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Outage Probability Analysis of Wireless Paths with Faulty Reconfigurable Intelligent Surfaces

Mounir Bensalem, Admela Jukan

TL;DR

This work addresses outage probability in RIS-aided wireless networks when RIS elements may fail and obstacles degrade connections. It develops a end-to-end channel/CSI model for a base station, multiple RISs partitioned into blocks, and a user, using outdated CSI to select the best RIS block and a 1-hop path. A closed-form outage probability is derived for an arbitrary RIS path, incorporating element failure as a binomial process and obstacle-induced degradation, with expressions expressed via the modified Bessel function $K_1$. Numerical results reveal how failure probability $p$, RIS size, distance, and CSI correlation influence reliability, showing that larger, highly correlated RISs improve outage performance while blockages and element failures worsen it, especially at low SNR. The findings offer practical guidance for designing robust RIS-aided systems under hardware faults and dynamic obstructions.

Abstract

We consider a next generation wireless network incorporating a base station a set of typically low-cost and faulty Reconfigurable Intelligent Surfaces (RISs). The base station needs to select the path including the RIS to provide the maximum signal-to-noise ratio (SNR) to the user. We study the effect of the number of elements, distance and RIS hardware failure on the path outage probability, and based on the known signal propagation model at high frequencies, derive the closed-form expression for the said probability of outage. Numerical results show the path outage likelihood as function of the probability of hardware failure of RIS elements, the number of elements, and the distance between mobile users and the RIS.

Outage Probability Analysis of Wireless Paths with Faulty Reconfigurable Intelligent Surfaces

TL;DR

This work addresses outage probability in RIS-aided wireless networks when RIS elements may fail and obstacles degrade connections. It develops a end-to-end channel/CSI model for a base station, multiple RISs partitioned into blocks, and a user, using outdated CSI to select the best RIS block and a 1-hop path. A closed-form outage probability is derived for an arbitrary RIS path, incorporating element failure as a binomial process and obstacle-induced degradation, with expressions expressed via the modified Bessel function . Numerical results reveal how failure probability , RIS size, distance, and CSI correlation influence reliability, showing that larger, highly correlated RISs improve outage performance while blockages and element failures worsen it, especially at low SNR. The findings offer practical guidance for designing robust RIS-aided systems under hardware faults and dynamic obstructions.

Abstract

We consider a next generation wireless network incorporating a base station a set of typically low-cost and faulty Reconfigurable Intelligent Surfaces (RISs). The base station needs to select the path including the RIS to provide the maximum signal-to-noise ratio (SNR) to the user. We study the effect of the number of elements, distance and RIS hardware failure on the path outage probability, and based on the known signal propagation model at high frequencies, derive the closed-form expression for the said probability of outage. Numerical results show the path outage likelihood as function of the probability of hardware failure of RIS elements, the number of elements, and the distance between mobile users and the RIS.
Paper Structure (12 sections, 2 theorems, 27 equations, 5 figures)

This paper contains 12 sections, 2 theorems, 27 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. System Model
  4. CSI Model
  5. SNR model
  6. Element failure model
  7. Path selection
  8. Outage Probability Analysis
  9. Outage considering connection degradation
  10. Outage considering Element failure
  11. Numerical Evaluation
  12. Conclusion

Key Result

Proposition 1

The probability mass function $P_{Q;M'}(q)$ that $q$ element out of $M'$ fails is given as follows:

Figures (5)

  • Figure 1: The reference RIS-assited wireless network system: a. system architecture, b. hardware failure and connection degradation case.
  • Figure 2: Outage probability of best RIS vs the normalized average SNR of U-RIS and RIS-B, with different probability of failures, for $d_{UR_{k,j}} = 4$ m.
  • Figure 3: Outage probability of best RIS vs the normalized average SNR of U-RIS and RIS-B, with different reliability scenarios, for $d_{UR_{k,j}} = 4$ m.
  • Figure 4: Outage probability of best RIS vs number of elements $M$
  • Figure 5: Outage probability of best RIS vs distance $d_{UR_{k,j}}$ with and without obstacle, $\gamma_T=3$ and $\lambda_U=0.05$

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof