Source enumeration in large arrays using corrected Rao's score test and relatively few samples

Abstract

We focus on the problem of source enumeration in large arrays with relatively few samples, which is solved in this paper by using a statistic of corrected Rao's score test (CRST) via the generalized Bayesian information criterion (GBIC). Under the white noise assumption, the covariance matrix of the noise subspace components of the observations is proportional to an identity matrix, and this structure can be tested by the CRST statistic for the sphericity hypothesis test. The observations are decomposed into signal and noise subspace components by unitary coordinate transformation under a presumptive number of sources. Only when there is no signal in the presumptive noise subspace components, the corresponding CRST statistic is asymptotic normal distribution. The CRST statistic of the presumptive noise subspace components also is a statistic of the sample eigenvalues, and can be used as the statistic in the GBIC for estimating the number of sources. Simulation results demonstrate that the proposed method can achieve more accurate detection of the number of sources in the case of a large number of sensors with relatively few samples, especially when the number of samples is smaller than the number of sensors.