Efficient use of signal-free samples for DOA estimation and detection in colored noise

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, such as directions of arrivals (DOAs), 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. This is shown in an earlier work, together with the introduction of an optimal weighting for weighted subspace fitting (WSF), when based on whitened data. An asymptotically valid approximative maximum likelihood method (AML) for the DOA estimation problem is derived in this paper. The resulting criterion can be concentrated with respect to the signal parameters. In numerical experiments, AML shows very promising small-sample performance compared to earlier methods. The associated criterion function is well suited for numerical optimization and 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. This non-iterative resulting procedure retains the asymptotic properties of maximum likelihood, and numerical simulations indicate superior threshold performance when compared to an optimally weighted 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 correctly weighting 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 promising performance for the AML-detection scheme