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Relay Selection for Cooperative NOMA
Zhiguo Ding, Huaiyu Dai, H. Vincent Poor
TL;DR
The paper studies how relay selection affects cooperative NOMA in a downlink with two users and multiple relays. It proposes a two-stage strategy that first meets user 1’s target rate and then maximizes user 2’s rate. Analytical and simulation results show maximal diversity, minimal outage probability, and gains over max-min selection and OMA.
Problem
The paper examines relay-selection strategies for cooperative NOMA, focusing on their effect on outage probability and diversity gain.
Method
The paper proposes two-stage relay selection: filter relays by user 1’s target-rate requirement, then select the eligible relay maximizing user 2’s rate.
Results
The two-stage scheme achieves diversity gain N and minimizes overall outage probability; simulations show it outperforms max-min selection and OMA in supported comparisons.
Takeaways & Limitations
Two-stage relay selection provides the reported optimal outage and diversity performance for the addressed cooperative NOMA scenario, while max-min selection matches it only under symmetrical setups.
Abstract
from arXiv · showhide
This letter studies the impact of relay selection (RS) on the performance of cooperative non-orthogonal multiple access (NOMA). In particular, a two-stage RS strategy is proposed, and analytical results are developed to demonstrate that this two-stage strategy can achieve the minimal outage probability among all possible RS schemes, and realize the maximal diversity gain. The provided simulation results show that cooperative NOMA with this two-stage RS scheme outperforms that with the conventional max-min approach, and can also yield a significant performance gain over orthogonal multiple access.
I. INTRODUCTION
Cooperative NOMA extends NOMA through relay-assisted transmission, exploiting spatial degrees of freedom even with single-antenna nodes. This letter studies relay selection for a downlink with one base station, two users, and multiple relays.
- NOMA is positioned as a technology for improving 5G spectral efficiency and has been included in 4G LTE.
- Prior cooperative NOMA designs use cooperating users, dedicated relays, multiple-antenna relays, or wireless power transfer as an incentive.
- The paper compares conventional max-min relay selection with a two-stage strategy that first ensures one user’s target rate and then opportunistically maximizes the other user’s rate.
- Analytical results state that the two-stage strategy achieves maximal diversity gain and optimal outage probability, while max-min selection is generally worse except under symmetry.
II. SYSTEM MODEL
The system is a single-antenna downlink with no direct BS–user link, where relays forward a superimposed NOMA signal under fixed power allocation. Users are differentiated by QoS requirements rather than channel ordering.
- The model contains one BS, two users, and N relays, with single antennas, no direct BS–user link, and independent identically distributed Rayleigh fading on both hops.
- User 1 requires quick low-rate small-packet service, while user 2 is served opportunistically according to QoS requirements.
- The BS transmits the superimposed signal α1s1 + α2s2, where si is user i’s signal and αi is its power allocation coefficient.
- During the second slot, a relay that decodes both signals forwards the superimposed signal to the users through relay–user channels.
- The paper uses fixed power allocation; optimizing coefficients or using different policies across time slots is outside its scope.
1) Max-min relay selection:
The conventional max-min strategy selects the relay with the strongest minimum channel quality across the BS–relay and both relay–user links.
- Max-min relay selection chooses the relay maximizing min{|hn|2, |gn,1|2, |gn,2|2}.
- This criterion jointly considers the BS–relay link and the two relay–user links when selecting a relay.
2) Two-stage relay selection:
The two-stage strategy first filters relays according to user 1’s target-rate requirement, then selects among the eligible relays to maximize user 2’s rate.
- 2) Two-stage relay selection:: The first stage constructs a relay subset focused on realizing user 1’s targeted data rate.
- 2) Two-stage relay selection:: The second stage selects from that subset the relay that maximizes user 2’s rate.
III. PERFORMANCE ANALYSIS
The analysis derives the outage probability of the two-stage relay-selection scheme, establishes its maximal diversity gain and outage optimality, and compares it with max-min selection under symmetric conditions.
- Outage characterization: The overall outage event is decomposed into O1, where s1 fails, and O2, where s2 fails while s1 succeeds at the relevant nodes.O2 is further written using relay decoding and user-2 decoding events when the selected-relay subset is nonempty.
- Outage characterization: The two-stage scheme’s outage probability is obtained in closed form by combining the probabilities of the categorized outage events and the relay-subset size.The derivation uses the CDF of the selected relay’s variable and the probability of having l relays in the first-stage subset.
- Diversity gain: N is the achieved diversity gain of the two-stage relay-selection scheme, which equals the maximal diversity gain available with N relays.This conclusion follows from the high-SNR approximation of the outage probability.
- Optimality: The two-stage relay-selection scheme minimizes the overall outage probability for the addressed cooperative NOMA scenario.The proof argues that no alternative relay can avoid O2 when the relay selected by the two-stage criterion causes O2.
- Comparison with max-min selection: The two-stage scheme outperforms max-min selection in simulations, while both schemes achieve the same performance for symmetric setups such as ξ1 = ξ2.Under ξ1 = ξ2, the max-min outage probability is shown to equal the expression from Lemma 1.
IV. NUMERICAL STUDIES
Simulations compare cooperative NOMA using max-min and two-stage relay selection, including against OMA. The two-stage scheme performs better when user target rates differ, with larger gains as more relays are added, while equal targets yield identical performance.
- Cooperative NOMA efficiently reduces outage probability compared with OMA in the simulations.The OMA comparison uses four time slots and max-min relay selection.
- When ξ1 ≠ ξ2, two-stage relay selection outperforms max-min relay selection.
- The performance gap between the two relay-selection schemes is small with few relays but increases when more relays are used.
- When ξ1 = ξ2, the two relay-selection schemes achieve the same performance.
- Simulation results perfectly match the analytical results developed in Lemma 1.This agreement demonstrates the accuracy of the analytical results.
V. CONCLUSIONS
The paper studies how relay selection affects cooperative NOMA and develops a closed-form outage expression for the two-stage scheme. The analysis shows that this scheme achieves optimal diversity gain and minimal outage probability, whereas max-min selection generally incurs an outage-probability loss except in symmetrical setups.
- The paper proposes and studies two relay-selection strategies for cooperative NOMA, including a two-stage scheme with a closed-form outage expression.
- The two-stage scheme achieves both optimal diversity gain and minimal outage probability.
- Max-min relay selection results in an outage-probability loss relative to the two-stage scheme, except in symmetrical setups.