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Movable-Antenna Position Optimization: A Graph-based Approach

Weidong Mei, Xin Wei, Boyu Ning, Zhi Chen, Rui Zhang

TL;DR

This work addresses maximizing received power in an MA-enhanced MISO system by optimizing discrete MA positions within a discretized transmit region. It reformulates the discrete point-selection as a fixed-hop shortest-path problem on a DAG and solves it with a polynomial-time graph-based algorithm, complemented by a linear-time suboptimal sequential update for reduced complexity. The proposed methods yield significant gains over conventional fixed-position antennas with and without antenna selection, and insights into the optimal MA placement along the array are provided. The framework lays groundwork for efficient MA deployment and can be extended to more general multi-user or MIMO settings in the future.

Abstract

Fluid antennas (FAs) and movable antennas (MAs) have emerged as promising technologies in wireless communications, which offer the flexibility to improve channel conditions by adjusting transmit/receive antenna positions within a spatial region. In this letter, we focus on an MA-enhanced multiple-input single-output (MISO) communication system, aiming to optimize the positions of multiple transmit MAs to maximize the received signal power. Unlike the prior works on continuously searching for the optimal MA positions, we propose to sample the transmit region into discrete points, such that the continuous antenna position optimization problem is transformed to a discrete sampling point selection problem based on the point-wise channel information. However, such a point selection problem is combinatory and challenging to be optimally solved. To tackle this challenge, we ingeniously recast it as an equivalent fixed-hop shortest path problem in graph theory and propose a customized algorithm to solve it optimally in polynomial time. To further reduce the complexity, a linear-time sequential update algorithm is also proposed to obtain a high-quality suboptimal solution. Numerical results demonstrate that the proposed algorithms can yield considerable performance gains over the conventional fixed-position antennas with/without antenna selection.

Movable-Antenna Position Optimization: A Graph-based Approach

TL;DR

This work addresses maximizing received power in an MA-enhanced MISO system by optimizing discrete MA positions within a discretized transmit region. It reformulates the discrete point-selection as a fixed-hop shortest-path problem on a DAG and solves it with a polynomial-time graph-based algorithm, complemented by a linear-time suboptimal sequential update for reduced complexity. The proposed methods yield significant gains over conventional fixed-position antennas with and without antenna selection, and insights into the optimal MA placement along the array are provided. The framework lays groundwork for efficient MA deployment and can be extended to more general multi-user or MIMO settings in the future.

Abstract

Fluid antennas (FAs) and movable antennas (MAs) have emerged as promising technologies in wireless communications, which offer the flexibility to improve channel conditions by adjusting transmit/receive antenna positions within a spatial region. In this letter, we focus on an MA-enhanced multiple-input single-output (MISO) communication system, aiming to optimize the positions of multiple transmit MAs to maximize the received signal power. Unlike the prior works on continuously searching for the optimal MA positions, we propose to sample the transmit region into discrete points, such that the continuous antenna position optimization problem is transformed to a discrete sampling point selection problem based on the point-wise channel information. However, such a point selection problem is combinatory and challenging to be optimally solved. To tackle this challenge, we ingeniously recast it as an equivalent fixed-hop shortest path problem in graph theory and propose a customized algorithm to solve it optimally in polynomial time. To further reduce the complexity, a linear-time sequential update algorithm is also proposed to obtain a high-quality suboptimal solution. Numerical results demonstrate that the proposed algorithms can yield considerable performance gains over the conventional fixed-position antennas with/without antenna selection.
Paper Structure (9 sections, 1 theorem, 9 equations, 6 figures, 1 algorithm)

This paper contains 9 sections, 1 theorem, 9 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Problem Formulation
  5. Proposed Algorithms for (P1)
  6. Optimal Solution by Graph Optimization
  7. Suboptimal Solution by Sequential Update
  8. Numerical Results
  9. Conclusion

Key Result

Lemma 1

Denote by $p^k(0,i)$ the $k$-hop shortest path from vertex 0 to another vertex $i, i \in \tilde{V}$. Then, if $k=0$, we have $p^k(0,i)=(0,i)$. If $(0,i)$ does not exist, we assume that there exists a virtual edge from vertex 0 to vertex $i$ with an infinite weight. For $k \ge 1$, let ${\cal N}_i=\{j

Figures (6)

  • Figure 1: MA-enhanced MISO communication system.
  • Figure 2: Received SNR versus the number of sampling points.
  • Figure 3: Optimized antenna positions in different schemes.
  • Figure 4: Received SNR versus the number of MAs.
  • Figure 5: Received SNR versus the length of transmit array.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Lemma 1: cheng2004finding