Fading Channel Capacity and Passive Sonar Performance Bounds

Passive sonar algorithms attempt to estimate the location of a sound source from pressure observations at a hydrophone array and knowledge of the acoustic environment. Traditionally, the mean squared error (MSE) of these position estimates has been the performance metric of interest, and performance bounds set lower limits on the MSE. Information theory provides an alternative perspective on passive sonar performance. In this approach, the search volume is partitioned into disjoint cells, each of which has an a priori probability of containing the source. The sonar algorithm then estimates which partition cell contains the unknown source based on the array observations. The goal is to minimize the probability of error (P_epsi) in making this assignment. A necessary condition to achieve arbitrarily small P_epsi is that the mutual information between the actual and estimated cell containing the source must exceed the entropy of the cells computed from the a priori probabilities. For a fixed size search region, this necessary condition implies a lower bound on the cell size which can achieve arbitrarily small P_epsi. If the average source level is known, but not the individual source levels, the mutual information is bounded by the capacity of a fading channel. The cell sizes satisfying the necessary condition for arbitrarily small P_epsi for the fading channel model are substantially larger than those for the case when the source level is known. The resulting performance bound is evaluated for a typical coastal shallow water environment