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Performance Analysis of Intelligent Reflecting Surface Aided Communication Systems
Qin Tao, Junwei Wang, Caijun Zhong
TL;DR
IRS-aided SISO systems require analytical performance characterization that accounts for both Rician IRS links and the direct transmitter–receiver link. The paper derives a closed-form ergodic-capacity upper bound and outage approximation, finding that more reflecting elements, stronger LOS components, and IRS placement near either endpoint improve performance.
Problem
Few analytical studies characterize IRS-aided system performance, while prior SISO analyses assume that the direct transmitter–receiver link does not exist.
Method
The paper analyzes IRS-aided SISO systems under mixed Rayleigh and Rician fading, deriving a closed-form ergodic-capacity upper bound, outage approximation, and asymptotic expressions.
Results
Increasing the number of reflecting elements boosts ergodic capacity and improves outage probability, while stronger LOS components and endpoint-proximal IRS placement are beneficial.
Takeaways & Limitations
The analysis indicates that IRS size, LOS strength, and deployment position are important determinants of IRS-aided SISO performance.
Abstract
from arXiv · showhide
This letter presents a detailed performance analysis of the intelligent reflecting surface (IRS) aided single-input single-output communication systems, taking into account of the direct link between the transmitter and receiver. A closed-form upper bound is derived for the ergodic capacity, and an accurate approximation is obtained for the outage probability. In addition, simplified expressions are presented in the asymptotic regime. Numerical results are provided to validate the correctness of the theoretical analysis. It is found that increasing the number of reflecting elements can significantly boost the ergodic capacity and outage probability performance, and a strong line-of-sight component is also beneficial. In addition, it is desirable to deploy the IRS close to the transmitter or receiver, rather than in the middle.
I. INTRODUCTION
The paper addresses limited analytical performance studies of IRS-aided systems by analyzing SISO communication under Rician fading while retaining the direct transmitter–receiver link.
- IRS technology manipulates propagation channels into favorable configurations for next-generation wireless communication systems.
- Prior IRS research largely focuses on phase-shift matrices, transmit beamformers, energy efficiency, statistical CSI, and multi-antenna systems.
- Few studies analytically characterize IRS-aided performance; existing SISO analyses often omit the direct transmitter–receiver link.
- Rician fading is motivated by IRS deployments having line-of-sight paths to both the transmitter and receiver.
- The paper analyzes IRS-aided SISO systems in Rician fading while accounting for the direct channel and derives capacity and outage-performance expressions.It also reports asymptotic expressions, an effective SNR gain of N2, and diversity order N + 1.
II. SYSTEM MODEL
The system is a three-node SISO link with an N-element IRS, a direct channel, optimized phase shifts, and mixed Rayleigh–Rician fading assumptions.
- The considered network contains a single-antenna transmitter, single-antenna receiver, and IRS with N reflecting elements.
- The receiver combines signals from both the transmitter–IRS–receiver path and the direct transmitter–receiver path.
- The model defines the transmit signal, direct channel, two IRS-related channel vectors, phase-shift matrix, element phases, and Gaussian noise.
- The IRS-related channels use Rician fading because of line-of-sight deployment, whereas the direct channel uses Rayleigh fading without a line-of-sight path.
- Channel parameters include link distances, path-loss exponents, Rician factors, normalized line-of-sight components, and normalized non-line-of-sight components.
- With perfect CSI at the IRS, the phase-shift matrix is selected to maximize the received SNR.
III. PERFORMANCE ANALYSIS
The performance analysis evaluates two system metrics: ergodic capacity and outage probability.
- The analysis focuses on ergodic capacity and outage probability as the two principal performance metrics.
A. Ergodic Capacity
The paper derives a tractable closed-form upper bound for ergodic capacity and uses it to characterize how IRS size, fading, and channel parameters affect performance.
- A. Ergodic Capacity: The ergodic capacity is expressed through the system’s maximum-SNR formulation.
- A. Ergodic Capacity: Jensen’s inequality provides a tractable bound because the exact distribution of the maximum SNR is intractable.
- A. Ergodic Capacity: Theorem 1 gives a closed-form upper bound applicable to arbitrary system configurations using elementary functions.
- A. Ergodic Capacity: The closed-form bound enables efficient ergodic-capacity evaluation and analysis of key parameter effects.
- A. Ergodic Capacity: The ergodic-capacity upper bound increases monotonically with N and, for sufficiently large N, is dominated by log2 γ1N2.
- A. Ergodic Capacity: The IRS provides an effective SNR gain of N2 through beamforming and aperture gains from collecting more signal power.
- A. Ergodic Capacity: A strong LOS component enhances ergodic capacity, while the upper bound has symmetric dependence on the two Rician factors K1 and K2.
B. Outage Probability
The paper analyzes outage probability using approximations because the exact distribution of the maximum instantaneous SNR is unknown. It derives large-N and high-SNR approximations, showing diversity order N + 1 and a coding-gain dependence on the LOS component.
- Outage probability is defined as the probability that instantaneous SNR falls below the threshold γth.
- Because the exact distribution of γmax is unknown, the analysis uses tight outage-probability approximations.
- When N →∞, Theorem 2 approximates outage probability with a closed-form expression that uses only elementary functions.The approximation can therefore be efficiently evaluated.
- The outage approximation is also examined in the high-SNR regime, where γ0 →∞.
- A diversity order of N + 1 is achieved, while the LOS component mainly affects the system’s achievable coding gain.
IV. SIMULATION RESULTS
Numerical results validate the analytical approximations and show that reflecting-element count, Rician factor, IRS placement, and SNR materially affect capacity and outage performance.
- Ergodic capacity: The ergodic-capacity upper bound remains tight across configurations, validating the closed-form expression in Theorem 1.Capacity increases monotonically with both the number of reflecting elements N and Rician factor K.
- IRS location: Ergodic capacity is minimized when the IRS is deployed midway between transmitter and receiver, under d1 + d2 = 300 m.The capacity is symmetric with respect to d1 and d2, and higher capacity is obtained near either endpoint.
- Outage probability: The outage approximation works well even for moderate N when K = 1.Figure 4 evaluates Pout,1 under this setting.
- Outage probability: Outage probability decreases sharply as SNR increases, with a faster decrease for larger N.The high-SNR approximation is also reported as accurate, and diversity order N + 1 is observed.
V. CONCLUSION
The paper analyzes IRS-aided SISO systems under mixed Rayleigh and Rician fading, deriving efficient performance expressions and identifying design factors that improve capacity and outage performance.
- The study analyzes ergodic capacity and outage probability for IRS-aided SISO systems under mixed Rayleigh and Rician fading channels.
- Closed-form expressions and asymptotic forms provide efficient means to evaluate system performance.
- The IRS contributes an effective SNR gain of N2, while diversity order can increase to N + 1.
- Higher performance is associated with deploying the IRS near the transmitter or receiver and with a strong LOS path.
APPENDIX A PROOF OF THEOREM 1
The proof derives the ergodic-capacity upper bound by applying Jensen’s inequality and decomposing the expected maximum SNR into tractable components.
- Jensen’s inequality is applied to obtain an upper bound on the ergodic capacity.
- The expected maximum SNR is computed using the system relationship and the binomial expansion theorem.
- The proof evaluates x1, x2, and x3 separately before combining them into the desired result.
- Independence of h1 and h2 is used when evaluating the relevant expectation terms.
- The Rayleigh distribution of |g| supplies the term needed to calculate x3.
APPENDIX B PROOF OF THEOREM 2
The proof approximates the IRS-reflected contribution with a normal distribution for sufficiently large N, then combines it with the Rayleigh direct-link term to obtain the outage result.
- The outage probability is first transformed into a distribution-based expression.
- For sufficiently large N, the reflected contribution u is approximated by a normal distribution using the central limit theorem.
- The cumulative distribution function of z is calculated by combining independent u and |g| components.
- The direct-link term |g| is modeled through its Rayleigh cumulative distribution function.
- Algebraic manipulation yields the desired outage-probability result.
APPENDIX C PROOF OF THEOREM 3
The proof characterizes the high-SNR outage behavior by analyzing the PDF near the origin for individual SNR branches, with separate cases based on index relationships.
- Conclusion: The desired high-SNR outage results follow from the case-specific PDF behavior after algebraic manipulation and an outage approximation result.The analysis treats γmax as the effective SNR of an equal-gain-combining SIMO system.
- PDF asymptotics: The high-SNR outage approximation is determined by the near-origin PDF parameters a and t.The PDF is expressed as f_β(β) = aβ^t + O(β^(t+ε)) near β = 0.
- PDF asymptotics: The outage analysis reduces to characterizing the PDFs of |g|^2 and |h_2,n|^2|h_1,n|^2 near the origin.The exponential distribution of |g|^2 is handled directly, so the proof focuses on the product term.
- Case analysis: The product-variable PDF is derived using results for β = dα_1 and relationships of the Bessel-K function.The derivation then considers separate cases according to whether n > p, n < p, or n = p.
- Case analysis: For n > p, the dominant contribution is determined by p = 0.The proof separately derives the n < p case using symmetry and observes that the n = p case is dominated by n = p = 0.