Unimodular Sequences Design with Good Correlation Properties via Consensus-PDMM Algorithm

Unimodular sequences with good correlation properties are desired in wireless communication and radar applications. In this paper, we focus on designing these kinds of sequences and the main content is as follows: first, we formulate the design problem as a quartic polynomial minimization problem with constant modulus constraints. Then, by introducing auxiliary variables, the polynomial minimization problem is equivalent to a nonconvex consensus problem. Second, we develop a low-complexity consensus parallel direction method of multipliers (consensus-PDMM) algorithm, in which all subproblems can be performed in parallel with analytical solutions. Moreover, we prove that consensus-PDMM's output is some stationary point of the original nonconvex problem if it is convergent. Third, two variant PDMM algorithms, based on stochastic block coordinate descent and accelerated gradient descent, are proposed to reduce the computational complexity and speed up the convergence rate. Numerical simulation results show that the proposed algorithm offers better performance than the state-of-the-art approaches.