Abstract
Information theory provides a novel perspective on passive sonar. 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. The goal is to assign the source to the correct partition with the minimum possible probability of error (Pe). Prior work [Buck, Proc. IEEE SAM Workshop, 2002] described necessary conditions for achieving arbitrarily small Pe as a tradeoff between SNR and the range extent, or resolution, of the partitions. This paper presents a method to extend these results using rate distortion theory to find necessary conditions for any Pe, not just arbitrarily small ones. The Gaussian channel bound sets an upper limit on the rate of information received at the array, which implies a lower bound on Pe for a given partition. For a given range resolution, this method provides the minimum achievable Pe for a given SNR, or the minimum SNR to achieve a given Pe. Examples of these bounds will be given for typical shallow water environments. [Work supported by ONR Code 321US.]