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Wireless Information and Power Transfer in Cooperative Networks with Spatially Random Relays

Z. Ding, I. Krikidis, B. Sharif, H. V. Poor

arXiv:1403.6164v1cs.IT

TL;DR

The paper asks how SWIPT can support cooperative networks with randomly located decode-forward relays while maintaining reliable transmission and effective relay allocation. It uses stochastic geometry to analyze single-source networks and coalition formation games for multiple sources. Under stated geometric assumptions, energy-harvesting relays retain the diversity gain of conventional relays, while distributed game-theoretic algorithms address relay competition among sources.

  • Problem

    The paper investigates SWIPT in cooperative networks with spatially random relays and the allocation of scarce relays among multiple competing sources.

  • Method

    It applies stochastic geometry to outage and diversity analysis for one source-destination pair, and develops distributed coalition formation algorithms for multiple sources.

  • Results

    Under α = 2 and relay-destination distances much larger than source-relay distances, energy-harvesting relays achieve the same diversity gain as conventional self-powered relays.

  • Takeaways & Limitations

    SWIPT can preserve cooperative diversity, while relay-allocation fairness should account for both relay SNR gains and their significance relative to coalition-wide SNR.

Abstract

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In this paper, the application of wireless information and power transfer to cooperative networks is investigated, where the relays in the network are randomly located and based on the decode-forward strategy. For the scenario with one source-destination pair, three different strategies for using the available relays are studied, and their impact on the outage probability and diversity gain is characterized by applying stochastic geometry. By using the assumptions that the path loss exponent is two and that the relay-destination distances are much larger than the source-relay distances, closed form analytical results can be developed to demonstrate that the use of energy harvesting relays can achieve the same diversity gain as the case with conventional self-powered relays. For the scenario with multiple sources, the relays can be viewed as a type of scarce resource, where the sources compete with each other to get help from the relays. Such a competition is modeled as a coalition formation game, and two distributed game theoretic algorithms are developed based on different payoff functions. Simulation results are provided to confirm the accuracy of the developed analytical results and facilitate a better performance comparison.

I. INTRODUCTION

The paper applies SWIPT to cooperative networks with randomly located relays, studying reliability, diversity, relay selection, and relay allocation. It combines stochastic geometry for one source-destination pair with coalition formation for multiple sources.

  • Motivation: SWIPT addresses wireless networks whose nodes lack access to external energy sources by combining information decoding with energy harvesting.The paper applies this concept to cooperative networks in which relay transmissions are powered by harvested relay-observation energy.
  • Single-source cooperative networks: For one source-destination pair, the paper models randomly deployed relays using stochastic geometry and studies three relay-use strategies.The analysis characterizes outage probability and diversity gain while accounting for spatially random relay locations.
  • Single-source cooperative networks: Under path loss exponent α = 2 and relay-destination distances much larger than source-relay distances, closed-form high-SNR results are derived for outage behavior.These assumptions are used to obtain analytical insight from otherwise complicated general expressions.
  • Relay selection: More sophisticated relay selection can improve reception reliability, but it requires additional system overhead to obtain the needed channel-state information.The paper also reports that second-order channel statistics alone do not improve diversity order under the stated asymptotic conditions.
  • Single-source cooperative networks: A randomly chosen energy-harvesting relay yields an outage decay rate proportional to log SNR / SNR^2, matching the diversity gain of conventional cooperative relaying.The result preserves diversity gain, although the outage expression includes a logarithmic factor.
  • Multiple-source cooperative networks: For multiple sources sharing relays, the paper formulates relay allocation as a coalition formation game and develops distributed algorithms with different payoff functions.The fairness analysis considers both a relay's SNR contribution and its significance relative to coalition-wide SNR to avoid unbalanced allocations.

A. Random relay selection

Randomly selecting an energy-harvesting relay yields an exact outage formulation and, under α = 2 with RD << d, diversity gain 2. Its high-SNR outage decay is slower than in conventional cooperative relaying.

  • A. Random relay selection: The outage probability accounts for no deployed relay, destination failure after successful relay decoding, and joint relay-destination detection failure.The exact expression applies to arbitrary path-loss exponents and distances but involves multiple integrals.
  • A. Random relay selection: The closed-form insight relies on α = 2 and a relay region whose radius is much smaller than the source-destination distance.Without these assumptions, the exact outage expression remains valid but is too complicated for straightforward insight development.
  • A. Random relay selection: Energy-harvesting relays preserve the conventional diversity gain, but their outage probability decreases at a slower high-SNR rate involving ln SNR than the conventional SNR^-2 behavior.The comparison follows from the dominant high-SNR factor in the derived outage approximation.

B. Relay selection based on the second order statistics of the channels

Using channel second-order statistics, selecting the relay nearest to the source minimizes high-SNR outage under the paper’s asymptotic assumptions. This improves outage performance but not diversity order, which remains 2.

  • B. Relay selection based on the second order statistics of the channels: At high SNR, selecting the relay closest to the source minimizes outage probability when N ≥1, α = 2, and RD << d.The criterion depends only on source-relay distances because relay-destination distances are approximated as equal.
  • B. Relay selection based on the second order statistics of the channels: Knowledge of channel second-order statistics improves outage performance over random relay selection but does not improve diversity order.The exact outage expression is difficult because the nearest-relay source-channel density is more complicated.

C. Distributed beamforming

With global CSI, qualified energy-harvesting relays use distributed beamforming, and the resulting outage analysis requires bounds because source-relay and relay-destination effects are coupled. Under α = 2 and RD << d, the scheme achieves maximum diversity gain N + 1.

  • C. Distributed beamforming: With global CSI, the paper uses distributed beamforming across relays that successfully decode the source message.The strategy is analogous to maximal-ratio combining in a single-input multiple-output setting.
  • C. Distributed beamforming: The beamforming power is normalized so each relay’s transmission power remains below its harvested available power.The destination combines the first- and second-slot observations using maximal-ratio combining.
  • C. Distributed beamforming: Because energy harvesting couples source-relay channels with destination SNR, the outage analysis develops lower and upper bounds that converge at high SNR.The calculation requires distributions for both relay-related channel variables and partition-dependent quantities.
  • C. Distributed beamforming: Under α = 2, RD << d, and N ≥1, distributed beamforming achieves the maximum diversity gain N + 1.The result shows full diversity remains attainable even though relaying transmissions are powered by harvested energy.

III. ENERGY HARVESTING COOPERATIVE NETWORKS WITH MULTIPLE SOURCES

For multiple sources sharing energy-harvesting relays, relay assignment is modeled as coalition formation because relays are scarce and sources compete for assistance. Two payoff designs address opportunistic allocation and user fairness.

  • III. ENERGY HARVESTING COOPERATIVE NETWORKS WITH MULTIPLE SOURCES: M sources communicate with one destination through N energy-harvesting relays using two transmission phases and disjoint relay groups.Sources first broadcast over orthogonal channels, followed by relay beamforming over corresponding orthogonal channels.
  • III. ENERGY HARVESTING COOPERATIVE NETWORKS WITH MULTIPLE SOURCES: Relay scarcity and source competition are modeled as a coalition formation game, with each coalition containing one source and its willing relays.A network partition consists of M source-relay coalitions.
  • A. A baseline approach without considering user fairness: The baseline relay payoff measures the SNR gain from joining a coalition minus a coordination cost proportional to the number of decoding relays.The coalition’s receive SNR is determined by distributed beamforming.
  • III. ENERGY HARVESTING COOPERATIVE NETWORKS WITH MULTIPLE SOURCES: The baseline payoff can neglect fairness, allowing relays to favor sources with strong connections while leaving critically underserved sources unsupported.The paper introduces an alternative payoff to account for user fairness and encourage help for sources needing it more urgently.
  • III. ENERGY HARVESTING COOPERATIVE NETWORKS WITH MULTIPLE SOURCES: In the illustrative two-source, two-relay case, the fairness-aware payoff assigns the second relay to the disadvantaged second source.The example reports φ2(S1) = 50 and φ2(S2) = 1 under the fairness-aware definition, leading the second relay to join S2.

C. A distributed coalition formation algorithm

The proposed coalition formation process lets relays choose among source coalitions using individual-payoff and network-benefit criteria, while simulations compare relay-use strategies and path-loss effects. The distributed algorithm converges to a Nash-stable partition, and relay-selection strategies exhibit distinct diversity behavior.

  • C. A distributed coalition formation algorithm: Relay preferences require increased individual payoff while preventing a reduction in overall network benefit when changing coalitions.These criteria can conflict: a relay’s preferred move may be blocked if it lowers the network benefit.
  • C. A distributed coalition formation algorithm: When a relay chooses between coalitions, Proposition 2 gives a critical case where higher relay payoff coincides with a lower total coalition value after the move.The condition assumes one source receives no help except from that relay, making the move consequential for that source’s SNR.
  • C. A distributed coalition formation algorithm: The algorithm randomly initializes relay assignments, then lets each relay iteratively stay or join another source coalition according to the preference criteria.This implements distributed coalition adjustment rather than centralized relay allocation.
  • C. A distributed coalition formation algorithm: Starting from any initial partition, the coalition formation algorithm converges to a final network partition that is Nash stable.The convergence argument relies on the overall network benefit being non-decreasing after each iteration.
  • IV. NUMERICAL RESULTS: In the numerical evaluation, Monte Carlo simulations use 10^5 runs for all figures except Fig. 2, which uses 10^8 runs.The simulations evaluate analytical results and compare performance across two scenarios.
  • A. Energy harvesting cooperative networks with one source: The cooperative scheme in Fig. 2 has a larger outage-curve slope than direct transmission, indicating a larger diversity gain and improved destination reception reliability.The analytical results are particularly close to simulations at high SNR.
  • A. Energy harvesting cooperative networks with one source: Fig. 2 compares outage probability versus SNR for random relay selection, showing analytical Theorem 1 results alongside simulations and a non-cooperative baseline.The plotted setting uses R = 0.1 BPCU, η = 0.5, α = 2, RD = 1.5m, and λφ = 1.
  • A. Energy harvesting cooperative networks with one source: Fig. 3 compares distance-based selection, distributed beamforming, and random relay selection for different relay counts; distance-based curves have the same slope, while beamforming diversity scales with relay availability.The comparison uses R = 1 BPCU, d = 5m, and RD = 2.5m, with simulation-based curves.

B. Energy harvesting cooperative networks with multiple sources

For multiple sources sharing randomly located energy-harvesting relays, coalition formation models relay allocation and evaluates its outage performance. Simulations show benefits from more relays and a payoff design that balances relay assistance across sources.

  • Outage performance: Increasing the number of relays improves the outage performance of both coalition formation schemes.More relays are available to assist source transmissions.
  • Payoff comparison: The payoff function in (18) yields better outage performance than the payoff function in (16).It evaluates a relay’s SNR gain relative to the coalition’s overall SNR and encourages balanced relay allocation.
  • Convergence and coordination cost: The proposed coalition formation algorithm converges quickly, while increasing κ increases coordination overhead and affects outage performance.The outage probability is sensitive to κ when κ is of the order of 0.001.
  • System model and approach: Relay allocation is modeled as a coalition formation game because multiple sources compete for scarce energy-harvesting relays.Two distributed algorithms use different payoff functions.
  • Energy-transfer strategy: Simultaneous information and power transfer can use residual relay observations more efficiently than a decoupled information-and-energy strategy.Relays can decode using part of their observations and harvest energy from the rest.

APPENDIX

The appendix derives outage expressions and high-SNR approximations for randomly located relays using stochastic-geometry and fading analyses. It then obtains diversity gains through asymptotic evaluation and upper-bound arguments.

  • Theorem 1: Relay locations are modeled as independent points in a disc generated by a homogeneous Poisson point process.The relay location determines source-relay and relay-destination distances.
  • Theorem 1: Theorem 1 derives the outage probability for an energy-harvesting protocol with a randomly chosen relay.The derivation combines the outage-event decomposition with the relay-location density and Poisson distribution.
  • Asymptotic analysis: High-SNR approximations use series expansions, vanishing q(d_i, θ_i), and the approximation RD << d to simplify relay-destination distances.The closed-form steps also specialize to α = 2.
  • Proposition 1: Proposition 1 completes its argument by showing that outage probability decreases with the source-relay distance.The proof treats source-relay and relay-destination distances as constants before differentiating the outage expression.
  • Theorem 2: Theorem 2 analyzes the relay closest to the source by deriving its conditional distance distribution and substituting it into the outage probability.The resulting asymptotic expression yields the diversity gain after identifying terms independent of ϵ.
  • Theorem 3: Theorem 3 upper-bounds outage probability and shows that the achievable diversity gain is (N + 1), equal to the network’s maximum diversity gain.The proof uses stochastic-geometry and high-SNR steps analogous to the earlier theorems.
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