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Active RIS-Aided Massive MIMO With Imperfect CSI and Phase Noise

Zhangjie Peng, Jianchen Zhu, Cunhua Pan, Zaichen Zhang, Daniel Benevides da Costa, Maged Elkashlan, George K. Karagiannidis

TL;DR

This work studies an active RIS-aided uplink massive MIMO system under imperfect CSI and RIS phase noise. It adopts a two-timescale design in which BS beamforming uses instantaneous aggregated CSI while RIS phase shifts are computed from statistical CSI, reducing overhead. A closed-form lower bound on the achievable rate is derived via the UatF bound, using LMMSE channel estimation, and a GA-based algorithm is proposed to optimize RIS phase shifts. Numerical results show that active RIS offers significant performance gains over passive RIS despite phase noise, but the usual power-scaling intuition does not hold in large-scale active-RIS deployments, highlighting practical power trade-offs and the value of the GA-based design for fairness and efficiency.

Abstract

Active reconfigurable intelligent surface (RIS) has attracted significant attention as a recently proposed RIS architecture. Owing to its capability to amplify the incident signals, active RIS can mitigate the multiplicative fading effect inherent in the passive RIS-aided system. In this paper, we consider an active RIS-aided uplink multi-user massive multiple-input multiple-output (MIMO) system in the presence of phase noise at the active RIS. Specifically, we employ a two-timescale scheme, where the beamforming at the base station (BS) is adjusted based on the instantaneous aggregated channel state information (CSI) and the statistical CSI serves as the basis for designing the phase shifts at the active RIS, so that the feedback overhead and computational complexity can be significantly reduced. The aggregated channel composed of the cascaded and direct channels is estimated by utilizing the linear minimum mean square error (LMMSE) technique. Based on the estimated channel, we derive the analytical closed-form expression of a lower bound of the achievable rate. The power scaling laws in the active RIS-aided system are investigated based on the theoretical expressions. When the transmit power of each user is scaled down by the number of BS antennas M or reflecting elements N, we find that the thermal noise will cause the lower bound of the achievable rate to approach zero, as the number of M or N increases to infinity. Moreover, an optimization approach based on genetic algorithms (GA) is introduced to tackle the phase shift optimization problem. Numerical results reveal that the active RIS can greatly enhance the performance of the considered system under various settings.

Active RIS-Aided Massive MIMO With Imperfect CSI and Phase Noise

TL;DR

This work studies an active RIS-aided uplink massive MIMO system under imperfect CSI and RIS phase noise. It adopts a two-timescale design in which BS beamforming uses instantaneous aggregated CSI while RIS phase shifts are computed from statistical CSI, reducing overhead. A closed-form lower bound on the achievable rate is derived via the UatF bound, using LMMSE channel estimation, and a GA-based algorithm is proposed to optimize RIS phase shifts. Numerical results show that active RIS offers significant performance gains over passive RIS despite phase noise, but the usual power-scaling intuition does not hold in large-scale active-RIS deployments, highlighting practical power trade-offs and the value of the GA-based design for fairness and efficiency.

Abstract

Active reconfigurable intelligent surface (RIS) has attracted significant attention as a recently proposed RIS architecture. Owing to its capability to amplify the incident signals, active RIS can mitigate the multiplicative fading effect inherent in the passive RIS-aided system. In this paper, we consider an active RIS-aided uplink multi-user massive multiple-input multiple-output (MIMO) system in the presence of phase noise at the active RIS. Specifically, we employ a two-timescale scheme, where the beamforming at the base station (BS) is adjusted based on the instantaneous aggregated channel state information (CSI) and the statistical CSI serves as the basis for designing the phase shifts at the active RIS, so that the feedback overhead and computational complexity can be significantly reduced. The aggregated channel composed of the cascaded and direct channels is estimated by utilizing the linear minimum mean square error (LMMSE) technique. Based on the estimated channel, we derive the analytical closed-form expression of a lower bound of the achievable rate. The power scaling laws in the active RIS-aided system are investigated based on the theoretical expressions. When the transmit power of each user is scaled down by the number of BS antennas M or reflecting elements N, we find that the thermal noise will cause the lower bound of the achievable rate to approach zero, as the number of M or N increases to infinity. Moreover, an optimization approach based on genetic algorithms (GA) is introduced to tackle the phase shift optimization problem. Numerical results reveal that the active RIS can greatly enhance the performance of the considered system under various settings.
Paper Structure (9 sections, 11 theorems, 83 equations, 6 figures, 3 algorithms)

This paper contains 9 sections, 11 theorems, 83 equations, 6 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Estimation
  4. Analysis Of The Achievable Rate
  5. Derivation of the Rate
  6. Power Scaling Laws
  7. Design Of The RIS Phase Shifts
  8. Numerical Results
  9. Conclusion

Key Result

Lemma 1

The mean vectors and covariance matrices required for calculating the LMMSE estimator are expressed as

Figures (6)

  • Figure 1: An active RIS-aided uplink communication system.
  • Figure 2: NMSE of user 1 versus the number of antennas $M$ and the number of RIS elements $N$.
  • Figure 3: Uplink achievable sum rate versus total power consumption.
  • Figure 4: Uplink achievable sum rate versus the number of antennas $M$.
  • Figure 5: Uplink achievable sum rate versus the number of RIS elements $N$.
  • ...and 1 more figures

Theorems & Definitions (11)

  • Lemma 1
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Lemma 2
  • Theorem 2
  • Corollary 3
  • Corollary 4
  • Corollary 5
  • Lemma 3
  • ...and 1 more