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RIS-assisted Cell-Free Massive MIMO Systems With Two-Timescale Design and Hardware Impairments

Jianxin Dai, Jin Ge, Kangda Zhi, Cunhua Pan, Youguo Wang

TL;DR

The paper addresses capacity limits in RIS-assisted CF-mMIMO under transceiver hardware impairments and RIS phase noise. It develops a two-timescale design, deriving a closed-form approximate uplink rate with MRC detection and providing power-scaling insights under HWIs. An accelerated gradient ascent method is proposed to optimize RIS phase shifts, yielding improvements in both sum rate and user fairness. Numerical results confirm the theoretical insights, showing that imperfect RISs can still provide substantial gains and offering practical guidelines for deployment and energy efficiency.

Abstract

Integrating the reconfigurable intelligent surface (RIS) into a cell-free massive multiple-input multiple-output (CF-mMIMO) system is an effective solution to achieve high system capacity with low cost and power consumption. However, existing works of RIS-assisted systems mostly assumed perfect hardware, while the impact of hardware impairments (HWIs) is generally ignored. In this paper, we consider the general Rician fading channel and uplink transmission of the RIS-assisted CF-mMIMO system under transceiver impairments and RIS phase noise. To reduce the feedback overhead and power consumption, we propose a two-timescale transmission scheme to optimize the passive beamformers at RISs with statistical channel state information (CSI), while transmit beamformers at access points (APs) are designed based on instantaneous CSI. Also, the maximum ratio combining (MRC) detection is applied to the central processing unit (CPU). On this basis, we derive the closed-form approximate expression of the achievable rate, based on which the impact of HWIs and the power scaling laws are analyzed to draw useful theoretical insights. To maximize the users' sum rate or minimum rate, we first transform our rate expression into a tractable form, and then optimize the phase shifts of RISs based on an accelerated gradient ascent method. Finally, numerical results are presented to demonstrate the correctness of our derived expressions and validate the previous analysis, which provide some guidelines for the practical application of the imperfect RISs in the CF-mMIMO with transceiver HWIs.

RIS-assisted Cell-Free Massive MIMO Systems With Two-Timescale Design and Hardware Impairments

TL;DR

The paper addresses capacity limits in RIS-assisted CF-mMIMO under transceiver hardware impairments and RIS phase noise. It develops a two-timescale design, deriving a closed-form approximate uplink rate with MRC detection and providing power-scaling insights under HWIs. An accelerated gradient ascent method is proposed to optimize RIS phase shifts, yielding improvements in both sum rate and user fairness. Numerical results confirm the theoretical insights, showing that imperfect RISs can still provide substantial gains and offering practical guidelines for deployment and energy efficiency.

Abstract

Integrating the reconfigurable intelligent surface (RIS) into a cell-free massive multiple-input multiple-output (CF-mMIMO) system is an effective solution to achieve high system capacity with low cost and power consumption. However, existing works of RIS-assisted systems mostly assumed perfect hardware, while the impact of hardware impairments (HWIs) is generally ignored. In this paper, we consider the general Rician fading channel and uplink transmission of the RIS-assisted CF-mMIMO system under transceiver impairments and RIS phase noise. To reduce the feedback overhead and power consumption, we propose a two-timescale transmission scheme to optimize the passive beamformers at RISs with statistical channel state information (CSI), while transmit beamformers at access points (APs) are designed based on instantaneous CSI. Also, the maximum ratio combining (MRC) detection is applied to the central processing unit (CPU). On this basis, we derive the closed-form approximate expression of the achievable rate, based on which the impact of HWIs and the power scaling laws are analyzed to draw useful theoretical insights. To maximize the users' sum rate or minimum rate, we first transform our rate expression into a tractable form, and then optimize the phase shifts of RISs based on an accelerated gradient ascent method. Finally, numerical results are presented to demonstrate the correctness of our derived expressions and validate the previous analysis, which provide some guidelines for the practical application of the imperfect RISs in the CF-mMIMO with transceiver HWIs.
Paper Structure (15 sections, 6 theorems, 102 equations, 11 figures, 1 table)

This paper contains 15 sections, 6 theorems, 102 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Model
  4. Uplink Transmission
  5. Uplink Achievable Rate Analysis
  6. Phase Shifts Design
  7. Numerical Results
  8. The Balance between System Capacity and User Fairness
  9. The Interplay between RISs and CF-mMIMO in the Presence of HWIs
  10. The Impact of HWIs
  11. The Power Scaling Laws
  12. Conclusion
  13. Derivations of $\mathbb{E}\left\{\left\|{\bf q}_k\right\|^{2}\right\}$
  14. Derivations of $\mathbb{E}\left\{\left|{{\bf q}_k^{H}\widehat{\bf q}_k}\right|^{2} \right\}$ and $\mathbb{E}\left\{\left|{{\bf q}_k^{H}\widehat{\bf q}_i}\right|^{2} \right\}$
  15. Derivations of $\mathbb{E}\left\{\left|{\mathbf{q}}_{k}^{H}\widehat{\mathbf{q}}_{i}{\mathbb{\eta}}_{\it i,t}\right|^{2}\right\}$ and $\mathbb{E}\left\{\left|{\mathbf{q}}_{k}^{H}{\bm{\eta}}_{\it r}\right|^{2}\right\}$

Key Result

Theorem 1

Based on (rek), the closed-form approximate expression of the achievable rate for user $k$ is given by where ${E}_{k}^{(\mathrm{signal})}({\bf\Phi})$ = $\mathbb{E}\{\left|{{\bf q}}_k^{H} \widehat{\mathbf{q}}_k\right|^{2}\}$, $E_{k}^{(\mathrm{noise})}({\bf\Phi})$ = $\mathbb{E}\{\left\|{\bf q}_k\right\|^{2}\}$, $E_{k}^{(\mathrm{hwi})}({\bf\Phi})=\mathbb{E}\{\sum\limits_{i=1}^{K}\left|{\mathbf{q}}_{

Figures (11)

  • Figure 1: The RIS-assisted CF-mMIMO system under uplink transmission.
  • Figure 2: The simulation scenario of the RIS-assisted CF-mMIMO system.
  • Figure 3: Desired signal power, inter-user interference power, noise power and HWI power for user $k$ under random channel realizations.
  • Figure 4: The rate performance versus the Rician factor of RISs-APs channels.
  • Figure 5: Achievable rate versus transmit power $P$.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Corollary 3
  • Corollary 4
  • Corollary 5