DOA Estimation of Quasi-Stationary Signals With Less Sensors Than Sources and Unknown Spatial Noise Covariance: A Khatri–Rao Subspace Approach

Abstract

In real-world applications such as those for speech and audio, there are signals that are nonstationary but can be modeled as being stationary within local time frames. Such signals are generally called quasi-stationary or locally stationary signals. This paper considers the problem of direction-of-arrival (DOA) estimation of quasi-stationary signals. Specifically, in our problem formulation we assume: i) sensor array of uniform linear structure; ii) mutually uncorrelated wide-sense quasi-stationary source signals; and iii) wide-sense stationary noise process with unknown, possibly nonwhite, spatial covariance. Under the assumptions above and by judiciously examining the structures of local second-order statistics (SOSs), we develop a Khatri-Rao (KR) subspace approach that has two notable advantages. First, through an identifiability analysis, it is proven that this KR subspace approach can operate even when the number of sensors is about half of the number of sources. The idea behind is to make use of a ¿virtual¿ array structure provided inherently in the local SOS model, of which the degree of freedom is about twice of that of the physical array. Second, the KR formulation naturally provides a simple yet effective way of eliminating the unknown spatial noise covariance from the signal SOSs. Extensive simulation results are provided to demonstrate the effectiveness of the KR subspace approach under various situations.