Min-Max Optimization for MIMO Radar Waveform Design With Improved Power Efficiency

Transmit waveform design with power efficiency constraint is a prominent problem for colocated multiple-input-multiple-output (MIMO) radar. Though there are extensive relevant works in the literature, the existing peak-to-average-power ratio (PAR) constraint is insufficient in controlling the transmit power uniformity and the conventional constant modulus (CM) is imposed on both waveform temporal and spatial dimensions, resulting in an unnecessary loss of degrees of freedom. Thereby, we introduce an individual antenna power control (IAPC) scheme with a new peak-to-valley-power-ratio (PVR) constraint to flexibly control the transmit power uniformity along the spatial dimension. We then devise two min-max waveform designs for shaped transmit beampattern synthesis. To tackle the resultant non-convex problems, we propose a surrogate primal alternating direction method of multipliers (SP-ADMM) to approximately solve a surrogate primal subproblem for PVR projection since the standard ADMM is unable to tackle the intricate primal problems directly. We theoretically prove the convergence behavior of the SP-ADMM. Finally, experiments verify the effectiveness and improved performance of the developed methods against their counterparts, especially in the metric of sidelobe level.