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Movable Antenna Enhanced AF Relaying: Two-Stage Antenna Position Optimization

Nianzu Li, Weidong Mei, Boyu Ning, Peiran Wu

TL;DR

This work addresses maximizing the end-to-end rate of a two-stage movable-antenna (MA) enhanced AF relay by jointly optimizing the relay weight matrix $\mathbf{W}$ and the MA positions $\tilde{\mathbf{r}}$, $\tilde{\mathbf{t}}$ in two stages. It develops an alternating-optimization framework that decouples the problem into subproblems, solving $\mathbf{W}$ via semidefinite relaxation (SDR) with a Charnes-Cooper reformulation (Proposition 1 guarantees a rank-1 solution) and updating MA positions with gradient ascent-based GA in each stage. The main contributions include (i) a new formulation (P1) for MA-enhanced AF relaying with two-stage positioning, (ii) a tight SDR-based solution for the relay beamformer, (iii) a gradient-ascent GA approach for MA placements, and (iv) convergence guarantees for the AO procedure and insights from simulations showing significant gains over fixed-position relays, with OTPA occasionally offering near-optimal performance. Overall, the proposed framework demonstrates substantial rate improvements and provides practical guidance on MA placement in relay systems.

Abstract

The movable antenna (MA) technology has attracted increasing attention in wireless communications due to its capability for flexibly adjusting the positions of multiple antennas in a local region to reconfigure channel conditions. In this paper, we investigate its application in an amplify-and-forward (AF) relay system, where a multi-MA AF relay is deployed to assist in the wireless communications from a source to a destination. In particular, we aim to maximize the achievable rate at the destination, by jointly optimizing the AF weight matrix at the relay and its MAs' positions in two stages for receiving the signal from the source and transmitting its amplified version to the destination, respectively. However, compared to the existing one-stage antenna position optimization, the two-stage position optimization is more challenging due to its intricate coupling in the achievable rate at the destination. To tackle this challenge, we decompose the considered problem into several subproblems by invoking the alternating optimization (AO) and solve them by using the semidefinite programming and the gradient ascent. Numerical results demonstrate the superiority of our proposed system over the conventional relaying system with fixed-position antennas (FPAs) and also drive essential insights.

Movable Antenna Enhanced AF Relaying: Two-Stage Antenna Position Optimization

TL;DR

This work addresses maximizing the end-to-end rate of a two-stage movable-antenna (MA) enhanced AF relay by jointly optimizing the relay weight matrix and the MA positions , in two stages. It develops an alternating-optimization framework that decouples the problem into subproblems, solving via semidefinite relaxation (SDR) with a Charnes-Cooper reformulation (Proposition 1 guarantees a rank-1 solution) and updating MA positions with gradient ascent-based GA in each stage. The main contributions include (i) a new formulation (P1) for MA-enhanced AF relaying with two-stage positioning, (ii) a tight SDR-based solution for the relay beamformer, (iii) a gradient-ascent GA approach for MA placements, and (iv) convergence guarantees for the AO procedure and insights from simulations showing significant gains over fixed-position relays, with OTPA occasionally offering near-optimal performance. Overall, the proposed framework demonstrates substantial rate improvements and provides practical guidance on MA placement in relay systems.

Abstract

The movable antenna (MA) technology has attracted increasing attention in wireless communications due to its capability for flexibly adjusting the positions of multiple antennas in a local region to reconfigure channel conditions. In this paper, we investigate its application in an amplify-and-forward (AF) relay system, where a multi-MA AF relay is deployed to assist in the wireless communications from a source to a destination. In particular, we aim to maximize the achievable rate at the destination, by jointly optimizing the AF weight matrix at the relay and its MAs' positions in two stages for receiving the signal from the source and transmitting its amplified version to the destination, respectively. However, compared to the existing one-stage antenna position optimization, the two-stage position optimization is more challenging due to its intricate coupling in the achievable rate at the destination. To tackle this challenge, we decompose the considered problem into several subproblems by invoking the alternating optimization (AO) and solve them by using the semidefinite programming and the gradient ascent. Numerical results demonstrate the superiority of our proposed system over the conventional relaying system with fixed-position antennas (FPAs) and also drive essential insights.
Paper Structure (10 sections, 31 equations, 7 figures, 2 algorithms)

This paper contains 10 sections, 31 equations, 7 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Proposed Solution for (P1)
  4. Optimizing $\mathbf{W}$ with Given $\{\mathbf{r}_n\}$ and $\{\mathbf{t}_n\}$
  5. Optimizing $\{\mathbf{r}_n\}_{n=1}^N$ with Given $\mathbf{W}$ and $\{\mathbf{t}_n\}$
  6. Optimizing $\{\mathbf{t}_n\}_{n=1}^N$ with Given $\mathbf{W}$ and $\{\mathbf{r}_n\}$
  7. Overall Algorithm
  8. Simulation Results
  9. Conclusion
  10. Proof of Proposition 1

Figures (7)

  • Figure 1: MA-enhanced AF relay system.
  • Figure 2: Convergence plot of our proposed AO algorithm.
  • Figure 3: Optimized positions of the MAs at the relay.
  • Figure 4: Achievable rates versus the relay power budget.
  • Figure 5: Achievable rates versus the number of antennas.
  • ...and 2 more figures