MIMO Radar Beampattern Design Via PSL/ISL Optimization

TLDR

The design incorporates constraints on main‑beam width and transmitted power to shape the beampattern. The paper aims to robustly design MIMO waveform covariance matrices that minimize worst‑case PSL or ISL under steering mismatches. The authors model steering‑vector uncertainty with double‑sided quadratic constraints and develop polynomial‑time algorithms to synthesize optimal covariance matrices. They show that the designs, though non‑convex, possess hidden convexity enabling polynomial‑time solutions, and the resulting waveforms outperform existing methods in worst‑case beampattern performance.

Abstract

We deal with the robust design of multiple-input multiple-output (MIMO) waveform covariance matrices that optimize the worst case (over steering mismatches) transmit beampattern assuming either the peak sidelobe level (PSL) or the integrated sidelobe level (ISL) as figure of merit. To this end, we model the uncertainty set associated with each steering vector through two double-sided, potentially non-convex, quadratic constraints. In addition, 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 both the mentioned waveform covariance designs lead to non-convex optimization problems which remarkably share some hidden convexity properties. Hence, we devise polynomial time procedures aimed at synthesizing the desired optimal MIMO waveform covariance matrices. Finally, at the analysis stage, we assess the performance of the proposed techniques showing their capability to ensuring improved worst case performance than some counterparts available in open literature.