  In this paper, we design constant modulus probing waveforms with good
correlation properties for collocated multi-input multi-output (MIMO) radar
systems. The main content is as follows: first, we formulate the design problem
as a fourth order polynomial minimization problem with constant modulus
constraints. Then, by exploiting introduced auxiliary variables and their
inherent structures, the polynomial optimization model is equivalent to a
non-convex consensus minimization problem. Second, a customized alternating
direction method of multipliers (ADMM) algorithm is proposed to solve the
non-convex problem approximately. In the algorithm, all the subproblems can be
solved analytically. Moreover, all subproblems except one subproblem can be
performed in parallel. Third, we prove that the customized ADMM algorithm is
theoretically-guaranteed convergent if proper parameters are chosen. Fourth,
two variant ADMM algorithms, based on stochastic block coordinate descent and
accelerated gradient descent, are proposed to reduce computational complexity
and speed up the convergence rate. Numerical examples show the effectiveness of
the proposed consensus-ADMM algorithm and its variants.
