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IRS-Aided Overloaded Multi-Antenna Systems: Joint User Grouping and Resource Allocation

Ying Gao, Qingqing Wu, Wen Chen, Yang Liu, Ming Li, Daniel Benevides da Costa

TL;DR

This paper studies an IRS-aided overloaded multi-antenna SWIPT downlink under phase errors, proposing two UG schemes (non-overlapping and overlapping) to manage overload by dividing IUs into groups served in orthogonal time slots. It jointly optimizes time allocation, AP transmit precoding, and IRS phase shifts to maximize the minimum IU throughput while guaranteeing EU energy harvesting, incorporating robust design to account for phase uncertainties. Efficient suboptimal algorithms based on big-M, penalty methods, block coordinate descent, and successive convex approximation are developed; a feasibility test guides applicability, and overlapping UG is shown to offer significant gains in suitable regimes. Simulation results confirm the importance of robustness, demonstrate UG advantages over benchmarks, and reveal when overlapping UG outperforms non-overlapping UG, especially for moderate $|K-M|$ and loose EH constraints.

Abstract

This paper studies an intelligent reflecting surface (IRS)-aided multi-antenna simultaneous wireless information and power transfer (SWIPT) system where an $M$-antenna access point (AP) serves $K$ single-antenna information users (IUs) and $J$ single-antenna energy users (EUs) with the aid of an IRS with phase errors. We explicitly concentrate on overloaded scenarios where $K + J > M$ and $K \geq M$. Our goal is to maximize the minimum throughput among all the IUs by optimizing the allocation of resources (including time, transmit beamforming at the AP, and reflect beamforming at the IRS), while guaranteeing the minimum amount of harvested energy at each EU. Towards this goal, we propose two user grouping (UG) schemes, namely, the non-overlapping UG scheme and the overlapping UG scheme, where the difference lies in whether identical IUs can exist in multiple groups. Different IU groups are served in orthogonal time dimensions, while the IUs in the same group are served simultaneously with all the EUs via spatial multiplexing. The two problems corresponding to the two UG schemes are mixed-integer non-convex optimization problems and difficult to solve optimally. We propose efficient algorithms for these two problems based on the big-M formulation, the penalty method, the block coordinate descent, and the successive convex approximation. Simulation results show that: 1) the non-robust counterparts of the proposed robust designs are unsuitable for practical IRS-aided SWIPT systems with phase errors since the energy harvesting constraints cannot be satisfied; 2) the proposed UG strategies can significantly improve the max-min throughput over the benchmark schemes without UG or adopting random UG; 3) the overlapping UG scheme performs much better than its non-overlapping counterpart when the absolute difference between $K$ and $M$ is small and the EH constraints are not stringent.

IRS-Aided Overloaded Multi-Antenna Systems: Joint User Grouping and Resource Allocation

TL;DR

This paper studies an IRS-aided overloaded multi-antenna SWIPT downlink under phase errors, proposing two UG schemes (non-overlapping and overlapping) to manage overload by dividing IUs into groups served in orthogonal time slots. It jointly optimizes time allocation, AP transmit precoding, and IRS phase shifts to maximize the minimum IU throughput while guaranteeing EU energy harvesting, incorporating robust design to account for phase uncertainties. Efficient suboptimal algorithms based on big-M, penalty methods, block coordinate descent, and successive convex approximation are developed; a feasibility test guides applicability, and overlapping UG is shown to offer significant gains in suitable regimes. Simulation results confirm the importance of robustness, demonstrate UG advantages over benchmarks, and reveal when overlapping UG outperforms non-overlapping UG, especially for moderate and loose EH constraints.

Abstract

This paper studies an intelligent reflecting surface (IRS)-aided multi-antenna simultaneous wireless information and power transfer (SWIPT) system where an -antenna access point (AP) serves single-antenna information users (IUs) and single-antenna energy users (EUs) with the aid of an IRS with phase errors. We explicitly concentrate on overloaded scenarios where and . Our goal is to maximize the minimum throughput among all the IUs by optimizing the allocation of resources (including time, transmit beamforming at the AP, and reflect beamforming at the IRS), while guaranteeing the minimum amount of harvested energy at each EU. Towards this goal, we propose two user grouping (UG) schemes, namely, the non-overlapping UG scheme and the overlapping UG scheme, where the difference lies in whether identical IUs can exist in multiple groups. Different IU groups are served in orthogonal time dimensions, while the IUs in the same group are served simultaneously with all the EUs via spatial multiplexing. The two problems corresponding to the two UG schemes are mixed-integer non-convex optimization problems and difficult to solve optimally. We propose efficient algorithms for these two problems based on the big-M formulation, the penalty method, the block coordinate descent, and the successive convex approximation. Simulation results show that: 1) the non-robust counterparts of the proposed robust designs are unsuitable for practical IRS-aided SWIPT systems with phase errors since the energy harvesting constraints cannot be satisfied; 2) the proposed UG strategies can significantly improve the max-min throughput over the benchmark schemes without UG or adopting random UG; 3) the overlapping UG scheme performs much better than its non-overlapping counterpart when the absolute difference between and is small and the EH constraints are not stringent.
Paper Structure (23 sections, 3 theorems, 39 equations, 9 figures, 2 algorithms)

This paper contains 23 sections, 3 theorems, 39 equations, 9 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Problem Formulation
  5. Feasibility Checking for (P1) and (P2)
  6. Optimizing $\left\lbrace \{\mathbf W_{\mathrm E,\ell}\}, \{\tau_\ell\} \right\rbrace$ for Given $\{\mathbf v_\ell\}$
  7. Optimizing $\{\mathbf v_\ell\}$ for Given $\left\lbrace \{\mathbf W_{\mathrm E,\ell}\},\{\tau_\ell\} \right\rbrace$
  8. Overall Algorithm
  9. Proposed Algorithm for (P1)
  10. Optimizing $\tilde{\mathcal{Z}}$ for Given $\{\mathbf v_{\ell}\}$
  11. Optimizing $\{\mathbf v_{\ell}\}$ for Given $\tilde{\mathcal{Z}}$
  12. Overall Algorithm
  13. Proposed Algorithm for (P2)
  14. Simulation Results
  15. Achievable Max-Min Harvested Energy
  16. ...and 8 more sections

Key Result

Theorem 1

The expectations of $\gamma_{k,\ell}$ and $Q_j$ are respectively given by where $\mathbf X_{k,\ell} = \mathbf H_k^H{\rm diag}\left(\mathbf v_\ell\right)\mathbf Z{\rm diag}\left(\mathbf v_{\ell}^H\right)\mathbf H_k$, $\mathbf Y_{j,\ell} = \mathbf G_j^H{\rm diag}\left(\mathbf v_\ell\right)\mathbf Z{\rm diag}\left(\mathbf v_{\ell}^H\right)\mathbf G_j$, and

Figures (9)

  • Figure 1: Illustration of an IRS-aided SWIPT system with different UG strategies: (a) Non-overlapping UG; (b) Overlapping UG.
  • Figure 2: Illustration of the transmission protocol.
  • Figure 3: Simulation setup. The AP, IRS elements, EUs, and IUs are marked by orange '$\blacklozenge$', green '$\blacksquare$'s, red '$\bullet$'s, and blue '$\blacktriangle$'s, respectively.
  • Figure 4: Average max-min harvested energy versus the number of EUs for $L = 5$.
  • Figure 5: Average max-min throughput versus the number of IUs for $J = 8$ and $L = 3$.
  • ...and 4 more figures

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Remark 1
  • Theorem 2
  • proof