Probabilistically Robust Joint Transmit Code and Receive Filter Design for Extended Targets: A Mixed-Integer Programming Approach

This article proposes a probabilistically robust joint transmit code (TC) and receive filter (RF) design approach for extended targets detection. The goal is to maximize the probability that the radar output signal-to-interference-pulse-noise ratio exceeds a given threshold, under the target impulse response with a complex Gaussian distribution. By restricting the transmit waveform to discrete phase codes, we construct a joint transmit–receive vector with respect to the TC and RF. Based on the joint vector, the probabilistically robust joint design problem is reformulated as a mixed-integer programming (MIP) problem. Subsequently, we linearize the nonlinear mixed-integer constraint using a linearization technique and derive an approximate analytical expression for the intractable probabilistic objective function. Finally, the MIP problem is solved using the bisection method, yielding high quality (suboptimal) solutions. Numerical experiments are presented to demonstrate the effectiveness and superiority of the proposed method in extended targets detection.