Multi-sensor beamsteering based on the asymptotic likelihood for colored signals

In this work, we derive a maximum likelihood formula for beamsteering in a multi-sensor array. The novelty of the work is that the impinging signal and noises are wide sense stationary (WSS) time series with unknown power spectral densities, unlike in previous work that typically considers white signals. Our approach naturally provides a way of fusing frequency-dependent information to obtain a broadband beamformer. In order to obtain the compressed likelihood, it is necessary to find the maximum likelihood estimates of the unknown parameters. However, this problem turns out to be an ML estimation of a block-Toeplitz matrix, which does not have a closed-form solution. To overcome this problem, we derive the asymptotic likelihood, which is given in the frequency domain. Finally, some simulation results are presented to illustrate the performance of the proposed technique. In these simulations, it is shown that our approach presents the best results.