Quasi-maximum-Likelihood Estimator of PPS on the Uniform Linear Array

In this paper, an idea from the quasi-maximum-likelihood (QML) algorithm has been applied to estimation of the direction of arrival (DOA) and parameters of the polynomial phase signals (PPS) impinging on the uniform linear array. The algorithm uses a search over a set of possible DOA values. For considered value, the DOA is compensated and resulted signal parameters are estimated using the original QML approach. In this way, several sets of potential estimates are obtained. Optimal DOA and PPS parameters belong to set that maximizes the proposed cost function. In the proposed approach, parameters are estimated using 2-D search over DOA and window widths used for calculation of the short Fourier transform in the QML that is an important advantage with respect to existing strategies like, for example, the polynomial beamformer requiring multi-dimensional or metaheuristic search strategies. Numerical validation of the proposed approach for both mono- and multi-component signals is provided in the paper. Both far- and near-field scenarios are considered.