Model-Based Learning for MIMO Radar Waveform Design in the Presence of Multiple Targets

This study addresses detecting multiple targets in the presence of signal-dependent clutter using a multiple-input–multiple-output radar system. Our primary objective is to design transmit waveforms that maximize the worst-case signal-to-interference-noise-ratio (SINR) across multiple targets. Practical constraints enforced in our work are the waveform similarity constraint and the constant modulus constraint. We confront a complex max–min and fractional nonconvex optimization problem. For tractability, we introduce a surrogate cost function based on the sum-of-reciprocals of SINRs. We show that despite the fractional form, an exact gradient can be computed for this cost function, leading to a sum-of-reciprocals exact descent (SRED) numerical optimization approach. We then propose a model-based deep learning technique that evolves the iterative SRED algorithm into a sum-of-reciprocals exact learning (SREL) approach. SREL enhances waveform optimization by learning key parameters, including descent direction and step sizes, via distinct training frameworks for intratarget and intertarget parameters. We first develop intratarget training focusing on a single SINR maximization. Intertarget parameters are then trained to balance between the multiple gradients, each corresponding to a SINR reciprocal, in order to maximize the worst-case SINR. Numerical experiments conducted for benchmark scenarios demonstrate that both SRED and SREL surpass the state-of-the-art counterparts in achieving superior worst-case SINR and generating favorable range-azimuth beampattern profiles. Notably, SREL, by virtue of parameter learning, also brings computational benefits in that the SREL requires a smaller number of steps than SRED iterations.