IEEE Workshop on Underwater Acoustic Signal Processing, Fall 2005
Title: Rate distortion theory bounds on passive sonar performance
Authors: Tianzhu Meng, John R. Buck

Information theory provides a novel perspective on the performance bounds for passive sonar. Classical approaches use the minimum mean squared error to bound passive sonar performance. In contrast, the information theoretic 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 ( P_e ).

Prior work [Buck, Proc. IEEE SAM Workshop, 2002] described necessary conditions for achieving arbitrarily small P_e 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 P_e, not just arbitrarily small ones.

For a given partition, rate distortion theory provides an algorithm to calculate the minimum required information rate in order to achieve the desired P_e. The Gaussian channel capacity sets an upper limit on information rate received at the array, which implies a lower bound on P_e for a given partition. For a given environment and array geometry, the Gaussian channel capacity is determined by the SNR. Thus this method describes the tradeoff between the range resolution, SNR and P_e. Sepcifically, for a desired range resolution, this method provides the minimum achievable P_e for a given SNR, or the minimum SNR to achieve a given P_e. Examples of these bounds will be given for typical shallow water environments.

[Work supported by ONR Code 321US.]

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