Efficient joint transmit waveform and receive filter design based on a general L_p-norm metric for sidelobe level of pulse compression

Low sidelobe level is required for pulse compression (PC) radar systems since it can reduce false alarm triggered by the high sidelobe and improve the ability to detect weak targets nearby strong scattering points. In most of the existing literature, sidelobe suppression is achieved by either transmit waveform design at the transmitter or mismatched filter optimization at the receiver. Joint design of waveform and filter is an approach with limited discussion. Thus, this paper aims to jointly design transmit waveform and mismatched filter to achieve low sidelobe level. We first formulate an L_p-norm metric for PC model which suits for either the integrated sidelobe level or peak sidelobe level (PSL) minimization (only with different initializations of p). Then we present a new iterative method to deal with the problem by using Dinkelbach's scheme and majorization minimization method. The proposed method is shown to be convergent and the computational complexity is also analyzed. Numerical examples demonstrate that waveforms and filters designed by using the proposed method produce lower PSL than the existing techniques.