Sum-of-Reciprocal Exact Descent: Waveform Design for Multi-Target Detection

We consider the problem of multiple target detection in the presence of signal-dependent clutter for a Multiple-Input Multiple-Output (MIMO) radar. Specifically, we design transmit waveforms for each antenna to maximize the worst-case Signal-to-Interference-Noise-Ratio (SINR) over multiple targets. To ensure hardware compatibility, the essential constant modulus constraint (CMC) is proposed. A hard max-min and fractional non-convex optimization problem emerges as a function of the transmit waveform. To address the difficulty of max-min optimization, we exploit SINR properties to develop a new sum-of-reciprocals cost function surrogate. Subsequently, we compute the exact gradient of each fractional term in the sum paving the way for a sum-of-reciprocals, exact descent (SRED) numerical op-timization technique that preserves the CMC. Numerical results over a well-known benchmark simulation scenario establish the ability of SRED to outperform state-of-the-art alternatives both in worst-case SINR and desirable beampattern profiles.