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Asymptotic Analysis of Reduced-Feedback Strategies for MIMO Gaussian Broadcast Channels

机译：MIMO高斯广播信道的减少反馈策略的渐近分析

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摘要

Achieving the sum-capacity of a multiple-input–multiple- output (MIMO) Gaussian broadcast channel is known to require full channel state information (CSI) at the base station, which implies the need of a large amount of feedback information from the users. Different asymptotics of the sum-capacity, such as its scaling law with respect to the number of users $n$ or the multiplexing gain, are conventionally used to assess the performance of suboptimal schemes with reduced feedback, or equivalently with partial channel state information at the transmitter. In this correspondence, the optimal scaling law of the sum-rate with respect to $n$ , for fixed signal-to-noise ratio (SNR), fixed number of transmit antennas $M$ and any number of receiving antennas $N$ (i.e., $Mlog log nN$), is proved to be achievable with a deterministic feedback of only one bit per user. Moreover, the amount of feedback is shown to be further reduced with no asymptotic optimality loss by applying the selective feedback principle, leading to an average feedback rate that scales as $log n$. Finally, the asymptotic performance with respect to SNR is studied, by assessing how fast the number of users needs to increase with the SNR in order to guarantee a noninterference limited behavior.
机译：已知实现多输入多输出（MIMO）高斯广播信道的总容量要求基站具有完整的信道状态信息（CSI），这意味着需要来自用户的大量反馈信息。传统上，总容量的不同渐近性，例如其相对于用户数量$ n $的缩放定律或多路复用增益，通常用于评估反馈减少或与部分信道状态信息等效的次优方案的性能。发射器。在这种对应关系中，对于固定信噪比（SNR），固定数量的发射天线$ M $和任意数量的接收天线$ N $（例如，$ Mlog log nN $）被证明是可以实现的，每个用户只有一个位的确定性反馈。此外，通过应用选择性反馈原理，显示出反馈量将进一步减少而不会出现渐近最优性，从而导致平均反馈率成$ log n $。最后，通过评估用户数需要随SNR增加多快来保证无干扰受限行为，研究了与SNR相关的渐近性能。

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