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.

中文翻译：

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通过 Consensus-ADMM/PDMM 方法设计具有优化自动/互相关属性的单模序列

具有良好自相关/互相关特性的单模序列在无线通信和雷达应用中是有利的。在本文中，我们专注于设计计算复杂度低但理论上有保证的算法来实现这些类型的序列。主要内容如下：首先，我们将设计问题表述为具有恒模约束的四次多项式最小化问题；其次，通过引入辅助相位变量，多项式最小化问题等价于一个共识非凸优化问题；第三，为了有效地实现其良好的近似解，我们提出了基于乘法器交替方向法（ADMM）和乘法器平行方向法（PDMM）的两种有效算法；第四，我们证明了consensus-ADMM算法可以收敛到原始非凸问题的某个驻点，并且consensus-PDMM的输出是原始非凸问题的某个驻点，如果它是收敛的。此外，我们还分析了所提出的共识 ADMM/PDMM 方法的非凸优化模型的局部最优性和计算复杂性。仿真结果表明，所提出的 ADMM/PDMM 方法在设计单模序列的计算成本或相关性方面均优于最先进的方法。s 所提出的共识 ADMM/PDMM 方法的局部最优性和计算复杂性。仿真结果表明，所提出的 ADMM/PDMM 方法在设计单模序列的计算成本或相关性方面均优于最先进的方法。s 所提出的共识 ADMM/PDMM 方法的局部最优性和计算复杂性。仿真结果表明，所提出的 ADMM/PDMM 方法在设计单模序列的计算成本或相关性方面均优于最先进的方法。