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Cooperative Non-Orthogonal Multiple Access with Simultaneous Wireless Information and Power Transfer
Yuanwei Liu, Zhiguo Ding, Maged Elkashlan, H. Vincent Poor
TL;DR
The paper addresses cooperative NOMA with spatially random users whose near relays are energy constrained. It proposes cooperative SWIPT NOMA with location-based selection and derives outage, throughput, and diversity results. The reported results show that SWIPT preserves diversity relative to conventional cooperation, while opportunistic location-based selection outperforms random selection in outage and throughput.
Problem
Cooperative NOMA must improve far-user reliability while near users are energy constrained and harvest energy from received RF signals.
Method
The paper proposes cooperative SWIPT NOMA with three location-based user selection schemes and derives closed-form outage and delay-sensitive throughput expressions using stochastic geometry.
Results
The three schemes have the same diversity order as conventional cooperative networks, while NNNF achieves the lowest outage probability and highest throughput for both near and far users.
Takeaways & Limitations
Opportunistic use of node locations can provide lower outage probability and higher throughput than random selection without jeopardizing the diversity gain from cooperative transmission.
Abstract
from arXiv · showhide
In this paper, the application of simultaneous wireless information and power transfer (SWIPT) to non-orthogonal multiple access (NOMA) networks in which users are spatially randomly located is investigated. A new cooperative SWIPT NOMA protocol is proposed, in which near NOMA users that are close to the source act as energy harvesting relays to help far NOMA users. Since the locations of users have a significant impact on the performance, three user selection schemes based on the user distances from the base station are proposed. To characterize the performance of the proposed selection schemes, closed-form expressions for the outage probability and system throughput are derived. These analytical results demonstrate that the use of SWIPT will not jeopardize the diversity gain compared to the conventional NOMA. The proposed results confirm that the opportunistic use of node locations for user selection can achieve low outage probability and deliver superior throughput in comparison to the random selection scheme.
I. INTRODUCTION
The paper proposes cooperative SWIPT NOMA, using energy-harvesting near users as relays for far users in spatially random networks. It develops location-aware user selection and analytical performance measures for this protocol.
- I. INTRODUCTION: The protocol combines NOMA’s power-domain access with cooperative relaying, where near users decode far-user information before forwarding it.Successive interference cancellation at near users makes the far-user information available for decode-and-forward relaying.
- A. Motivation and Contributions: Cooperative SWIPT NOMA uses energy-constrained near users as energy-harvesting relays to improve far-user reliability without consuming extra energy.The near users harvest energy from received RF signals and forward information to far users.
- A. Motivation and Contributions: Three user selection schemes opportunistically account for near and far users’ locations in the stochastic-geometry model.Near users are deployed close to the base station, while far users are deployed near the cell edge using homogeneous PPPs.
- A. Motivation and Contributions: Closed-form outage probabilities and delay-sensitive throughput expressions are derived for the three proposed selection schemes.The analysis covers outage at both near and far users and throughput based on those outage probabilities.
- A. Motivation and Contributions: All three selection schemes have the same diversity order, and far-user diversity matches that of conventional cooperative networks without radio-frequency energy harvesting.This establishes that adding SWIPT does not reduce the stated diversity gain for far users.
B. Phase 2: Cooperative Transmission
During cooperative transmission, the selected near user forwards the far user’s decoded message using harvested energy. The destination combines direct and relayed signals, while the analysis characterizes selection-dependent outage behavior.
- B. Phase 2: Cooperative Transmission: The near user forwards the far user’s message using energy harvested during the direct transmission phase.The forwarded signal travels over the near-to-far channel before destination combining.
- B. Phase 2: Cooperative Transmission: The far user combines direct and cooperative transmissions using maximal-ratio combining.The resulting received SINR combines the direct-phase SNR with the cooperative-phase SINR.
- B. Phase 2: Cooperative Transmission: The paper characterizes performance under three user selection schemes, including random selection of one near and one far user.Random selection requires no instantaneous channel-state information and gives each user a fair access opportunity.
- B. Phase 2: Cooperative Transmission: Near-user outage can result either from failing to decode the far-user message or from failing to decode the near-user message after successful first decoding.The NOMA power-allocation condition |p_i1|^2−|p_i2|^2τ_1 > 0 is required for implementation.
1) Outage Probability of the Near Users of RNRF:
The RNRF analysis derives approximate outage probabilities for near users under arbitrary path-loss exponent α and simplifies them for α = 2. The near-user outage is characterized through decoding thresholds and conditioned spatial user distributions.
- Theorem 1 provides an approximate near-user outage probability for RNRF under an arbitrary path-loss exponent α, conditioned on the PPPs.The result applies when εAi ≥ εBi; otherwise PBi = 1.
- The near-user outage probability is defined through the CDF of the channel-related variable Yi and the decoding thresholds εAi and εBi.For εAi < εBi, the near-user outage probability is always one.
- The analysis models near and far NOMA users as independently distributed points in their respective spatial regions under homogeneous PPPs.Their location information is represented by the random variables WAi and WBi.
- Gaussian-Chebyshev quadrature is used to approximate the outage expression when exact closed-form expressions are challenging for α > 2.The approximation introduces parameters controlling the complexity-accuracy tradeoff.
- For α = 2, Corollary 1 gives a specialized outage expression for the near users, with outage equal to one when εAi < εBi.The special-case result follows from the general expression after setting α = 2.
3) Diversity Analysis of RNRF:
The RNRF diversity analysis evaluates high-SNR outage behavior for near and far users. It finds that energy harvesting preserves the near-user diversity gain and that far users retain the cooperative-network diversity order.
- Near users: The near-user diversity gain is one, so NOMA with energy harvesting does not decrease the near-user diversity gain.This follows from the high-SNR approximation of the near-user outage probability.
- Far users: The far-user diversity gain of RNRF is two, matching the conventional cooperative network without radio-frequency energy harvesting.Thus, using an energy-harvesting relay does not affect the far-user diversity gain.
- Far users: At high SNR, the dominant far-user outage term is proportional to 1/(ρ^2 ln ρ), so outage decays at a rate involving ln SNR.A conventional cooperative system without energy harvesting can achieve a faster decreasing rate proportional to 1/SNR^2.
- Throughput: The paper evaluates system throughput in the delay-sensitive mode from the derived near- and far-user outage probabilities.In this mode, transmission uses a fixed information rate and throughput is determined through outage probability.
- Location-based selection: NNNF selects the nearest near user and nearest far user, because near users also harvest energy to relay information to far users.The selection is intended to minimize outage probability for both user types.
1) Outage Probability of the Near Users of NNNF:
The NNNF analysis derives approximate outage probabilities for users selected by nearest-distance criteria. It provides arbitrary-α theorems and α = 2 corollaries for both near and far users.
- NNNF selects the near user with the shortest distance to the BS within disc DB and derives its outage probability conditioned on the PPPs.The nearest-user distance distribution is obtained from the event that no point lies closer than a specified radius.
- Theorem 3 gives an approximate near-user outage probability for NNNF under an arbitrary path-loss exponent α.The expression uses the distribution of the nearest selected near user and applies a complexity-accuracy approximation.
- The NNNF outage analysis uses the nearest selected near user as an energy-harvesting relay and characterizes its distance through a conditional PDF.The PDF is based on the shortest distance from the selected near user to the BS.
- For α = 2, Corollary 3 provides a simplified outage probability for the selected near user.The result follows after substituting the nearest-user distance distribution into the general outage expression.
- Theorem 4 derives an approximate far-user outage probability for NNNF conditioned on the PPPs and assuming RDC ≫ RDB.A corresponding α = 2 simplification is given in Corollary 4.
3) Diversity Analysis of NNNF:
The NNNF diversity analysis examines high-SNR outage behavior for both selected near and far users. Distance-based nearest-user selection preserves the diversity gains of the corresponding cooperative scheme.
- Near users: The near-user diversity gain of NNNF is one, indicating that NNNF does not affect near-user diversity.This result is obtained from the high-SNR approximation of the NNNF near-user outage probability.
- Far users: The far-user diversity gain of NNNF remains two, so NNNF does not affect far-user diversity.The far-user result is obtained by substituting the NNNF outage approximation into the diversity definition.
- Throughput: The throughput of NNNF in delay-sensitive transmission is determined from its near- and far-user outage probabilities.The relevant probabilities are those derived for the selected users.
- Selection schemes: NNNF uses the nearest near user and nearest far user, while NNFF uses the nearest near user and farthest far user.The NNFF far-user choice is motivated by creating more distinct user channel conditions.
- NNFF: For NNFF, the near-user diversity gain is one and the far-user diversity gain is two, matching NNNF.Thus, opportunistic distance-based selection does not affect the diversity gain.
4) System Throughput in Delay-Sensitive Transmission Mode of NNFF:
The proposed cooperative SWIPT NOMA protocol is evaluated through analytical and numerical outage and throughput results for three location-based selection schemes. NNNF generally provides the best performance, while all schemes retain the same diversity gain and throughput depends critically on transmission-rate choices.
- Near-user outage: Simulation and analytical curves show precise agreement for near-user outage probability across the evaluated path-loss settings.Monte Carlo results verify the derived expressions, particularly across the plotted SNR conditions.
- Diversity gain: All three selection schemes have the same outage slopes and therefore the same diversity gains for near and far users.For far users, the diversity gain is two, matching the analytical result and a conventional cooperative network without RF energy harvesting.
- Selection performance: NNNF achieves the lowest outage probability and highest throughput because it selects users with the smallest path loss.NNFF outperforms RNRF for cooperative far-user transmission, although it performs worse than RNRF without cooperation.
- Rate and geometry effects: Increasing far-user rate R1 raises outage probability, while enlarging the far-user zone worsens performance through increased path loss.The near-user outage also becomes more frequent as R1 increases because the near relay must decode the far-user message first.
- Delay-sensitive throughput: Throughput ceilings appear at high SNR, and increasing R2 from 0.5 BPCU to 1 BPCU improves throughput whereas R2 = 2 BPCU lowers it.At the highest rate, insufficient remaining energy for near-user decoding causes outage and reduces throughput.
APPENDIX A: PROOF OF THEOREM 2
The proof derives outage-probability expressions through successive substitutions, distribution calculations, high-SNR approximations, and Gaussian-Chebyshev quadrature. It concludes by combining the resulting terms to obtain the theorem.
- The outage probability is first expressed by substituting earlier results into the governing equation.
- High-SNR approximations use Bessel-function series representations and special-function identities.
- For arbitrary α, mathematically intractable integrals and cumulative distributions are approximated using Gaussian-Chebyshev quadrature.
- Combining the derived intermediate expressions yields the stated result, completing the proof.
APPENDIX B: PROOF OF COROLLARY 2
The corollary proof specializes the preceding derivation to α = 2. It rewrites the relevant expression after substituting the specialized parameter value.
- The proof rewrites the integral expression after applying α = 2.
- The specialization is obtained by substituting the preceding expression into the general derivation.
- The resulting formulation provides the starting point for the α = 2 corollary.
Z RDA
This section derives outage-probability expressions for the selected near user under the stated user-count conditions and distance approximation. The derivation uses stochastic-geometry distributions and Gaussian-Chebyshev quadrature.
- Conditioning on at least one user in each group, the outage probability is formed by replacing selected-user variables in the preceding expression.
- The selected-user distances are defined relative to the base station and between the selected near and far users.
- Because RDC ≫ RDB, the inter-user distance is approximated as d_Ai* ≈ d_Ci*.
- Stochastic geometry within the relevant ring yields the probability density of the nearest selected near user.
- Gaussian-Chebyshev quadrature is then applied to approximate the derived quantity Φ*.
R RDA
The derivation for the selected-user case evaluates intermediate outage terms conditioned on group occupancy. It combines cumulative-distribution calculations, quadrature approximations, and a high-SNR approximation to obtain the final result.
- Gaussian-Chebyshev quadrature approximates the intermediate quantities Δ* and Ψ*.
- Conditioning on the numbers of users in both groups produces Θ2* as a product of two conditional probabilities.
- The cumulative distribution of the selected near user is derived and then approximated using Gaussian-Chebyshev quadrature.
- A high-SNR approximation is applied after substituting the derived cumulative-distribution expressions.
- Combining the resulting expressions yields the stated equation and completes the proof.
APPENDIX D: PROOF OF THEOREM 5
The proof derives the outage probability for Ai′ by combining variable substitutions, distance approximations, stochastic-geometry calculations, and conditional probability expressions. It then obtains the general case and the special case α = 2.
- The outage probability for Ai′ is expressed by substituting Xi∗→Xi, Yi∗→Yi, and Zi∗→Zi in (A.1).
- The derivation uses distances from the BS to Ai′ and from Ai′ to Bi∗, with dAi′ ≈ dCi′ under RDC ≫ RDB.
- Stochastic geometry within the ring DA is used to calculate the PDF fdAi′(rA) for the farthest Ai′.
- Conditioning on the numbers of Ai′ and Bi∗ yields probability terms involving Xi′ < εAi and Yi∗ < εAi.
- The general case (42) and the special case α = 2, obtained using a similar method to (38), complete the proof.