Movable Antennas-Enabled Two-User Multicasting: Do We Really Need Alternating Optimization for Minimum Rate Maximization?

TL;DR

This paper addresses a two-user downlink multicasting problem with movable antennas at the source, aiming to maximize the minimum user rate by jointly optimizing antenna positions and transmit beamforming. It proves that antenna positions and beamforming can be optimized separately: first, maximize the correlation between the S→U1 and S→U2 channels using a successive convex approximation (SCA) framework to find the optimal MA locations ${\bf x}$; then derive a closed-form beamforming solution conditioned on ${\bf x}$ and a scalar parameter $t$. The core contributions are (i) a correlation-driven method for MA-position optimization with a tractable surrogate and gradient, (ii) a scalar, low-complexity beamforming step that achieves the same performance as traditional alternating optimization (AO), and (iii) evidence from simulations that the proposed approach matches AO while reducing computational burden and offering new insights into MA-enabled channel reconfiguration. The work has practical implications for efficiently exploiting movable antennas in multicasting and suggests a broader optimization flow based on channel correlation in MA systems.

Abstract

Movable antenna (MA) technology, which can reconfigure wireless channels by flexibly moving antenna positions in a specified region, has great potential for improving communication performance. In this paper, we consider a new setup of MAs-enabled multicasting, where we adopt a simple setting in which a linear MA array-enabled source (${\rm{S}}$) transmits a common message to two single-antenna users ${\rm{U}}_1$ and ${\rm{U}}_2$. We aim to maximize the minimum rate among these two users, by jointly optimizing the transmit beamforming and antenna positions at ${\rm{S}}$. Instead of utilizing the widely-used alternating optimization (AO) approach, we reveal, with rigorous proof, that the above two variables can be optimized separately: i) the optimal antenna positions can be firstly determined via the successive convex approximation technique, based on the rule of maximizing the correlation between ${\rm{S}}$-${\rm{U}}_1$ and ${\rm{S}}$-${\rm{U}}_2$ channels; ii) afterwards, the optimal closed-form transmit beamforming can be derived via simple arguments. Compared to AO, this new approach yields the same performance but reduces the computational complexities significantly. Moreover, it can provide insightful conclusions which are not possible with AO.

Figures (2)

• Figure 1: Illustration of the system model.
• Figure 2: (a) Beam gain of four schemes at different AoDs, $N = 5$ and $L = 4$; (b) Minimum rate versus the number of antennas at $\rm{S}$ ($N$), $L = 5$; (c) Minimum rate versus the total span of movable antennas at $\rm{S}$ ($L$), $N= 5$.

Theorems & Definitions (2)

• proof
• proof