Biorthogonal partners and applications

Two digital filters H(z) and F(z) are said to be biorthogonal partners of each other if their cascade H(z)F(z) satisfies the Nyquist or zero-crossing property. Biorthogonal partners arise in many different contexts such as filterbank theory, exact and least squares digital interpolation, and multiresolution theory. They also play a central role in the theory of equalization, especially, fractionally spaced equalizers in digital communications. We first develop several theoretical properties of biorthogonal partners. We also develop conditions for the existence of biorthogonal partners and FIR biorthogonal pairs and establish the connections to the Riesz basis property. We then explain how these results play a role in many of the above-mentioned applications

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

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

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

Synchronization and detection for two-dimensional magnetic recording

This thesis develops efficient synchronization and detection algorithms for two-dimensional magnetic recording (TDMR) under a low latency constraint. TDMR is a new technology for increasing data density of hard disk drives up to 10 Tera bits per square inch of the medium. TDMR read channel suffers from two-dimensional interference, bit position (timing) uncertainty, and data dependent noise, to name a few. The problem of timing uncertainty is addressed with synchronization. This thesis focuses on the synchronization component of the read channel and develops synchronization solutions which effectively compensate for the asynchrony between the phase of the received readback waveforms and the phase of the sampling clocks. In particular, this thesis proposes solutions to reduce the computational cost of current generation of read channels, where only one data track is detected at a time. For future generations of TDMR read channels, where multiple tracks will be detected jointly, this thesis provides a first-time solution to the synchronization problem for joint detection of multiple asynchronous tracks.Ph.D

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

Reduced-complexity signal processing techniques for multiple-input multiple-output storage and wireless communication systems

Ph.DNUS-TU/E JOINT PH.D. PROGRAMM

Graphical model driven methods in adaptive system identification

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2016Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible. This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler. Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods. Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGSRLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods. The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems. The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.The work in this thesis was supported primarily by the Office of Naval Research through an ONR Special Research Award in Ocean Acoustics; and at various times by the National Science Foundation, the WHOI Academic Programs Office and the MIT Presidential Fellowship Program