有限反馈迫零SDMA的稳定性和时滞
Stability and Delay of Zero-Forcing SDMA with Limited Feedback
摘要：
本文研究了突发业务下空分多址（SDMA）系统的稳定性和时延问题，其中迫零波束赋形使多个移动台同时传输。计算波束成形向量依赖于来自移动台的量化信道状态信息（CSI）反馈（有限反馈）。将SDMA的稳定区域定义为稳态队列长度有限的多用户分组到达率集合。在理想CSI反馈和调度队列上的等功率分配条件下，证明了系统的稳定域是一个具有导出顶点的凸多面体。对于任何一组的到达率在稳定区域，多用户队列被证明是稳定的联合调度和波束成形控制策略，最大限度地提高了离开率加权和队列长度。有限反馈的稳定区域被发现是完美的CSI区域乘以一减去一个小的因素。每个移动所需的反馈比特数被证明与上述因子的倒数成比例，并且与发射天线的数量减一成线性。有限反馈对延迟的影响也被量化。对于泊松到达过程，CSI量化误差乘以平均延迟大于一个因素。可以通过按照导出的关系调整每个移动站的反馈比特数来控制该因子。对于一般的到达过程，CSI错误被发现增加金曼的瞬时延迟的尾部概率的一个加一个小的因素。每个移动所需的反馈比特数示出与这个因子成比例。
英文摘要：
This paper addresses the stability and queueing delay of Space Division Multiple Access (SDMA) systems with bursty traffic, where zero-forcing beamforming enables simultaneous transmission to multiple mobiles. Computing beamforming vectors relies on quantized channel state information (CSI) feedback (limited feedback) from mobiles. Define the stability region for SDMA as the set of multiuser packet-arrival rates for which the steady-state queue lengths are finite. Given perfect CSI feedback and equal power allocation over scheduled queues, the stability region is proved to be a convex polytope having the derived vertices. For any set of arrival rates in the stability region, multiuser queues are shown to be stabilized by a joint queue-and-beamforming control policy that maximizes the departure-rate-weighted sum of queue lengths. The stability region for limited feedback is found to be the perfect-CSI region multiplied by one minus a small factor. The required number of feedback bits per mobile is proved to scale logarithmically with the inverse of the above factor as well as linearly with the number of transmit antennas minus one. The effects of limited feedback on queueing delay are also quantified. For Poisson arrival processes, CSI quantization errors are shown to multiply average queueing delay by a factor larger than one. This factor can be controlled by adjusting the number of feedback bits per mobile following the derived relationship. For general arrival processes, CSI errors are found to increase Kingman's bound on the tail probability of the instantaneous delay by one plus a small factor. The required number of feedback bits per mobile is shown to scale logarithmically with this factor.
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