Designing Unimodular Sequences With Optimized Auto/Cross-Correlation Properties via Consensus-ADMM/PDMM Approaches

Unimodular sequences with good auto/cross-correlation properties are favorable in wireless communication and radar applications. In this paper, we focus on designing low computational complexity but theoretically-guaranteed algorithms to achieve 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); and 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.