SIAM Journal on Optimization, Volume 31, Issue 2, Page 1519-1545, January 2021.
Multiple-input multiple-output (MIMO) detection is a fundamental problem in wireless communications and it is strongly NP-hard in general. Massive MIMO has been recognized as a key technology in fifth generation (5G) and beyond communication networks, which on one hand can significantly improve the communication performance and on the other hand poses new challenges of solving the corresponding optimization problems due to the large problem size. While various efficient algorithms such as semidefinite relaxation (SDR) based approaches have been proposed for solving the small-scale MIMO detection problem, they are not suitable to solve the large-scale MIMO detection problem due to their high computational complexities. In this paper, we propose an efficient quadratic programming (QP) relaxation based algorithm for solving the large-scale MIMO detection problem. In particular, we first reformulate the MIMO detection problem as a sparse QP problem. By dropping the sparse constraint, the resulting relaxation problem shares the same global minimizer with the sparse QP problem. In sharp contrast to the SDRs for the MIMO detection problem, our relaxation does not contain any (positive semidefinite) matrix variable and the numbers of variables and constraints in our relaxation are significantly less than those in the SDRs, which makes it particularly suitable for the large-scale problem. Then we propose a projected Newton based quadratic penalty method to solve the relaxation problem, which is guaranteed to converge to the vector of transmitted signals under reasonable conditions. By extensive numerical experiments, when applied to solve small-scale problems, the proposed algorithm is demonstrated to be competitive with the state-of-the-art approaches in terms of detection accuracy and solution efficiency; when applied to solve large-scale problems, the proposed algorithm achieves better detection performance than a recently proposed generalized power method.

中文翻译：

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一种用于大规模 MIMO 检测的高效二次规划松弛算法

SIAM Journal on Optimization，第 31 卷，第 2 期，第 1519-1545 页，2021 年 1 月。
多输入多输出 (MIMO) 检测是无线通信中的一个基本问题，通常是 NP-hard 问题。Massive MIMO已被公认为第五代（5G）及以后通信网络的关键技术，一方面可以显着提升通信性能，另一方面由于问题规模较大，对解决相应优化问题提出了新的挑战. 虽然已经提出了各种有效的算法，例如基于半定松弛（SDR）的方法来解决小规模 MIMO 检测问题，但由于它们的高计算复杂性，它们不适合解决大规模 MIMO 检测问题。在本文中，我们提出了一种基于有效二次规划 (QP) 松弛的算法来解决大规模 MIMO 检测问题。特别是，我们首先将 MIMO 检测问题重新表述为稀疏 QP 问题。通过删除稀疏约束，由此产生的松弛问题与稀疏 QP 问题共享相同的全局最小化器。与用于 MIMO 检测问题的 SDR 形成鲜明对比的是，我们的松弛不包含任何（半正定）矩阵变量，并且我们松弛中的变量和约束的数量明显少于 SDR 中的数量，这使得它特别适合于大规模的问题。然后我们提出了一种基于投影牛顿的二次惩罚方法来解决松弛问题，保证在合理条件下收敛到传输信号的向量。通过大量的数值实验，当应用于解决小规模问题时，所提出的算法在检测精度和求解效率方面与最先进的方法相比具有竞争力；当应用于解决大规模问题时，所提出的算法比最近提出的广义幂方法实现了更好的检测性能。