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Wireless Information and Power Transfer with Full Duplex Relaying
Caijun Zhong, Himal A. Suraweera, Gan Zheng, Ioannis Krikidis, Zhaoyang Zhang
TL;DR
The paper studies RF-powered dual-hop full-duplex relaying with time switching, comparing amplify-and-forward and decode-and-forward protocols across three transmission modes. It derives throughput and time-split characterizations, finding that optimized full-duplex relaying substantially outperforms half-duplex relaying, while instantaneous transmission achieves the highest throughput and only a small gap over delay-constrained transmission.
Problem
Natural-resource energy harvesting is random and weather-dependent, motivating reliable wireless power transfer for energy-constrained communication systems.
Method
The paper analyzes an RF-powered source-relay-destination dual-hop system using separate-antenna full-duplex relaying, time switching, and both amplify-and-forward and decode-and-forward protocols.
Results
Optimized full-duplex relaying substantially boosts throughput over half-duplex relaying; decode-and-forward always outperforms amplify-and-forward, and instantaneous transmission has the highest throughput with a small gap over delay-tolerant transmission.
Takeaways & Limitations
Using both relay antennas for energy harvesting is always beneficial, with the largest gain when source transmit power is small.
Abstract
from arXiv · showhide
We consider a dual-hop full-duplex relaying system, where the energy constrained relay node is powered by radio frequency signals from the source using the time-switching architecture, both the amplify-and-forward and decode-and-forward relaying protocols are studied. Specifically, we provide an analytical characterization of the achievable throughput of three different communication modes, namely, instantaneous transmission, delay-constrained transmission, and delay tolerant transmission. In addition, the optimal time split is studied for different transmission modes. Our results reveal that, when the time split is optimized, the full-duplex relaying could substantially boost the system throughput compared to the conventional half-duplex relaying architecture for all three transmission modes. In addition, it is shown that the instantaneous transmission mode attains the highest throughput. However, compared to the delay-constrained transmission mode, the throughput gap is rather small. Unlike the instantaneous time split optimization which requires instantaneous channel state information, the optimal time split in the delay-constrained transmission mode depends only on the statistics of the channel, hence, is suitable for practical implementations.
I. INTRODUCTION
The paper studies full-duplex relaying for RF-powered dual-hop systems, using time switching to balance energy harvesting and information transmission. It derives throughput characterizations and time-split optimizations across relaying protocols and transmission modes, and compares full- and half-duplex architectures.
- Motivation: The work addresses the lack of prior studies applying full-duplex relaying to RF energy-harvesting systems.The relay is powered by RF signals from the source and uses separate antennas for reception and transmission.
- Analysis: Throughput is analyzed for AF and DF relaying across instantaneous, delay-constrained, and delay tolerant transmission modes.The analysis includes outage probability for delay-constrained transmission and achievable rate for delay tolerant transmission.
- Optimization: Optimal time splits are obtained numerically for AF, while DF has a closed-form solution for instantaneous transmission and numerical solutions for the other modes.The time split determines the balance between harvested energy and communication time.
- Findings: DF always yields better throughput than AF, while instantaneous transmission exceeds delay tolerant transmission with a nonsignificant throughput benefit.The paper also evaluates dual-antenna energy harvesting and reports that it outperforms single-antenna harvesting, although the gap diminishes at sufficiently high source power.
- Findings: With optimized time splitting, full-duplex relaying can substantially boost throughput compared with half-duplex relaying.For practical operation, delay tolerant transmission avoids instantaneous CSI and requires optimization only once over a relatively long period.
- System model: The system uses time switching: αT is allocated to relay energy harvesting and (1 − α)T to information transmission.Full-duplex operation is applied during information transmission, while harvesting and transmission occupy disjoint periods.
III. ENERGY HARVESTING WITH SINGLE ANTENNA
This section studies full-duplex relaying with RF energy harvesting using three transmission modes and examines optimal time allocation. For instantaneous transmission, the optimal time split is characterized for AF and DF protocols, analytically for the key DF result and numerically where closed forms are unavailable.
- System model: The study considers instantaneous, delay-constrained, and delay tolerant transmission under a loopback-interference-dominated full-duplex model.The relay uses RF energy harvesting and single-antenna operation in this section.
- AF relaying: For AF relaying, the end-to-end SINR determines the instantaneous throughput used in the time-split optimization.The section gives the AF SINR and resulting throughput before formulating the optimization problem.
- AF relaying: The AF optimal time split is obtained numerically because the throughput expression is concave but lacks a closed-form solution.The optimum is found by solving the first-order condition numerically.
- DF relaying: For DF relaying, the optimal time split is obtained through the stated analytical key result, with Lambert W used in its expression.The Lambert W function satisfies W exp(W) = x.
B. Delay-constrained Transmission
This section characterizes delay-constrained and delay tolerant performance for AF and DF full-duplex relaying with RF energy harvesting. It derives outage and ergodic-capacity expressions and uses them to determine the time split, numerically when closed forms are unavailable.
- Delay-constrained transmission: In delay-constrained transmission, a constant source rate Rc experiences outage because of random wireless-channel fading.Average throughput is therefore formulated using the outage probability.
- Delay-constrained transmission: The remaining task is to characterize exact outage probabilities for AF and DF protocols.The section presents separate propositions for the two relaying protocols.
- Delay-constrained transmission: For both AF and DF protocols, the delay-constrained outage probability is expressed analytically.The AF expression involves a modified Bessel function of the second kind.
- Delay-constrained transmission: The optimal delay-constrained time split is obtained numerically because the outage-based optimization has no closed-form solution.This follows from the outage expressions for the system.
- Delay tolerant transmission: In delay tolerant transmission, sufficiently long codewords motivate ergodic capacity as the throughput measure.Residual loopback interference is treated as Gaussian noise.
- Delay tolerant transmission: The AF and DF ergodic capacities are characterized analytically, with an AF upper bound introduced because the exact expression generally contains an intractable integral.The AF capacity is represented using a Meijer G-function, and the upper bound uses exponential-integral and digamma functions.
IV. ENERGY HARVESTING WITH DUAL ANTENNAS
This section extends RF energy harvesting to a relay using both antennas during harvesting and characterizes throughput for instantaneous and delay-constrained transmission. Optimal time splits are obtained numerically, while AF and DF outage probabilities are given analytically.
- Dual-antenna energy harvesting: Both relay antennas are used during the energy-harvesting phase, after which throughput and optimal time allocation are studied for three transmission scenarios.The harvested energy is characterized for the dual-antenna configuration.
- Instantaneous transmission: For AF relaying, the interference-dominated end-to-end SINR determines the instantaneous throughput and time-split optimization.The optimal α is evaluated numerically because the expression is too complex for a closed-form solution.
- Instantaneous transmission: For DF relaying, the end-to-end SINR likewise yields the instantaneous throughput, after which the optimal α is determined through a proposition.The section presents the DF signal-quality expression before optimizing time allocation.
- Delay-constrained transmission: For delay-constrained transmission, the AF protocol's outage probability is characterized analytically.The result is stated as Proposition 7.
- Delay-constrained transmission: For delay-constrained transmission, the DF protocol's outage probability is also given analytically.The result is stated as Proposition 8.
C. Delay Tolerant Performance
This section develops AF and DF throughput expressions for full- and half-duplex relaying across the paper’s transmission settings. It also presents ergodic-capacity characterizations and uses half-duplex relaying as a performance benchmark.
- Full-duplex performance: The AF ergodic capacity is characterized analytically, with a closed-form upper bound provided as an alternative.The section states Proposition 9 and Corollary 2 for AF relaying.
- Full-duplex performance: The DF ergodic capacity is likewise expressed analytically through Proposition 10.The proposition gives the achievable-rate characterization for DF relaying.
- Half-duplex benchmark: The half-duplex system is analyzed as a benchmark, using the same three transmission modes as the full-duplex system.The remaining information-transmission time is split equally between source-to-relay and relay-to-destination slots.
- Half-duplex benchmark: For half-duplex AF relaying, the end-to-end SNR and instantaneous throughput are explicitly characterized.The AF relay amplifies its input signal before transmitting.
- Half-duplex benchmark: For half-duplex DF relaying, the end-to-end SNR and instantaneous throughput are also characterized.The section presents the corresponding DF expressions separately from AF.
B. Delay-constrained Transmission
The section characterizes half-duplex throughput and outage performance for AF and DF relaying, including achievable-rate expressions for delay-tolerant operation and analytical outage results for delay-constrained operation.
- HD throughput and outage analysis: The HD throughput expressions account for the half-duplex constraint through a 1/2 factor.
- HD throughput and outage analysis: The AF protocol’s HD outage probability is given analytically, with the result presented as Lemma 1.
- HD throughput and outage analysis: The DF protocol’s HD outage probability is also derived analytically from the end-to-end SNR.
- Delay-tolerant achievable rates: For AF delay-tolerant operation, an alternative achievable-rate expression reduces the required calculation from a double integral to a single integral.
- Delay-tolerant achievable rates: For delay-tolerant operation, the DF achievable rate is expressed analytically from the end-to-end SNR distribution.
VI. NUMERICAL RESULTS
The numerical results validate the analytical approximations and examine how antenna configuration, loopback interference, transmit power, and transmission rate affect throughput across relaying modes.
- Validation and antenna effects: The interference-limited approximation closely matches exact outage-probability and achievable-rate performance.With fixed α, dual antennas help at low SNR but can hurt at high SNR because excessive harvested energy strengthens loopback interference.
- Validation and antenna effects: The analytical instantaneous-capacity solutions exactly agree with simulations for the stated channel realization and Ps/N0 = 10 dB.The optimal α for the FD two-antenna case is smaller than for the HD case in this setting.
- Optimized throughput comparisons: Instantaneous optimization gives the highest throughput, but its advantage over delay-tolerant transmission is limited.The delay-constrained throughput is upper bounded by Rc = 3 bps/Hz; DF slightly outperforms AF, while dual antennas provide the greatest gain at low SNR.
- Interference and transmit-power effects: Increasing λr decreases DF throughput because stronger residual loopback interference degrades performance.At high source transmit power, the throughput difference between FD antenna configurations becomes insignificant.
- Interference and transmit-power effects: At high source transmit power, FD delay-constrained systems approach 3 bps/Hz, nearly doubling the HD maximum throughput.
- Delay-tolerant comparisons: Delay-tolerant FD throughput can exceed HD throughput at high SNR, while HD dual antennas remain similar at low SNR and require two RF-chain pairs.With weak loopback interference, FD dual antennas outperform HD dual antennas from Ps/N0 ≥ 10 dB; with strong interference, the threshold is Ps/N0 ≥ 20 dB.
- Transmission-rate effects: Delay-constrained throughput first increases and then decreases with Rc, producing a unique maximizing transmission rate for fixed transmit power.The optimal Rc is the same for both FD schemes and smaller than for HD schemes at Ps/N0 = 40 dB.
- Overall conclusions: The study concludes that using both relay antennas for energy harvesting is always beneficial, with the largest throughput gain at low source transmit power.
APPENDIX A PROOF OF PROPOSITION 1
The proof partitions the time-split domain into two regions and analyzes throughput behavior in each region to determine the optimal α.
- The throughput analysis considers the regions 0 < α < 1 and 1+α0 ≤ α < 1 separately.
- The first-region optimization differentiates CID(α), transforms the resulting condition algebraically, and recognizes a Lambert W function form.
- In the second region, the derivative of CID(α) is strictly smaller than zero, so throughput decreases with α.
APPENDIX B PROOF OF PROPOSITION 2
The proof derives outage probability and ergodic-capacity expressions by transforming channel-related random variables and averaging over their distributions.
- The outage analysis defines x = |h1|2|g|2 and y = | ˆf|2, then conditions on y before averaging over it.
- The ergodic-capacity derivation uses the distribution of x and evaluates conditional integrals to obtain the desired expression.
- The alternative SINR representation introduces random variables whose distributions support the outage-probability calculation.
- A change-of-variables argument establishes independence of U and V, with U following a uniform distribution.
APPENDIX E PROOF OF PROPOSITION 8
The proof rewrites the end-to-end SNR and ergodic capacity using auxiliary variables, then evaluates the resulting expectations and integrals.
- The end-to-end SNR is expressed using T and W, allowing outage probability to be computed from their independent distributions.
- The ergodic capacity is decomposed into expectation terms involving W and evaluated through integral identities.
- The capacity expression includes terms of the form E {log2 (1 + kaW)} and related constants involving k and a.
- The proof combines the evaluated components to obtain the final desired result.
APPENDIX G PROOF OF COROLLARY 2
The proof evaluates terms in the ergodic-capacity expression using integral identities and bounds the remaining term through convexity.
- The first item in the capacity expression is computed using an integral representation and a supporting identity.
- An additional term is evaluated with an integral identity, yielding an expression involving ψ(1), ψ(2), and ln kλr.
- The third item is lower bounded because f(x, y) = log2(1 + ex + ey) is convex in x and y.
- Combining the evaluated and bounded terms yields the desired result.