Rate Distortion Bounds on Passive Sonar Performance

Information theory provides a novel perspective on passive sonar performance analysis. This approach begins by partitioning the search space and then considers the problem of assigning a source to the correct partition based on pressure observations from a hydrophone array. Prior work described necessary conditions for achieving arbitrarily small probability of error (P-e) as a tradeoff between signal-to-noise ratio (SNR) and the range accuracy of the partitions. This paper presents a method to extend these results using the rate-distortion function to find necessary conditions for any P-e. The Gaussian channel bound sets an upper limit on the information rate received at the array. Through the rate-distortion function, this upper limit on the information rate implies a lower bound on P-e for a given partition. Furthermore, the current work describes a tradeoff between range accuracy, P-e and SNR. Examples of this tradeoff are evaluated for both one-dimensional (bearing) and two-dimensional (range-depth) estimation problems.