PaperlayerView exact revision on arXiv

Source-linked AI summary

Simultaneous Information and Energy Transfer in Large-Scale Networks with/without Relaying

Ioannis Krikidis

arXiv:1310.6511v2cs.IT

TL;DR

RF energy-harvesting research has largely focused on specific small-scale networks, leaving large-scale random networks insufficiently characterized. This paper uses stochastic geometry to analyze power-splitting information-and-energy transfer with direct transmission and random relay assistance. It derives outage and harvested-energy results, formulates closed-form minimum-power optimization, and reports that relay density and selection area affect cooperative performance.

  • Problem

    Existing RF energy-harvesting studies mainly use specific small-scale network structures, limiting characterization of general large-scale networks.

  • Method

    The paper applies stochastic geometry to random transmitter-receiver networks with power-splitting receivers, analyzing non-cooperative direct links and cooperative transmission with randomly selected relays.

  • Results

    The paper derives closed-form outage and average harvested-energy expressions, solves constrained minimum-transmit-power optimization in closed form, and analyzes cooperative selection combining.

  • Takeaways & Limitations

    Network density, power-splitting ratio, relay density, and relay selection area affect the outage-probability and average-harvested-energy trade-off.

Abstract

from arXiv · show

Energy harvesting (EH) from ambient radio-frequency (RF) electromagnetic waves is an efficient solution for fully autonomous and sustainable communication networks. Most of the related works presented in the literature are based on specific (and small-scale) network structures, which although give useful insights on the potential benefits of the RF-EH technology, cannot characterize the performance of general networks. In this paper, we adopt a large-scale approach of the RF-EH technology and we characterize the performance of a network with random number of transmitter-receiver pairs by using stochastic-geometry tools. Specifically, we analyze the outage probability performance and the average harvested energy, when receivers employ power splitting (PS) technique for "simultaneous" information and energy transfer. A non-cooperative scheme, where information/energy are conveyed only via direct links, is firstly considered and the outage performance of the system as well as the average harvested energy are derived in closed form in function of the power splitting. For this protocol, an interesting optimization problem which minimizes the transmitted power under outage probability and harvesting constraints, is formulated and solved in closed form. In addition, we study a cooperative protocol where sources' transmissions are supported by a random number of potential relays that are randomly distributed into the network. In this case, information/energy can be received at each destination via two independent and orthogonal paths (in case of relaying). We characterize both performance metrics, when a selection combining scheme is applied at the receivers and a single relay is randomly selected for cooperative diversity.

I. INTRODUCTION

The paper addresses the open problem of analyzing RF energy harvesting in large-scale networks with practical power-splitting techniques. It uses stochastic geometry to study outage probability, harvested energy, optimization, and relay assistance.

  • Practical simultaneous information and energy transfer can use power splitting, assigning part of the received signal to decoding and the remainder to RF harvesting.
  • Existing RF energy-harvesting studies mostly examine fixed single- or multiple-user configurations rather than general large-scale networks.
  • The paper models random transmitter-receiver locations with stochastic geometry and analyzes the trade-off between outage probability and average harvested energy.
  • The non-cooperative protocol derives closed-form outage and harvesting expressions and solves minimum-power optimization under outage and harvesting constraints.
  • The cooperative protocol uses randomly distributed potential DF relays, orthogonal paths, selection combining, and random single-relay selection.

II. SYSTEM MODEL

The system is a slotted two-dimensional network with randomly located transmitter-receiver pairs and power-splitting receivers. Its model includes direct-link fading, path loss, interference, noise, and RF-to-DC conversion.

  • Transmitters form a homogeneous PPP of intensity λ, each paired with a receiver at distance d0, while all sources transmit simultaneously without coordination.
  • Desired direct links experience small-scale fading and large-scale path loss, whereas interference links are modeled as path-loss dominated.
  • Each receiver uses power splitting: one signal portion supports information decoding and the other drives the rectenna for energy conversion.
  • Decoding succeeds when SINR reaches threshold Ω, while harvesting is evaluated through long-term average harvested energy.
  • The RF-to-DC conversion efficiency is ζ, assumed equal to 1 for analytical convenience, and harvested AWGN energy is neglected.

III. NON-COOPERATIVE PROTOCOL FOR SIMULTANEOUS INFORMATION/ENERGY TRANSFER

The non-cooperative protocol sends information and energy directly in one slot while all sources transmit simultaneously. Its analysis derives outage and average harvested-energy metrics for the typical link and network.

  • All sources simultaneously transmit to associated receivers in a single time slot without cooperation.
  • Network outage is defined through the probability that instantaneous SINR falls below the detection threshold Ω.
  • The outage probability for the non-cooperative protocol is derived analytically in Proposition 1.
  • As Pt →∞ with νd > 0, the system becomes interference limited and outage converges to a constant error floor.
  • The average harvested energy is derived analytically for the non-cooperative protocol in Proposition 2.

1) Optimization problem- minimum transmitted power:

The protocol’s optimization minimizes transmitted power subject to outage and average-harvesting requirements. Feasibility depends on the outage floor, while adaptive power splitting increases implementation complexity.

  • Optimization problem- minimum transmitted power:: The QoS constraint limits outage probability below CI, while the harvesting constraint requires average harvested energy at least CH.
  • Optimization problem- minimum transmitted power:: If the outage-probability floor exceeds CI, no transmitted power can satisfy the optimization problem, making it infeasible.
  • Optimization problem- minimum transmitted power:: Constant power splitting offers lower implementation complexity and suits systems with predefined, non-adaptable rectenna parameters.
  • Optimization problem- minimum transmitted power:: General optimization requires adaptive and dynamic RF power splitting, which entails higher implementation complexity.
  • Optimization problem- minimum transmitted power:: At the optimum, the inequality constraint holds with equality because otherwise transmitted power could be reduced further.

IV. COOPERATIVE PROTOCOL FOR SIMULTANEOUS INFORMATION/ENERGY TRANSFER

The cooperative protocol adds randomly located decode-and-forward relays to support simultaneous information and energy transfer. It uses a two-phase design, random single-relay selection, and selection combining at receivers.

  • System model: A homogeneous PPP models dedicated single-antenna decode-and-forward relays randomly distributed throughout the network.The relays have no own traffic and assist transmitters.
  • First phase: In the first phase, transmitters broadcast simultaneously, while relays inside each transmitter’s circular-sector area treat its signal as useful information.Other received signals are treated as interference.
  • Relay eligibility: Relays join a transmitter’s potential relay set when their received SINR reaches the decoding threshold.Relays use all received signal power for information decoding because they have no energy-harvesting requirements.
  • Second phase: One successfully decoding relay is selected uniformly at random to retransmit in the second phase, without instantaneous channel feedback or geometry knowledge.If no relay decodes the message, the second-phase transmission is omitted and cooperative diversity is unavailable.
  • Receiver processing: Receivers use selection combining to decode from the better direct or relaying path, while the branch allocated to selection combining is not reused for RF energy harvesting.Selection combining avoids continuous channel-state estimates and reduces power consumption relative to maximum-ratio combining.
  • Relay selection area: The relay selection area is a circular sector with radius η > r0 oriented toward the associated receiver, and its angle can constrain relaying paths to be shorter than the direct link.The sector geometry therefore avoids selected relays suffering more severe path loss than direct transmission.

A. Outage probability and average harvested energy

The cooperative analysis derives outage and average harvested-energy expressions for two-phase relaying with selection combining. Harvesting remains active even when no relay retransmits, while the relaying optimization lacks an elegant closed-form solution.

  • Outage probability: Cooperative outage occurs when the direct link fails and either no relay decodes or both direct and relaying links fail.These cases distinguish inactive and active relaying transmissions.
  • Outage probability: Proposition 3 gives the outage probability for the cooperative protocol, with component expressions for the first-hop and second-hop outage probabilities.The first hop concerns source-to-relay decoding, while the second concerns relay-to-destination transmission.
  • Outage probability: When C → 0 with positive direct and relay power-splitting ratios, outage converges to an interference-limited constant floor.The result characterizes the high-interference limiting behavior of the cooperative system.
  • Average harvested energy: Average harvested energy includes contributions from both cooperative phases, and harvesting remains active even when the relay set is empty.With no retransmitting relay, the receiver does not apply power splitting and uses all received energy.
  • Average harvested energy: Proposition 4 gives the average harvested energy for the cooperative protocol, including the relaying-link attenuation term.The derivation uses the average attenuation for the relaying link, for which both exact and simplified forms are available.
  • Optimization limitation: The relaying optimization can minimize total transmitted power Pt + Pr, but the cooperative outage expressions do not yield an elegant closed-form solution.This contrasts with the closed-form optimization available for the non-cooperative protocol.

V. NUMERICAL RESULTS

Simulations evaluate the proposed schemes under the system and cooperative-protocol models. The reported setup uses equal source and relay powers and fixed geometric, channel, noise, and decoding parameters.

  • Simulation setup: The channel and decoding parameters are C = 1, Ω = −30 dB, α = 4, and ζ = 1.These parameters are used for the numerical evaluation of the proposed protocols.
  • Cooperative setup: Relay nodes transmit with Pr = Pt, assuming computational and complexity characteristics similar to the transmitters.The relaying sector uses η = 8 m and satisfies the stated angle condition with θ0 ≤ cos−1(1/5) = 0.4359π.
  • Interpretation of results: The presented results concern the typical link x0 → r(x0) and refer to any link in the transmitter process under Slivnyak’s theorem.This identifies the representative link used for the numerical results.

A. Non-cooperative protocol

The non-cooperative protocol is interference-limited: increasing network density worsens outage probability but increases harvested RF energy. Power splitting and joint optimization of transmit power and splitting ratio determine the balance between decoding, harvesting, and constraint satisfaction.

  • Network density: As Pt increases, outage probability converges to a constant floor because uncoordinated transmissions make the system interference limited.The figure compares non-cooperative performance across network densities, with analytical results shown by dashed lines.
  • Network density: 6×10^-4 versus 6×10^-2: outage probability converges to the lower value at λ = 10^-5 and the higher value at λ = 10^-3.The increase is attributed to stronger multi-user interference at higher network density.
  • Network density: 1.5 %: at λ = 10^-3, the direct-link share of harvested energy is almost negligible because interference dominates the harvesting process.At smaller densities, the direct component contributes significantly more to total average harvested energy.
  • Power splitting: As νd increases, outage performance improves while RF harvesting becomes less efficient; decreasing νd produces the inverse behavior.The power splitting ratio allocates received energy between information decoding and RF-to-DC rectification.
  • Power optimization: Optimization II yields much lower P ∗t than Optimization I because the power splitting parameter is optimized alongside transmit power.Optimization II satisfies both outage and harvesting constraints with equality, while the dominant constraint determines the equality condition in Optimization I.

B. Cooperative protocol

The cooperative protocol uses randomly distributed relays to improve outage and harvested-energy performance, with outcomes governed by relay density and selection-area angle. Simulations compare these effects against non-cooperative transmission.

  • Simulation assumptions: The simulations assume fixed network densities, typically with relay density λr higher than transmitter density λ to expose cooperation benefits.Very small λr yields almost no successful relay decoding, while larger λ increases multi-user interference.
  • Performance evaluation: The cooperative protocol is evaluated for outage probability and average harvested energy as functions of transmitted power Pt.Figure 5 fixes Pr = Pt, λr = 10^-2, η = 8 m, and θ0 = π/3; analytical results are shown with dashed lines.
  • Outage performance: 6 × 10^-4 versus 3 × 10^-4 is the high-power outage floor for non-cooperative versus cooperative transmission at λ = 10^-5.The cooperative gain is attributed to retransmission from a shorter distance and an independent fading channel.
  • Energy harvesting: 275 Watt versus 450 Watt is the average harvested energy at λ = 10^-3 and Pt = 60 dB without versus with cooperation.Receivers without relay assistance harvest all received power during the cooperative protocol’s second phase.
  • Cooperative diversity: At Pt → ∞, the non-cooperative/cooperative performance gap is attributed to cooperative diversity in the cooperative scheme.This comparison is described as fair in the high-power limit.
  • Relay-density and angle trade-off: The combination (λr, θ0) = (10^-1, π/2) achieves the best reported outage-performance balance.Higher relay density supports a non-empty relay set, while a smaller selection angle limits large-distance relays.

VI. CONCLUSION

The conclusion summarizes a stochastic-geometry analysis of power-splitting energy harvesting in large-scale networks, covering direct transmission and orthogonal relay assistance. It reports closed-form non-cooperative analysis, constrained power optimization, and cooperative performance trade-offs.

  • Scope: The paper studies power-splitting RF harvesting for multiple transmitter-receiver pairs with simultaneous quality-of-service and energy-harvesting requirements.The network is analyzed using stochastic geometry.
  • Non-cooperative protocol: The non-cooperative protocol is analyzed for outage performance and average harvested energy when transmitters communicate simultaneously without coordination.The analysis includes the direct-link setting.
  • Trade-off and optimization: Network density and power-splitting ratio significantly affect the outage-versus-energy-harvesting trade-off.The transmitted-power minimization problem under outage and harvesting constraints is solved in closed form.
  • Cooperative protocol: The cooperative protocol uses a random set of orthogonal relays and random relay selection within a sectorized area.Analytical and simulation results assess relay density and selection-area effects on outage and harvested energy.

PROTOCOL: PROOF OF PROPOSITION I

The proof derives the non-cooperative outage probability by characterizing normalized interference and applying exponential-fading and Laplace-transform results. The resulting proposition provides the outage expression for the typical transmitter-receiver pair.

  • Interference characterization: The derivation begins by calculating the Laplace transform of the normalized interference term I0.The interference is generated by transmitters modeled through a Poisson point process.
  • Interference characterization: The Laplace-transform calculation uses the probability generating functional of a PPP and successive integral transformations.The derivation also uses integration by parts and the lower incomplete gamma function.
  • Outage derivation: The outage probability is then obtained for the typical transmitter-receiver pair.The calculation combines the unit-variance exponential fading CDF with the previously derived Laplace transform.
  • Outage derivation: Proposition 1 states the resulting closed-form outage probability for the non-cooperative protocol.The proposition is the endpoint of the interference-transform and fading-CDF derivation.

APPENDIX B MEAN OF THE INTERFERENCE TERM I0

The appendix develops geometric and point-process ingredients for relay-assisted analysis, including interference means, relay-region geometry, successful-relay thinning, and relaying-hop outage evaluation.

  • Interference mean: The mean normalized interference I0 is computed for a transmitter PPP using Campbell’s theorem.The transmitter process has density λ, and interference contributions are summed through path-loss terms d(x)^-α.
  • Relay geometry: The relay-receiver distance is expressed from transmitter-relay distance, direct-link distance, and angle using the cosine rule.This geometry determines whether the relay-receiver distance satisfies the d0 requirement.
  • Relay geometry: A sectorized selection area is bounded by applying the relay-distance condition at the sector border, yielding a maximum supported angle range.The selected area is parameterized by radius η and central angle θ0.
  • Successful-relay process: Relays that successfully decode the source form a thinned PPP with an intensity determined by the decoding probability.The thinning procedure is applied to the homogeneous relay process.
  • Successful-relay process: The probability of an empty relaying set is derived using fundamental properties of a PPP.This quantity determines whether cooperative retransmission is available.
  • Relaying-hop analysis: For relaying transmissions, selected relays form a PPP with density λ(1 − Πc), and the relaying-hop outage uses the direct-link expressions.The density reflects one selected relay per transmitter with probability 1 − Πc.
  • Relay attenuation: Jensen’s inequality simplifies the average relay-receiver attenuation by exploiting convexity and E[cos(θ)] = sin(θ0)/θ0.The attenuation expression incorporates the considered propagation model.
Loading 1310.6511v2…