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Wireless-Powered Relays in Cooperative Communications: Time-Switching Relaying Protocols and Throughput Analysis

Ali Arshad Nasir, Xiangyun Zhou, Salman Durrani, Rodney A. Kennedy

arXiv:1310.7648v5cs.IT

TL;DR

The paper addresses protocol design that allows energy accumulation at the relay. It proposes time-switching EH and IT protocols, derives achievable-throughput expressions, verifies them analytically and by simulation, and reports improved throughput over fixed time-duration EH.

  • Problem

    Designing protocols that allow energy accumulation at the relay remains an open problem.

  • Method

    The paper proposes time-switching protocols for energy harvesting and information transmission with continuous-time and discrete-time EH modes.

  • Results

    The proposed protocols' achievable-throughput expressions are verified against simulations and analytical results, including tight lower bounds on actual throughput.

  • Takeaways & Limitations

    The proposed protocols outperform fixed time-duration EH protocols by adapting switching between EH and IT to the available harvested energy.

Abstract

from arXiv · show

We consider wireless-powered amplify-and-forward and decode-and-forward relaying in cooperative communications, where an energy constrained relay node first harvests energy through the received radio-frequency signal from the source and then uses the harvested energy to forward the source information to the destination node. We propose time-switching based energy harvesting (EH) and information transmission (IT) protocols with two modes of EH at the relay. For continuous time EH, the EH time can be any percentage of the total transmission block time. For discrete time EH, the whole transmission block is either used for EH or IT. The proposed protocols are attractive because they do not require channel state information at the transmitter side and enable relay transmission with preset fixed transmission power. We derive analytical expressions of the achievable throughput for the proposed protocols. The derived expressions are verified by comparison with simulations and allow the system performance to be determined as a function of the system parameters. Finally, we show that the proposed protocols outperform the existing fixed time duration EH protocols in the literature, since they intelligently track the level of the harvested energy to switch between EH and IT in an online fashion, allowing efficient use of resources.

I. INTRODUCTION

Wireless-powered relaying addresses energy constraints at relay nodes, but practical receiver separation and protocols supporting energy accumulation remain important challenges. This paper proposes time-switching protocols for AF and DF relaying that adapt EH and IT online while avoiding transmitter-side CSI.

  • Practical receiver design: Energy harvesting through an information decoder is practically infeasible with current electronic circuits, motivating separate EH and information decoding.Time-switching and power-splitting receiver designs separate the two processes.
  • Motivation: RF energy harvesting can support cooperative relaying when relay nodes have limited battery reserves and require external charging.RF signals can carry both energy and information, making wireless-powered relaying relevant to energy-constrained networks.
  • Related work: Prior relaying studies considered energy harvesting under varied models but often assumed sufficient relay energy, simultaneous decoding and extraction, perfect channel knowledge, or full-duplex operation.These assumptions limit practical applicability because they impose capabilities or information unavailable in the targeted relay setting.
  • Open problem: Existing protocols did not provide analytical achievable-throughput expressions in several settings and commonly used fixed EH durations without allowing relay energy accumulation.The resulting open problem is to design protocols that accumulate surplus harvested energy for future use.
  • Proposed protocols: The paper proposes time-switching EH and IT protocols for energy-constrained AF and DF relaying with continuous-time and discrete-time EH modes.Continuous EH permits any percentage of a transmission block for harvesting, whereas discrete EH uses each whole block exclusively for EH or IT.
  • Contributions: The protocols avoid transmitter-side CSI, support preset fixed relay transmission power, accumulate energy at the relay, and outperform fixed-duration EH protocols through online EH–IT switching.Analytical throughput expressions are derived as functions of system parameters, including relay transmission and noise powers.

II. SYSTEM MODEL AND ASSUMPTIONS

The system models communication from a source to a destination through an energy-constrained relay when no direct link is available. It adopts time-switching EH/IT, specified channel and energy assumptions, and continuous or discrete EH modes.

  • System scenario: Communication uses a two-hop S→R→D link because the source and destination have no direct connection.The relay is energy constrained, whereas the source and destination are not.
  • Relay model: The relay harvests enough source-transmitted energy before forwarding information with preset fixed power Pr, assuming an infinite-capacity battery.Relay circuitry energy consumption is treated as negligible relative to transmission energy.
  • Relay model: The relay separately performs energy harvesting and information processing, allocating part of each block to EH and the remainder to IT.The receiver uses a time-switching architecture with separate circuits.
  • Channel model: Channels are quasi-static over each T-second block, independently identically distributed across blocks, and modeled with path loss and Rayleigh small-scale fading.Closed-form throughput expressions are valid specifically for Rayleigh-distributed channel gains, although the protocols support other fading distributions.
  • Channel model: Transmitter-side CSI is unavailable, while receiver-side CSI is obtained through channel estimation and assumed perfect.AF does not require S→R channel estimation, whereas DF requires it for decoding.
  • Protocol framework: The protocols are proposed for both AF and DF relaying, with throughput efficiency defined as the average fraction of block time supporting successful information transmission.Switching decisions depend online on available harvested energy and preset relay transmit power Pr.

III. AMPLIFY-AND-FORWARD RELAYING

This section formulates the wireless-powered AF relay signal model and introduces throughput analysis for continuous- and discrete-time EH protocols. AF forwarding uses the received signal and can obtain its power constraint from the received signal without necessarily estimating the S→R channel.

  • Section scope: The AF relay model is developed before proposing and analytically characterizing two time-switching EH/IT protocols.The protocols cover continuous-time and discrete-time EH.
  • AF signal model: The relay receives the source signal, amplifies it after harvesting sufficient energy, and forwards the amplified signal to the destination.The destination signal model includes the R→D fading gain and destination noise.
  • AF signal model: AF forwarding is constrained by preset relay power Pr and a power constraint factor derived from the received signal.The relay need not necessarily estimate the source-to-relay channel to obtain this factor.
  • Performance metric: An outage occurs when the destination SNR γd,i falls below the threshold SNR γo.The outage indicator uses an indicator function that equals 1 when its argument is true.

B. Protocol 1: TS-based Protocol for EH and IT with Continuous Time EH in AF Relaying

Protocol 1 continuously adjusts each block’s EH duration so the AF relay harvests only the energy required for preset-power forwarding. This creates a single EH-IT block whose IT time varies with the source-to-relay channel.

  • Protocol operation: The relay harvests only the energy needed for its transmission, consuming all harvested energy during IT and maintaining Eo = Ei(0) = 0.Thus, each EH-IT pattern contains one block without accumulated harvested energy.
  • Protocol operation: Each block begins with EH for αiT seconds and continues with IT for the remaining (1−αi)T seconds.The IT interval is split equally between S→R and R→D transmission.
  • Energy allocation: 0 < αi < 1 guarantees that the relay can harvest the required energy and transmit with preset power Pr within every block.The protocol derives αi by equating harvested energy with the energy required for relay transmission.
  • Throughput behavior: Larger αi leaves less IT time and transmits fewer packets, whereas smaller αi leaves more IT time and transmits more packets.The packet count varies with αi, which depends on the source-to-relay channel quality.
  • Throughput behavior: Although finite packet transmission makes αi discrete mathematically, small packets relative to the block allow αi to be treated approximately as continuous.This approximation relies on quasi-static fading and many packets per block.
  • Throughput analysis: The section analytically evaluates throughput and states a closed-form result involving modified Bessel functions for the continuous-time AF protocol.The parameter ν may require numerical integration because a closed-form expression does not appear tractable for given system parameters.

C. Protocol 2: TS-based Protocol for EH and IT with Discrete Time EH in AF Relaying

Protocol 2 uses discrete time switching: each block is entirely devoted to EH or IT, with switching determined by the relay’s available energy. Its throughput is analytically characterized using the distributions of residual energy and required EH blocks.

  • Protocol operation: Each block is dedicated either to EH (αi = 1) or IT (αi = 0), and IT uses T/2 for relay-to-destination transmission.The relay transmits with preset power Pr, consuming PrT/2 energy during IT.
  • Protocol operation: The EH-IT pattern contains X successive EH blocks before IT, where X depends on the residual energy Eo.Larger Eo makes fewer EH blocks more likely; a single IT block occurs when Ei(0) exceeds the required transmission energy.
  • Protocol operation: The relay checks available energy only at each block start, unlike Protocol 1’s continuous within-block checking.Once sufficient energy is available, it sends a one-bit indication that IT starts; the control channel is assumed error-free.
  • Throughput analysis: Eo is exponentially distributed with mean ρ, while the conditional number of additional EH blocks follows a Poisson model when Eo < PrT/2.These distributions provide the probabilistic ingredients for the discrete-time protocol’s throughput analysis.
  • Throughput analysis: Theorem 2 gives the throughput for the discrete-time EH protocol in AF relaying using the derived energy and block-count distributions.The result is presented as an analytical expression averaged over channel history and block throughput.

IV. DECODE-AND-FORWARD RELAYING

The DF-relaying model accounts for relay decoding success in addition to harvested energy. The proposed protocols use relay-outage detection to decide whether a block performs EH, IT, or both.

  • DF operation: In DF relaying, IT depends on whether the source-to-relay channel is in outage.A relay outage causes the relay to alert the source and destination and dedicate the entire block to EH.
  • Continuous-time EH: Continuous-time DF patterns include a single EH-IT block, outage-induced EH blocks followed by an EH-IT block, and accumulated EH blocks followed by IT.The number n of outage-induced EH blocks is random and occurs irrespective of accumulated energy.

3) Throughput Analysis:

For continuous-time DF, exact throughput analysis is intractable, so the paper derives a lower bound by neglecting extra energy accumulated during outage-related EH blocks. The bound is evaluated through a rapidly convergent summation.

  • Continuous-time DF analysis: The exact throughput for Protocol 3 is not tractable, motivating a lower-bound analysis.The analysis treats the extra harvested energy in a particular outage pattern as negligible.
  • Continuous-time DF analysis: The lower-bound assumption sets Eo = 0 when the relevant outage-related EH-IT pattern occurs.Poor channel quality and the low probability of successive outages support neglecting the energy accumulated in those blocks.
  • Continuous-time DF analysis: Theorem 3 provides a lower bound on throughput for continuous-time EH in DF relaying.The expression includes the outage-block count n and the exponential-integral function.
  • Continuous-time DF analysis: The summation term decays rapidly for moderate or large n because long sequences of relay outages are unlikely.The paper states that n = 10 terms are sufficient for accurate evaluation.
  • Continuous-time DF analysis: The n = 10 analytical throughput is an accurate lower bound on simulation-based actual throughput.This comparison validates the truncated analytical evaluation for the continuous-time DF protocol.

3) Throughput Analysis:

For discrete-time DF, the paper derives a lower bound by approximating the residual-energy distribution as in Protocol 2 and accounting for outage-induced EH blocks. Simulations show close agreement with the analysis and reveal an optimal preset relay power.

  • Discrete-time DF analysis: The outage count Y has a geometric-type PMF determined by the relay outage probability po,r = 1 − e^−ā.Y counts successive outage blocks after sufficient energy has been harvested for IT.
  • Discrete-time DF analysis: The exact distribution of Eo is not tractable for Protocol 4 because outage-related EH blocks add extra harvested energy.The analysis neglects that additional energy and reuses the PDF from Lemma 1.
  • Discrete-time DF analysis: Theorem 4 gives a lower bound on throughput for discrete-time EH in DF relaying.The bound combines the distributions of residual energy, energy-required EH blocks, and outage-induced blocks.
  • Numerical results: The analytical throughput in Theorem 4 is an accurate lower bound on simulation-based actual throughput.The numerical results evaluate the proposed protocols under independently generated fading channels and realistic parameter settings.
  • Numerical results: The AF analytical results match simulations perfectly, whereas the DF analytical results closely track actual throughput as lower bounds.The AF expressions are exact; the DF expressions are lower-bound calculations.
  • Numerical results: Throughput varies significantly with preset relay power Pr, and maximum throughput requires selecting an optimal relay transmission power.The optimal power is obtained offline for given system parameters because closed-form optimization is intractable.
  • Numerical results: Because αi differs across blocks, throughput cannot be plotted directly against a single energy-harvesting time for Protocols 1–4.The paper instead uses throughput versus preset relay power for these protocols.

B. Performance of the Proposed Protocols

The proposed protocols’ throughput depends on relay and destination noise, relaying type, EH mode, and adaptive energy use. They outperform fixed-duration EH by adapting EH time to harvested energy while maintaining preset relay power.

  • DF relaying outperforms AF relaying as relay noise variance increases or destination noise variance decreases.
  • For AF relaying, continuous time EH outperforms discrete time EH except at very low relay or destination noise variance.
  • For DF relaying, continuous and discrete time EH protocols have the same performance except under the stated low-noise conditions.
  • The proposed protocols outperform fixed time-duration EH by approximately 0.2−0.5 dB for continuous EH and almost 3−7 dB for discrete EH over stated SNR-threshold ranges.
  • The proposed protocols accumulate relay energy and adapt EH duration to meet a preset transmission power, improving energy-and-throughput efficiency.
  • At γo = 50 dB, the proposed discrete time EH protocols achieve optimal throughput efficiency around 0.35−0.4, implying average successful IT for 40% of block time.
  • The improvement requires the relay to send a single IT-alert bit, while fixed relay power eases hardware design compared with variable transmission power.

APPENDIX A

Appendix A derives analytical throughput expressions for the proposed protocols using channel and harvested-energy distributions, including the discrete EH process’s repeated EH–IT patterns.

  • The appendix derives analytical expressions for throughput τ by evaluating inner and outer expectations over fading and EH time.
  • Under the stated model, channel gains are exponential random variables with unit mean, with PDF f_hi(z) ≜ e^−z for |hi|^2.
  • For Protocol 2, harvested energy available at the start of any EH–IT pattern is exponentially distributed.
  • The memoryless property preserves the exponential distribution of leftover harvested energy across successive EH–IT patterns.
  • The proof establishes this distribution recursively by considering EH blocks followed by IT or a single IT block.

APPENDIX C

Appendix C derives the throughput expression for a protocol whose EH time depends on accumulated energy from prior source-to-relay channel realizations.

  • The block outage indicator is independent of EH time because outage depends on current fading channels, whereas EH time depends on accumulated prior harvested energy.
  • Throughput is obtained by separately evaluating the expected no-outage factor and the expected fraction of a block used for information transmission.
  • The appendix substitutes the evaluated expectations into the throughput expression to obtain the analytical result in (16).
  • A lower-bound throughput expression is derived under the assumption Eo = 0, which simplifies the accumulated-energy state.

APPENDIX E

Appendix E derives a lower-bound throughput expression by analyzing information-transmission probability while neglecting harvested energy from successive EH blocks caused by relay outage.

  • The block outage indicator depends on the current relay-to-destination fading channel, while EH time depends on current and previous source-to-relay channels and accumulated energy.
  • The probability that a block is used for IT is expressed through the expected lengths of EH–IT patterns.
  • The derivation assumes independent random variables X and Y because source-to-relay channels are independent across blocks.
  • Neglecting harvested energy from Y successive EH blocks due to relay outage produces the inequality in the lower-bound derivation.
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