[论文解读] On Design of Distributed Beamforming for Two-Way Relay Networks

Meng Zeng, Rui Zhang+1 more|arXiv (Cornell University)|May 11, 2010

Cooperative Communication and Network Coding参考文献 15被引用 14

一句话总结

本文针对单天线中继簇在双向中继网络中，于信道互惠与非互惠条件下的最优分布式波束成形，提出了闭式解。通过求解加权和倒谱信噪比（inverse-SNR）最小化问题，推导出全局最优波束成形向量，从而表征完整的二维可实现速率区域，实现了仅需局部信道状态信息和一个全局参数的半分布式算法，显著提升了相较于以往纯数值方法的设计效率。

ABSTRACT

We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay node multiplies its received signal by a complex coefficient and retransmits the signal to the two source nodes, which leads to a distributed two-way beamforming system. By applying the principle of analog network coding, each receiver at S1 and S2 cancels the ``self-interference'' in the received signal from the relay cluster and decodes the message. This paper studies the 2-dimensional achievable rate region for such a two-way relay network with distributed beamforming. With different assumptions of channel reciprocity between the source-relay and relay-source channels, the achievable rate region is characterized under two setups. First, with reciprocal channels, we investigate the achievable rate regions when the relay cluster is subject to a sum-power constraint or individual-power constraints. We show that the optimal beamforming vectors obtained from solving the weighted sum inverse-SNR minimization (WSISMin) problems are sufficient to characterize the corresponding achievable rate region. Furthermore, we derive the closed form solutions for those optimal beamforming vectors and consequently propose the partially distributed algorithms to implement the optimal beamforming, where each relay node only needs the local channel information and one global parameter. Second, with the non-reciprocal channels, the achievable rate regions are also characterized for both the sum-power constraint case and the individual-power constraint case. Although no closed-form solutions are available under this setup, we present efficient algorithms to compute the optimal beamforming vectors, which are attained by solving SDP problems after semi-definite relaxation.

研究动机与目标

• 表征在总功率和个体功率约束下，双向中继网络中分布式波束成形的完整二维可实现速率区域。
• 在信道互惠条件下，推导出总功率与个体功率约束下的闭式最优波束成形向量。
• 提出仅需局部CSI和一个全局参数的半分布式算法。
• 将分析扩展至闭式解不可行的非互惠信道，采用半定松弛（SDR）与SDP-based计算方法。
• 通过加权和倒谱信噪比最小化，建立系统化框架以实现Pareto最优速率对。

提出的方法

• 将问题建模为加权和倒谱信噪比最小化（WSISMin），以表征Pareto最优速率区域。
• 利用拉格朗日对偶理论与相位对齐原理，在信道互惠条件下推导出闭式波束成形解。
• 提出半分布式算法，其中每个中继仅使用其局部CSI和一个全局权重参数。
• 对于非互惠信道，应用半定松弛（SDR）将非凸问题转化为一系列凸半定规划（SDP）。
• 利用倒谱信噪比区域与速率区域之间的几何对偶性，证明仅需从WSISMin解集中取边界点即可构造完整的速率区域。
• 采用凸包与对偶性论证，表明非WSISMin边界点在速率区域构造中冗余。

实验结果

研究问题

• RQ1 在总功率与个体功率约束下，分布式双向中继波束成形系统的完整二维可实现速率区域是什么？
• RQ2 当信道互惠时，能否为最优波束成形向量推导出闭式解？
• RQ3 如何以最小信令开销实现最优波束成形的半分布式实现？
• RQ4 在非互惠信道下，最优波束成形向量的结构如何？如何高效计算？
• RQ5 速率区域的所有边界点是否都对构造Pareto最优区域是必需的？还是可通过解的子集完全表征？

主要发现

• 在信道互惠条件下，推导出最优波束成形向量的闭式解，实现了对可实现速率区域的显式表征。
• 证明在互惠条件下，最优波束成形向量与等效信道增益呈相位对齐，简化了实现。
• 提出半分布式算法，每个中继仅需局部CSI和一个全局权重参数，显著降低了反馈开销。
• 对于非互惠信道，通过半定松弛（SDR）后，采用一系列半定规划（SDP）计算最优波束成形向量。
• 速率区域可由WSISMin问题的解完全表征；非WSISMin边界点在几何上冗余，无需用于凸包构造。
• 证明倒谱信噪比区域与速率区域之间存在对偶变换关系，从而可从倒谱信噪比解集中高效计算速率区域。