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Energy Efficiency Analysis of IRS-aided Wireless Communication Systems Under Statistical QoS Constraints: An Information-Theoretic Perspective

Wenhao Wang, Deli Qiao, Lei Yang, Yueying Zhan, Derrick Wing Kwan Ng

TL;DR

It is revealed that compared with the results applied to the low-power regime, higher effective capacity performance can be achieved in scenarios with sparse multipath fading while achieving the same minimum bit energy in the wideband regime.

Abstract

This paper investigates the information-theoretic energy efficiency of intelligent reflecting surface (IRS)-aided wireless communication systems, taking into account the statistical quality-of-service (QoS) constraints on delay violation probabilities. Specifically, effective capacity is adopted to capture the maximum constant arrival rate that can be supported by a time-varying service process while fulfilling these statistical QoS requirements. We derive the minimum bit energy required for the IRS-aided wireless communication system under QoS constraints and analyze the spectral efficiency and energy efficiency tradeoff at low but nonzero signal-to-noise ratio (SNR) levels by also characterizing the wideband slope values. Our analysis demonstrates that the energy efficiency for the considered system under statistical QoS constraints can approach that for a system without QoS limitations in the low-SNR regime. Additionally, deploying a sufficiently large number of practical IRS reflecting elements can substantially reduce energy consumption required to achieve desired spectral efficiency performance in the low-power regime, even with limited bit-resolution phase shifters. Besides, we reveal that compared with the results applied to the low-power regime, higher effective capacity performance can be achieved in scenarios with sparse multipath fading while achieving the same minimum bit energy in the wideband regime.

Energy Efficiency Analysis of IRS-aided Wireless Communication Systems Under Statistical QoS Constraints: An Information-Theoretic Perspective

TL;DR

It is revealed that compared with the results applied to the low-power regime, higher effective capacity performance can be achieved in scenarios with sparse multipath fading while achieving the same minimum bit energy in the wideband regime.

Abstract

This paper investigates the information-theoretic energy efficiency of intelligent reflecting surface (IRS)-aided wireless communication systems, taking into account the statistical quality-of-service (QoS) constraints on delay violation probabilities. Specifically, effective capacity is adopted to capture the maximum constant arrival rate that can be supported by a time-varying service process while fulfilling these statistical QoS requirements. We derive the minimum bit energy required for the IRS-aided wireless communication system under QoS constraints and analyze the spectral efficiency and energy efficiency tradeoff at low but nonzero signal-to-noise ratio (SNR) levels by also characterizing the wideband slope values. Our analysis demonstrates that the energy efficiency for the considered system under statistical QoS constraints can approach that for a system without QoS limitations in the low-SNR regime. Additionally, deploying a sufficiently large number of practical IRS reflecting elements can substantially reduce energy consumption required to achieve desired spectral efficiency performance in the low-power regime, even with limited bit-resolution phase shifters. Besides, we reveal that compared with the results applied to the low-power regime, higher effective capacity performance can be achieved in scenarios with sparse multipath fading while achieving the same minimum bit energy in the wideband regime.

Paper Structure

This paper contains 18 sections, 10 theorems, 45 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model
  4. Effective Capacity
  5. Spectral Efficiency and Energy Efficiency Tradeoff
  6. Energy Efficiency in the Low-Power Regime
  7. Energy Efficiency in the Wideband Regime
  8. Simulation Results
  9. Simulation Setup
  10. Spectral Efficiency versus Energy Efficiency in Low-Power Regime
  11. Spectral Efficiency versus Energy Efficiency in Wideband Regime
  12. Conclusion
  13. Proof of Lemma \ref{['optimal_theta']}
  14. Proof of Theorem \ref{['low_power']}
  15. Proof of Corollary \ref{['large_number_elements']}
  16. ...and 3 more sections

Key Result

Lemma 1

For a given transmit SNR, the $n$-th optimal phase shift adopted at the IRS is expressed as $\theta_n^{\star} = \arg( h ) - \arg( f_n ) - \arg( g_n )$, where $f_n$ and $g_n$ are the $n$-th element of channel vectors ${\mathbf{f}}$ and ${\mathbf{g}}$, respectively, $\forall n \in {\mathcal{N}}$.

Figures (5)

  • Figure 1: The normalized effective capacity (bit/s/Hz) versus the bit energy (dB) for the considered system in the low-power regime with $N=100$ and $B = 10^5$ Hz.
  • Figure 2: The normalized effective capacity (bit/s/Hz) versus the bit energy (dB) for comparison between the considered system and the non-IRS system in the low-power regime with $N=60$ and $B = 10^5$ Hz.
  • Figure 3: The normalized effective capacity (bit/s/Hz) versus the bit energy (dB) for the considered system by deploying the various number of the IRS reflecting elements in the low-power regime with $\mu=0.1$ and $B = 10^5$ Hz.
  • Figure 4: The minimum bit energy (dB) versus the number of IRS reflecting elements for case I in the scenario with sparse multipath fading in the wideband regime with $N_{\mathrm{c}}=5$ and $P/N_0 = 10^6$.
  • Figure 5: The normalized effective capacity (bit/s/Hz) versus the bit energy (dB) for a) case I and b) case II in the scenario with sparse multipath fading in the wideband regime with $N=500$ and $P/N_0 = 10^5$.

Theorems & Definitions (31)

  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Remark 1
  • Corollary 1
  • proof
  • Remark 2
  • Remark 3
  • Theorem 2
  • ...and 21 more