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arXiv 0704.0217cs.ITmath.IT
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采用量化预编码矩阵的多天线衰落信道容量

Capacity of a Multiple-Antenna Fading Channel with a Quantized Precoding Matrix

Wiroonsak Santipach, Michael L. Honig

摘要:

给定多输入多输出(MIMO)信道,来自接收器的反馈可用于指定发射预编码矩阵,其选择性地激活最强信道模式。在这里,我们分析的随机矢量量化(RVQ),其中的预编码矩阵是从包含独立的,各向同性分布的条目的随机码本中选择的性能。我们假设信道元素是独立同分布的。并且对于接收机是已知的,接收机使用B个比特将最优(速率最大化)预编码器码本索引中继到发射机。我们首先导出作为B的函数的波束成形(秩一预编码矩阵)的大系统容量,其中大系统将极限称为B,并且发射天线和接收天线的数量都以固定比率趋于无穷大。在波束成形的情况下,RVQ是渐近最优的,即,没有其它量化方案可以实现更大的渐近速率。RVQ的性能也比较了一个更简单的降秩标量量化方案,其中波束形成器被约束到位于一个随机子空间。随后,我们考虑一个预编码矩阵与任意秩,并近似的渐近RVQ性能与最佳和线性接收机(匹配滤波器和最小均方误差(MMSE))。数值例子表明,这些近似准确地预测有限尺寸系统的性能。给定目标频谱效率,数值例子表明,线性MMSE接收机所需的反馈量仅略多于最佳接收机所需的反馈量,而匹配滤波器可能需要更多的反馈。

英文摘要:

Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of Random Vector Quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are i.i.d. and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using B bits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of B, where large system refers to the limit as B and the number of transmit and receive antennas all go to infinity with fixed ratios. With beamforming RVQ is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. The performance of RVQ is also compared with that of a simpler reduced-rank scalar quantization scheme in which the beamformer is constrained to lie in a random subspace. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and Minimum Mean Squared Error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.

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