Array processing based on time-frequency analysis and higher-order statistics

Abstract

Five algorithms are proposed to solve three classes of array-processing problems. The first class of problem involves the parameter estimation of polynomial phase signals (PPS) impinged on sensor array. The first algorithm, which requires only a one-dimensional search, is proposed to estimate the direction of arrival (DOA), frequency and frequency rate of a second-order PPS. This algorithm performs more accurately at lower computational cost than most of the existing algorithms, which require a multidimensional search. The second algorithm is for parameter estimation of single PPS of any order impinged on sensor array. We introduced the spatial higher-order instantaneous moment operator, which essentially transforms the wideband array problem with one PPS into the classical narrowband array problem with one sinusoidal signal. The second class of problem is to recover the source signals even if the channel is underdetermined (wide matrix). The third proposed algorithm is applicable to time-frequency signals with disjoint/non-disjoint signatures. Our algorithm performs better than existing algorithm in speed and accuracy, because batch processing is used and the cross-terms of the multi-component signal are exploited. The third class of problem deals with DOA estimation under Gaussian noise, which is not necessary white. The fourth and fifth proposed algorithms use respectively the fourth- and mixed-order statistics for DOA estimation, and the algorithms are shown to be robust to any unknown Gaussian noise.