Probability distribution of multiple-target data snapshots applied to large-aperture array processing

Abstract

We consider sonar array target detection and azimuth estimation in experimental scenarios consisting of large-aperture horizontal line arrays of hydrophones in the water column. In such scenarios, successful distinction of quiet targets from the background noise strongly depends on having sufficient independent data snapshots available for computation of adaptive beamforming weights. In this work, the discrete Fourier transform matrix is used for projecting the array data into a sparse domain, from which the theoretical probability density function of each (sparse-domain) datum can be obtained. It is shown that the sparse data exhibits a scaled chi-squared distributed magnitude, with a scale factor that depends on signal-to-background noise ratio and array size. Using this theoretical distribution and Monte Carlo simulations, minimum experimental requirements for target detection are quantified and highlight the tradeoff between data sample size, array aperture, and signal-to-noise ratio. In addition, a s...