基于凸优化方法的认知雷达低峰均比波形设计

为了提高雷达发射波形的检测性能，同时使发射机发挥其最大效能，以发射波形的低峰均比(PAR)为约束条件，该文提出了一种信号相关杂波背景下的认知雷达发射波形和接收机滤波器联合优化方法。首先，面向距离扩展目标检测问题，构建关于雷达输出信干噪比(SINR)的优化模型；然后将该模型转化为Rayleigh商形式，给出了接收机权值的解析表达式；在此基础上，通过半正定松弛，将关于发射波形半正定矩阵的非凸问题转化为凸问题，求得发射波形的最优矩阵解；最后，将秩1近似法和最近邻方法相结合，从最优矩阵解中提取出发射波形的最优向量解。该方法在给定PAR取值范围内可使波形的输出SINR达到最大，PAR=2时波形的SINR值与能量约束下优化波形的SINR值相同，并且比PAR=1时所得波形高出约0.5 dB。仿真结果验证了所提方法的有效性。 

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

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.