A nonlinear-ADMM method for designing MIMO radar constant modulus waveform with low correlation sidelobes

Abstract

Abstract This paper investigates the design of constant modulus waveforms with low auto- and cross-correlation sidelobes for multiple-input multiple-output (MIMO) radar. The resulting weighted integrated sidelobe level (WISL) minimization problem involves a fourth-order objective function and nonconvex constant modulus constraint and, hence, is NP-hard. Unlike existing methods which indirectly solve an “almost equivalent” problem to the original one, we equivalently reformulate the nonconvex WISL minimization problem appropriately and propose a new method to directly deal with the problem. Specifically, in the proposed algorithm, the fourth-order problem is first converted into a bi-quadratic problem via introducing an auxiliary primal variable, and then a primal-dual framework, named as “nonlinear alternating direction method of multipliers (nonlinear-ADMM)”, is derived to handle the modified problem. More importantly, both the convergence and termination conditions of this algorithm are discussed. Numerical simulation are carried out to assess the performance of the proposed algorithm in terms of the WISL metric, auto- and cross- correlation properties and computational complexity.