DOA Estimation and Detection in Colored Noise Using Additional Noise-Only Data

In a typical array processing scenario, noise acting on the array can not be assumed spatially white. It is in many cases necessary to use quiet periods, when only noise is received, to estimate the noise covariance. If estimation of the signal parameters and noise covariance is performed jointly, performance can be improved. This is especially true when stationarity considerations limit the amount of available valid noise-only data. An asymptotically valid approximative maximum likelihood method (AML) for the estimation problem is derived in this work. The resulting criterion is, when concentrated with respect to the signal parameters, relatively simple. In numerical experiments, AML shows promising small-sample performance compared to earlier methods. The criterion function is also well suited for numerical optimization. The new criterion function allows for the development of a novel, MODE-like, non-iterative estimation procedure if the array belongs to the important class of uniform linear arrays. The resulting procedure retains the asymptotic properties of maximum likelihood, and numerical simulations indicate superior threshold performance when compared to an optimally weighted subspace fitting (WSF) formulation of MODE. For the detection problem, no method has been presented that takes the unknown noise covariance into account. Here, a well known detection scheme for WSF is extended to work in this scenario as well. The derivations of this scheme further stress the importance of using the correct weighting in WSF when the noise covariance is unknown. It is also shown that the minimum value of the criterion function associated with AML can be used for the detection purpose. Numerical experiments indicate very promising performance for the AML-detection scheme.