Regularized Weighted Descent: Model-Based Learner for Multi-Target Radar Waveform Design

This study focuses on multiple target detection in the presence of signal-dependent clutter using a Multiple-Input Multiple-Output (MIMO) radar system. The problem is formulated as worst-case SINR maximization (max-min optimization), which is a function of the MIMO waveform, under the hardware-inspired constant modulus constraint (CMC). While existing approaches invariably rely on computationally expensive iterative optimization over the waveform variable, we develop a model-based deep learning algorithm that shifts the computational burden to the neural network training, yielding fast inference. We utilize a surrogate cost function – the sum of SINR-Reciprocals (SRs) – that enables converting the max-min problem into the minimization of the sum of SRs. Our model-based learner unrolls an iterative optimization method that utilizes the SR descent vectors but with novel inter-target and inter-step parameters. The inter-target parameter weighs the SR descent vectors so that the net descent direction is dominated by the vector associated with the largest SR, thereby focusing on the worst-case SINR. The inter-step parameter ensures the update between the steps encourages a monotonic decrease in the cost function. To effectively guide the parameter learning, we introduce regularizers aligned with the learning goals, and consequently, we term the proposed method Regularized Weighted Descent (RWD). We demonstrate that the RWD achieves a larger worst-case SINR value (superior solution quality) in a shorter time (lower computational complexity) compared to the state-of-the-art alternatives.