Overview of signal processing in uncertain and random environments

This paper is an overview of optimum and/or robust signal-processing approaches for detecting signals in random and uncertain propagation and interference environments, a topic that is intertwined with statistical modeling of the medium and signals. The classical approach to processing of signals that have propagated through randomly fluctuating media is based on the concepts of randomly time-varying impulse responses, spreading functions, and scattering functions. This approach uses second-order statistics and gives insight into performance of active sonar. Implementation of maximum likelihood (ML) detectors for signals that have propagated through random environments requires knowledge of the probability density functions (pdf’s) of the random signal and noise parameters. Random signal parameters that are typically affected by medium randomness are amplitude, phase, and arrival time; pulse and Doppler spread; arrival angle bias and spread. Signal pdf’s can be derived from ocean acoustic models using the maximum entropy (ME) principle, which exploits what is known but is maximally noncommittal of what is uncertain. The ME method can be used to generate densities that belong to the exponential class, and for this class, ML detectors can be implemented as an estimator-correlator and estimator-noise canceler structure. [Work supported by The Undersea Signal Processing Program Office of Naval Research.]