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Ergodic Spectral Efficiency Analysis of Intelligent Omni-Surface Aided Systems Suffering From Imperfect CSI and Hardware Impairments

Qingchao Li, Mohammed El-Hajjar, Lajos Hanzo

TL;DR

The paper addresses ergodic spectral efficiency in IOS-aided systems under imperfect CSI and hardware impairments, introducing an LMMSE channel estimator and a two-timescale beamforming framework that leverages instantaneous equivalent-UE–AP CSI at the AP and statistical CSI for IOS. It derives a closed-form IOS phase-shift design to maximize an upper bound on ergodic SE, and establishes hardware-quality scaling laws that reveal AP HWIs can be mitigated by more AP antennas, while UE HWIs fundamentally limit performance at high power. The analysis combines MMSE combining at the AP with a statistical-CSI–based IOS optimization, yielding insights into how device quality and IOS element count shape achievable gains in realistic settings. Practically, the results guide IOS deployment and transceiver design by quantifying when increasing antennas or IOS elements delivers meaningful improvements versus when hardware impairments cap performance.

Abstract

In contrast to the conventional reconfigurable intelligent surfaces (RIS), intelligent omni-surfaces (IOS) are capable of full-space coverage of smart radio environments by simultaneously transmitting and reflecting the incident signals. In this paper, we investigate the ergodic spectral efficiency of IOS-aided systems for transmission over random channel links, while considering both realistic imperfect channel state information (CSI) and transceiver hardware impairments (HWIs). Firstly, we formulate the linear minimum mean square error estimator of the equivalent channel spanning from the user equipments (UEs) to the access point (AP), where the transceiver HWIs are also considered. Then, we apply a two-timescale protocol for designing the beamformer of the IOS-aided system. Specifically, for the active AP beamformer, the minimum mean square error combining method is employed, which relies on the estimated equivalent channels, on the statistical information of the channel estimation error, on the inter-user interference as well as on the HWIs at the AP and UEs. By contrast, the passive IOS beamformer is designed based on the statistical CSI for maximizing the upper bound of the ergodic spectral efficiency. The theoretical analysis and simulation results show that the transceiver HWIs have a significant effect on the ergodic spectral efficiency, especially in the high transmit power region. Furthermore, we show that the HWIs at the AP can be effectively compensated by deploying more AP antennas.

Ergodic Spectral Efficiency Analysis of Intelligent Omni-Surface Aided Systems Suffering From Imperfect CSI and Hardware Impairments

TL;DR

The paper addresses ergodic spectral efficiency in IOS-aided systems under imperfect CSI and hardware impairments, introducing an LMMSE channel estimator and a two-timescale beamforming framework that leverages instantaneous equivalent-UE–AP CSI at the AP and statistical CSI for IOS. It derives a closed-form IOS phase-shift design to maximize an upper bound on ergodic SE, and establishes hardware-quality scaling laws that reveal AP HWIs can be mitigated by more AP antennas, while UE HWIs fundamentally limit performance at high power. The analysis combines MMSE combining at the AP with a statistical-CSI–based IOS optimization, yielding insights into how device quality and IOS element count shape achievable gains in realistic settings. Practically, the results guide IOS deployment and transceiver design by quantifying when increasing antennas or IOS elements delivers meaningful improvements versus when hardware impairments cap performance.

Abstract

In contrast to the conventional reconfigurable intelligent surfaces (RIS), intelligent omni-surfaces (IOS) are capable of full-space coverage of smart radio environments by simultaneously transmitting and reflecting the incident signals. In this paper, we investigate the ergodic spectral efficiency of IOS-aided systems for transmission over random channel links, while considering both realistic imperfect channel state information (CSI) and transceiver hardware impairments (HWIs). Firstly, we formulate the linear minimum mean square error estimator of the equivalent channel spanning from the user equipments (UEs) to the access point (AP), where the transceiver HWIs are also considered. Then, we apply a two-timescale protocol for designing the beamformer of the IOS-aided system. Specifically, for the active AP beamformer, the minimum mean square error combining method is employed, which relies on the estimated equivalent channels, on the statistical information of the channel estimation error, on the inter-user interference as well as on the HWIs at the AP and UEs. By contrast, the passive IOS beamformer is designed based on the statistical CSI for maximizing the upper bound of the ergodic spectral efficiency. The theoretical analysis and simulation results show that the transceiver HWIs have a significant effect on the ergodic spectral efficiency, especially in the high transmit power region. Furthermore, we show that the HWIs at the AP can be effectively compensated by deploying more AP antennas.
Paper Structure (24 sections, 62 equations, 10 figures, 1 table)

This paper contains 24 sections, 62 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Prior Works
  3. Motivations and Contributions
  4. Organization and Notation
  5. System Model
  6. IOS Architecture
  7. Channel Model
  8. Channel Estimation and Beamforming Protocol
  9. Channel Estimation
  10. Beamforming Design
  11. AP Beamforming
  12. IOS Beamforming
  13. Hardware-Quality Scaling Law
  14. AP HWI
  15. UE HWI
  16. ...and 9 more sections

Figures (10)

  • Figure 1: System model of the considered IOS-aided wireless communication system, including an AP equipped with $M$ ULA antennas, an IOS employing the mode stitching protocol with a total of $N$ elements, a user located at the same side of the IOS, denoted as UE-R, and a user located at the other side of the IOS, denoted as UE-T.
  • Figure 2: Illustration of the employed two-timescale channel estimation and beamforming protocol.
  • Figure 3: Comparison of the N-MSE versus the transmit power.
  • Figure 4: Theoretical (\ref{['Beamforming_Design_9']}), (\ref{['Beamforming_Design_19']}) and simulation comparison of the ergodic sum-rate versus the transmit power in various combining methods.
  • Figure 5: Theoretical (\ref{['Beamforming_Design_9']}), (\ref{['Beamforming_Design_19']}) and simulation comparison of the ergodic sum-rate versus the transmit power under different number of IOS elements, hardware quality factor and Rician factor.
  • ...and 5 more figures