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Outage Performance for Cooperative NOMA Transmission with an AF Relay
Xuesong Liang, Yongpeng Wu, Derrick Wing Kwan Ng, Yiping Zuo, Shi Jin, Hongbo Zhu
TL;DR
Exact outage analysis is intractable because relevant random events are correlated; the paper derives a closed-form approximation and analyzes high-SNR behavior. Cooperative NOMA has the same diversity order as cooperative OMA but superior coding gain.
Problem
Exact outage probability is important for this system, but its analytical expression is intractable because the relevant random events are correlated.
Source: A. Outage Probability · p. 2, §III · p. 2Method
The paper derives a closed-form approximation for system outage probability and investigates its high-SNR asymptotic behavior.
Source: A. Outage Probability · p. 2, §V · p. 4Results
Cooperative NOMA and cooperative OMA have the same diversity order, 1, while cooperative NOMA has superior coding gain and outage performance.
Source: §IV · pp. 3–4Takeaways & Limitations
When relay transmit power is much smaller than BS transmit power, outage performance improves as the relay moves closer to the indirect-link user.
Source: §I · p. 1, §IV · p. 4
Abstract
from arXiv · showhide
This letter studies the outage performance of cooperative non-orthogonal multiple access (NOMA) network with the help of an amplify-and-forward relay. An accurate closed-form approximation for the exact outage probability is derived. Based on this, the asymptotic outage probability is investigated, which shows that cooperative NOMA achieves the same diversity order and the superior coding gain compared to cooperative orthogonal multiple access. It is also revealed that when the transmit power of relay is smaller than that of the base station, the outage performance improves as the distance between the relay and indirect link user decreases.
I. INTRODUCTION
Earlier cooperative NOMA work often assumed users lacked direct BS links, while AF-relaying NOMA outage results had not been reported. This letter studies a dedicated AF relay and compares cooperative NOMA with cooperative OMA.
I. INTRODUCTION
- Prior cooperative NOMA schemes with dedicated relays usually assumed no direct BS-user links, although typical small-cell scenarios can include both direct and indirect users.The letter identifies AF-relaying NOMA as an unreported case motivating this study.Source: §I · p. 1
- The letter studies downlink cooperative NOMA with direct and indirect users assisted by a dedicated AF relay.It compares overall outage probability with cooperative OMA and derives a closed-form approximation that closely matches exact results.Source: §I · p. 1
- 1 is the system's diversity order, while coding gain depends on relay location; with much lower relay power, performance improves as the relay nears the indirect-link user.Monte Carlo simulations validate the analytical results.Source: §I · p. 1
II. SYSTEM MODEL
The system has one base station, two users, and a half-duplex AF relay: UE1 has a direct BS link, whereas UE2 relies on the relay. It uses two equal-length time slots and NOMA superposition.
II. SYSTEM MODEL
- The model has one BS, UE1, UE2, and a single-antenna half-duplex AF relay; UE1 has a direct BS link, while UE2 has no direct path.The two phases are equal-length time slots.Source: §II · p. 1
- The BS broadcasts the superposition x1 + x2 to the relay and UE1, with x1 and x2 carrying UE1's and UE2's signals and P1 < P2.The total BS transmit power is PT = P1 + P2.Source: §II · p. 2
- The BS-to-UE1 and BS-to-relay channels are independent Rayleigh fading, and receiver noise at UE1 and the relay is zero-mean AWGN with variance N0.The relay-to-user channels are also described as independent Rayleigh fading.Source: §II · p. 2
- In the second slot, the BS is silent and the relay amplifies its received signal before broadcasting to UE1 and UE2.The relayed UE1 signal includes an effective channel and noise combining forwarded relay noise with receiver noise.Source: §II · p. 2
- UE1 decodes UE2's data first, applies successive interference cancellation, then decodes its own data; it combines its two received signals using maximum-ratio combining.UE2 decodes x2 from the relay transmission.Source: §II · p. 2
III. OUTAGE PERFORMANCE ANALYSIS
Exact outage analysis for the cooperative NOMA system is mathematically intractable. The paper therefore derives a closed-form approximation and uses it to discuss high-SNR outage behavior.
III. OUTAGE PERFORMANCE ANALYSIS
- The exact outage probability expression for the considered system is mathematically intractable.Outage probability is treated as an important performance metric for the system.Source: §III · p. 2
- A closed-form approximation is derived as an alternative to the exact outage probability expression.Source: §III · p. 2
- The approximation is used to discuss the system's asymptotic outage characteristics in the high-SNR regime.Source: §III · p. 2
A. Outage Probability
The system outage event covers failure to decode any required signal, but its exact probability is mathematically intractable. The paper derives a closed-form approximation and relates decoding probabilities to user outage estimates.
A. Outage Probability
- System outage occurs if UE1 fails to decode x2 or x1, or UE2 fails to decode x2.The decoding thresholds are f(R1) for x1 and f(R2) for x2.Source: A. Outage Probability · p. 2
- A closed-form outage-probability approximation is derived and reported to be sufficiently accurate against exact results.The exact expression is difficult to analyze because the outage events are correlated.Source: A. Outage Probability · p. 2
- When P2/P1 ≤ f(R2), x2 cannot be decoded by either UE, so the base station must assign it at least PT · f(R2)/(1 + f(R2)).Source: A. Outage Probability · p. 2
- P_A and P_B are the probabilities that UE1 decodes x1 and UE2 decodes x2, respectively, and 1 − P_A and 1 − P_B estimate their outage probabilities.Source: A. Outage Probability · p. 3
B. Asymptotic Analysis
The paper analyzes outage in the high-SNR regime using an asymptotic expression based on its approximation. It reports diversity order one and better outage performance when the relay is closer to UE2 under the stated condition.
B. Asymptotic Analysis
- For P2/P1 > f(R2), the asymptotic outage expression applies as the average SNR tends to infinity.The analysis fixes PR/PT and P1/PT while PT/N0 increases without bound.Source: B. Asymptotic Analysis · p. 3
- The asymptotic expression is obtained by approximating K1(x) as 1/x for small x and dropping higher-order Taylor terms.Source: B. Asymptotic Analysis · p. 3
- The cooperative NOMA system has diversity order one.Source: B. Asymptotic Analysis · p. 3
- When λ < 1, outage performance is superior with the relay closer to UE2 than to the base station, for a fixed sum distance.The paper attributes this to the relay's transmit power being fully utilized when it is near the user.Source: B. Asymptotic Analysis · p. 3
IV. NUMERICAL RESULTS
The numerical results show that the outage approximation closely matches cooperative NOMA simulations and that NOMA outperforms cooperative OMA across SNR regimes, with the same diversity order but superior coding gain. They also examine how relay location affects coding gain.
IV. NUMERICAL RESULTS
- The simulations average 105 independent channel realizations, set noise power to N0 = 1, and vary PT from 10 dB to 35 dB.Source: §IV · p. 3
- The numerical study defines Cases A, B, and C using channel-variance and power-ratio conditions, with distinct parameter settings for Cases A and C relative to Case B-I.Source: §IV · pp. 3–4
- For a fair comparison, cooperative OMA uses data requirements 1.5 times those of cooperative NOMA because OMA uses three equal-length slots rather than two.Source: §IV · p. 3
- Case B-I uses BS–R and R–UE2 distances of 30 m and 45 m, respectively; Case B-II reverses them, and coding gain improves when R is closer to UE2.Source: §IV · pp. 3–4, Figure 1 · p. 3
- The approximation closely matches exact cooperative NOMA outage, especially at high SNR, while NOMA outperforms cooperative OMA across SNR regimes with the same diversity order and superior coding gain.Source: §IV · pp. 3–4
V. CONCLUSION
The letter studies outage performance for downlink cooperative NOMA with an AF relay and derives a closed-form outage approximation verified by numerical simulations. Its high-SNR analysis indicates superior coding gain over cooperative OMA without loss of diversity order.
V. CONCLUSION
- The letter derives a closed-form approximation of outage probability for downlink cooperative NOMA with an AF relay, and numerical simulations verify its accuracy.Source: §V · p. 4
- At high SNR, cooperative NOMA is superior to cooperative OMA in coding gain without losing diversity order.Source: §V · p. 4
- The simulations examine how relay-location variations affect system coding gain.Source: §V · p. 4
APPENDIX A PROOF OF PROPOSITION 1
The proof assembles expressions for terms in (18) and substitutes them to obtain (17), completing the derivation.
APPENDIX A PROOF OF PROPOSITION 1
- The first term in (18) is given by (15), with η specified in the derivation.Source: Appendix A · p. 4
- The second term in (18) is given by (16), with λ = PR/PT and μ = 2θr.Source: Appendix A · p. 4
- Substituting (15) and (16) into (18) yields (17), completing the proof.Source: Appendix A · p. 4