Detection of the number of noncoherent and coherent signals with a simple planar array

In this paper, we investigate the number detection of a mixture of noncoherent and coherent signals impinging on a simple planar array consisting of two parallel uniform linear arrays (ULAs). Firstly, the numbers of noncoherent signals and coherent groups are obtained from the ranks of two outer-product matrices. Then a new oblique projector is obtained to suppress the noncoherent signals in the received array data and the number of coherent signals is obtained from the rank of another outer-product matrix which only contains the information of coherent signals. The number of noncoherent signals and that of coherent signals are estimated separately and the effectiveness of the proposed method is substantiated through numerical examples where the simulation results show that the proposed method performs well with a small number of snapshots and/or at relatively low signal-to-noise ratio (SNR).

I. Introduction

In array signal processing, detection of the number of incident signals from the noisy array data is a fundamental problem and it has been investigated widely in [1]–[5] (and references therein). The information theoretic criteria based methods such as the Akaike information criterion (AIC) and minimum description length (MDL) [1] are benchmarks for estimating the number of incident signals, and their performance has been extensively investigated in the literature [2]. However, they are not applicable to the case of coherent (i.e., fully correlated) signals which is encountered in multipath propagation scenario. We proposed a nonparametric method for estimating the number of signals without eigendecomposition (MENSE) [3], and it can resolve the number detection of coherent signals.