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Distributed Transmit Beamforming Using Feedback Control

机译：使用反馈控制的分布式发射波束成形

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摘要

The concept of distributed transmit beamforming is implicit in many key results of network information theory. However, its implementation in a wireless network involves the fundamental challenge of ensuring phase coherence of the radio frequency signals from the different transmitters in the presence of unknown phase offsets between the transmitters and unknown channel gains from the transmitters to the receiver. In this paper, it is shown that such phase alignment can be achieved using distributed adaptation by the transmitters with minimal feedback from the receiver. Specifically, each transmitter independently makes a small random adjustment to its phase at each iteration, while the receiver broadcasts a single bit of feedback, indicating whether the signal-to-noise ratio (SNR) improved or worsened after the current iteration. The transmitters keep the ¿good¿ phase adjustments and discard the ¿bad¿ ones, thus implementing a distributed ascent algorithm. It is shown that, for a broad class of distributions for the random phase adjustments, this procedure leads to asymptotic phase coherence with probability one. A simple analytical model, borrowing ideas from statistical mechanics, is used to characterize the progress of the algorithm, and to provide guidance on parameter choices. This analytical model is based on a conjecture on the distribution of the received phases when the number of transmitters becomes large. Finally, the proposed system is shown to be scalable: the random phase perturbations can be chosen such that the convergence time is linear in the number of collaborating nodes.
机译：网络信息理论的许多关键结果都暗含了分布式发射波束成形的概念。然而，其在无线网络中的实现涉及根本的挑战，即在发射机之间存在未知的相位偏移以及从发射机到接收机的未知信道增益的情况下，确保来自不同发射机的射频信号的相位相干性。在本文中，示出了可以使用发送器的分布式自适应以最小的接收器反馈来实现这种相位对准。具体来说，每个发射器在每次迭代时都对其相位进行随机的小调整，而接收器广播一个反馈位，以指示在当前迭代之后信噪比（SNR）是提高还是变差。发射器保持“好”相位调整并丢弃“坏”相位调整，从而实现了分布式上升算法。结果表明，对于随机相位调整的广泛分布类别，该过程导致概率为1的渐近相位相干。一个简单的分析模型（借鉴了统计力学的思想）用于表征算法的进度，并为参数选择提供指导。当发射机数量变大时，该分析模型基于对接收相位分布的推测。最后，所提出的系统显示为可伸缩的：可以选择随机相位扰动，以使收敛时间在协作节点的数量中是线性的。

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