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Multi-Cell Random Beamforming: Achievable Rate and Degrees of Freedom Region

机译:多单元随机波束成形:可达到的速度和自由度区域

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Random beamforming (RBF) is a practically favorable transmission scheme for multiuser multiantenna downlink systems since it requires only partial channel state information (CSI) at the transmitter. Under the conventional single-cell setup, RBF is known to achieve the optimal sum-capacity scaling law as the number of users goes to infinity, thanks to the multiuser diversity enabled transmission scheduling that virtually eliminates the intra-cell interference. In this paper, we extend the study of RBF to a more practical multi-cell downlink system with single-antenna receivers subject to the additional inter-cell interference (ICI). First, we consider the case of finite signal-to-noise ratio (SNR) at each receiver. We derive a closed-form expression of the achievable sum-rate with the multi-cell RBF, based upon which we show an asymptotic sum-rate scaling law as the number of users goes to infinity. Next, we consider the high-SNR regime and for tractable analysis assume that the number of users in each cell scales in a certain order with the per-cell SNR. Under this setup, we characterize the achievable degrees of freedom (DoF) (which is defined as the sum-rate normalized by the logarithm of the SNR as SNR goes to infinity) for the single-cell case with RBF. Then, we extend the analysis to the multi-cell RBF case by characterizing the DoF region, which consists of all the achievable DoF tuples for all the cells subject to their mutual ICI. It is shown that the DoF region characterization provides a useful guideline on how to design a cooperative multi-cell RBF system to achieve optimal throughput tradeoffs among different cells. Furthermore, our results reveal that the multi-cell RBF scheme achieves the “interference-free” DoF region upper bound for the multi-cell system, provided that the per-cell number of users has a sufficiently large scaling order with the SNR. Our result thus confirms the optimality of multi-cell RBF in this regime even without- the complete CSI at the transmitter, as compared to other full-CSI requiring transmission schemes such as interference alignment.
机译:随机波束成形(RBF)是多用户多天线下行链路系统的一种实用的传输方案,因为它在发射机处仅需要部分信道状态信息(CSI)。在传统的单小区设置下,由于启用了多用户分集的传输调度实际上消除了小区内干扰,因此,随着用户数量达到无穷大,RBF可以实现最佳的总容量缩放定律。在本文中,我们将RBF的研究扩展到具有单天线接收器且受到额外小区间干扰(ICI)的更实用的多小区下行链路系统。首先,我们考虑在每个接收器处的有限信噪比(SNR)的情况。我们使用多小区RBF得出可实现的总和率的封闭式表达式,在此基础上,随着用户数量达到无穷大,我们显示出渐近的总和率定标定律。接下来,我们考虑高SNR机制,并且为了便于分析,假设每个小区中的用户数量以每个小区SNR的特定顺序扩展。在这种设置下,我们描述了带有RBF的单小区情况下可实现的自由度(DoF)(定义为通过SNR的对数归一化的总和率)。然后,通过表征DoF区域,将分析扩展到多小区RBF情况,该区域由受其相互ICI约束的所有小区的所有可实现的DoF元组组成。结果表明,DoF区域表征为如何设计协作式多小区RBF系统以实现不同小区之间的最佳吞吐量折衷提供了有用的指导。此外,我们的结果表明,只要每小区用户数具有足够大的SNR缩放比例,多小区RBF方案就可以实现多小区系统的“无干扰” DoF区域上限。因此,与其他要求传输方案(如干扰对准)的全CSI相比,即使在发射机处没有完整的CSI的情况下,我们的结果也证实了该方案中多小区RBF的最优性。

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