Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Spatially Correlated RIS-Aided Secure Massive MIMO Under CSI and Hardware Imperfections

Dan Yang, Jindan Xu, Wei Xu, Bin Sheng, Xiaohu You, Chau Yuen, Marco Di Renzo

TL;DR

This work analyzes secure communications in RIS-aided multiuser massive MIMO under practical impairments: CSI imperfection, transceiver hardware impairments (HWI), RIS phase noise, and spatially correlated fading. It develops LMMSE-based channel estimation for the aggregate RIS-BS-user channel, and a downlink transmission scheme using MRT with null-space AN to enhance secrecy, deriving a lower bound on the ergodic secrecy rate and an upper bound on Eve's capacity. The study reveals key scaling laws: a non-zero secrecy rate can be maintained when total transmit power scales as $P_t \propto 1/N$, and the legitimate-rate grows as $O(\log_2 M)$ as $N$ grows large, while correlation among RIS elements can degrade performance. An optimized power-allocation rule between data and AN is proposed, demonstrating that RIS elements can counteract HWI and RIS phase noise, providing design guidance for robust, secure RIS-enabled massive MIMO systems.

Abstract

This paper investigates the integration of a reconfigurable intelligent surface (RIS) into a secure multiuser massive multiple-input multiple-output (MIMO) system in the presence of transceiver hardware impairments (HWI), imperfect channel state information (CSI), and spatially correlated channels. We first introduce a linear minimum-mean-square error estimation algorithm for the aggregate channel by considering the impact of transceiver HWI and RIS phase-shift errors. Then, we derive a lower bound for the achievable ergodic secrecy rate in the presence of a multi-antenna eavesdropper when artificial noise (AN) is employed at the base station (BS). In addition, the obtained expressions of the ergodic secrecy rate are further simplified in some noteworthy special cases to obtain valuable insights. To counteract the effects of HWI, we present a power allocation optimization strategy between the confidential signals and AN, which admits a fixed-point equation solution. Our analysis reveals that a non-zero ergodic secrecy rate is preserved if the total transmit power decreases no faster than $1/N$, where $N$ is the number of RIS elements. Moreover, the ergodic secrecy rate grows logarithmically with the number of BS antennas $M$ and approaches a certain limit in the asymptotic regime $N\rightarrow\infty$. Simulation results are provided to verify the derived analytical results. They reveal the impact of key design parameters on the secrecy rate. It is shown that, with the proposed power allocation strategy, the secrecy rate loss due to HWI can be counteracted by increasing the number of low-cost RIS elements.

Spatially Correlated RIS-Aided Secure Massive MIMO Under CSI and Hardware Imperfections

TL;DR

This work analyzes secure communications in RIS-aided multiuser massive MIMO under practical impairments: CSI imperfection, transceiver hardware impairments (HWI), RIS phase noise, and spatially correlated fading. It develops LMMSE-based channel estimation for the aggregate RIS-BS-user channel, and a downlink transmission scheme using MRT with null-space AN to enhance secrecy, deriving a lower bound on the ergodic secrecy rate and an upper bound on Eve's capacity. The study reveals key scaling laws: a non-zero secrecy rate can be maintained when total transmit power scales as , and the legitimate-rate grows as as grows large, while correlation among RIS elements can degrade performance. An optimized power-allocation rule between data and AN is proposed, demonstrating that RIS elements can counteract HWI and RIS phase noise, providing design guidance for robust, secure RIS-enabled massive MIMO systems.

Abstract

This paper investigates the integration of a reconfigurable intelligent surface (RIS) into a secure multiuser massive multiple-input multiple-output (MIMO) system in the presence of transceiver hardware impairments (HWI), imperfect channel state information (CSI), and spatially correlated channels. We first introduce a linear minimum-mean-square error estimation algorithm for the aggregate channel by considering the impact of transceiver HWI and RIS phase-shift errors. Then, we derive a lower bound for the achievable ergodic secrecy rate in the presence of a multi-antenna eavesdropper when artificial noise (AN) is employed at the base station (BS). In addition, the obtained expressions of the ergodic secrecy rate are further simplified in some noteworthy special cases to obtain valuable insights. To counteract the effects of HWI, we present a power allocation optimization strategy between the confidential signals and AN, which admits a fixed-point equation solution. Our analysis reveals that a non-zero ergodic secrecy rate is preserved if the total transmit power decreases no faster than , where is the number of RIS elements. Moreover, the ergodic secrecy rate grows logarithmically with the number of BS antennas and approaches a certain limit in the asymptotic regime . Simulation results are provided to verify the derived analytical results. They reveal the impact of key design parameters on the secrecy rate. It is shown that, with the proposed power allocation strategy, the secrecy rate loss due to HWI can be counteracted by increasing the number of low-cost RIS elements.
Paper Structure (13 sections, 12 theorems, 70 equations, 10 figures, 1 table)

This paper contains 13 sections, 12 theorems, 70 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Channel Estimation and Data Transmission
  4. Uplink Channel Estimation
  5. Downlink Data Transmission
  6. Achievable Ergodic Secrecy Rate Analysis
  7. Achievable Rate of the Legitimate Users
  8. Upper Bounded Capacity at Eve
  9. Ergodic Secrecy Rate Analysis
  10. New Characteristics of Integrating RIS
  11. Optimized Transmission Design
  12. Numerical Results
  13. Conclusion

Key Result

Lemma 1

The LMMSE estimate of ${\bf h}_k$ is obtained as where and with $\varrho=\frac{I_1(\nu_p)}{I_0(\nu_p)}$ for the von Mises distribution and $\varrho=\frac{\sin(\iota_p)}{\iota_p}$ for the uniform distribution.

Figures (10)

  • Figure 1: RIS-aided downlink secure massive MIMO system in the presence of an $M_{\rm E}$-antenna Eve
  • Figure 2: NMSE versus SNR with different transceiver hardware parameters.
  • Figure 3: NMSE versus the number of RIS elements with different transceiver hardware parameters and pilot lengths.
  • Figure 4: Ergodic secrecy rate and lower bound versus SNR ($M=128$, $N=196$, $K=6$).
  • Figure 5: Ergodic secrecy rate versus the number of BS antennas ($N=196$, $K=6$, $M_{\rm E}=4$, SNR$=0$ dB).
  • ...and 5 more figures

Theorems & Definitions (14)

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