MIMO Radar Beampattern Design via Algorithm Unrolling

Optimizing a transmit multiple-input–multiple-output (MIMO) radar waveform subject to the nonconvex constant modulus constraint (CMC) remains a problem of enduring interest. The past decade has seen a variety of tailored iterative approaches with various performance–complexity tradeoffs. Despite promising work, iterative algorithms have a speed handicap and require meticulous parameter tuning. Deep learning has recently been proposed for MIMO radar waveform design, where iterative optimization is replaced by a neural network that regresses from the problem specification to the desired waveform. Once trained, a deep network can quickly regress the desired waveform coefficients, but it is a black box and may excel only when generous training is available. We present a fast, learned, and explainable deep (FLED) learning approach by unrolling a state-of-the-art iterative algorithm. We particularly leverage the recently proposed projection–descent–retraction (PDR) algorithm and design a neural network where each PDR iteration is mapped to a step of the network while preserving the CMC. Alongside an interpretable network architecture, we propose learning of key algorithm parameters such as the direction of descent, while introducing learning of FLED initialization and solution refinement through trainable prune–expand blocks. By enforcing appropriate regularizers in the learning of these parameters, FLED breaks the tradeoff between computational speed and performance. Compared to the state-of-the-art alternatives, it is near real time with boosted performance—fidelity to the desired beampattern. Crucially, the benefits of FLED over competing deep learning techniques are enhanced in the regime of limited training, i.e., FLED exhibits superior generalizability.