MIMO Radar Robust Waveform-Filter Design for Extended Targets Based on Lagrangian Duality

In this article, we address the robust waveform-filter design problem for extended targets with a colocated multiple-input–multiple-output 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 constraint imposed on the waveform, which results in a nonconvex 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 semidefinite relaxation (SDR) technique, we devise the Lagrangian duality semidefinite relaxation (LDSDR) and the Lagrangian duality double SDRalgorithms 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.