Approximate Maximum-likelihood DOA Estimation for a Single Narrow-band Amplitude-distorted Wavefront

This chapter extends the author's previous work on signal-to-noise ratio (SNR) estimation, in developing a novel stochastic maximum-likelihood-based (SML-based) approach for estimating the direction-of-arrival (DOA) of a single narrow-band amplitude-distorted wavefront received by an arbitrary antenna array. The distorted amplitude wavefront is assumed to vary according to the complex-valued circular AR (1) model with unknown coefficients. The chapter’s contribution consists of developing an approximate SML-based approach to estimate the DOA in a high SNR scenario. It shows how to eliminate the noise and AR (1) nuisance (distortion) parameters from the considered approximate stochastic likelihood function, thus obtaining an SML DOA estimate through a simple one-dimensional (1-D) search. Compact Cramer-Rao lower bound (CRB) expressions for the DOA parameter alone are derived for different kinds of time-varying fading amplitudes. High and low SNR approximation expressions for the are also derived, which enables the derivation of several CRB properties. Finally, simulation results show the performance of the proposed approach and validate the theoretical analysis.