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Wireless Information and Power Transfer in Two-Way Amplify-and-Forward Relaying Channels
Zhiyong Chen, Biao Wang, Bin Xia, Hui Liu
TL;DR
Ambient RF signals offer energy that devices can harvest while processing information, motivating green wireless information and power transfer. This paper develops and analyzes a two-way amplify-and-forward relaying protocol with an energy-harvesting relay, deriving performance expressions and bounds. Compared with non-cooperative relaying, the protocol improves ergodic capacity and outage performance without additional energy, time, or spectrum resources.
Problem
Wireless devices need a way to harvest energy from ambient RF signals while processing information simultaneously for green communications.
Method
The paper designs a two-way AF protocol in which an energy-constrained relay harvests received-signal energy and uses it to forward the sources’ signals.
Results
The protocol improves ergodic capacity and achieves higher outage performance than non-cooperative relaying without additional energy, time, or radio spectrum resources.
Takeaways & Limitations
Exact outage probability, ergodic capacity, and finite-SNR DMT expressions, plus tight bounds, characterize the proposed energy-harvesting relaying protocol.
Abstract
from arXiv · showhide
The various wireless networks have made the ambient radio frequency signals around the world. Wireless information and power transfer enables the devices to recycle energy from these ambient radio frequency signals and process information simultaneously. In this paper, we develop a wireless information and power transfer protocol in two-way amplify-and-forward relaying channels, where two sources exchange information via an energy harvesting relay node. The relay node collects energy from the received signals and uses it to provide the transmission power to forward the received signals. We analytically derive the exact expressions of the outage probability, the ergodic capacity and the finite-SNR diversity-multiplexing trade-off (DMT). Furthermore, the tight closed-form upper and lower bounds of the outage probability and the ergodic capacity are then developed. Moreover, the impact of the power splitting ratio is also evaluated and analyzed. Finally, we show that compared to the non-cooperative relaying scheme, the proposed protocol is a green solution to offer higher transmission rate and more reliable communication without consuming additional resource.
I. INTRODUCTION
The paper motivates wireless information and power transfer as a way to harvest ambient RF energy while processing information, then applies it to two-way AF relaying with an energy-constrained relay. The protocol is analyzed as a resource-conscious alternative for exchanging information between two sources.
- Motivation: Ambient RF signals carry both information and energy, enabling simultaneous energy recycling and information processing.The paper presents this capability as a route toward green communications.
- Related work: Prior work extended wireless information and power transfer to MIMO, cooperative, and OFDM systems and studied rate-energy tradeoffs and relay-channel performance.The cited research includes outage probability, throughput, and energy-efficient power allocation analyses.
- Protocol: The proposed protocol uses amplify-and-forward relaying so two sources exchange information through an energy-constrained relay.The relay harvests energy from received signals and uses it to support forwarding.
- Analysis: The paper derives exact outage probability, ergodic capacity, and finite-SNR DMT expressions, along with tight upper and lower bounds for outage probability and ergodic capacity.It also evaluates how the power splitting ratio affects harvesting energy, forwarding power, ergodic capacity, and finite-SNR DMT.
- System model: The system uses half-duplex operation with multiple-access and broadcasting stages for source-to-relay reception and relay-to-destination transmission.Both sources transmit simultaneously in the multiple-access stage, after which the relay broadcasts to them.
B. Energy Harvesting Relaying Protocol
The energy-harvesting relay splits received signal power between harvesting and information processing, then forwards both sources’ signals using the harvested energy. The resulting relay constraint limits signal-quality amplification, while the protocol’s performance depends on channel conditions and power splitting.
- Energy harvesting: The relay has no fixed power supply and scavenges energy from the simultaneous source transmissions during the multiple-access stage.The relay also processes information using the harvested energy.
- Channel and decoding: The source-to-relay channels are modeled as reciprocal quasi-static Rayleigh fading channels, and each source can cancel its known self-interference.The received signals include Gaussian noise at the sources.
- Power splitting: The relay uses power splitting to divide received signal power between energy harvesting and information processing.The harvesting fraction is denoted by λ, with 0 < λ < 1.
- Relay transmission: The harvested energy determines the relay’s transmitted power, with η representing energy-conversion efficiency.The efficiency satisfies 0 < η ⩽ 1.
- Relay transmission: The relay forwards both sources’ signals, while passband-to-baseband conversion introduces additive white Gaussian noise and a relay power-constraint factor.The remaining received signal power is used for information processing before broadcasting.
- Performance implication: The relay cannot purely enlarge signal quality without consuming additional energy, although path loss can let the protocol outperform non-cooperative relaying.The bound applies to the end-to-end SNRs, while the comparison is reported for the proposed protocol under path-loss effects.
III. INFORMATION-THEORETIC METRICS
The paper evaluates the proposed energy-harvesting relaying protocol using outage probability, ergodic capacity, and finite-SNR diversity-multiplexing trade-off as its information-theoretic performance metrics.
- Performance metrics: The performance analysis focuses on outage probability, ergodic capacity, and finite-SNR diversity-multiplexing trade-off.These are the stated information-theoretic metrics of interest.
A. Outage Probability
The paper defines outage for two-way AF relaying as failure of either source’s target-rate condition, then derives an exact expression and computationally simpler bounds. The high-SNR analysis shows the exact expression and both bounds share the same approximation.
- Outage definition: Outage occurs when either source’s instantaneous rate falls below its target rate, combining the two individual outage events by inclusion–exclusion.The thresholds are τ_i = 2^(2T_i) − 1 for i = 1, 2.
- Exact expression: Theorem 1 gives an exact outage-probability expression for two-way AF relaying with energy harvesting.The expression uses intermediate quantities V_1 = Y_0 and V_2 = X_0.
- Bounds: Closed-form lower and upper bounds are derived to reduce the computational complexity of evaluating the exact outage probability.The exact expression involves an integral evaluated numerically before the bounds are introduced.
- High-SNR behavior: At high SNR, the exact outage probability and both bounds are approximated by the same asymptotic expression.This follows from X_0 → 0, Y_0 → 0, and xK_1(x) → 1 as x → 0.
B. Ergodic Capacity
The paper derives the ergodic capacity of the energy-harvesting two-way AF relay and provides an exact expression together with bounds and an efficient approximation. The bounds closely match the exact capacity at high power-splitting ratios but separate at low ratios.
- Exact capacity: Theorem 2 gives an exact ergodic-capacity expression for two-way AF relaying with energy harvesting.The expression uses the confluent hypergeometric function and Euler’s constant.
- Capacity bounds: Proposition 2 provides upper and lower bounds for the total ergodic capacity.These bounds are developed because an intermediate quantity cannot be obtained in closed form.
- Bound accuracy: The upper bound closely matches the exact ergodic capacity at high SNR and high power-splitting-ratio regimes.The stated reason is x ∝ σ^2/(λP_1) and xK_1(x) → 1 as x → 0.
C. Finite-SNR DMT
The paper characterizes the finite-SNR diversity–multiplexing trade-off for symmetric two-way AF relaying with energy harvesting. It evaluates the trade-off using the outage bound because the exact outage expression is difficult to use directly.
- DMT formulation: The finite-SNR DMT is defined through the diversity gain for two-way AF relaying channels with energy harvesting.The multiplexing gain is expressed using the rate and instantaneous SNR.
- Symmetric relaying: The analysis assumes symmetric relaying, with equal normalized source powers and equal target rates.Specifically, P_1/σ^2 = P_2/σ^2 = γ and T_1 = T_2 = R.
- Evaluation: The finite-SNR DMT is evaluated from the outage lower bound because numerical results show that the bound is close to the exact outage probability.Under the symmetric assumptions, X_0 equals Y_0 and simplifies the calculation.
IV. NUMERICAL RESULTS
Numerical results validate the analytical expressions and show that the power-splitting ratio λ substantially affects ergodic capacity and diversity gain. The proposed relay improves ergodic capacity and outage performance over non-cooperative relaying without additional resource consumption.
- The analytical outage-probability results closely match simulations, and the derived lower and upper bounds are tight, especially for asymmetric relaying traffic.
- For P1/σ2 = P2/σ2 = 20 dB, λ values from 0.3 to 0.6 provide reasonable ergodic capacity, whereas extreme values significantly degrade it.Larger λ increases harvested energy but reduces forward signal power.
- The ergodic-capacity analytical result agrees closely with simulation, while the upper and lower bounds become tight at high λ but diverge more at low λ.
- Diversity gain increases with SNR, and its dependence on λ reflects a trade-off that varies with relay position.
- Compared with non-cooperative relaying, the proposed relay improves ergodic capacity and outage performance without consuming additional energy, time, or radio-spectrum resources.
V. CONCLUSION
The paper concludes that its energy-harvesting two-way AF protocol improves transmission efficiency and reliability without additional resources. It characterizes exact performance metrics, develops tight bounds, verifies the analysis numerically, and examines λ's effects on capacity and finite-SNR DMT.
- The protocol improves transmission efficiency and communication reliability without consuming additional resources.
- Exact expressions are characterized for outage probability, ergodic capacity, and finite-SNR DMT.
- Tight bounds are derived for outage probability and ergodic capacity, and numerical results verify the theoretical predictions.
- The power-splitting ratio λ affects ergodic capacity and finite-SNR DMT, as illustrated by the numerical results.
APPENDIX A PROOF OF THEOREM 1
Appendix A derives the required theorem by solving equations around a solution point, partitioning the calculation into integrals, and approximating difficult terms with second-order Taylor expansions.
- The proof identifies a solution point (X0, Y0) and derives inequalities for X > X0 and Y > Y0.
- The calculation proceeds by evaluating integrals using V1 = Y0 and V2 = X0.
- Because closed forms for I1 and I2 are difficult to obtain, second-order Taylor expansions of Hi,j(z) provide approximations.
- The proof applies Lemma 1 and subsequent bounds to complete the theorem derivation.
APPENDIX C PROOF OF THEOREM 2
Appendix C derives the closed-form expression by expanding K1(x), decomposing the resulting terms, and evaluating them with special-function identities and series relations.
- The proof begins by applying a series expansion of K1(x).
- The expanded expression is decomposed into three terms labeled Q1, Q2, and Q3.
- Q1 is evaluated using the definition of the confluent hypergeometric function, while Gamma-function identities support the remaining manipulations.
- The same procedure yields the corresponding closed-form integral expression for the remaining term.