Simultaneous optimization of radar waveform and mismatched filter with range and delay-Doppler sidelobes suppression

Since radar transmit circuit often operates in the saturation mode to maximize transmit power, radar is more suitable for transmitting constant modulus waveforms, which makes it difficult to suppress the range sidelobes. The mismatched filter method in the receive end can suppress range sidelobes significantly, but it is often designed with a prescribed waveform. Hence, in this paper, we firstly present an approach to simultaneously optimize radar waveform and mismatched filter (SORW-MF) under a signal-to-noise ratio (SNR) loss constraint. However, most of existing mismatched filter design works including the aforementioned SORW-MF work neglect Doppler mismatch issue. To address this problem, during SORW-MF process, another approach is developed to suppress delay-Doppler sidelobes and control SNR loss. Both design approaches are non-convex optimization problems, and we solve them by a least-pth minimax algorithm and a double least-pth minimax algorithm, respectively. Numerical results indicate that the first approach can further reduce the range sidelobes compared with the separate/iterative design methods, and the second approach can efficiently suppress delay-Doppler sidelobes over different specifications of Doppler mismatch.