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 an unknown 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 SNR and the range precision of the partitions. The current work presents a method to extend these results using the rate distortion function to find necessary conditions for any P_e, not just arbitrarily small ones. 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 information rate implies a lower bound on P_e for a given partition. Furthermore, the current work describes a tradeoff among range precision, P_e and SNR. Examples of this tradeoff are given for a typical 2-dimensional (range and depth) shallow water environment