Robust Radar Waveform Optimization Under Target Interpulse Fluctuation and Practical Constraints via Sequential Lagrange Dual Approximation

Abstract

This correspondence considers the problem of robust radar waveform design against target interpulse fluctuation with constraints on the transmit energy, similarity, and signal dynamic range. We aim to make robust the transmit waveform and receive filter with respect to the Target Amplitude Vector (TAV) uncertainties by enhancing the worst-case Signal-to-Noise-Ratio (SNR) over the modeled ellipsoidal set. First of all, the filter is directly solved leveraging on the existence of saddle point condition, which leads to a suitable simplification of the original non-convex problem. Then, to handle the resultant max-min problem, the Sequential Lagrange Dual Approximation (SLDA) procedure is devised. Specifically, we update the transmit waveform via solving a sequence of max-min approximate problems, which are proven to be hidden convex relying on the theory of Lagrange duality. Finally, the filter is synthesized after solving a Quadratical Constraint Quadratic Programming (QCQP) problem based on the optimized waveform. Numerical results highlight the robustness of the proposed design which guarantees an enhanced worst-case SNR with respect to TAV uncertainties.