In this paper, we propose a deep learning (DL)-based approach for efficiently computing the inverse of Hermitian matrices using truncated polynomial expansion (TPE). Our model-driven approach involves optimizing the coefficients of the TPE during an offline training procedure for a given number of TPE terms. We apply this method to signal detection in uplink massive multiple-input multiple-output (MIMO) systems, where the matrix inverse operation required by linear detectors, such as zero-forcing (ZF) and minimum mean square error (MMSE), is approximated using TPE. Our simulation results demonstrate that the proposed learned TPE-based method outperforms the conventional TPE method with optimal coefficients in terms of asymptotic convergence speed and reduces the computational complexity of the online detection stage, albeit at the expense of the offline training stage. However, the limited number of trainable parameters leads to a swift offline training process.

我们提出了一种基于深度学习的方法，用于高效计算埃尔米特矩阵的逆矩阵，采用截断多项式展开。模型驱动方法通过离线训练过程来优化给定数量的多项式展开项的系数。我们将该方法应用于上行大规模多输入多输出（MIMO）系统中的信号检测，其中线性检测器（如零强制和最小均方误差）所需的矩阵逆运算使用截断多项式展开进行近似。我们的仿真结果表明，所提出的学习多项式展开方法在渐近收敛速度方面优于传统的多项式展开方法，并减少了在线检测阶段的计算复杂度，尽管离线训练阶段的时间稍长。然而，由于可训练参数的数量有限，离线训练过程很快。

基于截断多项式扩展的大规模MIMO检测：一种基于模型的深度学习方法