[论文解读] Quantization Design and Channel Estimation for Massive MIMO Systems with One-Bit ADCs

Feiyu Wang, Jun Fang+2 more|arXiv (Cornell University)|Apr 16, 2017

Advanced MIMO Systems Optimization参考文献 23被引用 6

一句话总结

本文提出了一种适用于单比特大规模MIMO系统的自适应与随机量化方案，以在严重量化失真条件下实现高效的信道估计。通过基于信道统计特性优化量化阈值，所提方法使估计误差控制在理想无量化情况下的π/2倍以内，并显著降低训练开销，仅需每位用户约五个导频符号即可实现接近完美的CSI性能。

ABSTRACT

We consider the problem of channel estimation for uplink multiuser massive MIMO systems, where, in order to significantly reduce the hardware cost and power consumption, one-bit analog-to-digital converters (ADCs) are used at the base station (BS) to quantize the received signal. Channel estimation for one-bit massive MIMO systems is challenging due to the severe distortion caused by the coarse quantization. It was shown in previous studies that an extremely long training sequence is required to attain an acceptable performance. In this paper, we study the problem of optimal one-bit quantization design for channel estimation in one-bit massive MIMO systems. Our analysis reveals that, if the quantization thresholds are optimally devised, using one-bit ADCs can achieve an estimation error close to (with an increase by a factor of $π/2$) that of an ideal estimator which has access to the unquantized data. The optimal quantization thresholds, however, are dependent on the unknown channel parameters. To cope with this difficulty, we propose an adaptive quantization (AQ) approach in which the thresholds are adaptively adjusted in a way such that the thresholds converge to the optimal thresholds, and a random quantization (RQ) scheme which randomly generate a set of nonidentical thresholds based on some statistical prior knowledge of the channel. Simulation results show that, our proposed AQ and RQ schemes, owing to their wisely devised thresholds, present a significant performance improvement over the conventional fixed quantization scheme that uses a fixed (typically zero) threshold, and meanwhile achieve a substantial training overhead reduction for channel estimation. In particular, even with a moderate number of pilot symbols (about 5 times the number of users), the AQ scheme can provide an achievable rate close to that of the perfect channel state information (CSI) case.

研究动机与目标

• 解决由于大规模MIMO系统中使用单比特ADC而导致的严重信道估计失真问题。
• 减少传统固定阈值量化方案所需的过长训练序列。
• 设计在信道参数未知条件下最小化估计误差的量化阈值。
• 在最小导频开销下实现高 spectral efficiency 和接近完美CSI的可实现速率。
• 开发实用的、自适应的和随机的量化策略，利用统计先验知识使阈值收敛至最优值。

提出的方法

• 提出一种自适应量化（AQ）方案，通过迭代调整阈值以基于信道估计收敛至最优值。
• 引入一种随机量化（RQ）方案，利用信道的统计先验知识生成非相同的阈值。
• 推导单比特量化系统的Cramér-Rao界（CRB），以建立估计精度的理论极限。
• 使用最大似然（ML）估计方法建模单比特量化下的信道估计问题。
• 优化量化矩阵A，以最小化Fisher信息矩阵的逆矩阵的迹，从而确保高效估计。
• 建立理论边界，表明最优单比特量化可使估计误差控制在理想无量化情况下的π/2倍以内。

实验结果

研究问题

• RQ1 单比特量化能否实现接近理想无量化系统的估计精度？
• RQ2 在缺乏完美信道知识的情况下，如何设计量化阈值以最小化信道估计误差？
• RQ3 能否在不牺牲估计精度的前提下，显著减少单比特大规模MIMO系统中的训练开销？
• RQ4 单比特量化下信道估计的理论性能极限是什么？
• RQ5 自适应与随机量化方案与固定阈值方法相比，在训练开销和估计精度方面表现如何？

主要发现

• 最优单比特量化阈值可使估计误差控制在理想无量化估计器的π/2倍以内。
• 自适应量化（AQ）方案收敛至最优阈值，并仅需每位用户约五个导频符号即可实现接近完美CSI的可实现速率。
• 基于统计先验知识的随机量化（RQ）方案显著优于传统固定阈值量化。
• AQ与RQ方案相较于传统方法可大幅降低训练开销，后者在训练序列中所需符号数可达用户数的50倍。
• 理论分析证实，最优单比特量化下的最小估计误差被限制为理想估计器误差的π/2倍。
• 所提方法即使在中等导频开销下也能实现近似最优性能，证明了其在单比特大规模MIMO系统中的实际可行性。