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

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 (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{S}}$</tex-math></inline-formula>) transmits a common message to two single-antenna users <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{U}}_{1}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{U}}_{2}$</tex-math></inline-formula>. We aim to maximize the minimum rate among these two users, by jointly optimizing the transmit beamforming and antenna positions at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{S}}$</tex-math></inline-formula>. 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{S}}$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{U}}_{1}$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{S}}$</tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathrm{{U}}_{2}$</tex-math></inline-formula> 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.