In this work, we study complex-valued data detection performance in massive multiple-input multiple-output (MIMO) systems. We focus on the problem of recovering an $n$-dimensional signal whose entries are drawn from an arbitrary constellation $\mathcal{K} \subset \mathbb{C}$ from $m$ noisy linear measurements, with an independent and identically distributed (i.i.d.) complex Gaussian channel. Since the optimal maximum likelihood (ML) detector is computationally prohibitive for large dimensions, many convex relaxation heuristic methods have been proposed to solve the detection problem. In this paper, we consider a regularized version of this convex relaxation that we call the regularized convex relaxation (RCR) detector and sharply derive asymptotic expressions for its mean square error and symbol error probability. Monte-Carlo simulations are provided to validate the derived analytical results.

翻译：在这项工作中,我们研究了大规模多投入多重产出(MIMO)系统中的复杂价值数据探测性能。我们集中研究从一个任意的星座 $\ mathcal{K}\ subset\ mathbb{C} 美元抽取的一元元信号的回收问题,该信号的输入来自一个任意的星座 $\ mathcal{K}\ subset\ mathbb{C} 美元, 以独立和相同的分布( i. d. ) 复杂的高西亚频道。 由于计算上的最大可能性( ML) 探测器对于大尺寸来说是令人窒息的, 已经提出了许多convex 放松超热度方法来解决探测问题。 在本文中,我们考虑的是这种二次曲线放松的常规版本, 我们称之为正统的 convex 放松( RCR) 探测器, 并快速得出其平均方形误差和符号误差概率的微表达方式。 提供蒙特- Carlo 模拟来验证分析结果。