In this paper, we consider massive multiple-input-multiple-output (MIMO) communication systems with a uniform planar array (UPA) at the base station (BS) and investigate the downlink precoder design with imperfect channel state information (CSI). By exploiting channel estimates and statistical parameters of channel estimation error, we aim to design precoding vectors to maximize the utility function on the ergodic rates of users subject to a total transmit power constraint. By employing an upper bound of the ergodic rate, we leverage the corresponding Lagrangian formulation and identify the structural characteristics of the optimal precoder as the solution to a generalized eigenvalue problem. The Lagrange multipliers play a crucial role in determining both precoding directions and power parameters, yet are challenging to be solved directly. To figure out the Lagrange multipliers, we develop a general framework underpinned by a properly designed neural network that learns directly from CSI. To further relieve the computational burden, we obtain a low-complexity framework by decomposing the original problem into computationally efficient subproblems with instantaneous and statistical CSI handled separately. With the offline pre-trained neural network, the online computational complexity of precoder is substantially reduced compared with the existing iterative algorithm while maintaining nearly the same performance.

中文翻译：

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基于深度学习的大规模 MIMO 鲁棒预编码


在本文中，我们考虑在基站（BS）处具有均匀平面阵列（UPA）的大规模多输入多输出（MIMO）通信系统，并研究具有不完善信道状态信息（CSI）的下行链路预编码器设计。通过利用信道估计和信道估计误差的统计参数，我们的目标是设计预编码向量，以最大化受总发射功率约束的用户遍历速率的效用函数。通过采用遍历率的上限，我们利用相应的拉格朗日公式并确定最佳预编码器的结构特征作为广义特征值问题的解决方案。拉格朗日乘子在确定预编码方向和功率参数方面发挥着至关重要的作用，但直接求解具有挑战性。为了计算出拉格朗日乘数，我们开发了一个通用框架，该框架以正确设计的神经网络为基础，可直接从 CSI 中学习。为了进一步减轻计算负担，我们通过将原始问题分解为计算高效的子问题来获得一个低复杂度的框架，并分别处理瞬时CSI和统计CSI。通过离线预训练的神经网络，预编码器的在线计算复杂度与现有迭代算法相比大幅降低，同时保持了几乎相同的性能。