This paper addresses the design of transmit precoder and receive combiner matrices to support $N_{\rm s}$ independent data streams over a time-division duplex (TDD) point-to-point massive multiple-input multiple-output (MIMO) channel with either a fully digital or a hybrid structure. The optimal precoder and combiner design amounts to finding the top-$N_{\rm s}$ singular vectors of the channel matrix, but the explicit estimation of the entire high-dimensional channel would require significant pilot overhead. Alternatively, prior works seek to find the precoding and combining matrices directly by exploiting channel reciprocity and by using the power iteration method, but its performance degrades in the low SNR regime. To tackle this challenging problem, this paper proposes a learning-based active sensing framework, where the transmitter and the receiver send pilots alternately using sensing beamformers that are actively designed as functions of previously received pilots. This is accomplished by using recurrent neural networks to summarize information from the historical observations into hidden state vectors, then using fully connected neural networks to learn the appropriate sensing beamformers in the next pilot stage and finally the transmit precoding and receive combiner matrices for data communications. Simulations demonstrate that the learning-based method outperforms existing approaches significantly and maintains superior performance even in low SNR regimes both in fully digital and hybrid MIMO scenarios.

翻译：本文研究在时分双工(TDD)点对点大规模多输入多输出(MIMO)信道中，支持$N_{\rm s}$个独立数据流的发射预编码器和接收合并器矩阵的设计问题，系统可采用全数字或混合结构。最优预编码器和合并器设计等价于寻找信道矩阵的前$N_{\rm s}$个奇异向量，但完整估计高维信道需要大量导频开销。为此，现有研究尝试通过信道互易性和幂迭代法直接求解预编码与合并矩阵，然而该方法在低信噪比条件下性能显著下降。针对这一挑战，本文提出一种基于学习的有源感知框架：收发双方交替发送导频，并采用根据历史接收导频主动设计的感知波束赋形器。该框架通过循环神经网络将历史观测信息汇总为隐状态向量，进而利用全连接神经网络学习下一导频阶段的感知波束赋形器，最终生成数据通信所需的发射预编码与接收合并矩阵。仿真结果表明，在低信噪比场景下，该学习方法在全数字与混合MIMO系统中均显著优于现有方案，并保持卓越性能。