Source-linked AI summary
Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface Assisted NOMA Networks
Xinwei Yue, Jin Xie, Yuanwei Liu, Zhihao Han, Rongke Liu, Zhiguo Ding
TL;DR
The paper addresses STAR-RIS-NOMA performance when signals serve nearby and distant users across both sides of the surface, including imperfect SIC. It derives outage and ergodic-rate approximations over Rician fading and reports improved outage and ergodic-rate performance over OMA and conventional cooperative communication baselines.
Problem
Reflection-only RIS restricts users to one side of the source, while existing STAR-RIS-NOMA analysis assumes pSIC despite residual interference in practical receivers.
Method
The paper derives approximate and asymptotic outage probabilities, diversity orders, ergodic rates, and throughput for STAR-RIS-NOMA over Rician fading with ipSIC and pSIC.
Results
STAR-RIS-NOMA outage probability outperforms STAR-RIS-OMA and conventional cooperative communication, while its ergodic rates exceed STAR-RIS-OMA.
Takeaways & Limitations
Increasing reflecting elements K and Rician factor κ enhances STAR-RIS-NOMA performance, while residual interference can produce a zero diversity order for user n with ipSIC.
Abstract
from arXiv · showhide
Simultaneously transmitting/refracting and reflecting reconfigurable intelligent surface (STAR-RIS) has been introduced to achieve full coverage area. This paper investigate the performance of STAR-RIS assisted non-orthogonal multiple access (NOMA) networks over Rician fading channels, where the incidence signals sent by base station are reflected and transmitted to the nearby user and distant user, respectively. To evaluate the performance of STAR-RIS-NOMA networks, we derive new approximate expressions of outage probability and ergodic rate for a pair of users, in which the imperfect successive interference cancellation (ipSIC) and perfect SIC (pSIC) schemes are taken into consideration. Based on the asymptotic expressions, the diversity orders of the nearby user with ipSIC/pSIC and distant user are achieved carefully. The high signal-to-noise ratio slopes of ergodic rates for nearby user with pSIC and distant user are equal to $one$ and $zero$, respectively. In addition, the system throughput of STAR-RIS-NOMA is discussed in delay-limited and delay-tolerant modes. Simulation results are provided to verify the accuracy of the theoretical analyses and demonstrate that: 1) The outage probability of STAR-RIS-NOMA outperforms that of STAR-RIS assisted orthogonal multiple access (OMA) and conventional cooperative communication systems; 2) With the increasing of reflecting elements $K$ and Rician factor $κ$, the STAR-RIS-NOMA networks are capable of attaining the enhanced performance; and 3) The ergodic rates of STAR-RIS-NOMA are superior to that of STAR-RIS-OMA.
I. INTRODUCTION
The paper motivates combining NOMA with STAR-RIS to extend coverage beyond reflection-only RIS constraints, and analyzes outage, ergodic-rate, and throughput performance under practical SIC conditions.
- STAR-RIS reflects and refracts incident signals toward users on the same and opposite sides of the source, extending coverage to the entire space.
- Existing STAR-RIS-NOMA outage analysis considered perfect SIC, whereas practical receivers may experience residual interference from imperfect SIC.
- The paper derives approximate outage probabilities and asymptotic diversity orders for nearby user n with ipSIC/pSIC and distant user m over Rician fading channels.
- STAR-RIS-NOMA with pSIC has lower outage probability than STAR-RIS-OMA and conventional cooperative communication systems, while increasing K and κ enhances outage performance.
- The paper derives ergodic-rate expressions and evaluates system throughput in both delay-limited and delay-tolerant modes.
A. Signal Model
The signal model considers a STAR-RIS-assisted downlink NOMA pair in which nearby user n receives direct and reflected signals, while distant user m receives transmitted STAR-RIS signals.
- The base station broadcasts superposed signals through STAR-RIS to nearby user n and distant user m.
- The STAR-RIS has 2K configurable elements divided between reflecting and transmitting links, with Rician fading used for the wireless channels.
- User m receives only the signal transmitted by STAR-RIS, whereas user n can receive both the BS signal and the signal reflected by STAR-RIS.
- User n performs SIC by first detecting user m’s signal, subtracting it, and then decoding its own information.
- Imperfect SIC is modeled through residual interference, while pSIC and ipSIC correspond to zero and nonzero residual-interference operations, respectively.
B. STAR-RIS-OMA
The paper uses STAR-RIS-OMA as a comparison baseline and models the Rician and cascaded-Rician channel statistics needed to evaluate outage behavior.
- STAR-RIS-OMA is selected as a baseline, with detecting SNRs specified for users n and m under the same system assumptions.
- The channel statistical properties of Rician and cascaded-Rician channels are developed for evaluating STAR-RIS-NOMA outage behavior.
- The direct BS-to-user-n channel follows a Rician distribution described through its PDF and CDF.
- The analysis uses coherent phase shifting, matching each element’s phase to incoming and outgoing channel phases.
- The cascaded-channel analysis uses modified Bessel functions, element-level variables X_k, and their mean μ_ϕ and variance Ω_ϕ.
III. OUTAGE PROBABILITY
This section derives approximate outage probabilities for the nearby user under imperfect and perfect SIC in STAR-RIS-NOMA over Rician fading. It formulates the nearby user's outage through successive decoding events and provides quadrature-based expressions, including a pSIC special case.
- User n outage formulation: The nearby user first detects the distant user’s signal and then decodes its own signal under SIC.Outage occurs if distant-user detection fails or if that detection succeeds but nearby-user decoding fails.
- User n outage formulation: The nearby-user outage probability is decomposed into failure to detect xm or successful xm detection followed by failure to decode xn.The corresponding thresholds are γthn = 2Rn − 1 and γthm = 2Rm − 1.
- Approximate expressions: Approximate outage expressions are derived for user n with ipSIC and pSIC under Rician fading.The pSIC result is presented as a special case obtained by setting the residual-interference parameter to zero and applying Gaussian-Chebyshev quadrature.
- Approximate expressions: The analytical expressions use Gauss-Laguerre quadrature parameters whose choices provide a complexity-accuracy tradeoff.The quadrature uses abscissas and weights associated with Laguerre polynomial zeros.
B. The Outage Probability of User m
This section derives outage expressions for the distant user and combines user-level results into system outage probabilities for STAR-RIS-NOMA and STAR-RIS-OMA. The NOMA distant-user outage is determined by failure to decode its refracted signal.
- User m outage: The distant-user outage event occurs when user m cannot detect its refracting signal xm.Its outage probability is represented as Pr(γm < γthm).
- User m outage: An approximate expression for user m’s outage probability is derived under Rician fading.The derivation uses a lower incomplete Gamma function and assumes am > γthm an.
- System outage: The STAR-RIS-NOMA system outage probability combines the nearby-user ipSIC or pSIC outage with the distant-user outage.The component probabilities are taken from the derived expressions for users n and m.
- STAR-RIS-OMA comparison: STAR-RIS-OMA uses two time slots, with separate transmissions for users n and m through the STAR-RIS.Its user outage is defined by the instantaneous SNR falling below a target threshold, and approximate expressions are derived for both users.
- STAR-RIS-OMA comparison: The STAR-RIS-OMA system outage probability is obtained by combining the separately derived outage probabilities of users n and m.The resulting expression parallels the STAR-RIS-NOMA system-outage construction.
D. Diversity Analysis
The diversity analysis characterizes how outage probability decays with increasing SNR and examines asymptotic behavior for both SIC schemes and both users. It also introduces ergodic-rate approximations and identifies an exact-solution difficulty for one expression.
- Diversity analysis: Diversity order measures how quickly outage probability decreases with increasing SNR, with larger order indicating faster decay and greater fading robustness.The analysis uses high-SNR asymptotic outage expressions to obtain these orders.
- Diversity analysis: User n with ipSIC achieves zero diversity order because residual interference makes its high-SNR outage probability approach a constant.This behavior is stated to be consistent with conventional cooperative NOMA communications.
- Diversity analysis: User n with pSIC achieves diversity order K + 1, linked to the number of configurable elements K and the direct communication link.The pSIC asymptotic expression is obtained using the Laplace transform and convolution theorem.
- Diversity analysis: User m achieves diversity order K, which depends only on the number of configurable elements.For STAR-RIS-OMA, the corresponding diversity orders are K + 1 for user n and K for user m.
- Ergodic-rate analysis: Approximate ergodic-rate expressions are provided for user n with pSIC and for user m under Rician fading.The ergodic-rate analysis also considers ipSIC and pSIC, while the user-n expression is difficult to solve exactly in closed form.
A. Slope Analysis
The high-SNR ergodic-rate slopes are one for user n with pSIC, zero for user m, and one half for both users in STAR-RIS-OMA.
- Slope Analysis: One is the high-SNR slope of user n with pSIC in STAR-RIS-NOMA.The direct BS–user n link does not improve this slope.
- Slope Analysis: Zero is the high-SNR slope of user m in STAR-RIS-NOMA.
- Slope Analysis: One half is the high-SNR slope of both users in STAR-RIS-OMA.
B. Delay-tolerant Transmission
The paper formulates STAR-RIS-NOMA throughput for delay-tolerant transmission, where the base station sends information at a constant data rate constrained by channel conditions.
- Delay-tolerant Transmission: Delay-tolerant transmission uses a constant data rate constrained by the user’s channel conditions.The corresponding STAR-RIS-NOMA throughput with pSIC is obtained from the ergodic-rate and outage expressions.
V. SIMULATION RESULTS
Simulations verify the theoretical STAR-RIS-NOMA analyses and examine the effects of configurable elements, Rician factor, interference, propagation conditions, and power allocation. The results show improved outage performance under pSIC versus OMA and cooperative benchmarks, while channel and allocation conditions materially affect users differently.
- V. SIMULATION RESULTS: The simulations use summarized parameters and validate the analytical outage and ergodic-rate expressions for STAR-RIS-NOMA.The approximation tradeoff parameters are P = 300 and U = 50.
- V. SIMULATION RESULTS: The asymptotic outage probabilities match exact curves at high SNR, while ipSIC produces an error floor and zero diversity gain for user n.Increasing residual interference worsens user n’s ipSIC outage performance.
- V. SIMULATION RESULTS: STAR-RIS-NOMA with pSIC has better outage performance than STAR-RIS-OMA and conventional cooperative communication systems.The comparison includes HD/FD decode-and-forward and amplify-and-forward relays.
- V. SIMULATION RESULTS: Increasing channel-estimation errors from Ωe = −30 dB to Ωe = −20 dB increases pSIC outage probability and produces high-SNR error floors.
- V. SIMULATION RESULTS: Increasing the Rician factor from κ = 0 dB to κ = 5 dB decreases outage probability for users n and m.The paper attributes this behavior to dominant line-of-sight components in Rician fading channels.
- V. SIMULATION RESULTS: Increasing the dynamic power-allocation factor improves user n with pSIC but gradually worsens user m’s outage behavior.User m suffers more interference when detecting its own information, motivating balanced power allocation.
B. Ergodic Rate
The ergodic-rate analysis shows distinct high-SNR behavior for the two users and compares STAR-RIS-NOMA with orthogonal users. System throughput improves with perfect SIC and increasing reconfigurable elements in both transmission modes.
- Ergodic-rate behavior: User m's ergodic rate converges to a throughput ceiling, yielding a zero high-SNR slope.This behavior is attributed to the rate discussion in Remark 6.
- Ergodic-rate behavior: User n with ipSIC approaches a constant ergodic rate at high SNR because of residual interference.
- Ergodic-rate comparison: At high SNR, user n with pSIC outperforms orthogonal users, whereas user m is inferior to its orthogonal counterpart.The comparison is linked to the larger high-SNR slope of user n with pSIC and the zero slope of user m.
- System throughput: In delay-limited transmission, the pSIC system-throughput curves are superior to the corresponding ipSIC curves.The comparison uses Rn = Rm = 0.5 BPCU, K = 5, and κ = −5 dB.
- System throughput: Increasing the number of reconfigurable elements enhances the system throughput of STAR-RIS-NOMA by lowering outage probabilities for both users.
- System throughput: In delay-tolerant transmission, STAR-RIS-NOMA with pSIC outperforms its ipSIC and STAR-RIS-OMA counterparts.The cited discussion considers K = 5 and κ = −5 dB.
APPENDIX A: PROOF OF THEOREM 1
The appendix derives approximate outage probabilities for the nearby and distant users under ipSIC by transforming the cascaded Rician-channel variables and evaluating the resulting integrals numerically.
- User n with ipSIC: The ipSIC outage probability of user n is first obtained by substituting the system expressions into the outage condition.
- User n with ipSIC: A Laguerre-polynomial series approximates the PDF of X because the cascaded Rician PDF is difficult to calculate directly.The appendix characterizes this PDF as unimodal with tails extending on both sides.
- User n with ipSIC: The PDF of Z is derived by combining the transformed variables and applying algebraic manipulations.
- User n with ipSIC: Gauss-Chebyshev and Gauss-Laguerre quadratures approximate the definite and indefinite integrals needed for the closed-form outage expression.
- User m: The outage probability of user m is derived from its system expression using coherent phase shifting for correlated Rician fading channels.
APPENDIX C: PROOF OF COROLLARY 3
The appendix develops high-SNR asymptotic outage analysis using Laplace transforms, convolution, inverse transforms, and series approximations for the relevant cascaded Rician variables.
- High-SNR asymptotics: The asymptotic outage calculation begins by approximating the PDF and CDF of variable V at high SNR.
- High-SNR asymptotics: The Laplace transform of the PDF for Xk is derived using a hypergeometric-function expression and its large-s approximation.
- High-SNR asymptotics: The convolution theorem yields the Laplace transform of X, which is then approximated by retaining the first series term.
- High-SNR asymptotics: The PDF of |hsn| is expressed as a series involving little-O notation before constructing the high-SNR PDF of V.
- High-SNR asymptotics: Applying the inverse Laplace transform produces the high-SNR PDF of V, which is substituted into the outage expression to complete the proof.
- User m ergodic rate: For user m's ergodic rate, coherent phase shifting and the CDF of X2 lead to an approximation evaluated with Gauss-Chebyshev quadrature.