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Capacity Maximization for FAS-assisted Multiple Access Channels

Hao Xu, Kai-Kit Wong, Wee Kiat New, Farshad Rostami Ghadi, Gui Zhou, Ross Murch, Chan-Byoung Chae, Yongxu Zhu, Shi Jin

TL;DR

The paper tackles capacity maximization in a mmWave multiuser uplink where each user employs a fluid antenna system (FAS) while the base station uses fixed antennas. It develops upper bounds and large-antenna approximations to illuminate the problem and then proposes practical optimization frameworks in both single-antenna and multi-antenna FAS regimes, including alternating optimization, rank-one reformulations, and penalty-based DC methods. The results show that FAS can dramatically boost sum capacity in MAC settings, with the proposed algorithms outperforming fixed-antenna benchmarks and aligning closely with the derived bounds in favorable regimes. This work highlights the potential of FAS to introduce new degrees of freedom for uplink capacity in mmWave systems and lays groundwork for broader FAS-enabled network design.

Abstract

This paper investigates a multiuser millimeter-wave (mmWave) uplink system in which each user is equipped with a multi-antenna fluid antenna system (FAS) while the base station (BS) has multiple fixed-position antennas. Our primary objective is to maximize the system capacity by optimizing the transmit covariance matrices and the antenna position vectors of the users jointly. To gain insights, we start by deriving upper bounds and approximations for the capacity. Then we delve into the capacity maximization problem. Beginning with the simple scenario of a single user equipped with a single-antenna FAS, we demonstrate that a closed-form optimal solution exists when there are only two propagation paths between the user and the BS. In the case where multiple propagation paths are present, a near-optimal solution can also be obtained through a one-dimensional search method. Expanding our focus to multiuser cases, in which users are equipped with either single- or multi-antenna FAS, we show that the original capacity maximization problems can be reformulated into distinct rank-one programmings. Then, we propose alternating optimization algorithms to deal with the transformed problems. Simulation results indicate that FAS can improve the capacity of the multiple access channel (MAC) greatly, and the proposed algorithms outperform all the benchmarks.

Capacity Maximization for FAS-assisted Multiple Access Channels

TL;DR

The paper tackles capacity maximization in a mmWave multiuser uplink where each user employs a fluid antenna system (FAS) while the base station uses fixed antennas. It develops upper bounds and large-antenna approximations to illuminate the problem and then proposes practical optimization frameworks in both single-antenna and multi-antenna FAS regimes, including alternating optimization, rank-one reformulations, and penalty-based DC methods. The results show that FAS can dramatically boost sum capacity in MAC settings, with the proposed algorithms outperforming fixed-antenna benchmarks and aligning closely with the derived bounds in favorable regimes. This work highlights the potential of FAS to introduce new degrees of freedom for uplink capacity in mmWave systems and lays groundwork for broader FAS-enabled network design.

Abstract

This paper investigates a multiuser millimeter-wave (mmWave) uplink system in which each user is equipped with a multi-antenna fluid antenna system (FAS) while the base station (BS) has multiple fixed-position antennas. Our primary objective is to maximize the system capacity by optimizing the transmit covariance matrices and the antenna position vectors of the users jointly. To gain insights, we start by deriving upper bounds and approximations for the capacity. Then we delve into the capacity maximization problem. Beginning with the simple scenario of a single user equipped with a single-antenna FAS, we demonstrate that a closed-form optimal solution exists when there are only two propagation paths between the user and the BS. In the case where multiple propagation paths are present, a near-optimal solution can also be obtained through a one-dimensional search method. Expanding our focus to multiuser cases, in which users are equipped with either single- or multi-antenna FAS, we show that the original capacity maximization problems can be reformulated into distinct rank-one programmings. Then, we propose alternating optimization algorithms to deal with the transformed problems. Simulation results indicate that FAS can improve the capacity of the multiple access channel (MAC) greatly, and the proposed algorithms outperform all the benchmarks.
Paper Structure (37 sections, 7 theorems, 110 equations, 8 figures, 1 table, 4 algorithms)

This paper contains 37 sections, 7 theorems, 110 equations, 8 figures, 1 table, 4 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Signal Model
  4. Channel Model
  5. Problem Formulation
  6. Upper Bound and Approximation
  7. Single-Antenna FAS
  8. Single-User Case
  9. Two Paths
  10. Multiple Paths
  11. Multiuser Case
  12. Alternative Optimization
  13. Joint Optimization
  14. Convergence and Complexity Analysis
  15. Convergence Analysis
  16. ...and 22 more sections

Key Result

Theorem 1

The sum capacity of the considered system is upper bounded by the optimal objective function value of the following convex problem: where ${\tilde{\bm Q}}_u \in {\mathbb C}^{L_u \times L_u}$, ${\tilde{\bm Q}}_{\cal U} = \{{\tilde{\bm Q}}_1, \dots, {\tilde{\bm Q}}_U\}$, and

Figures (8)

  • Figure 1: A FAS-assisted uplink MAC where the users have FAS for transmission but the BS uses multiple fixed-position antennas for reception.
  • Figure 2: Single-antenna FAS & Single-user: average capacity versus $M$ with $U=1$, $N=1$, ${\text{SNR}} =10$ dB, $W=10 \lambda$, and $L=5$.
  • Figure 3: Single-antenna FAS & Multiuser: average capacity versus $M$ with $U=2$, $N=1$, ${\text{SNR}}=10$ dB, $W=10 \lambda$, and $L=5$.
  • Figure 4: Single-antenna FAS & Multiuser: average capacity versus $L$ with $U=2$, $N=1$, ${\text{SNR}}=10$ dB, and $W=10 \lambda$.
  • Figure 5: Multi-antenna FAS & Single-user: average capacity versus $M$ with $U=1$, $N=4$, ${\text{SNR}}=10$ dB, $W=10 \lambda$, and $L=5$.
  • ...and 3 more figures

Theorems & Definitions (9)

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