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

机译:带有量化预编码矩阵的多天线衰落信道的容量

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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 independent and identically distributed (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. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. 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.
机译:给定多输入多输出(MIMO)通道,可以使用来自接收器的反馈来指定发射预编码矩阵,该矩阵有选择地激活最强的信道模式。在这里,我们分析了随机矢量量化(RVQ)的性能,其中,预编码矩阵是从包含独立的各向同性分布条目的随机码本中选择的。我们假设信道元素是独立的并且是均匀分布的(i.i.d.)并为接收者所知,后者使用$ B $位将最佳(速率最大化)预编码器代码本索引中继到发送器。我们首先得出波束成形(秩预编码矩阵)的大系统容量作为$ B $的函数,其中大型系统将限制称为$ B $,并且发射和接收天线的数量均以固定比率变为无穷大。 。用于波束成形的RVQ是渐近最优的,即没有其他量化方案可以实现更大的渐近率。随后,我们考虑了具有任意秩的预编码矩阵,并使用最佳和线性接收器(匹配滤波器和最小均方误差(MMSE))来近似渐近RVQ性能。数值示例表明,这些近似值可以准确预测目标有限尺寸系统的性能。给定目标频谱效率,数值示例表明,线性MMSE接收机所需的反馈量仅比最佳接收机所需的反馈量稍多,而匹配滤波器可能需要更多的反馈。

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