Fractional biorthogonal partners in channel equalization and signal interpolation

The concept of biorthogonal partners has been introduced recently by the authors. The work presented here is an extension of some of these results to the case where the upsampling and downsampling ratios are not integers but rational numbers, hence, the name fractional biorthogonal partners. The conditions for the existence of stable and of finite impulse response (FIR) fractional biorthogonal partners are derived. It is also shown that the FIR solutions (when they exist) are not unique. This property is further explored in one of the applications of fractional biorthogonal partners, namely, the fractionally spaced equalization in digital communications. The goal is to construct zero-forcing equalizers (ZFEs) that also combat the channel noise. The performance of these equalizers is assessed through computer simulations. Another application considered is the all-FIR interpolation technique with the minimum amount of oversampling required in the input signal. We also consider the extension of the least squares approximation problem to the setting of fractional biorthogonal partners

Performance Evaluation of Adaptive Equalizer in a Communication System

This project deals with the study of the various kinds of interferences in a communication channel viz. Inter symbol Interference, Multipath Interference and Additive Interference. It deals with the design of an Adaptive Equalizer. The idea of the equalizer is to build (another) filter in the receiver that counteracts the effect of the channel. In essence, the equalizer must “unscatter” the impulse response. This can be stated as the goal of designing the equalizer E so that the impulse response of the combined channel and equalizer CE has a single spike. This can be solved using different techniques. In this project, we have implemented an ‘Adaptive Equalizer’ using four different algorithms in Matlab. We have suggested different ways to decide the coefficients of the equalizer. The first procedure (LEAST SQUARE ALGORITHM) minimizes the square of the symbol recovery error over a block of data which can be done by using matrix pseudo inversion. The second method (LEAST MEAN SQUARE ALGORITHM) involves minimizing the square of the error between the received data values and the transmitted values which are achieved via an adaptive element. The third method (DECISION DIRECTED ALGORITHM) and the fourth method (DISPERSION MINIMIZING ALGORITHM) are used when there is no training sequence and other performance functions are appropriate. In addition to this we have undertaken a study and realization of the Bit Error Rate of a communication system using VisSim Software

Channel estimation for SISO and MIMO OFDM communications systems.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2010.Telecommunications in the current information age is increasingly relying on the wireless link. This is because wireless communication has made possible a variety of services ranging from voice to data and now to multimedia. Consequently, demand for new wireless capacity is growing rapidly at a very alarming rate. In a bid to cope with challenges of increasing demand for higher data rate, better quality of service, and higher network capacity, there is a migration from Single Input Single Output (SISO) antenna technology to a more promising Multiple Input Multiple Output (MIMO) antenna technology. On the other hand, Orthogonal Frequency Division Multiplexing (OFDM) technique has emerged as a very popular multi-carrier modulation technique to combat the problems associated with physical properties of the wireless channels such as multipath fading, dispersion, and interference. The combination of MIMO technology with OFDM techniques, known as MIMO-OFDM Systems, is considered as a promising solution to enhance the data rate of future broadband wireless communication Systems. This thesis addresses a major area of challenge to both SISO-OFDM and MIMO-OFDM Systems; estimation of accurate channel state information (CSI) in order to make possible coherent detection of the transmitted signal at the receiver end of the system. Hence, the first novel contribution of this thesis is the development of a low complexity adaptive algorithm that is robust against both slow and fast fading channel scenarios, in comparison with other algorithms employed in literature, to implement soft iterative channel estimator for turbo equalizer-based receiver for single antenna communication Systems. Subsequently, a Fast Data Projection Method (FDPM) subspace tracking algorithm is adapted to derive Channel Impulse Response Estimator for implementation of Decision Directed Channel Estimation (DDCE) for Single Input Single Output - Orthogonal Frequency Division Multiplexing (SISO-OFDM) Systems. This is implemented in the context of a more realistic Fractionally Spaced-Channel Impulse Response (FS-CIR) channel model, as against the channel characterized by a Sample Spaced-Channel Impulse Response (SS)-CIR widely assumed by other authors. In addition, a fast convergence Variable Step Size Normalized Least Mean Square (VSSNLMS)-based predictor, with low computational complexity in comparison with others in literatures, is derived for the implementation of the CIR predictor module of the DDCE scheme. A novel iterative receiver structure for the FDPM-based Decision Directed Channel Estimation scheme is also designed for SISO-OFDM Systems. The iterative idea is based on Turbo iterative principle. It is shown that improvement in the performance can be achieved with the iterative DDCE scheme for OFDM system in comparison with the non iterative scheme. Lastly, an iterative receiver structure for FDPM-based DDCE scheme earlier designed for SISO OFDM is extended to MIMO-OFDM Systems. In addition, Variable Step Size Normalized Least Mean Square (VSSNLMS)-based channel transfer function estimator is derived in the context of MIMO Channel for the implementation of the CTF estimator module of the iterative Decision Directed Channel Estimation scheme for MIMO-OFDM Systems in place of linear minimum mean square error (MMSE) criterion. The VSSNLMS-based channel transfer function estimator is found to show improved MSE performance of about -4 MSE (dB) at SNR of 5dB in comparison with linear MMSE-based channel transfer function estimator

UNDERWATER COMMUNICATIONS WITH ACOUSTIC STEGANOGRAPHY: RECOVERY ANALYSIS AND MODELING

In the modern warfare environment, communication is a cornerstone of combat competence. However, the increasing threat of communications-denied environments highlights the need for communications systems with low probability of intercept and detection. This is doubly true in the subsurface environment, where communications and sonar systems can reveal the tactical location of platforms and capabilities, subverting their covert mission set. A steganographic communication scheme that leverages existing technologies and unexpected data carriers is a feasible means of increasing assurance of communications, even in denied environments. This research works toward a covert communication system by determining and comparing novel symbol recovery schemes to extract data from a signal transmitted under a steganographic technique and interfered with by a simulated underwater acoustic channel. We apply techniques for reliably extracting imperceptible information from unremarkable acoustic events robust to the variability of the hostile operating environment. The system is evaluated based on performance metrics, such as transmission rate and bit error rate, and we show that our scheme is sufficient to conduct covert communications through acoustic transmissions, though we do not solve the problems of synchronization or equalization.Lieutenant, United States NavyApproved for public release. Distribution is unlimited

Development of Fuzzy System Based Channel Equalisers

Channel equalisers are used in digital communication receivers to mitigate the effects of inter symbol interference (ISI) and inter user interference in the form of co-channel interference (CCI) and adjacent channel interference (ACI) in the presence of additive white Gaussian noise (AWGN). An equaliser uses a large part of the computations involved in the receiver. Linear equalisers based on adaptive filtering techniques have long been used for this application. Recently, use of nonlinear signal processing techniques like artificial neural networks (ANN) and radial basis functions (RBF) have shown encouraging results in this application. This thesis presents the development of a nonlinear fuzzy system based equaliser for digital communication receivers. The fuzzy equaliser proposed in this thesis provides a parametric implementation of symbolby-symbol maximum a-posteriori probability (MAP) equaliser based on Bayes’s theory. This MAP equaliser is also called Bayesian equaliser. Its decision function uses an estimate of the noise free received vectors, also called channel states or channel centres. The fuzzy equaliser developed here can be implemented with lower computational complexity than the RBF implementation of the MAP equaliser by using scalar channel states instead of channel states. It also provides schemes for performance tradeoff with complexity and schemes for subset centre selection. Simulation studies presented in this thesis suggests that the fuzzy equaliser by using only 10%-20% of the Bayesian equaliser channel states can provide near optimal performance. Subsequently, this fuzzy equaliser is modified for CCI suppression and is termed fuzzy–CCI equaliser. The fuzzy–CCI equaliser provides a performance comparable to the MAP equaliser designed for channels corrupted with CCI. However the structure of this equaliser is similar to the MAP equaliser that treats CCI as AWGN. A decision feedback form of this equaliser which uses a subset of channel states based on the feedback state is derived. Simulation studies presented in this thesis demonstrate that the fuzzy–CCI equaliser can effectively remove CCI without much increase in computational complexity. This equaliser is also successful in removing interference from more than one CCI sources, where as the MAP equalisers treating CCI as AWGN fail. This fuzzy–CCI equaliser can be treated as a fuzzy equaliser with a preprocessor for CCI suppression, and the preprocessor can be removed under high signal to interference ratio condition

Artificial Neural Network Based Channel Equalization

The field of digital data communications has experienced an explosive growth in the last three decade with the growth of internet technologies, high speed and efficient data transmission over communication channel has gained significant importance. The rate of data transmissions over a communication system is limited due to the effects of linear and nonlinear distortion. Linear distortions occure in from of inter-symbol interference (ISI), co-channel interference (CCI) and adjacent channel interference (ACI) in the presence of additive white Gaussian noise. Nonlinear distortions are caused due to the subsystems like amplifiers, modulator and demodulator along with nature of the medium. Some times burst noise occurs in communication system. Different equalization techniques are used to mitigate these effects. Adaptive channel equalizers are used in digital communication systems. The equalizer located at the receiver removes the effects of ISI, CCI, burst noise interference and attempts to recover the transmitted symbols. It has been seen that linear equalizers show poor performance, where as nonlinear equalizer provide superior performance. Artificial neural network based multi layer perceptron (MLP) based equalizers have been used for equalization in the last two decade. The equalizer is a feed-forward network consists of one or more hidden nodes between its input and output layers and is trained by popular error based back propagation (BP) algorithm. However this algorithm suffers from slow convergence rate, depending on the size of network. It has been seen that an optimal equalizer based on maximum a-posterior probability (MAP) criterion can be implemented using Radial basis function (RBF) network. In a RBF equalizer, centres are fixed using K-mean clustering and weights are trained using LMS algorithm. RBF equalizer can mitigate ISI interference effectively providing minimum BER plot. But when the input order is increased the number of centre of the network increases and makes the network more complicated. A RBF network, to mitigate the effects of CCI is very complex with large number of centres. To overcome computational complexity issues, a single neuron based chebyshev neural network (ChNN) and functional link ANN (FLANN) have been proposed. These neural networks are single layer network in which the original input pattern is expanded to a higher dimensional space using nonlinear functions and have capability to provide arbitrarily complex decision regions. More recently, a rank based statistics approach known as Wilcoxon learning method has been proposed for signal processing application. The Wilcoxon learning algorithm has been applied to neural networks like Wilcoxon Multilayer Perceptron Neural Network (WMLPNN), Wilcoxon Generalized Radial Basis Function Network (WGRBF). The Wilcoxon approach provides promising methodology for many machine learning problems. This motivated us to introduce these networks in the field of channel equalization application. In this thesis we have used WMLPNN and WGRBF network to mitigate ISI, CCI and burst noise interference. It is observed that the equalizers trained with Wilcoxon learning algorithm offers improved performance in terms of convergence characteristic and bit error rate performance in comparison to gradient based training for MLP and RBF. Extensive simulation studies have been carried out to validate the proposed technique. The performance of Wilcoxon networks is better then linear equalizers trained with LMS and RLS algorithm and RBF equalizer in the case of burst noise and CCI mitigations

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications