4
0这份文本资料深入探讨了多组多播波束成形的复杂挑战，特别是针对广义效用函数的优化问题。作者分析了最优波束成形结构，并揭示了在不同信噪比和天线数量下渐近最优的低维波束成形形式。在此基础上，文章提出了一种名为SCA-HFPI的高效算法，该算法通过逐次凸近似（SCA）框架和超平面不动点迭代（HFPI）来解决非光滑非凸问题，显著降低了计算复杂度，使其特别适用于6G超大规模MIMO应用。研究结果表明，这些新算法在保持或提升性能的同时，极大地减少了计算时间。
Optimal Beamforming Structure and Efficient Optimization Algorithms for Generalized Multi-Group Multicast Beamforming Optimization
Abstract:
In this work, we focus on solving non-smooth non-convex maximization problems in multi-group multicast transmission. By leveraging Karush-Kuhn-Tucker (KKT) optimality conditions, we thoroughly analyze the optimal beamforming structure for a set of optimization problems characterized by a general utility-based objective function. By exploiting the identified optimal structure, we further unveil inherent low-dimensional beamforming structures within the problems, which are asymptotically optimal in various regimes of transmit signal-to-noise ratios (SNRs) or the number of transmit antennas. Building upon the discovered optimal and low-dimensional beamforming structures, we then propose highly efficient optimization algorithms to solve a specific multi-group multicast optimization problem based on the weighted power mean (WPM) utility function. The proposed algorithms first use the successive convex approximation (SCA) framework to decompose the problem into a sequence of convex subproblems, each with an optimal closed-form beamforming solution structure. Then, we propose a hyperplane fixed point iteration (HFPI) algorithm to compute the optimal Lagrangian dual variables for each subproblem. Numerical results show that the proposed algorithms maintain comparable or improved utility performance compared to baseline algorithms, while dramatically reducing the computational complexity. Notably, the proposed ultra-low-complexity algorithms based on low-dimensional beamforming structures achieve near optimal utility performance with extremely low computational complexity. This complexity remains independent of the number of transmit antennas, making them promising and practical for extremely large multiple-input multiple-output (XL-MIMO) applications in 6G.
Published in: IEEE Transactions on Signal Processing ( Volume: 73)
Page(s): 2719 - 2735
Date of Publication: 25 June 2025
ISSN Information:
Print ISSN: 1053-587X
Electronic ISSN: 1941-0476
Publisher: IEEE
Funding Agency:
10.13039/501100001809-National Nature Science Foundation of China (Grant Number: 62201347)
