Source-linked AI summary
Spectral and Energy Efficiency of IRS-Assisted MISO Communication with Hardware Impairments
Shaoqing Zhou, Wei Xu, Kezhi Wang, Marco Di Renzo, Mohamed-Slim Alouini
TL;DR
The paper addresses how hardware impairments affect spectral and energy efficiency in IRS-assisted MISO downlink communication. It models AP RF impairments and IRS phase noise, derives the corresponding efficiency expressions and optimal transmit power, and reports bounded spectral efficiency with impairment severity affecting the energy-efficiency optimum.
Problem
The paper examines the effects of hardware impairments at the AP and IRS on IRS-assisted MISO spectral and energy efficiency.
Method
The paper derives spectral- and energy-efficiency expressions for the impaired system and obtains a closed-form optimal transmit power.
Results
Spectral efficiency is upper bounded as the numbers of AP antennas and IRS elements grow, while the impact of imperfect IRS diminishes at high SNR.
Takeaways & Limitations
The optimal transmit power for maximizing energy efficiency increases as RF impairments become more severe.
Abstract
from arXiv · showhide
In this letter, we analyze the spectral and energy efficiency of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) downlink system with hardware impairments. An extended error vector magnitude (EEVM) model is utilized to characterize the impact of radio-frequency (RF) impairments at the access point (AP) and phase noise is considered for the imperfect IRS. We show that the spectral efficiency is limited due to the hardware impairments even when the numbers of AP antennas and IRS elements grow infinitely large, which is in contrast with the conventional case with ideal hardware. Moreover, the performance degradation at high SNR is shown to be mainly affected by the AP hardware impairments rather than the phase noise of IRS. We further obtain the optimal transmit power in closed form for energy efficiency maximization. Simulation results are provided to verify these results.
I. INTRODUCTION
The paper studies IRS-assisted MISO communication with AP and IRS hardware impairments, addressing unclear RF-impairment effects and deriving spectral- and energy-efficiency results.
- The study focuses on an IRS-assisted MISO system with hardware impairments at both the AP and IRS.
- Theoretical spectral-efficiency expressions are derived for the non-ideal system.
- Spectral-efficiency growth is limited as the numbers of reflecting elements increase.
- At high SNR, the impact of IRS phase noise diminishes.
- A closed-form optimal transmit power is obtained for energy-efficiency maximization, and this power increases with RF impairments.
A. Signal Model
The signal model describes a LoS AP–IRS–user MISO link with an N-element IRS, AP RF-chain impairments modeled by EEVM, and IRS phase errors.
- The system is a MISO downlink with an M-antenna AP, a single-antenna user, and an IRS containing N reflecting elements.
- The IRS reflection matrix uses per-element amplitude coefficients and phase shifts, with unit amplitudes assumed for all elements.
- Both AP-to-IRS and IRS-to-user channels are modeled as line-of-sight links under flat fading.
- AP RF-chain impairments are represented with the EEVM model, including attenuation, phase rotation, and additive distortion noise.
- IRS phase errors are incorporated by adding phase noise to each practical reflecting-element phase shift.
B. Power Consumption Model
The total power model combines transmit-power consumption with static circuit power while treating the IRS as passive and imposing amplifier and rate-independence assumptions.
- The IRS consumes no transmit power because it operates through passive reflection.
- Total power consumption is modeled as P_T = μP + P_C.
- The coefficient μ accounts for transmit-power-amplifier efficiency under RF impairments, while P_C is static hardware power.
- The model assumes that the transmit amplifier operates within its linear region and that static power does not depend on communication rate.
III. SPECTRAL AND ENERGY EFFICIENCY ANALYSIS
The analysis quantifies how AP and IRS hardware impairments affect downlink spectral and energy efficiency, using the ideal system as a comparison case.
- The paper quantitatively analyzes downlink spectral and energy efficiency under hardware impairments at both the AP and IRS.
- The ideal spectral and energy-efficiency results are recovered as a special case for comparison.
- The analysis compares impaired-system performance with the corresponding ideal-hardware case.
A. Spectral Efficiency Analysis
The analysis derives downlink spectral efficiency under AP and IRS hardware impairments, then characterizes how these impairments constrain performance as system dimensions and SNR increase.
- Maximum ratio transmission is used for AP transmit beamforming, while IRS phases are optimized to maximize received signal power.
- Theorem 1 gives the downlink spectral efficiency for massive IRS-assisted MISO systems with large M and N under hardware impairments.
- In the ideal case, setting η = 1, σ = 0, and δψ = δˆθ = 0 reduces the impaired spectral-efficiency expression to the ideal form.
- At high SNR, spectral efficiency follows R → log2 P + 2 log2 η + 2 log2 sinc(δψ) − log2 σ2.
- Unlike the ideal case, impaired spectral efficiency is ultimately upper bounded as the numbers of AP antennas and IRS elements increase.
- High-SNR performance is mainly limited by AP RF impairments rather than IRS phase noise, supporting low-resolution IRS phase shifts with limited degradation.
B. Energy Efficiency Analysis
The energy-efficiency analysis defines energy efficiency as spectral efficiency divided by power consumption and derives a closed-form optimal transmit-power solution.
- Energy efficiency is defined as the ratio of spectral efficiency to total power consumption, EE ≜ BR/PT.
- At high SNR, energy efficiency is expressed as B(log2 P + 2 log2 η + 2 log2 sinc(δψ) − log2 σ2).
- Theorem 2 provides the unique closed-form optimal transmit power that maximizes energy efficiency using Lambert’s W-function.
- In the ideal case, continuous IRS phase increases the IRS’s static hardware power consumption.
- More severe RF impairments increase the optimal transmit power and decrease the corresponding optimal energy efficiency.
IV. SIMULATION RESULTS
Simulations validate the theoretical spectral- and energy-efficiency results under hardware impairments. Increasing IRS size eventually limits spectral-efficiency growth, while more severe RF impairments require higher optimal transmit power and reduce energy efficiency.
- Theorem 1, special cases, and simulations show that both non-ideal and ideal spectral efficiency increase with transmit power, but at different scales.
- The simplified spectral-efficiency expression is fairly tight at high SNR.
- As the number of IRS reflecting elements increases, hardware impairments limit spectral-efficiency growth, unlike the ideal case, which continues increasing logarithmically with the squared element count.
- Theorem 2's optimal transmit power matches the highest point of the energy-efficiency curve, while worse RF impairments require higher optimal power and reduce corresponding energy efficiency.
- The ideal case can have poorer energy-efficiency performance because continuous-phase IRS hardware consumes more static power.
V. CONCLUSION
The paper analyzes IRS-assisted downlink spectral and energy efficiency with hardware impairments. It finds that spectral efficiency is upper bounded as AP antennas and IRS elements grow, imperfect-IRS effects diminish at high SNR, and optimal transmit power rises with impairment severity.
- The non-ideal spectral efficiency is upper bounded for large numbers of AP antennas and IRS elements.
- At high SNR, the impact of an imperfect IRS diminishes.
- The optimal transmit power for maximizing energy efficiency increases as RF impairments become more severe.
APPENDIX A PROOF OF THEOREM 1
The appendix derives the asymptotic spectral-efficiency expression by evaluating phase-noise expectations and applying convergence results. It then obtains the energy-efficiency optimum from a stationary-point equation and proves uniqueness.
- The spectral-efficiency expression is rewritten by substituting the channel relations and expectation terms.
- The phase-noise expectations reduce to sinc^2(δψ) using symmetry and the phase-noise probability density.
- The Strong Law of Large Numbers and Continuous Mapping Theorem establish the required convergence for continuous matrix functions.
- The energy-efficiency optimum is obtained by setting its partial derivative to zero and rearranging with the inverse Lambert W-function.
- Monotonicity of g(P) shows that the stationary-point equation has at most one solution, which is the closed-form optimum.