[Paper Review] Performance Analysis of Reconfigurable Intelligent Surfaces over Nakagami-m Fading Channels

Monjed H. Samuh, Anas M. Salhab|arXiv (Cornell University)|Oct 15, 2020

Advanced Wireless Communication TechnologiesEngineering19 citations

TL;DR

This paper analyzes reconfigurable intelligent surface (RIS)-assisted networks over Nakagami-m fading channels by deriving closed-form approximations for outage probability, average symbol error probability (ASEP), and channel capacity. It reveals that the system achieves a diversity order of (a+1)/2, where a depends on the Nakagami-m parameter m and the number of reflecting elements N, with m having a stronger impact on performance than N.

ABSTRACT

This letter studies the performance of reconfigurable intelligent surface (RIS)-aided networks over Nakagami-m fading channels. First, we derive accurate closed-form approximations for the system channel distributions, and then, use them in deriving closed-form approximations for the outage probability, average symbol error probability (ASEP), and average channel capacity. In addition, to get more insights at the system performance, we derive asymptotic expression for the outage probability at high signal-to-noise ratio (SNR) regime, and provide closed-form expressions for the system diversity order and coding gain. Results show that the considered RIS scenario can provide a diversity order of (a+1)/2, where a is a function of the Nakagami-m fading parameter m and the number of reflecting elements N. Furthermore, results illustrate that m is more impactful on the diversity order and the system performance than N. Finally, the provided results are valid for arbitrary number of reflecting elements N and non-integer m.

Motivation & Objective

• To analyze the performance of reconfigurable intelligent surface (RIS)-assisted networks in Nakagami-m fading environments.
• To derive accurate closed-form approximations for key system metrics: outage probability, average symbol error probability (ASEP), and average channel capacity.
• To investigate the diversity order and coding gain in the high signal-to-noise ratio (SNR) regime for RIS-aided systems.
• To quantify the relative impact of the Nakagami-m fading parameter m and the number of reflecting elements N on system performance.
• To ensure the derived expressions are valid for arbitrary N and non-integer m values.

Proposed method

• Derive closed-form approximations for the system channel distribution in RIS-aided networks over Nakagami-m fading channels.
• Utilize the derived channel distribution to analytically compute outage probability, ASEP, and average channel capacity in closed form.
• Apply asymptotic analysis at high SNR to derive the outage probability expression and extract the diversity order and coding gain.
• Express the diversity order as (a+1)/2, where a is a function of the Nakagami-m parameter m and the number of reflecting elements N.
• Validate the analytical expressions through mathematical derivation and asymptotic analysis, ensuring applicability for non-integer m and arbitrary N.

Experimental results

Research questions

• RQ1 What are the closed-form expressions for outage probability, ASEP, and average channel capacity in RIS-aided systems over Nakagami-m fading?
• RQ2 How does the diversity order scale with the Nakagami-m fading parameter m and the number of reflecting elements N?
• RQ3 What is the relative impact of m versus N on system diversity gain and overall performance?
• RQ4 How do the asymptotic outage performance and coding gain behave at high SNR in the considered RIS scenario?
• RQ5 Are the derived expressions valid for non-integer values of the Nakagami-m fading parameter m and arbitrary numbers of reflecting elements N?

Key findings

• The system achieves a diversity order of (a+1)/2, where a depends on the Nakagami-m fading parameter m and the number of reflecting elements N.
• The Nakagami-m fading parameter m has a more significant impact on the diversity order and overall system performance than the number of reflecting elements N.
• Closed-form expressions for outage probability, ASEP, and average channel capacity are derived and validated for arbitrary N and non-integer m.
• Asymptotic analysis confirms the diversity order and coding gain in the high SNR regime, providing performance insights for system design.
• The derived expressions are accurate and applicable across a wide range of system configurations, including non-integer m and arbitrary N.
• The results demonstrate that system performance is more sensitive to fading severity (controlled by m) than to the number of reflecting elements.