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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通过凸集上的优越投影进行多组多播波束成形

在本文中，我们提出了一种迭代算法来解决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表示为实际Hilbert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一个点。受高级方法的启发，我们将此映射用作基本算法，并在每次迭代中添加一个小的扰动，目的是减小目标值和到非凸秩约束集的距离。我们证明了扰动序列是有界的，因此可以保证算法收敛到松弛半定程序的可行点。