Estimation in randomly time-varying systems with application to digital communications

Many systems in digital signal processing, communications and control can be modeled as a linear randomly time-varying system. Ionospheric channels for communications, target models in synthetic aperture radars, geological systems and especially urban communication channels are examples of randomly time-varying systems.; The impulse response for this class of systems is a stochastic process with two independent parameters, or a two-dimensional random field. This reflects randomness and time variations of the system. We can transform one of the variables to the frequency domain and use time-frequency analysis techniques.; The mathematical analysis of the linear time-varying random systems is based on multi-parameter martingale theory. Interpretation of stochastic processes in Hilbert space, spectral multiplicity and canonical decompositions are important concepts in estimation theory. This framework is used to discuss the estimation and detection in wide sense stationary uncorrelated scatterer systems. Linear randomly time-varying operators are used in the study of communications through multipath fading channels. This includes modeling of the channel for wideband signals, optimum signal and receiver design for communications through multipath fading channels, and estimation techniques, including Wiener and Kalman filtering.; An important application of this theory is in digital mobile communication which suffers from significant Rayleigh fading. We compare different estimation and equalization techniques using Kalman filtering and other adaptive signal processing techniques such as Least Mean Square and modified Recursive Least Square and analyze their performance and complexity for dispersive fading channels. Finally, simulations of some of the suggested algorithms are presented. The simulations model the entire digital mobile communication system including transmitter, channel and receiver.