In this paper, we propose an iterative algorithm to address the nonconvex multi-group multicast beamforming problem with quality-of-service constraints and per-antenna power constraints. We formulate a convex relaxation of the problem as a semidefinite program in a real Hilbert space, which allows us to approximate a point in the feasible set by iteratively applying a bounded perturbation resilient fixed-point mapping. Inspired by the superiorization methodology, we use this mapping as a basic algorithm, and we add in each iteration a small perturbation with the intent to reduce the objective value and the distance to nonconvex rank-constraint sets. We prove that the sequence of perturbations is bounded, so the algorithm is guaranteed to converge to a feasible point of the relaxed semidefinite program. Simulations show that the proposed approach outperforms existing algorithms in terms of both computation time and approximation gap in many cases.

中文翻译：

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通过凸集上的高级投影进行多组组播波束成形


在本文中，我们提出了一种迭代算法来解决具有服务质量约束和每天线功率约束的非凸多组多播波束成形问题。我们将问题的凸松弛公式化为真实希尔伯特空间中的半定程序，这使我们能够通过迭代应用有界扰动弹性定点映射来逼近可行集中的点。受优越化方法的启发，我们使用这种映射作为基本算法，并在每次迭代中添加一个小扰动，旨在减少目标值和与非凸秩约束集的距离。我们证明扰动序列是有界的，因此保证算法收敛到松弛半定规划的可行点。仿真表明，在许多情况下，所提出的方法在计算时间和近似间隙方面都优于现有算法。