Formulation of the maximum signal-to-noise ratio array processor in beam space

Abstract

The maximum signal-to-noise ratio (SNR) processor as formulated by Edelblute et al. [J. Acoust. Soc. Am. 41, 199–206 (1967)] has proved extremely useful in the analysis and interpretation of sonar data. In a known noise field this processor uses an optimum set of weights (or shading coefficients) derived from the crosspower spectral matrix of receiver noise outputs. In this paper an alternative maximum SNR processor is derived. This processor transforms the outputs of a conventional frequency domain beamformer in such a way that the SNR in the transformed beam is maximized. Expressions for the transformation (i.e., the complex beam weights) and the resulting array gain are derived. Some general properties of the beam space formulation are discussed and conditions for its equivalence to the element space formulation of Edelblute et al. are determined. Examples using both simulated and sonar data are given to compare the beam and element space formulations.