IEEE Workshop on Underwater Acoustic Signal Processing, Fall 2005
Title: Fading Channel Capacity and Passive Sonar Resolution
Author: John R. Buck

Passive sonar algorithms process the pressure field observed on an array of hydrophones and estimate the location of the acoustic source from this information and knowledge of the acoustic environment. Historically, the performance of passive sonar algorithms has been quantified in terms of the mean squared error between the estimated source location and its true location. An alternative perspective is to divide the search region in disjoint partitions, then attempt to assign the source to the correct partition with the minimum probability of error ( P_e ). Within this perspective, information theory provides important necessary conditions characterizing the tradeoff between the SNR and the number of partitions if the sources are to be assigned to the correct partition with arbitrarily small P_e. Previous work [Buck, IEEE Proc. SAM 2002] described how to compute these performance bounds for a given environment and array geometry.

A shortcoming of the approach described in [Buck, IEEE Proc. SAM 2002] was that the source level was presumed to be known. In practice, the absolute level of the acoustic source would not be known. This restriction can be mapped onto the fading channel problem in communication theory. Recent results [Abou-Faycal et. al, IEEE Trans. Info. Th., May 2001] presented upper bounds on the channel capacity for a fading channel. For the SNRs typical in passive sonar, there is much less mutual information available for the unknown source level scenario than the previously presented known source level scenario. This implies substantially less resolution is possible while achieving arbitrarily small P_e. Results will be presented from typical shallow water environments contrasting the unknown source level case with the known source level case for single-frequency stationary sources.

[Work supported by ONR Code 321US.]

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