Ultra-Low-Complexity Algorithms with Structurally Optimal Multi-Group Multicast Beamforming in Large-Scale Systems

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 optimal structure obtained recently [2], convert original problem into a non-convex weight optimization of lower dimension and two fast first-order algorithms to solve it. Both are based on successive convex approximation (SCA) provide iterative updates each SCA subproblem. The first algorithm uses saddle point reformulation dual domain applies extragradient method with an adaptive step-size procedure find simple closed-form updates. second adopts alternating direction multipliers (ADMM) converting subproblem favorable ADMM structure. leads updates, where update block can be further decomposed parallel subproblems small sizes, which obtained. We also efficient initialization methods obtain initial points that facilitate convergence. Furthermore, taking advantage proposed algorithms, max-min fair (MMF) scaling scheme directly solution from QoS avoiding conventional computationally expensive iteratively solves inverse problem. develop upper bounds performance scheme. Simulation results show offer near-optimal substantially computational complexity than state-of-the-art