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The relative motion between the transmitter and the receiver modifies the nonstationarity properties of the transmitted signal. In particular, the almost-cyclostationarity property exhibited by almost all modulated signals adopted in communications, radar, sonar, and telemetry can be transformed into more general kinds of nonstationarity. A proper statistical characterization of the received signal allows for the design of signal processing algorithms for detection, estimation, and classification that significantly outperform algorithms based on classical descriptions of signals.Generalizations of Cyclostationary Signal Processing addresses these issues and includes the following key features: Presents the underlying theoretical framework, accompanied by details of their practical application, for the mathematical models of generalized almost-cyclostationary processes and spectrally correlated processes; two classes of signals finding growing importance in areas such as mobile communications, radar and sonar. Explains second- and higher-order characterization of nonstationary stochastic processes in time and frequency domains. Discusses continuous- and discrete-time estimators of statistical functions of generalized almost-cyclostationary processes and spectrally correlated processes. Provides analysis of mean-square consistency and asymptotic Normality of statistical function estimators. Offers extensive analysis of Doppler channels owing to the relative motion between transmitter and receiver and/or surrounding scatterers. Performs signal analysis using both the classical stochastic-process approach and the functional approach, where statistical functions are built starting from a single function of time.
Many processes in nature arise from the interaction of periodic phenomena with random phenomena. The results are processes that are not periodic, but whose statistical functions are periodic functions of time. These processes are called cyclostationary and are an appropriate mathematical model for signals encountered in many fields including communications, radar, sonar, telemetry, acoustics, mechanics, econometrics, astronomy, and biology. Cyclostationary Processes and Time Series: Theory, Applications, and Generalizations addresses these issues and includes the following key features. Presents the foundations and developments of the second- and higher-order theory of cyclostationary signals Performs signal analysis using both the classical stochastic process approach and the functional approach for time series Provides applications in signal detection and estimation, filtering, parameter estimation, source location, modulation format classification, and biological signal characterization Includes algorithms for cyclic spectral analysis along with Matlab/Octave code Provides generalizations of the classical cyclostationary model in order to account for relative motion between transmitter and receiver and describe irregular statistical cyclicity in the data
From this book, you will learn new concepts, methods, and algorithms for performing signal processing tasks and designing and analyzing communications systems.
Symmetries and Groups in Signal Processing: An Introduction deals with the subject of symmetry, and with its place and role in modern signal processing. In the sciences, symmetry considerations and related group theoretic techniques have had a place of central importance since the early twenties. In engineering, however, a matching recognition of their power is a relatively recent development. Despite that, the related literature, in the form of journal papers and research monographs, has grown enormously. A proper understanding of the concepts that have emerged in the process requires a mathematical background that goes beyond what is traditionally covered in an engineering undergraduate curriculum. Admittedly, there is a wide selection of excellent introductory textbooks on the subject of symmetry and group theory. But they are all primarily addressed to students of the sciences and mathematics, or to students of courses in mathematics. Addressed to students with an engineering background, this book is meant to help bridge the gap.
The growing interest in smart grid applications has drawn considerable attention to power line communications (PLC) as a central communications medium for smart grids. Specifically, network control and grid applications are allocated the frequency band of 0 − 500 kHz, commonly referred to as the narrowband PLC channel. As this frequency band is characterized by strong cyclostationary noise, multipath signal propagation, and periodically time varying channel conditions, narrowband PLC channels fall into the class of periodic channels with finite memory. In this dissertation we study communications over periodic channels with finite memory, utilizing the theory of cyclostationary processes to address two major aspects: information-theoretic performance bounds, and practical algorithms for realizing the predicted performance gains. In the first part of the dissertation, we study the fundamental rate limits of periodic channels with finite memory, focusing on the capacity of point-to-point (PtP) periodic channels, i.e., without security constraints, as well as the secrecy capacity of periodic wiretap channels, i.e., with security constraints. By proving a bijection between PtP periodic channels and time-invariant multiple input-multiple output (MIMO) channels with finite memory, we characterize the capacity of periodic channels via the capacity of the equivalent time-invariant MIMO channels. As part of the capacity derivation, we characterize the capacity achieving transmission scheme, which leads to a practical code construction that approaches capacity. Motivated by the bijection between periodic channels and time-invariant MIMO channels with finite memory, we study the secrecy capacity of time-invariant Gaussian MIMO channels with finite memory. Although the time-invariant Gaussian MIMO channel with finite memory is a very common channel model in wireless communications, as well as in wireline communications, this is the first time that the secrecy capacity has been characterized for this channel model. As the resulting secrecy capacity expression is given by a non-convex optimization problem, we derive a simple necessary and sufficient condition for positive secrecy capacity, and obtain an explicit expression for the secrecy capacity in the scalar case. Then, we show how our result directly leads to the secrecy capacity of periodic channels. In the second part of the dissertation, we study practical algorithms which utilize the theory of cyclostationarity to approach the predicted performance gains in periodic channels. First, we propose a receiver algorithm for the recovery of orthogonal frequency division multiplexing (OFDM) modulated signals in periodic channels. The proposed receiver uses frequency-shift filtering to exploit the cyclostationary properties of both the additive channel noise and the information signal. We explicitly derive the coefficients of the filter which minimize the time-averaged mean-squared error (TA-MSE), and propose an adaptive implementation, which is based on the recursive least-squares (RLS) algorithm. Numerical simulations show that the proposed receiver demonstrates a substantial performance gain over previously proposed receivers. Finally, motivated by the fact that most adaptive algorithms, such as the least mean-squares (LMS) and the RLS, are designed for stationary signals, we rigorously study the optimal adaptive filtering of cyclostationary signals. We first identify the relevant objective as the TA-MSE, and obtain an adaptive algorithm, which we refer to as time-averaged LMS (TA-LMS), as the stochastic approximation of the TA-MSE minimizer. We provide a comprehensive transient and steady-state performance analysis, and derive conditions for convergence and stability, which are shown to accurately characterize the performance of the adaptive algorithm in a simulation study.-- abstract.
Our focus in this ARO research project is to investigate and study the application of cyclostationary signal processing in digital communication systems. We consider several important areas of application including channel equalization, co-channel interference rejection, and antenna beamforming. During this report period, we developed a number of new algorithm for the blind identification and equalization of multiple input multiple output systems. These methods are more robust and accurate than many existing methods. Blind separation of signals using both the higher order and second order (cyclostationary) statistics are studied. Several simple methods are proposed. We also developed a finite window decorrelator receiver for asynchronous CDMA systems. This new algorithm is near far resistant even when the processing window is rather short, overcoming the weakness of the conventional decorrelator that relies on large (almost infinite) window size. In another important study, we investigate the applicability of blind equalization algorithms in practical wireless cellular systems such as the GSM. Since the GSM transmission is nonlinear and is in burst mode, blind equalization algorithms must be adopted for this nonlinear modulation and must converge within each frame of data burst. Using a linearization method, we simplied the nonlinear GMSK signal into an equivalent linear QAM signal. A de-rotation scheme further allowed channel diversity be extracted without the need of additional downlink antennae. Successful blind equalization and semi-blind equalization results for GSM are established.