MIMO radar robust waveform-filter design for extended targets based on Lagrangian duality

Abstract

We address the robust waveform-filter design problem for extended targets with a colocated Multiple-Input Multiple-Output (MIMO) radar . The goal is to maximize the worst-case Signal-to-Interference-pulse-Noise Ratio (SINR) at the receiver against the uncertain Target Impulse Response (TIR) with the Peak-to-Average Ratio (PAR) constraint imposed on the waveform, which results in a non-convex minimax optimization problem. Two kinds of uncertainty sets for the TIR, namely, the spherical set and the annular set, are considered. Combing the duality theory in optimization and the Semi-Definite Relaxation (SDR) technique, we devise the Lagrangian Duality Semi-Definite Relaxation (LDSDR) and the Lagrangian Duality Double SemiDefinite Relaxation (LDDSDR) algorithms to tackle the associated waveform-filter design problems against the spherical and the annular sets, respectively. The convergences of the proposed algorithms are proved theoretically. Numerical results verify the effectiveness of the proposed algorithms. Compared with the current algorithms for the spherical set, the proposed LDSDR algorithm achieves the highest worst-case SINR with a reduced computational complexity