This paper considers the problem of symbol detection in massive multiple-input multiple-output (MIMO) wireless communication systems. We consider hard-thresholding preceeded by two variants of the regularized least squares (RLS) decoder; namely the unconstrained RLS and the RLS with box constraint. For all schemes, we focus on the evaluation of the mean squared error (MSE) and the symbol error probability (SEP) for M-ary pulse amplitude modulation (M-PAM) symbols transmitted over a massive MIMO system when the channel is estimated using linear minimum mean squared error (LMMSE) estimator. Under such circumstances, the channel estimation error is Gaussian which allows for the use of the convex Gaussian min-max theorem (CGMT) to derive asymptotic approximations for the MSE and SER when the system dimensions and the coherence duration grow large with the same pace. The obtained expressions are then leveraged to derive the optimal power distribution between pilot and data under a total transmit energy constraint. In addition, we derive an asymptotic approximation of the goodput for all schemes which is then used to jointly optimize the number of training symbols and their associated power. Numerical results are presented to support the accuracy of the theoretical results.

翻译：本文研究了大规模多输入多输出（MIMO）无线通信系统中的符号检测问题。我们考虑两种正则化最小二乘（RLS）解码器变体前的硬阈值处理，即无约束RLS和带箱式约束的RLS。针对所有方案，我们重点评估了在线性最小均方误差（LMMSE）估计器进行信道估计的大规模MIMO系统中，M进制脉冲幅度调制（M-PAM）符号传输时的均方误差（MSE）和符号错误概率（SEP）。在此条件下，信道估计误差服从高斯分布，这使得我们可以利用凸高斯最小最大定理（CGMT）来推导当系统维度与相干时间以相同速度增长时的MSE与SER的渐近近似表达式。随后利用这些表达式，在总发射能量约束下推导出导频与数据之间的最优功率分配。此外，我们为所有方案推导了有效吞吐量的渐近近似，并将其用于联合优化训练符号数量及其对应功率。数值结果验证了理论分析的准确性。