniques
Bell Laboratories Layered Space-Time (BLAST), Gerard. J. Foschini (1996), sees also V-blast.
Per Antenna Rate Control (PARC), Varanasi, Guess (1998), Chung, Huang, Lozano (2001).
Selective Per Antenna Rate Control (SPARC), Ericsson (2004).
Some limitations
The physical antenna spacing are selected to be large; multiple wavelengths at the base station. The antenna separation at the receiver is heavily space constrained in hand sets, though advanced antenna design and algorithm techniques are under discussion.
3.4 MIMO channel capacity
In are MIMO systems, a transmitter send multiple streams by multiple transmit antennas. The transmit streams go through a matrix channel which consists of all Nt , Nr paths between the Nt transmit antennas at the transmitter and Nr accept antennas at the receiver. Then, the receiver gets the received signal vectors by the multiple receive antennas and decodes the received signal vectors into the original information. A narrowband flat fading MIMO system modeled as
y = Hx + n ………(1)
Equation No. (1) Where y and x are a received and transmit vectors, respectively, and H and n are the channel matrix and the noise vector, respectively.
Referring to information theory, the argotic channel capacity of MIMO systems where both the transmitter and the receiver have perfect instantaneous channel state information is[20]
C_(perfect-CSI )= E [max┬(Q;tr(Q)≤1)⁡log_2⁡〖del(I+ρHQH^H)]〗 = E[log_2⁡〖del(I+ρDSD)]〗 ……(2)
Where denotes Hermitical transpose and is the ratio between transmit power and noise power (i.e., transmit SNR). The optimal signal covariance is achieved through singular value decomposition of the channel matrix and an optimal diagonal power allocation matrix . The optimal power allocation is achieved through water filling, that is
S_i = (μ- 1/(ρd_i^2 ))+
for i =1 ,….min(N_(t,) N_r)
Where are the diagonal elements of D, is zero if its argument is negative, and is selected such that .
If the transmitter has only statistical channel state information, then the argotic channel capacity will decrease as the signal covariance Q can only be optimized in terms of the average mutual information.
C_(statistical-CSI) = max┬Q⁡〖E [log_2⁡〖del(I+ ρHQH^H)]〗 〗 ……….(3)
The spatial correlation of the channel has a strong impact on the argotic channel capacity with statistical information.
If the transmitter has no channel state information it can select the signal covariance Q to maximize channel capacity under worst-case statistics, which means Q=1/Nt I and accordingly
C_(no-CSI) = E [ log_2⁡〖del(I+ ρ/N_t 〗 〖HH〗^H)] ……(4)
Depending on the statistical properties of the channel, the argotic capacity is no greater than min (Nt, Nr) times larger than that of a SISO system.
MIMO signal testing focuses first on the transmitter/receiver system. The random phases of the sub-carrier signals can produce instantaneous power levels that cause the amplifier to compress, momentarily causing distortion and ultimately symbol errors. Signals with a high PAR (peak-to-average ratio) can cause amplifiers to compress unpredictably during transmission. OFDM signals are very dynamic and compression problems can be hard to detect because of their noise-like nature.
Knowing the quality of the signal channel is also critical. A channel emulator can simulate how a device performs at the cell edge, can add noise or can simulate what the channel looks like at speed. To fully qualify the performance of a receiver, a calibrated transmitter, such as a vector signal generator (VSG), and channel emulator can be used to test the receiver under a variety of different conditions. Conversely, the transmitter’s performance under a number of different conditions can be verified using a channel emulator and a calibrated receiver, such as a vector signal analyzer (VSA).
Understanding the channel allow for manipulation of the phase and amplitude of each transmitter in order to form a beam. To correctly form a beam, the transmitter needs to understand the characteristics of the channel. This process is called channel sounding or channel estimation. A known signal is sent to the mobile device that enables it to build a picture of the channel environment. The mobile device sends back the channel characteristics to the transmitter. The transmitter can then apply the correct phase and amplitude adjustments to form a beam directed at the mobile device. This is called a closed-loop MIMO system. For beam forming, it is required to adjust the phases and amplitude of each transmitter. In a beam former optimized for spatial diversity or spatial multiplexing, each antenna element simultaneously transmits a weighted combination of two data symbols.
3.5 MIMO-OFDM channel model
Multiple input, multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) is the dominant air interface for 4G and 5G broadband wireless communications. It combines multiple input, multiple output (MIMO) technology, which multiplies capacity by transmitting different signals over multiple antennas, and orthogonal frequency division multiplexing (OFDM), which divides a radio channel into a large number of closely spaced sub channels to provide more reliable communications at high speeds. Research conducted during the mid-1990s showed that while MIMO can be used with other popular air interfaces such as time division multiple accesses (TDMA) and code division multiple access (CDMA), the combination of MIMO and OFDM is most practical at higher data rates.
MIMO-OFDM is the foundation for most advanced wireless local area network (Wireless LAN) and mobile broadband network standards because it achieves the greatest spectral efficiency and, therefore, delivers the highest capacity and data throughput. Greg Raleigh invented MIMO in 1996 when he showed that different data streams could be transmitted at the same time on the same frequency by taking advantage of the fact that signals transmitted through space bounce off objects (such as the ground) and take multiple paths to the receiver. That is, by using multiple antennas and preceding the data, different data streams could be sent over different paths. Raleigh suggested and later proved that the processing required by MIMO at higher speeds would be most manageable using OFDM modulation, because OFDM converts a high-speed data channel into a number of parallel, lower-speed channels.
In modern usage, the term “MIMO” indicates more than just the presence of multiple transmit antennas (multiple input) and multiple receive antennas (multiple output). While multiple transmit antennas can be used for beam forming, and multiple receive antennas can be used for diversity, the word “MIMO” refers to the simultaneous transmission of multiple signals (spatial multiplexing) to multiply spectral efficiency (capacity).
Traditionally, radio engineers treated natural multipath propagation as an impairment to be mitigated. MIMO is the first radio technology that treats multipath propagation as a phenomenon to be exploited. MIMO multiplies the capacity of a radio link by transmitting multiple signals over multiple, co-located antennas. This is accomplished without the need for additional power or bandwidth. Space-time codes are employed to ensure that the signals transmitted over the different antennas are orthogonal to each other, making it easier for the receiver to distinguish one from another. Even when there is line of sight access between two stations, dual antenna polarization may be used to ensure that there is more than one robust path.
OFDM enables reliable broadband communications by distributing user data across a number of closely spaced, narrowband sub channels. This arrangement makes it possible to eliminate the biggest obstacle to reliable broadband communications, inter symbol interference (ISI). ISI occurs when the overlap between consecutive symbols is large compared to the symbols’ duration. Normally, high data rates require shorter duration symbols, increasing the risk of ISI. By dividing a high-rate data stream into numerous low-rate data streams, OFDM enables longer duration symbols. A cyclic prefix (CP) may be inserted to create a (time) guard interval that prevents ISI entirely. If the guard interval is longer than the delay spread—the difference in delays experienced by symbols transmitted over the channel—then there will be no overlap between adjacent symbols and consequently no inter symbol interference. Though the CP slightly reduces spectral capacity by consuming a small percentage of the available bandwidth, the elimination of ISI makes it an exceedingly worthwhile tradeoff.
A key advantage of OFDM is that Fast Fourier Transforms (FFTs) may be used to simplify implementation. Fourier transforms convert signals back and forth between the time domain and frequency domain. Consequently, Fourier transforms can exploit the fact that any complex waveform may be decomposed into a series of simple sinusoids. In signal processing applications, discrete Fourier transforms (DFTs) are used to operate on real-time signal samples. DFTs may be applied to composite OFDM signals, avoiding the need for the banks of oscillators and demodulators associated with individual subcarriers. Fast Fourier transforms are numerical algorithms used by computers to perform DFT calculations.
FFTs also enable OFDM to make efficient use of bandwidth. The sub channels must be spaced apart in frequency just enough to ensure that their time-domain waveforms are orthogonal to each other. In practice, this means that the sub channels are allowed to partially overlap in frequency.
MIMO-OFDM is a particularly powerful combination because MIMO does not attempt to mitigate multipath propagation and OFDM avoids the need for signal equalization. MIMO-OFDM can achieve very high spectral efficiency even when the transmitter does not possess channel state information (CSI). When the transmitter does possess CSI (which can be obtained through the use of training sequences), it is possible to approach the theoretical channel capacity. CSI may be used, for example, to allocate different size signal constellations to the individual subcarriers, making optimal use of the communications channel at any given moment of time.
More recent MIMO-OFDM developments include multi-user MIMO (MU-MIMO), higher order MIMO implementations (greater number of spatial streams), and research concerning “massive MIMO” and “Cooperative MIMO” for inclusion in coming 5G standards.
MU-MIMO is part of the IEEE 802.11ac standard, the first Wi-Fi standard to offer speeds in the gigabit per second range. MU-MIMO enables an access point (AP) to transmit to up to four client devices simultaneously. This eliminates contention delays, but requires frequent channel measurements to properly direct the signals. Each user may employ up to four of the available eight spatial streams.
For example, an AP with eight antennas can talk to two client devices with four antennas, providing four spatial streams to each. Alternatively, the same AP can talk to four client devices with two antennas each, providing two spatial streams to each. Multi-user MIMO beams forming even benefits single spatial stream devices. Prior to MU-MIMO beam forming, an access point communicating with multiple client devices could only transmit to one at a time. With MU-MIMO beam forming, the access point can transmit to up to four single stream devices at the same time on the same channel.
The 802.11ac standard also supports speeds up to 6.93 GBit/s using eight spatial streams in single-user mode. The maximum data rate assumes use of the optional 160 MHz channel in the 5 GHz band and 256 QAM (quadrature amplitude modulation). Chipsets supporting six spatial streams have been introduced and chipsets supporting eight spatial streams are under development.
Massive MIMO consists of a large number of base station antennas operating in a MU-MIMO environment. While LTE networks already support handsets using two spatial streams, and handset antenna designs capable of supporting four spatial streams have been tested, massive MIMO can deliver significant capacity gains even to single spatial stream handsets. Again, MU-MIMO beam forming is used to enable the base station to transmit independent data streams to multiple handsets on the same channel at the same time. However, one question still to be answered by research is: When is it best to add antennas to the base station and when is it best to add small cells.
Another focus of research for 5G wireless is Cooperative MIMO (CO-MIMO). In CO-MIMO, clusters of base stations work together to boost performance. This can be done using macro diversity for improved reception of signals from handsets or multi-cell multiplexing to achieve higher downlink data rates. However, CO-MIMO requires high-speed communication between the cooperating base stations.
3.5.1 AWGN Channel
Additive white Gaussian noise (AWGN) is a basic noise model used in Information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics:
‘Additive’ because it is added to any noise that might be intrinsic to the information system.
‘White’ refers to idea that it has uniform power across the frequency band for the information system. It is an analogy to the color white which has uniform emissions at all frequencies in the visible spectrum.
‘Gaussian’ because it has a normal distribution in the time domain with an average time domain value of zero.
Wideband noise comes from many natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson-Nyquist noise), shot noise, black body radiation from the earth and other warm objects, and from celestial sources such as the Sun. The central limit theorem of probability theory indicates that the summation of many random processes will tend to have distribution called Gaussian or Normal.
AWGN is often used as a channel model in which the only impairment to communication is a linear addition of wideband or white noise with a constant spectral density (expressed as watts per hertz of bandwidth) and a Gaussian distribution of amplitude. The model does not account for fading, frequency selectivity, interference, nonlinearity or dispersion. However, it produces simple and tractable mathematical models which are useful for gaining insight into the underlying behavior of a system before these other phenomena are considered.
The AWGN channel is a good model for many satellite and deep space communication links. It is not a good model for most terrestrial links because of multipath, terrain blocking, interference, etc. However, for terrestrial path modeling, AWGN is commonly used to simulate background noise of the channel under study, in addition to multipath, terrain blocking, interference, ground clutter and self interference that modern radio systems encounter in terrestrial operation.
3.5.2 Rayleigh fading channel
Rayleigh fading is a statistical model for the effect of a 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 communications channel) will vary randomly, or fade, according to a Rayleigh distribution, the radial component of the sum of two uncorrelated Gaussian random variables.
Rayleigh fading is viewed as a reasonable model for troposphere and ionosphere signal propagation as well as the effect of heavily built-up urban environments on radio signals.[1][2] Rayleigh fading is most applicable when there is no dominant propagation along a line of sight between the transmitter and receiver. If there is a dominant line of sight, Rician fading may be more applicable.
Since it is based on a well-studied distribution with special properties, the Rayleigh distribution lends itself to analysis, and the key features that affect the performance of a wireless network have analytic expressions. The parameters discussed here are for a non-static channel. If a channel is not changing with time, it does not fade and instead remains at some particular level. Separate instances of the channel in this case will be uncorrelated with one another, owing to the assumption that each of the scattered components fades independently. Once relative motion is introduced between any of the transmitter, receiver, and caterers, the fading becomes correlated and varying in time.
3.5.3 Rician fading channel
Rician fading is a stochastic model for radio propagation anomaly caused by partial cancellation of a radio signal by itself — the signal arrives at the receiver by several different paths (hence exhibiting multipath interference), and at least one of the paths is changing (lengthening or shortening). Rician fading occurs when one of the paths, typically a line of sight signal, is much stronger than the others. In Rician fading, the amplitude gain is characterized by a Rician distribution.
Rayleigh fading is the specialized model for stochastic fading when there is no line of sight signal, and is sometimes considered as a special case of the more generalized concept of Rician fading. In Rayleigh fading, the amplitude gain is characterized

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