[论文解读] On the Information Rate of MIMO Systems with Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy

Wei Dai, Youjian Liu+2 more|ArXiv.org|Mar 9, 2006

Advanced MIMO Systems Optimization参考文献 29被引用 5

一句话总结

本文研究了采用波束成形与功率开关策略的有限速率信道状态反馈MIMO系统。推导出渐近公式，表明在高信噪比下，最优激活波束数收敛于系统维度的恒定比例，从而可通过一种新型的功率效率因子准确表征信息速率，该因子量化了反馈不完善的影响。

ABSTRACT

It is well known that Multiple-Input Multiple-Output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. When CSIT is obtained by feedback, it is practical to assume that the channel state feedback rate is finite and the CSIT is not perfect. For such a system, we consider beamforming and power on/off strategy for its simplicity and near optimality, where power on/off means that a beamforming vector (beam) is either turned on with a constant power or turned off. The main contribution of this paper is to accurately evaluate the information rate as a function of the channel state feedback rate. Name a beam turned on as an on-beam and the minimum number of the transmit and receive antennas as the dimension of a MIMO system. We prove that the ratio of the optimal number of on-beams and the system dimension converges to a constant for a given signal-to-noise ratio (SNR) when the numbers of transmit and receive antennas approach infinity simultaneously and when beamforming is perfect. Asymptotic formulas are derived to evaluate this ratio and the corresponding information rate per dimension. The asymptotic results can be accurately applied to finite dimensional systems and suggest a power on/off strategy with a constant number of on-beams. For this suboptimal strategy, we take a novel approach to introduce power efficiency factor, which is a function of the feedback rate, to quantify the effect of imperfect beamforming. By combining power efficiency factor and the asymptotic formulas for perfect beamforming case, the information rate of the power on/off strategy with a constant number of on-beams is accurately characterized.

研究动机与目标

• 解决在实际有限速率信道状态反馈下实现MIMO系统高 spectral efficiency 的挑战。
• 评估在功率开关与波束成形策略下反馈带来的性能增益，这些策略简化了实现过程，同时保持接近最优的性能。
• 表征信息速率与反馈速率的关系，特别是在高维MIMO系统中的表现。
• 构建一个准确建模有限反馈导致波束成形不完善影响的框架。

提出的方法

• 通过令发射与接收天线数同时趋于无穷大，采用渐近分析方法，推导最优激活波束数的极限行为。
• 引入一个作为反馈速率函数的功率效率因子，以量化因波束成形不完善导致的性能损失。
• 利用随机矩阵理论的技术，推导在理想波束成形条件下最优激活波束数及其对应信息速率的渐近公式。
• 通过将这些渐近结果与功率效率因子结合，将其应用于有限维系统，以建模反馈不完善的影响。
• 采用奇异值分解将MIMO信道分解为并行子信道，从而实现波束成形与功率控制的设计。
• 证明在理想波束成形下，最优激活波束数是非递减的，并且在高信噪比下收敛于系统维度的恒定比例。

实验结果

研究问题

• RQ1 当系统维度趋于无穷大时，在有限速率反馈与理想波束成形条件下，MIMO系统中最优激活波束数是多少？
• RQ2 在采用功率开关与波束成形策略时，信息速率如何随反馈速率变化？
• RQ3 反馈量化误差对波束成形性能有何影响，如何对其进行定量建模？
• RQ4 为大系统推导出的渐近公式能否准确应用于具有有限反馈的有限维MIMO系统？
• RQ5 对于具有有限速率反馈的MIMO系统，恒定数量的激活波束是否近似最优？

主要发现

• 当发射与接收天线数趋于无穷大时，最优激活波束数与系统维度的比值在给定信噪比下收敛于一个常数。
• 在理想波束成形条件下，最优激活波束数是信噪比的非递减函数。
• 推导出的渐近公式能够准确预测最优激活波束数及其对应的单位维度信息速率。
• 作为反馈速率函数的功率效率因子，能有效量化因波束成形不完善导致的性能下降。
• 所提出的方法能够准确表征在有限维MIMO系统中采用恒定激活波束数的功率开关策略下的信息速率。
• 结果表明，即使在有限反馈条件下，恒定波束数策略也近似最优且具有实际可行性。