Optimal relay location and power allocation for low SNR broadcast relay channels
Optimal relay location and power allocation for low SNR broadcast relay channels
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DOI：
10.1109/infcom.2011.5935119
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发表时间：
2010-08
期刊：
影响因子：
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通讯作者：
Mohit Thakur;N. Fawaz;M. Médard
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文献类型：
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作者：
Mohit Thakur;N. Fawaz;M. Médard
我们考虑广播中继信道（BRC），其中一个单一的源发送到多个目的地的帮助下，一个中继，在一个大的带宽限制。我们解决的问题，最佳的中继定位和功率分配在源和中继，最大限度地提高组播速率从源到所有目的地。为了解决这样的网络规划问题，我们开发了一个三方面的基础上的信息理论模型，计算几何方面，网络优化工具的方法。首先，假设叠加编码和频率划分之间的源和中继，信息理论框架产生一个超图模型的宽带BRC，它捕获的依赖性，可实现的速率元组的网络拓扑结构。随着中继位置的变化，构成超图的超弧集合也会变化，从而呈现优化问题的组合性质。我们表明，在2-D平面中的所有节点的凸船体C可以被划分成不同的超弧集对应的不相交的区域。这些集合是通过叠加C的所有k阶Voronoi细分而获得的。我们提出了一个简单而有效的算法来计算所有的超弧集，并证明了它们是多项式有界的。然后，我们通过引入连续开关函数来规避问题的组合性质，这允许以连续的方式适应网络超图。使用这种切换超图的方法，我们建模的原始问题作为一个连续的但非凸的网络优化程序。最后，利用几何规划和p-范数替代逼近技术，得到了一个良好的凸逼近。我们提供了一个详细的表征共线定位的目的地的问题，然后给出了一个概括的任意位置的目的地。最后，我们表现出强大的收益相比，看似有趣的位置的最佳中继定位。
We consider the broadcast relay channel (BRC), where a single source transmits to multiple destinations with the help of a relay, in the limit of a large bandwidth. We address the problem of optimal relay positioning and power allocations at source and relay, to maximize the multicast rate from source to all destinations. To solve such a network planning problem, we develop a three-faceted approach based on an underlying information theoretic model, computational geometric aspects, and network optimization tools. Firstly, assuming superposition coding and frequency division between the source and the relay, the information theoretic framework yields a hypergraph model of the wideband BRC, which captures the dependency of achievable rate-tuples on the network topology. As the relay position varies, so does the set of hyperarcs constituting the hypergraph, rendering the combinatorial nature of optimization problem. We show that the convex hull C of all nodes in the 2-D plane can be divided into disjoint regions corresponding to distinct hyperarcs sets. These sets are obtained by superimposing all k-th order Voronoi tessellation of C. We propose an easy and efficient algorithm to compute all hyperarc sets, and prove they are polynomially bounded. Then, we circumvent the combinatorial nature of the problem by introducing continuous switch functions, that allows adapting the network hypergraph in a continuous manner. Using this switched hypergraph approach, we model the original problem as a continuous yet non-convex network optimization program. Ultimately, availing on the techniques of geometric programming and p-norm surrogate approximation, we derive a good convex approximation. We provide a detailed characterization of the problem for collinearly located destinations, and then give a generalization for arbitrarily located destinations. Finally, we show strong gains for the optimal relay positioning compared to seemingly interesting positions.