Source Detection and Parameter Estimation in Array Processing in the Presence of Nonuniform Noise
S. Aouada · Technischen Universität Darmstadt · 2008
We address the problem of source detection in array signal processing when the noise over the sensors does not have a uniform power. Such spatial nonuniformity is observed in several applications including communications, radar, sonar and biomedical engineering. The problem of interest is theoretically non-identifiable, however, the only case of non-identifiability is very unrealistic in practical coupled arrays. Estimation of the number of sources is equivalent to the determination of the dimension of the signal subspace. Considering the ideal uniform scenario, we evaluate the effect of noise-power perturbation on the quality of the estimated signal subspace and identify practical limits to the separability between the noise and signal subspaces. Based on this analysis, under the Gaussian-data scenario, we propose a sequential hypothesis test for source detection, deriving an expression for the asymptotic distribution of the proposed test statistics. The latter follows from a transformation of the array and Gerschgorin's theorem. When the data are assumed non-Gaussian, or when no sufficient prior knowledge of the distribution of the data is available, we propose to employ the bootstrap to empirically estimate the distributions of interest. To support the approach, we use a set of real data from a nuclear power plant. Based on the same measure of quality of the estimated signal subspace, we also propose a set of information theoretic criteria and analyze their asymptotic performance both analytically and through simulation. Given a criterion for source detection is available, we investigate the problem of parameter estimation in nonuniform noise and apply a modified approximate maximum likelihood estimator in the stochastic Gaussian case. Simulation examples are provided to illustrate the characteristics, advantages and limitations of the different methods, and compare them to existing methods.