[Paper Review] STAR-RISs: A Correlated T&R Phase-Shift Model and Practical Phase-Shift Configuration Strategies

Jiaqi Xu, Yuanwei Liu+3 more|arXiv (Cornell University)|Dec 1, 2021

Advanced Wireless Communication TechnologiesEngineering24 references12 citations

TL;DR

This paper proposes a correlated transmission and reflection (T&R) phase-shift model for passive, lossless STAR-RISs, which accounts for electromagnetic constraints limiting independent control of transmitted and reflected signals. It introduces three practical phase-shift configuration (PSC) strategies—PS-PSC, DP-PSC, and TR-PSC—and demonstrates that the DP-PSC strategy achieves full diversity order for users on both sides of the STAR-RIS, matching the performance upper bound of the independent phase-shift model with only 4 dB power degradation.

ABSTRACT

A correlated transmission and reflection (T&R) phase-shift model is proposed for passive lossless simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs). A STAR-RIS-aided two-user downlink communication system is investigated for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA). To evaluate the impact of the correlated T&R phase-shift model on the communication performance, three phase-shift configuration strategies are developed, namely the primary-secondary phase-shift configuration (PS-PSC), the diversity preserving phase-shift configuration (DP-PSC), and the T/R-group phase-shift configuration (TR-PSC) strategies. Furthermore, we derive the outage probabilities for the three proposed phase-shift configuration strategies as well as for those of the random phase-shift configuration and the independent phase-shift model, which constitute performance lower and upper bounds, respectively. Then, the diversity order of each strategy is investigated based on the obtained analytical results. It is shown that the proposed DP-PSC strategy achieves full diversity order simultaneously for users located on both sides of the STAR-RIS. Moreover, power scaling laws are derived for the three proposed strategies and for the random phase-shift configuration. Numerical simulations reveal a performance gain if the users on both sides of the STAR-RIS are served by NOMA instead of OMA. Moreover, it is shown that the proposed DP-PSC strategy yields the same diversity order as achieved by STAR-RISs under the independent phase-shift model and a comparable power scaling law with only 4 dB reduction in received power.

Motivation & Objective

• To address the lack of realistic hardware models for passive, lossless STAR-RISs that account for electromagnetic coupling between transmission and reflection.
• To develop practical phase-shift configuration (PSC) strategies that respect physical constraints of passive STAR-RIS elements.
• To evaluate the performance of these strategies in terms of outage probability, diversity order, and power scaling laws under OMA and NOMA.
• To establish performance bounds using random and independent phase-shift models as lower and upper bounds, respectively.

Proposed method

• Proposes a correlated T&R phase-shift model based on electromagnetic theory, enforcing energy conservation and boundary conditions for passive lossless elements.
• Develops three PSC strategies: PS-PSC (primary-secondary), DP-PSC (diversity preserving), and TR-PSC (T/R-group) to manage phase shifts under physical constraints.
• Derives asymptotic outage probability expressions for OMA and NOMA using Laplace transforms and Taylor expansion of PDFs near the origin.
• Analyzes diversity order by examining the asymptotic behavior of outage probability at high SNR.
• Derives power scaling laws showing M² scaling for DP-PSC and PS-PSC, and M scaling for random PSC.
• Validates analytical results with simulations, including beam pattern analysis and performance comparison across strategies.

Experimental results

Research questions

• RQ1 How does the correlated T&R phase-shift model affect the performance of STAR-RIS-aided systems under practical hardware constraints?
• RQ2 Can practical PSC strategies achieve full diversity order for users on both sides of the STAR-RIS?
• RQ3 What is the power scaling law of the proposed PSC strategies compared to the independent phase-shift model and random configuration?
• RQ4 How does the presence of direct links affect the diversity order and outage performance?
• RQ5 What is the performance gain of NOMA over OMA in STAR-RIS-aided systems under the proposed model?

Key findings

• The DP-PSC strategy achieves full diversity order (M+1) for users on both sides of the STAR-RIS, even with direct links, provided the direct link is sufficiently strong (η ≥ 0.5).
• The DP-PSC strategy achieves the same diversity order as the independent phase-shift model, confirming its optimality in diversity gain.
• The DP-PSC strategy exhibits a power scaling law of M², matching the performance upper bound of the independent phase-shift model.
• The DP-PSC strategy incurs only 4 dB power degradation compared to the upper bound, with 10 log₁₀(4/π²) ≈ -3.9 dB loss.
• Numerical results confirm a performance gain when using NOMA instead of OMA, especially under the DP-PSC strategy.
• The random PSC strategy shows only M scaling, resulting in 5 dB power gain when doubling M from 15 to 30, compared to 10 dB for DP-PSC.