Near-field performance of passive coherence processing sonars

Recently, passive sonar systems using two or more stationary receivers have been used for the detection and localization of moving acoustic targets. In far-field configurations, where the receivers are remotely located from the source, the use of the magnitude-squared coherence function (MSCF) has proved attractive. In this paper near-field configurations are considered, where the interreceiver spacing is not appreciably greater than the distance from the source. The concept of an extended MSCF (EMSCF) is introduced to take into account the relative Doppler shift and time delay between the signals at two receivers. Asymptotic expressions are derived for the EMSCF as the number of data segments becomes large. The effect on the EMSCF of noise in the received signals is analyzed by obtaining approximate expressions for the mean and variance of the density function of the EMSCF. An example is presented to illustrate the use of these expressions in the evaluation of the performance of passive sonar detectors.