Robust Joint Design of Waveform and Mismatched Filter for ISRJ Suppression via Stochastic Majorization Minimization

In this paper, we propose a joint design of a unimodular waveform and a mismatched filter to suppress interrupted sampling repeater jamming (ISRJ).The goal of our design is to achieve high target detection accuracy, effective ISRJ suppression, and robustness against variations in ISRJ forwarding times, while effectively controlling signal-to-noise ratio loss caused by mismatched filter. To satisfy all the aforementioned requirements, we employ a weighted sum of three metrics related to integrated sidelobe level, jamming integrated level, and signal-to-interference-plus-noise ratio as the objective. Based on this, we formulate the joint design as a non-convex optimization problem with constraints on waveform modulus, filtering energy and mainlobe peak level. To address this problem, we reformulate the optimization as minimizing the expected value of the objective over ISRJ forwarding times and apply the stochastic majorization-minimization technique. This approach involves sampling ISRJ forwarding times from the specified interval and systematically transforming the reformulated problem into a sequence of distinct sub-problems based on these samples. Our contributions also lie in elaborating the majorant for each sub-problem and deriving a closed-form solution. Simulation results verify the effectiveness of the proposed design.