Successive QCQP Refinement for MIMO Radar Waveform Design Under Practical Constraints

The authors address the problem of designing a waveform for multiple-input multiple-output (MIMO) radar under the important practical constraints of constant modulus and waveform similarity. Incorporating these constraints in an analytically tractable manner is a longstanding open challenge. This is due to the fact that the optimization problem that results from signal-to-interference-plus-noise ratio (SINR) maximization subject to these constraints is a hard non-convex problem. The authors develop a new analytical approach that involves solving a sequence of convex quadratically constrained quadratic programing (QCQP) problems, which they prove converges to a sub-optimal solution. Because an improvement in SINR results via solving each problem in the sequence, they call the method Successive QCQP Refinement (SQR). Furthermore, the proposed SQR method can be easily extended to incorporate emerging requirements of spectral coexistence, as shown briefly in this paper. The authors evaluate SQR against other candidate techniques with respect to SINR performance, beam pattern, and pulse compression properties in a variety of scenarios. Results show that SQR outperforms state-of-the-art methods that also employ constant modulus and/or similarity constraints while being computationally less burdensome.