In this paper, we study the channel estimation problem in correlated massive multiple-input-multiple-output (MIMO) systems with a reduced number of radio-frequency (RF) chains. Importantly, other than the knowledge of channel correlation matrices, we make no assumption as to the structure of the channel. To address the limitation in the number of RF chains, we employ hybrid beamforming, comprising a low dimensional digital beamformer followed by an analog beamformer implemented using phase shifters. Since there is no dedicated RF chain per transmitter/receiver antenna, the conventional channel estimation techniques for fully-digital systems are impractical. Exploiting the fact that the channel entries are uncorrelated in its eigen-domain, we seek to estimate the channel entries in this domain. Due to the limited number of RF chains, channel estimation is typically performed in multiple time slots. Under a total energy budget, we aim to design the hybrid precoder and the receive combiner in each training time slot, in order to estimate the channel using the minimum mean squared error criterion. To this end, we choose the precoder and combiner in each time slot such that they are aligned to transmitter and receiver eigen-directions, respectively. Further, we derive a water-filling type expression for the optimal energy allocation at each time slot. This expression illustrates that, with a low training energy budget, only significant components of the channel need to be estimated. Simulation results indicate that the proposed channel estimation scheme can efficiently estimate correlated massive MIMO channels within a few training time slots.

中文翻译：

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用于相关大规模 MIMO 系统中信道估计的混合模拟和数字波束成形设计

在本文中，我们研究了相关大规模多输入多输出 (MIMO) 系统中射频 (RF) 链数量减少的信道估计问题。重要的是，除了信道相关矩阵的知识外，我们不对信道的结构做任何假设。为了解决 RF 链数量的限制，我们采用了混合波束成形，包括一个低维数字波束成形器，然后是一个使用移相器实现的模拟波束成形器。由于每个发射器/接收器天线没有专用的 RF 链，因此用于全数字系统的传统信道估计技术是不切实际的。利用信道条目在其特征域中不相关的事实，我们试图估计该域中的信道条目。由于射频链的数量有限，信道估计通常在多个时隙中执行。在总能量预算下，我们的目标是在每个训练时隙中设计混合预编码器和接收组合器，以便使用最小均方误差准则来估计信道。为此，我们在每个时隙中选择预编码器和组合器，使它们分别与发射机和接收机的本征方向对齐。此外，我们推导出了每个时隙最佳能量分配的注水类型表达式。该表达式说明，在训练能量预算较低的情况下，只需要估计通道的重要组成部分。仿真结果表明，所提出的信道估计方案可以在几个训练时隙内有效地估计相关的大规模 MIMO 信道。