Joint Design of Doppler Resilient Unimodular Discrete Phase Sequence Waveform and Receiving Filter for Multichannel Radar

Design of discrete phase sequence waveform (DPSW) with desirable co- and cross-ambiguity function (AF) properties has been a longstanding and critical challenge in the field of high-performance multichannel electronic systems, e.g. radar systems. This paper focuses on the joint design of Doppler-resilient DPSW and receiving filter with low weighted integrated sidelobe level (WISL) for multichannel radar system. This design aims to construct DPSWs of "thumbtack" shape and all-zero AFs within the desired Range-Doppler region for both co-channels and cross-channels, respectively. A peak constraint function, i.e. the penalty function, is incorporated into the objective function to control the signal-to-noise ratio loss (SNRL) due to mismatched filtering. In the design, unimodular and discrete phase constraints are imposed on each element of the sequences, while the receiving filters are subject to the energy constraint and the mismatch constraint of SNRL. Different constraints on transmitted sequences and receiving filters make the optimization problem difficult to solve. Here, an alternatively iterative algorithm based on the majorization-minimization (MM) and the coordinate descent (CD) frameworks is proposed to handle the differently constrained optimization problem. Moreover, by incorporating a general acceleration scheme and the fast Fourier transform (FFT), the computational efficiency of the proposed algorithm can be further improved. Simulation and practical experiments are conducted to validate the designed DPSWs showing superior performance when compared to that by the latest and representative methods.