Channel estimation and data transmission constitute the most fundamental functional modules of multiple-input multiple-output (MIMO) communication systems. The underlying key tasks corresponding to these modules are training sequence optimization and transceiver optimization. Hence, we jointly optimize the linear transmit precoder and the training sequence of MIMO systems using the metrics of their effective mutual information (MI), effective mean squared error (MSE), effective weighted MI, effective weighted MSE, as well as their effective generic Schur-convex and Schur-concave functions. Both statistical channel state information (CSI) and estimated CSI are considered at the transmitter in the joint optimization. A unified framework termed as joint matrix-monotonic optimization is proposed. Based on this, the optimal precoder matrix and training matrix structures can be derived for both CSI scenarios. Then, based on the optimal matrix structures, our linear transceivers and their training sequences can be jointly optimized. Compared to state-of-the-art benchmark algorithms, the proposed algorithms visualize the bold explicit relationships between the attainable system performance of our linear transceivers conceived and their training sequences, leading to implementation ready recipes. Finally, several numerical results are provided, which corroborate our theoretical results and demonstrate the compelling benefits of our proposed pilot-aided MIMO solutions.

翻译：信道估计与数据传输构成了多输入多输出（MIMO）通信系统中最基本的两个功能模块。这些模块所对应的核心关键任务分别是训练序列优化与收发机优化。因此，我们利用有效互信息（MI）、有效均方误差（MSE）、有效加权互信息、有效加权均方误差，以及有效通用舒尔凸函数与舒尔凹函数等度量指标，对MIMO系统的线性发射预编码器与训练序列进行联合优化。在联合优化中，发射端同时考虑统计信道状态信息（CSI）与估计信道状态信息。本文提出了一种称为联合矩阵单调优化的统一框架。基于此框架，可以推导出两种CSI场景下的最优预编码器矩阵与训练矩阵结构。进而，基于最优矩阵结构，我们能够联合优化线性收发机及其训练序列。与现有最优基准算法相比，所提算法清晰揭示了设计的线性收发机可达系统性能与其训练序列之间显式的直接关系，从而形成了可立即实现的解决方案。最后，提供了若干数值结果，这些结果验证了我们的理论分析，并展示了所提出的导频辅助MIMO方案的显著优势。