Estimating parameters of multiple wideband polynomial-phase sources in sensor arrays

In this paper, we consider the problem of estimating the parameters of multiple wideband polynomial-phase signal (PPS) sources in sensor arrays. A new maximum likelihood (NIL) direction-of-arrival (DOA) estimator is introduced, and the exact Cramer-Rao bound (CRB) is derived for the general case of multiple constant-amplitude polynomial-phase sources. Since the proposed exact NM estimator is computationally intensive, an approximate solution is proposed, originating from the analysis of the log-likelihood (LL) function in the single chirp signal case. As a result, a new form of spatio-temporal matched filter (referred to as the chirp beamformer) is derived, which is applicable to "well-separated" sources that have distinct time-frequency or/and spatial signatures. This beamforming approach requires solving a three-dimensional (3-D) optimization problem and, therefore, enjoys essentially simpler implementation than that entailed by the exact NIL. Simulation results are presented, illustrating the performance of the estimators and validating our theoretical CRB analysis.