Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission
Nonsmooth Optimization for Efficient Beamforming in Cognitive Radio Multicast Transmission
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DOI：
10.1109/tsp.2012.2189857
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发表时间：
2012-06
影响因子：
5.4
通讯作者：
A. H. Phan;H. Tuan;H. H. Kha-H.;D. T. Ngo
中科院分区：
文献类型：
--
作者：
A. H. Phan;H. Tuan;H. H. Kha-H.;D. T. Ngo
已知认知无线电多播传输的最优发射波束形成向量的设计可以用不确定二次优化规划来表示。鉴于这些非凸问题的挑战，在文献中的传统方法是将它们转换为凸半定规划（SDP）与秩一约束。然后，这些非凸和不连续的约束被丢弃，允许实现一个池的放松的候选解决方案，从其中利用各种随机化技术，希望恢复最优解。然而，已经表明，这种方法在许多实际设置中未能提供令人满意的结果，其中发现所确定的解决方案与实际最优性相差甚远。相反，我们在这篇文章中通过将它们表示为具有额外的反向凸（但连续）约束的SDP来不同地处理上述最佳波束成形问题。非光滑优化算法，然后提出了一种有效的方式来定位这样的设计问题的最优解。我们彻底的数值例子验证，所提出的算法提供几乎全局最优，同时需要相对较低的计算负荷。
It is known that the design of optimal transmit beamforming vectors for cognitive radio multicast transmission can be formulated as indefinite quadratic optimization programs. Given the challenges of such nonconvex problems, the conventional approach in literature is to recast them as convex semidefinite programs (SDPs) together with rank-one constraints. Then, these nonconvex and discontinuous constraints are dropped allowing for the realization of a pool of relaxed candidate solutions, from which various randomization techniques are utilized with the hope to recover the optimal solutions. However, it has been shown that such approach fails to deliver satisfactory outcomes in many practical settings, wherein the determined solutions are found to be unacceptably far from the actual optimality. On the contrary, we in this contribution tackle the aforementioned optimal beamforming problems differently by representing them as SDPs with additional reverse convex (but continuous) constraints. Nonsmooth optimization algorithms are then proposed to locate the optimal solutions of such design problems in an efficient manner. Our thorough numerical examples verify that the proposed algorithms offer almost global optimality whilst requiring relatively low computational load.