Waveform Design for Cognitive Radar Under Low PAR Constraints by Convex Optimization

Abstract

To improve the detection performance of the radar transmit waveform while enabling the transmitter to perform at its maximal efficiency, a joint design method is proposed for the transmit and receive filter in the presence of signal-dependent clutter with a Peak-to-Average-power Ratio (PAR) constraint of the transmit waveform. First, an optimized model of the radar’s output Signal-to-Interference-plus-Noise Ratio (SINR) for range-extended target detection is established. Second, the analytic expression of the receiver is obtained by converting the optimization problem into the Rayleigh quotient model. The optimal matrix solution is then obtained by transforming the non-convex problem into a convex problem via the semi-definite matrix of the waveform. Finally, the optimal vector solution of the waveform is extracted from the optimal matrix solution by combining the rank-one approximation method combined with the nearest neighbor method. An optimal waveform with a maximal output SINR for a given PAR range is obtained using the proposed method. The SINR value of the waveform when PAR = 2 is the same as the SINR value of the optimized waveform under the energy constraint and is about 0.5 dB higher than the waveform when PAR = 1. Simulation results demonstrate the effectiveness of the proposed method.