Low-complexity Multicast Beamforming for Multi-stream Multi-group Communications
Hamidreza Bakhshzad Mahmoodi, Bikshapathi Gouda, MohammadJavad Salehi, and Antti Tolli

TL;DR
This paper introduces a low-complexity, closed-form multicast beamforming method for multi-stream multi-group communications, significantly improving computational efficiency and convergence speed over existing solutions.
Contribution
It develops a convex approximation and a closed-form solution for multi-stream multicast beamforming, avoiding generic solvers and bisection loops, thus enhancing efficiency.
Findings
Outperforms state-of-the-art in computational cost
Achieves faster convergence
Provides a practical closed-form solution
Abstract
In this paper, assuming multi-antenna transmitter and receivers, we consider multicast beamformer design for the weighted max-min-fairness (WMMF) problem in a multi-stream multi-group communication setup. Unlike the single-stream scenario, the WMMF objective in this setup is not equivalent to maximizing the minimum weighted SINR due to the summation over the rates of multiple streams. Therefore, the non-convex problem at hand is first approximated with a convex one and then solved using Karush-Kuhn-Tucker (KKT) conditions. Then, a practically appealing closed-form solution is derived, as a function of dual variables, for both transmit and receive beamformers. Finally, we use an iterative solution based on the sub-gradient method to solve for the mutually coupled and interdependent dual variables. The proposed solution does not rely on generic solvers and does not require any bisection…
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