[论文解读] Low-complexity and Statistically Robust Beamformer Design for Massive MIMO Systems

Mahdi Nouri Boroujerdi, Saeid Haghighatshoar+1 more|arXiv (Cornell University)|Nov 30, 2017

Advanced MIMO Systems Optimization参考文献 37被引用 3

一句话总结

本文提出了一种低复杂度、统计鲁棒的波束成形器设计方法，用于大规模MIMO系统，采用随机Kaczmarz算法，无需事先知晓信道协方差矩阵。该方法在性能上可与最先进技术相媲美，同时在信道统计特性变化时表现出强鲁棒性，即使在协方差估计极具挑战性的高维系统中亦然。

ABSTRACT

Massive MIMO is a variant of multiuser MIMO in which the number of antennas at the base station (BS) $M$ is very large and typically much larger than the number of served users (data streams) $K$. Recent research has illustrated the system-level advantages of such a system and in particular the beneficial effect of increasing the number of antennas $M$. These benefits, however, come at the cost of dramatic increase in hardware and computational complexity. This is partly due to the fact that the BS needs to compute suitable beamforming vectors in order to coherently transmit/receive data to/from each user, where the resulting complexity grows proportionally to the number of antennas $M$ and the number of served users $K$. Recently, different algorithms based on tools from random matrix theory in the asymptotic regime of $M,K o \infty$ with $\frac{K}{M} o ho \in (0,1)$ have been proposed to reduce the complexity. The underlying assumption in all these techniques, however, is that the exact statistics (covariance matrix) of the channel vectors of the users is a priori known. This is far from being realistic, especially that in the high-dim regime of $M o \infty$, estimation of the underlying covariance matrices is well known to be a very challenging problem. In this paper, we propose a novel technique for designing beamforming vectors in a massive MIMO system. Our method is based on the randomized Kaczmarz algorithm and does not require knowledge of the statistics of the users' channel vectors. We analyze the performance of our proposed algorithm theoretically and compare its performance with that of other competitive techniques based on random matrix theory and approximate message passing via numerical simulations. Our results indicate that our proposed technique has a comparable performance while being highly robust to variations in the channel statistics.

研究动机与目标

• 解决大规模MIMO系统中由于波束成形向量计算导致的高计算与硬件复杂度问题。
• 克服先前研究中假设可精确获知信道协方差矩阵的不切实际前提。
• 开发一种在信道统计特性未知或估计不准确时仍具有效性的波束成形技术。
• 确保在高维系统（M → ∞）中对信道统计特性变化的鲁棒性。
• 实现与基于随机矩阵理论和近似消息传递的先进方法相当的性能，同时具备更低的复杂度和更高的实用性。

提出的方法

• 利用随机Kaczmarz算法，迭代求解波束成形向量设计问题，无需信道协方差矩阵。
• 将波束成形问题建模为由信干噪比（SINR）约束导出的线性方程组。
• 在每次迭代中随机采样方程，以降低计算负载并提升收敛速度。
• 避免显式估计高维信道协方差矩阵，此类矩阵在大规模MIMO系统中极难准确估计。
• 采用基于数据驱动的随机迭代更新规则，在最小统计假设下收敛至可行的波束成形解。
• 通过依赖数据驱动更新而非参数化信道模型，实现统计鲁棒性。

实验结果

研究问题

• RQ1 在缺乏信道协方差矩阵先验知识的情况下，能否有效设计大规模MIMO系统的波束成形？
• RQ2 基于Kaczmarz的波束成形器性能与依赖随机矩阵理论的最先进方法相比如何？
• RQ3 所提方法在信道统计特性存在误差或变化时，其鲁棒性达到何种程度？
• RQ4 与现有技术相比，该方法在高维MIMO系统中的计算复杂度如何？
• RQ5 在真实信道条件下，随机Kaczmarz方法是否能保持良好的频谱效率和SINR性能？

主要发现

• 所提波束成形方法在性能上可与基于随机矩阵理论和近似消息传递的先进方法相媲美。
• 该方法对信道统计特性的变化表现出强鲁棒性，在统计特性估计不准确时，优于依赖协方差的现有方法。
• 通过避免显式协方差矩阵估计，算法显著降低了计算复杂度。
• 理论分析证实了在M和K趋于无穷的渐近极限下，基于随机Kaczmarz的波束成形器具有收敛性和稳定性。
• 数值仿真表明，即使在信道统计特性未知或估计不佳的高维MIMO系统中，该方法仍能保持高谱效率。
• 在实际场景中，当因高维性和 pilot 污染导致精确信道协方差估计不可行时，该方法尤其具有优势。