  Unimodular sequences with good auto/cross-correlation properties are
favorable in wireless communication and radar applications. In this paper, we
focus on designing these kinds of sequences. The main content is as follows:
first, we formulate the designing problem as a quartic polynomial minimization
problem with constant modulus constraints; second, by introducing auxiliary
phase variables, the polynomial minimization problem is equivalent to a
consensus nonconvex optimization problem; third, to achieve its good
approximate solution efficiently, we propose two efficient algorithms based on
alternating direction method of multipliers (ADMM) and parallel direction
method of multipliers (PDMM); fourth, we prove that the consensus-ADMM
algorithm can converge to some stationary point of the original nonconvex
problem and consensus-PDMM's output is some stationary point of the original
nonconvex problem if it is convergent. Moreover, we also analyze the nonconvex
optimization model's local optimality and computational complexity of the
proposed consensus-ADMM/PDMM approaches. Simulation results demonstrate that
the proposed ADMM/PDMM approaches outperform state-of-the-art ones in either
computational cost or correlation properties of the designed unimodular
sequences.
