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Feedback rate-capacity loss tradeoff for limited feedback MIMO systems

机译：有限反馈MIMO系统的反馈速率-容量损失的权衡

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Multiple-input-multiple-output (MIMO) communication systems can provide large capacity gains over traditional single-input-single-output (SISO) systems and are expected to be a core technology of next generation wireless systems. Often, these capacity gains are achievable only with some form of adaptive transmission. In this paper, we study the capacity loss (defined as the rate loss in bits/s/Hz) of the MIMO wireless system when the covariance matrix of the transmitted signal vector is designed using a low rate feedback channel. For the MIMO channel, we find a bound on the ergodic capacity loss when random codebooks, generated from the uniform distribution on the complex unit sphere, are used to convey the second order statistics of the transmitted signal from the receiver to the transmitter. In this case, we find a closed-form expression for the ergodic capacity loss as a function of the number of bits fed back at each channel realization. These results show that the capacity loss decreases at least as O(2/sup -B/(2MMt-2)/) where B is the number of feedback bits, M/sub t/ is the number of transmit antennas, and M=min{M/sub r/,M/sub t/} where M/sub r/ is the number of receive antennas. In the high SNR regime, we present a new bound on the capacity loss that is tighter than the previously derived bound and show that the capacity loss decreases exponentially as a function of the number of feedback bits.
机译：与传统的单输入单输出（SISO）系统相比，多输入多输出（MIMO）通信系统可以提供更大的容量增益，并且有望成为下一代无线系统的核心技术。通常，这些容量增益只有通过某种形式的自适应传输才能实现。在本文中，我们研究了使用低速率反馈信道设计发射信号矢量的协方差矩阵时，MIMO无线系统的容量损失（定义为比特/秒/赫兹的速率损失）。对于MIMO信道，当根据复杂单位球面上的均匀分布生成的随机码本用于将接收到的信号的二阶统计量从接收器传输到发送器时，我们会发现遍历容量损失的界限。在这种情况下，我们发现遍历容量损失的封闭式表达式是每个通道实现反馈的位数的函数。这些结果表明，容量损失至少随着O（2 / sup -B /（2MMt-2）/）而减小，其中B是反馈比特数，M / sub t /是发射天线数，M = min {M / sub r /，M / sub t /}，其中M / sub r /是接收天线的数量。在高SNR体制中，我们提出了一个比先前导出的界限更严格的容量损失新界限，并表明容量损失随反馈位数的增加呈指数下降。

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