PaperlayerView exact revision on arXiv

Source-linked AI summary

Relaying Protocols for Wireless Energy Harvesting and Information Processing

A. A. Nasir, X. Zhou, S. Durrani, R. A. Kennedy

arXiv:1212.5406v3cs.IT

TL;DR

The paper studies how an energy-constrained relay can harvest RF energy while forwarding information in an AF wireless network. It proposes time-switching and power-splitting relaying protocols and analytically evaluates throughput in two transmission modes. Numerical results show that TSR outperforms PSR under relatively low SNR and high transmission rates, while relay placement and protocol parameters affect performance.

  • Problem

    The paper addresses wireless energy harvesting and information processing for an energy-constrained AF relay that must forward source information using harvested RF energy.

  • Method

    The paper proposes TSR and PSR protocols and evaluates throughput using outage probability for delay-limited and ergodic capacity for delay-tolerant transmission.

  • Results

    TSR outperforms PSR in throughput at relatively low SNR and high transmission rates, while relay placement and harvesting parameters provide practical performance insights.

  • Takeaways & Limitations

    The results identify protocol and relay-placement choices that affect throughput in RF-powered AF relay networks.

  • Takeaways & Limitations

    The model assumes CSI is available only at the destination and uses a fixed source transmission rate of R = 3 bits/sec/Hz unless otherwise stated.

Abstract

from arXiv · show

An emerging solution for prolonging the lifetime of energy constrained relay nodes in wireless networks is to avail the ambient radio-frequency (RF) signal and to simultaneously harvest energy and process information. In this paper, an amplify-and-forward (AF) relaying network is considered, where an energy constrained relay node harvests energy from the received RF signal and uses that harvested energy to forward the source information to the destination. Based on the time switching and power splitting receiver architectures, two relaying protocols, namely, i) time switching-based relaying (TSR) protocol and ii) power splitting-based relaying (PSR) protocol are proposed to enable energy harvesting and information processing at the relay. In order to determine the throughput, analytical expressions for the outage probability and the ergodic capacity are derived for delay-limited and delay-tolerant transmission modes, respectively. The numerical analysis provides practical insights into the effect of various system parameters, such as energy harvesting time, power splitting ratio, source transmission rate, source to relay distance, noise power, and energy harvesting efficiency, on the performance of wireless energy harvesting and information processing using AF relay nodes. In particular, the TSR protocol outperforms the PSR protocol in terms of throughput at relatively low signal-to-noise-ratios and high transmission rate.

I. INTRODUCTION

The paper addresses RF energy harvesting and information processing in an energy-constrained AF relay network. It proposes TSR and PSR protocols, derives throughput expressions for two transmission modes, and compares their performance.

  • Motivation: RF signals can simultaneously carry energy and information, allowing energy-constrained nodes to scavenge energy while processing information.
  • Related receiver architectures: Practical RF harvesting circuits cannot directly decode carried information, motivating separate information decoding and energy harvesting receiver designs.
  • System and contribution: The considered AF network has an energy-constrained relay that harvests energy from the source RF signal and uses it to forward information to the destination.
  • Protocols: The proposed TSR and PSR protocols separate energy harvesting from information processing through time switching and power splitting, respectively.
  • Analysis: Analytical throughput expressions are obtained from outage probability for delay-limited transmission and ergodic capacity for delay-tolerant transmission.
  • Results: TSR has superior throughput in delay-limited transmission at higher rates, relatively lower SNR, and lower energy harvesting efficiency.
  • Results: For both protocols, placing the relay closer to the source produces larger throughput in delay-limited and delay-tolerant transmission modes.

B. Related Works

The system model uses a single energy-constrained AF relay between source and destination, with practical separated harvesting and decoding and destination-only CSI. It defines TSR/PSR operation and two transmission modes.

  • System model: The model considers a source-to-destination link assisted by a single intermediate energy-constrained relay, with no direct source-destination link.
  • System model: The relay harvests energy from the source signal and uses the harvested energy as transmit power to forward source information.
  • Assumptions: The relay uses amplify-and-forward relaying because of its implementation simplicity, while relay processing power is assumed negligible relative to transmission power.
  • Assumptions: Channel gains are quasi-static, frequency-nonselective Rayleigh block-fading channels that remain constant during each block.
  • Assumptions: Channel state information is available only at the destination, which estimates the dual-hop channel using source pilots with negligible overhead.
  • Protocols and modes: TSR and PSR harvest energy using time switching and power splitting, and the analysis covers delay-limited and delay-tolerant transmission modes.
  • Transmission modes: Delay-limited decoding occurs block by block, whereas delay-tolerant transmission permits buffering and code lengths much larger than the block time.

III. TIME SWITCHING-BASED RELAYING (TSR) PROTOCOL

In TSR, the relay divides each block between RF energy harvesting and two-hop information transmission. Harvesting time controls the relay’s available forwarding power and destination throughput.

  • Protocol operation: TSR divides a block of duration T into an energy-harvesting fraction αT and an information-transmission period (1−α)T.
  • Protocol operation: The information period is split equally between source-to-relay and relay-to-destination transmission.
  • Energy use: All energy harvested during the harvesting phase is consumed while the relay forwards the source signal.
  • Design parameter: The harvesting fraction α affects achievable destination throughput by trading harvesting duration against information-transmission duration.
  • Receiver architecture: The TSR receiver first sends the received RF signal to the harvesting receiver and then to the information receiver.
  • Receiver architecture: The harvesting receiver rectifies the RF signal into direct current to charge the relay battery, while the information receiver down-converts and processes the signal.
  • Signal model: The relay’s transmitted power depends on the energy harvested during the harvesting interval and is used in the destination received-signal model.

C. Throughput Analysis

The TSR throughput analysis uses outage probability for delay-limited transmission and relates it to energy-harvesting time and fixed-rate communication parameters.

  • The received SNR determines throughput for both delay-limited and delay-tolerant transmission modes.
  • For delay-limited transmission, throughput is evaluated at a fixed source rate R using the outage probability at the destination.The detection threshold satisfies R ≜ log2(1 + γ0), with γ0 = 2^R − 1.
  • The TSR outage probability decreases as the energy-harvesting time α increases from 0 to 1.Larger α provides more relay transmission power, reducing the chance of outage.
  • The resulting throughput depends on source power, harvesting efficiency, α, relay distances, transmission rate, and noise power.Effective communication time is (1 − α)T/2 within a block of duration T.

2) Delay-Tolerant Transmission:

In delay-tolerant transmission, the paper evaluates ergodic capacity for TSR and describes PSR energy harvesting and information processing through power splitting at the relay.

  • The delay-tolerant mode uses ergodic capacity, which depends on random channel gains h and g.
  • For TSR, ergodic capacity increases as α increases from 0 to 1 because more harvesting time produces more relay transmission power.
  • Throughput is not necessarily increasing in α because effective communication time (1 − α)T/2 decreases as harvesting time grows.
  • PSR protocol: The PSR harvesting fraction affects achievable destination throughput, with energy conversion efficiency constrained by 0 < η < 1.

B. Energy Constrained Relay-Assisted Transmission

The PSR protocol models an energy-constrained amplify-and-forward relay that splits received signal power between harvesting and information processing before forwarding the source signal.

  • The relay amplifies the received signal and transmits using power determined by harvested energy.
  • The destination SNR is obtained from the signal and overall-noise components of the received signal.
  • For PSR delay-limited transmission, throughput is calculated from the destination SNR and outage probability.The analytical outage expression is provided through Proposition 3.
  • Although TSR and PSR outage expressions have similar forms, their constants differ and therefore yield different final expressions.

2) Delay-Tolerant Transmission:

The paper derives throughput expressions for TSR and PSR, discusses numerical optimization of harvesting controls, and bounds practical throughput because several system constraints are omitted.

  • PSR delay-tolerant transmission: For PSR delay-tolerant transmission, ergodic capacity is calculated analytically using the destination SNR and the same derivation framework as TSR.
  • The throughput formulas for TSR and PSR are summarized in Table I using protocol-dependent constants.
  • Optimal α for TSR and ρ for PSR are found offline by numerical evaluation over system parameters because closed-form optimization is intractable.Parameters include source power, harvesting efficiency, distances, transmission rate, and noise variances.
  • The derived throughput expressions represent an upper bound on practically achievable throughput.Propagation delay, finite-alphabet modulation, minimum harvesting power, and retransmissions can reduce achievable throughput.
  • Ideal receiver: The ideal-receiver analysis models simultaneous energy harvesting and information processing during the first half of the block, followed by forwarding during the second half.

1) Delay-Limited Transmission:

The delay-limited analysis evaluates TSR and PSR throughput using derived outage-probability expressions and numerical verification. Optimal harvesting and splitting parameters are investigated under specified system assumptions.

  • Design parameters: The study investigates optimal throughput, harvesting time α, and power-splitting ratio ρ across noise variances, link distances, transmission rates, and harvesting efficiencies.The optimal α and ρ are defined as the values maximizing destination throughput.
  • Analytical and simulation evaluation: Analytical and simulation results match for all tested α and ρ values in both TSR and PSR protocols.This agreement verifies the analytical expressions for outage probability and ergodic capacity used to calculate throughput.
  • Throughput comparison: Delay-tolerant throughput exceeds delay-limited throughput for both TSR and PSR protocols.The closed-form analytical approximations are also reported to be very close to the exact analytical results.

B. Effect of Energy Harvesting Time, α (TSR protocol) and Power Splitting Factor, ρ (PSR protocol)

Throughput varies non-monotonically with the TSR harvesting time α and PSR splitting ratio ρ, because energy harvesting and information-transmission resources trade off. Protocol comparisons also depend on noise conditions and transmission mode.

  • TSR protocol: TSR delay-limited throughput increases with α to an optimum of 0.28, then decreases as additional harvesting time reduces information-transmission time.The same qualitative trend is observed for TSR in delay-tolerant transmission.
  • PSR protocol: PSR delay-limited throughput increases with ρ to an optimum of 0.63, then decreases as excess harvesting leaves less power for information transmission.Below the optimum, insufficient harvested power reduces relay transmit power; above it, relay signal strength worsens and outage increases.
  • Protocol comparison: In delay-limited transmission, PSR generally exceeds TSR throughput at lower noise variance, whereas TSR becomes better at relatively large noise variance.The ideal receiver outperforms both proposed protocols across the considered noise variances.
  • Protocol comparison: In delay-tolerant transmission, PSR is superior to TSR for the considered noise-variance values.The reported comparison concerns optimal throughput under the considered parameter settings.
  • Noise effects: The optimal TSR α increases with conversion-noise variance, while the optimal PSR ρ follows a different trend across antenna- and conversion-noise variations.The difference is attributed to how antenna and conversion noise affect the received signal in the two architectures.

D. Effect of Relay Location

Relay placement strongly affects throughput when the relay harvests energy from the source signal. Increasing the source-to-relay distance reduces optimal throughput, and the best relay location is close to the source.

  • Relay location: For both TSR and PSR, optimal throughput decreases as source-to-relay distance d1 increases.Increasing d1 reduces both harvested energy and the signal strength received at the relay through larger path loss.
  • Relay location: Throughput changes little when d1 exceeds 1.2 because placing the relay closer to the destination reduces the harvested energy required for reliable relay-to-destination communication.The cited setting uses d2 = 2 − d1.
  • Relay location: With energy harvesting at the relay, the optimal relay location is close to the source node.This differs from the non-energy-harvesting case, where maximum throughput is achieved at the midpoint between source and destination.

E. Effect of the Source Transmission Rate in Delay-Limited Transmission

In delay-limited transmission, throughput initially increases with source transmission rate but eventually decreases as outage probability rises. The comparisons also show that protocol superiority depends on transmission mode and system parameters.

  • Effect of the Source Transmission Rate in Delay-Limited Transmission: Optimal throughput τ increases with source transmission rate R up to a threshold, then decreases for larger R.At high R, the receiver cannot correctly decode the larger data amount within the limited time.
  • Effect of the Source Transmission Rate in Delay-Limited Transmission: At relatively low transmission rates, PSR provides more throughput than TSR, whereas TSR is superior at larger transmission rates.The comparison is stated for the source-rate analysis in delay-limited transmission.
  • Effect of the Energy Harvesting Efficiency: For smaller energy harvesting efficiencies η in delay-limited transmission, TSR outperforms PSR in throughput.This comparison is reported from the optimal-throughput analysis across η.
  • Effect of the Energy Harvesting Efficiency: In delay-tolerant transmission, PSR outperforms TSR in throughput for all considered values of η and other system parameters.The paper contrasts this result with the delay-limited comparison.
  • Analysis Framework: The study derives throughput expressions using outage probability for delay-limited transmission and ergodic capacity for delay-tolerant transmission.The protocols are TSR and PSR, implemented at an energy-constrained AF relay.
  • Scope and Constraints: The reported throughput is an upper bound on practically achievable throughput because finite-alphabet modulation, minimum harvesting power, and retransmissions are excluded.The paper also assumes CSI is available only at the destination node.

APPENDIX A

The appendix derives analytical outage and ergodic-capacity expressions for the TSR protocol. It uses exponential channel distributions and also develops high-SNR approximations when the exact integrations cannot be simplified further.

  • Outage Probability: The appendix derives the destination outage probability expression for the TSR protocol from the system equations.The resulting expression is identified as Proposition 1 in (12).
  • Channel Statistics: The derivation models |h|^2 and |g|^2 as exponential random variables using their PDFs, CDF, and means.The CDF of |g|^2 is given as F_|g|^2(z) = 1−e^−z/λg.
  • High-SNR Approximation: The exact outage integration cannot be further simplified, so a high-SNR approximation is obtained by neglecting a noise-product term.The approximation simplifies the destination signal-to-noise ratio expression.
  • Ergodic Capacity: The appendix derives the TSR ergodic capacity by obtaining the PDF of γD from its CDF and integrating it.The resulting analytical capacity expression is presented as Proposition 2 in (16).
  • High-SNR Approximation: A high-SNR approximation is likewise applied to the TSR ergodic-capacity expression when the exact integration cannot be further simplified.The approximation is based on the previously described high-SNR treatment.
Loading 1212.5406v3…