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In this paper, we design constant modulus probing waveforms with goodcorrelation properties for collocated multi-input multi-output (MIMO) radarsystems. The main content is as follows: first, we formulate the design problemas a fourth order polynomial minimization problem with constant modulusconstraints. Then, by exploiting introduced auxiliary variables and theirinherent structures, the polynomial optimization model is equivalent to anon-convex consensus minimization problem. Second, a customized alternatingdirection method of multipliers (ADMM) algorithm is proposed to solve thenon-convex problem approximately. In the algorithm, all the subproblems can besolved analytically. Moreover, all subproblems except one subproblem can beperformed in parallel. Third, we prove that the customized ADMM algorithm istheoretically-guaranteed convergent if proper parameters are chosen. Fourth,two variant ADMM algorithms, based on stochastic block coordinate descent andaccelerated gradient descent, are proposed to reduce computational complexityand speed up the convergence rate. Numerical examples show the effectiveness ofthe proposed consensus-ADMM algorithm and its variants.

On the Design of Constant Modulus Probing Waveforms with Good Correlation Properties for MIMO Radar via Consensus-ADMM Approach