Joint Waveform Design and Antenna Selection for MIMO Radar Beam Scanning

A key task of antenna array is to radiate multiple patterns for beam scanning. While antenna selection can offer additional degrees of freedom in beampattern synthesis. This paper presents a method for antenna selection and beam scanning in a colocated wideband multiple-input multiple-output radar system. Our approach integrates the peak-to-average power ratio (PAPR), energy, and binary constraints, where the last one is employed for antenna selection, in the design. The aim is to match a set of given beampattern masks by jointly determining the antenna positions and a set of probing waveforms, allowing for effective beam scanning. The resultant problem is complex due to the involvement of large-scale, nonconvex, and nonsmooth optimization caused by the PAPR and nonconvex binary constraints, as well as max and modulus operations in the objective function. To address the issues, we start by converting the min-max optimization problem into an iteratively reweighted least squares (IRLS) problem using the Lawson algorithm. Then, we replace the nonsmooth nonconvex objective function with a convex majorization function. Finally, we apply the alternating direction method of multipliers to solve the majorized IRLS problem. Our convergence analysis shows that the proposed algorithms ensure a stationary solution. Additionally, we provide numerical examples to demonstrate the effectiveness of the algorithm.