[论文解读] Hybrid Analog and Digital Beamforming Design for Channel Estimation in Correlated Massive MIMO Systems

Javad Mirzaei, Shahram Shahbazpanahi+2 more|arXiv (Cornell University)|Jul 15, 2021

Advanced MIMO Systems Optimization参考文献 67被引用 24

一句话总结

本文提出了一种针对相关性大规模MIMO系统中混合模拟-数字波束成形的基于训练的信道估计方案。通过利用信道相关矩阵的特征分解，该方法设计与主导特征方向对齐的混合预编码器和合并器，在总能量预算下最小化均方误差，仅需少量训练时隙即可实现精确估计——尤其在训练能量受限时效果显著。

ABSTRACT

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. By 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 transmit beamformer (precoder) and the receive beamformer (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. In contrast, with a large training energy budget, the energy is almost equally distributed among all eigen-directions. Simulation results show that the proposed channel estimation scheme can efficiently estimate correlated massive MIMO channels within a few training time slots.

研究动机与目标

• 解决大规模MIMO系统中射频链路数量减少带来的信道估计挑战。
• 设计一种在射频链路受限条件下可行的基于训练的信道估计技术。
• 利用已知的信道相关矩阵，而不假设参数化或稀疏信道模型。
• 在总能量预算下最小化信道估计的均方误差（MSE）。
• 在多个训练时隙中优化混合预编码器与合并器的设计。

提出的方法

• 使用Kronecker模型表示发射端和接收端的信道相关矩阵。
• 将信道估计问题转换到特征域，使信道元素之间不相关。
• 在每个时隙中设计与信道最强特征方向对齐的混合波束成形器（预编码器与合并器）。
• 推导出一种类似水填满（water-filling）的能量分配规则，以最小化MSE。
• 在总能量和射频链路约束下，通过凸优化框架优化波束成形器设计。
• 利用相关矩阵的特征分解来指导波束成形器对齐与能量分配。

实验结果

研究问题

• RQ1 在射频链路有限的相关性大规模MIMO系统中，如何高效地进行信道估计？
• RQ2 如何在多个时隙中最优分配训练能量以最小化估计误差？
• RQ3 信道相关性的结构如何影响所需训练时隙的数量？
• RQ4 信道相关矩阵的特征方向能否用于指导混合波束成形器设计以提升估计性能？
• RQ5 在混合波束成形系统中，训练能量预算与估计精度之间存在何种权衡？

主要发现

• 所提方法仅需少量训练时隙即可实现低归一化均方误差（NMSE），尤其在低能量预算下表现优异。
• 在低训练能量下，仅估计最强的特征方向，从而实现显著的资源节省。
• 在高训练能量预算下，能量几乎平均分配至所有特征方向，表明超过某一点后收益递减。
• 所需训练时隙数量与复杂度呈线性关系，但当Q ≥ 32时性能增益趋于边际化。
• 当相关性较高（|ρ| ≈ 1）时，仅估计主导特征方向即可实现接近最优的性能。
• 该方法通过利用相关性结构，在不假设稀疏性或参数化模型的前提下，优于传统方法。