Optimal Quadratic Array Processing Using Time-Frequency and Time-Scale Representations

The use of sensor arrays in signal processing applications has received considerable attention, especially in radar/sonar processing. Sensor arrays are able to enhance desired signal reception while simultaneously suppressing undesired components through the use of directionality. The performance of traditional matched-eld beamformers is severely limited for many random signal models of interest and when loss of coherence between sensors is an issue. Quadratic array processing is optimal for many stochastic signals of interest, but direct implementation poses a signiicant computational burden, making it impractical in many situations. In this paper we demonstrate that quadratic time-frequency representations and timescale representations (TFRs and TSRs) provide a structured framework for detecting certain nonstationary signals in the presence of nonstationary noise using a partially coherent sensor array. This identiication of structure allows for eecient implementation, making quadratic array processing a viable alternative to suboptimal matched-lter techniques. In developing the TFR/TSR-based optimal quadratic array processor, we avoid narrowband signal assumptions, allow for the noise process to be partially correlated between sensors, and consider several types of array environments including those with full, partial, and no coherence.