PSL-based beampattern design for MIMO radar systems

We deal with the robust design of the Multiple-Input Multiple-Output (MIMO) waveform covariance matrix optimizing the worst case (over steering mismatches) transmit beampattern Peak Sidelobe Level (PSL). To this end, we model the uncertainty set associated with each steering vector through two double-sided, potentially non-convex, quadratic constraints. Additionally, we force two suitable constraints on the optimization variable. The former accounts for the width of the mainbeam, whereas the latter is either a uniform or a relaxed elemental power requirement allowing to control the amount of transmitted power. We prove that the mentioned design leads to a non-convex optimization problem which remarkably shares some hidden convexity. Hence, we devise a polynomial time procedure aimed at synthesizing an optimal MIMO waveform covariance. Finally, at the analysis stage, we assess the performance of the proposed design technique showing that it ensures an improved worst case performance than some counterparts available in open literature.