Towards an optimal beamforming algorithm for physical layer multicasting
Towards an optimal beamforming algorithm for physical layer multicasting
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DOI：
10.1109/itw.2011.6089487
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
M. Khojastepour;Alireza Salehi-Golsefidi;S. Rangarajan
中科院分区：
文献类型：
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作者：
M. Khojastepour;Alireza Salehi-Golsefidi;S. Rangarajan
无线网络中涉及组通信的应用的日益普及导致了对高效多播解决方案的需求。智能天线的波束形成能力，从而提高在客户端的信号质量，使他们特别有吸引力的组播应用。不幸的是，多播波束成形设计问题是一个非凸优化问题，文献中只提出了次优的解决方案。在这项工作中，我们发现了一个隐藏的凸性的问题在一定的信道条件下经常发生的实际系统与瑞利衰落信道模型。我们提出了一个解决方案，基于这个观察，其中包括两个步骤：（1）我们解决的对偶问题，并检查唯一性条件;如果满足，我们表明，对偶差距为零，并根据对偶问题的解决方案获得原始问题的解决方案;（2）如果唯一性条件不满足，我们使用梯度下降为基础的方法。我们的评估表明，该算法显着提高了组播性能的最先进的解决方案。仿真结果表明，在大多数感兴趣的情况下，该算法收敛在所需的限制在第一步的概率很高。我们还获得了性能界的基础上的对偶制定的原始问题。
The increasing popularity of applications involving group communications in wireless networks has led to the need for efficient multicasting solutions. The ability of smart antennas to beamform and hence improve the signal quality at the clients has made them especially attractive for multicasting applications. Unfortunately, the problem of multicast beamforming design is a non-convex optimization problem for which only suboptimal solutions has been proposed in the literature. In this work, we uncover a hidden convexity of the problem under certain channel conditions which happens frequently for practical systems with Rayleigh fading channel model. We propose a solution based on this observation which consists of two steps: (1) we solve the dual problem and check for a uniqueness condition; if satisfied, we show that the duality gap is zero and the solution of the primal problem is obtained based on the solution of the dual problem; (2) if the uniqueness condition is not satisfied, we use a gradient descent based approach. Our evaluations reveal that the proposed algorithm significantly improves the multicast performance over state-of-the-art solutions. Simulation results show that in most scenarios of interest the algorithm converges within a required limit in the first step with high probability. We also obtain the performance bounds for the primal problem based on the dual formulation.