# Reducing the Computational Complexity of Multicasting in Large-Scale Antenna Systems

## TL;DR

This paper introduces new low-complexity algorithms for physical layer multicasting in large-scale antenna systems, significantly improving computational efficiency and performance over traditional SDR-based methods.

## Contribution

The paper proposes two novel classes of algorithms that reduce computational complexity and outperform existing SDR-based solutions for multicasting in large-scale antenna systems.

## Key findings

- Proposed algorithms have lower computational complexity than SDR.
- Algorithms outperform SDR in large-scale scenarios.
- Duality between QoS and MMF problems is explicitly established.

## Abstract

In this paper, we study the physical layer multicasting to multiple co-channel groups in large-scale antenna systems. The users within each group are interested in a common message and different groups have distinct messages. In particular, we aim at designing the precoding vectors solving the so-called quality of service (QoS) and weighted max-min fairness (MMF) problems, assuming that the channel state information is available at the base station (BS). To solve both problems, the baseline approach exploits the semidefinite relaxation (SDR) technique. Considering a BS with $N$ antennas, the SDR complexity is more than $\mathcal{O}(N^{6})$, which prevents its application in large-scale antenna systems. To overcome this issue, we present two new classes of algorithms that, not only have significantly lower computational complexity than existing solutions, but also largely outperform the SDR based methods. Moreover, we present a novel duality between transformed versions of the QoS and the weighted MMF problems. The duality explicitly determines the solution to the weighted MMF problem given the solution to the QoS problem, and vice versa. Numerical results are used to validate the effectiveness of the proposed solutions and to make comparisons with existing alternatives under different operating conditions.