论文标题
具有结构上最佳的多组多播在大规模系统中的超低复杂算法
Ultra-Low-Complexity Algorithms with Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems
论文作者
论文摘要
在这项工作中，我们提出了用于大规模系统中多播多播的超低复杂设计解决方案。对于服务质量（QoS）问题，通过使用最近在[2]中获得的最佳多播束式结构，我们将原始问题转换为较低尺寸的非凸vex权重优化问题，并提出了两种快速的一阶算法来求解它。两种算法均基于连续的凸近似（SCA），并提供快速的迭代更新以求解每个SCA子问题。第一种算法在双域中使用鞍点重新构造，并使用自适应阶梯尺寸的过程应用外部方法，以使用简单的闭合形式更新来查找鞍点。第二算法通过将每个SCA子问题转换为有利的ADMM结构，采用了乘数（ADMM）方法的交替方向方法。该结构导致简单的封闭形式的ADMM更新，其中每个更新块中的问题可以进一步分解为小尺寸的平行子问题，为此获得了封闭形式的解决方案。我们还提出了有效的初始化方法，以获得有利的初始点，以促进快速收敛。此外，利用提出的快速算法，对于最大的Min Fair（MMF）问题，我们提出了一种简单的封闭形式缩放方案，该方案直接使用从QoS问题中获得的解决方案，避免了传统的计算昂贵的方法，以迭代迭代地求解了倒数QoS问题。我们进一步发展了该缩放方案性能的上限和上限。仿真结果表明，所提出的算法提供了几乎最佳的性能，其计算复杂性大大低于大规模系统的最新算法。
In this work, we propose ultra-low-complexity design solutions for multi-group multicast beamforming in large-scale systems. For the quality-of-service (QoS) problem, by utilizing the optimal multicast beamforming structure obtained recently in [2], we convert the original problem into a non-convex weight optimization problem of a lower dimension and propose two fast first-order algorithms to solve it. Both algorithms are based on successive convex approximation (SCA) and provide fast iterative updates to solve each SCA subproblem. The first algorithm uses a saddle point reformulation in the dual domain and applies the extragradient method with an adaptive step-size procedure to find the saddle point with simple closed-form updates. The second algorithm adopts the alternating direction method of multipliers (ADMM) method by converting each SCA subproblem into a favorable ADMM structure. The structure leads to simple closed-form ADMM updates, where the problem in each update block can be further decomposed into parallel subproblems of small sizes, for which closed-form solutions are obtained. We also propose efficient initialization methods to obtain favorable initial points that facilitate fast convergence. Furthermore, taking advantage of the proposed fast algorithms, for the max-min fair (MMF) problem, we propose a simple closed-form scaling scheme that directly uses the solution obtained from the QoS problem, avoiding the conventional computationally expensive method that iteratively solves the inverse QoS problem. We further develop lower and upper bounds on the performance of this scaling scheme. Simulation results show that the proposed algorithms offer near-optimal performance with substantially lower computational complexity than the state-of-the-art algorithms for large-scale systems.
