Joint design of phase coded waveform and mismatched filter

Pulse compression radar usually has undesirables range sidelobe, which makes it difficult to detect weak targets nearby strong targets. Low range sidelobe level at the radar receiving end can suppress the interference from strong target returns, and hence is an attractive feature for radar systems. In this paper, we study a waveform design method that jointly optimize a phase coded waveform and a mismatch filter. The principal idea is to minimize the peak sidelobe level (PSL) of the range sidelobes after mismatched filtering with a constraint of signal-to-noise ratio (SNR) loss with respect to that after matched filtering. The optimization problem is solved by a so-called least-pth minimax algorithm including the Limited-memory BFGS (L-BFGS) algorithm as its subalgorithm. Numerical results show that, compared with the methods designing the phase coded waveform and mismatched filter separately, the joint waveform design method can yield a much lower sidelobe level output with a given SNR loss.