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Antenna Elements' Trajectory Optimization for Throughput Maximization in Continuous-Trajectory Fluid Antenna-Aided Wireless Communications

Shuaixin Yang, Yijia Li, Yue Xiao, Yong Liang Guan, Kai-Kit Wong, Hyundong Shin, Chau Yuen

Abstract

Fluid antenna (FA) systems offer novel spatial degrees of freedom (DoFs) with the potential for significant performance gains. Compared to existing works focusing solely on optimizing FA positions at discrete time instants, we introduce the concept of continuous-trajectory fluid antenna (CTFA), which explicitly considers the antenna element's movement trajectory across continuous time intervals and incorporates the inherent kinematic constraints present in practical FA implementations. Accordingly, we formulate the total throughput maximization problem in CTFA-aided wireless communication systems, addressing the joint optimization of continuous antenna trajectories in conjunction with the transmit covariance matrices under kinematic constraints. To effectively solve this non-convex problem with highly coupled optimization variables, we develop an iterative algorithm based on block coordinate descent (BCD) and majorization-minimization (MM) principles with the aid of the weighted minimum mean square error (WMMSE) method. Finally, numerical results are presented to validate the efficacy of the proposed algorithms and to quantify the substantial total throughput advantages afforded by the conceived CTFA-aided system compared to conventional fixed-position antenna (FPA) benchmarks and alternative approaches employing simplified trajectories.

Antenna Elements' Trajectory Optimization for Throughput Maximization in Continuous-Trajectory Fluid Antenna-Aided Wireless Communications

Abstract

Fluid antenna (FA) systems offer novel spatial degrees of freedom (DoFs) with the potential for significant performance gains. Compared to existing works focusing solely on optimizing FA positions at discrete time instants, we introduce the concept of continuous-trajectory fluid antenna (CTFA), which explicitly considers the antenna element's movement trajectory across continuous time intervals and incorporates the inherent kinematic constraints present in practical FA implementations. Accordingly, we formulate the total throughput maximization problem in CTFA-aided wireless communication systems, addressing the joint optimization of continuous antenna trajectories in conjunction with the transmit covariance matrices under kinematic constraints. To effectively solve this non-convex problem with highly coupled optimization variables, we develop an iterative algorithm based on block coordinate descent (BCD) and majorization-minimization (MM) principles with the aid of the weighted minimum mean square error (WMMSE) method. Finally, numerical results are presented to validate the efficacy of the proposed algorithms and to quantify the substantial total throughput advantages afforded by the conceived CTFA-aided system compared to conventional fixed-position antenna (FPA) benchmarks and alternative approaches employing simplified trajectories.

Paper Structure

This paper contains 20 sections, 5 theorems, 71 equations, 3 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Channel Model
  5. Kinematic Constraints
  6. Problem Formulation
  7. Proposed BCD-MM-Based Algorithm
  8. Problem Reformulation and Optimization
  9. Optimize ${\mathbf Q}_n$
  10. Optimize ${\mathbf U}_n$ and ${\mathbf W}_n$
  11. Optimize $\left\{{{\mathbf q}}_{t,n}^{k},{{\mathbf v}}_{t,n}^{k},{{\mathbf a}}_{t,n}^{k}\right\}_{n=0}^N$
  12. Optimize $\left\{{{\mathbf q}}_{r,n}^{l},{{\mathbf v}}_{r,n}^{l},{{\mathbf a}}_{r,n}^{l}\right\}_{n=0}^N$
  13. Overall Algorithm
  14. Simulation Results
  15. Conclusion
  16. ...and 5 more sections

Key Result

Lemma 1

Define an $m$ by $m$ matrix function where $\mathbf Z$ is any positive definite matrix. It holds true that

Figures (3)

  • Figure 1: System model of the point-to-point CTFA-enabled MIMO system.
  • Figure 2: Simulation results for the $2\times2$ CTFA system.
  • Figure 3: Simulation results for the $4\times4$ CTFA system.

Theorems & Definitions (9)

  • Lemma 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • proof