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RF-based Energy Harvesting in Decode-and-Forward Relaying Systems: Ergodic and Outage Capacities
Yanju Gu, Sonia Aïssa
TL;DR
The paper addresses energy-constrained relaying under difficult battery replacement and interference conditions. It proposes harvesting energy from both information and CCI signals in DF relays, analyzes TS and PS, and derives capacity and throughput results. PS is superior at high SNR, whereas TS performs better at low SNR; capacity ordering also depends on interference-power distribution.
Problem
Energy-constrained relays need practical recharging, while interference reduces communication capacity despite also carrying harvestable energy.
Method
The paper studies DF relaying in which relays harvest information-signal and CCI energy, using separate TS and PS protocols, and derives ergodic and outage capacities.
Results
PS outperforms TS in throughput at high SNR, while TS outperforms PS at relatively low SNR; interference-power distributions also induce capacity orderings.
Takeaways & Limitations
Interference can function as harvested relay power during energy harvesting while remaining noise during information decoding, making its distribution relevant to throughput.
Abstract
from arXiv · showhide
Radio-frequency energy harvesting constitutes an effective way to prolong the lifetime of wireless networks, wean communication devices off the battery and power line, benefit the energy saving and lower the carbon footprint of wireless communications. In this paper, an interference aided energy harvesting scheme is proposed for cooperative relaying systems, where energy-constrained relays harvest energy from the received information signal and co-channel interference signals, and then use that harvested energy to forward the correctly decoded signal to the destination. The time-switching scheme (TS), in which the receiver switches between decoding information and harvesting energy, as well as the power-splitting scheme (PS), where a portion of the received power is used for energy harvesting and the remaining power is utilized for information processing, are adopted separately. Applying the proposed energy harvesting approach to a decode-and-forward relaying system with the three-terminal model, the analytical expressions of the ergodic capacity and the outage capacity are derived, and the corresponding achievable throughputs are determined. Comparative results are provided and show that PS is superior to TS at high signal-to-noise ratio (SNR) in terms of throughput, while at low SNR, TS outperforms PS. Furthermore, considering different interference power distributions with equal aggregate interference power at the relay, the corresponding system capacity relationship, i.e., the ordering of capacities, is obtained.
I. INTRODUCTION
The paper motivates RF energy harvesting for energy-constrained cooperative relays and studies how interference can serve both as a capacity-limiting disturbance and an energy source. It analyzes TS and PS protocols, derives capacity measures, and compares their throughput behavior.
- Motivation: RF energy harvesting is presented as a way to support energy-constrained communication devices using widely available ambient RF signals.Ambient RF radiation can be captured by receive antennas and converted into electrical energy.
- Harvesting protocols: Practical circuit limitations make simultaneous information decoding and energy harvesting difficult, motivating TS and PS as separate processing schemes.TS alternates decoding and harvesting over time, whereas PS divides received power between the two functions.
- Motivation: Cooperative relays can enhance communication range and capacity, but limited batteries and difficult wired charging motivate wireless energy harvesting at the relays.The relay must remain active while assisting transmission between source and destination.
- Interference-aided relaying: The proposed relay harvests energy from both the information signal and CCI, then uses it to decode and forward the source signal.Interference is useful during harvesting but acts as noise during information decoding.
- Analysis and contributions: Closed-form ergodic and outage capacities and their achievable throughputs are derived for both harvesting protocols, with interference-distribution effects studied using majorization theory.The study covers delay-insensitive and real-time performance metrics.
II. ENERGY-HARVESTING BASED RELAYING
The system is a three-terminal cooperative DF relay network with an energy-constrained half-duplex relay. Independent Rayleigh block fading models the two hops, while independent non-identically distributed CCI signals affect the relay.
- System model: The model considers source S communicating with destination D through an energy-constrained intermediate relay R.Each node has a single antenna and operates in half-duplex mode.
- Channel model: Both source-to-relay and relay-to-destination links undergo independent Rayleigh fading.The channel remains constant within each block and changes independently between blocks.
- Channel model: Channel state information is available only at the receiver.
- Interference model: The relay is affected by M independent CCI signals whose fading gains are not necessarily identically distributed.Each interferer-to-relay channel is modeled as a complex Gaussian fading gain.
B. Wireless Energy Harvesting at the Relay
The relay replenishes its forwarding energy from received information and interference signals under harvest-use operation. TS separates harvesting and transmission in time, while PS separates harvesting and detection in received power.
- Relay energy harvesting: The energy-constrained relay exploits received information and interference signals to replenish the energy needed for forwarding.The model assumes the relay may have limited battery reserves and require external charging.
- Time-Switching Scheme: Under TS, the relay harvests for αT, then divides the remaining time equally between the two communication hops.All energy collected during harvesting is consumed because no energy buffer is available.
- Relay energy harvesting: The relay forwards using all harvested energy, with transmit and receive circuitry power treated as negligible relative to signal-transmission power.
- Power-Splitting Scheme: Under PS, the relay harvests during T/2 while allocating fraction θ of received power to harvesting and the remainder to information detection.The same received block supports both functions through power division.
- Power-Splitting Scheme: The PS analysis assumes power splitting reduces signal power but not noise power, yielding a lower-bound performance measure for practical relaying networks.
III. ERGODIC CAPACITY
The paper derives end-to-end SNR distributions and capacity expressions for TS and PS energy-harvesting DF relaying, while examining how interference-power distributions affect performance.
- Capacity analysis: The analysis derives the exact closed-form CDF of the end-to-end SNR for TS and PS energy-harvesting DF relaying.
- Capacity analysis: Ergodic capacity and achievable throughput are analyzed for both harvesting protocols.The interference-power distribution is also considered in the ergodic-capacity and throughput analysis.
- Interference distribution: The relay interference power is modeled as a sum of M statistically independent, not necessarily identically distributed exponential random variables.Their means depend on the interferer powers, channel statistics, and relay noise variance.
- Interference distribution: When interfering signals are i.i.d., the interference power becomes a sum of M i.i.d. exponential random variables.
- Distribution derivation: The derivations use matrix-based distribution expressions involving distinct diagonal values, multiplicities, characteristic coefficients, and modified Bessel functions.
B. Ergodic Capacity and Achievable Throughput
The section formulates ergodic capacity by averaging instantaneous DF capacity over fading, with the weaker hop determining performance. It also relates achievable throughput to effective information-transmission time in TS and PS systems.
- Ergodic capacity: Ergodic capacity averages instantaneous capacity over fading states, with the minimum of the first- and second-hop SNRs determining instantaneous DF capacity.The two transmission phases introduce a factor of 1/2.
- Outage probability: Outage probability at a threshold γ is expressed as the probability that the source-relay link is below γ or that the relay succeeds but the relay-destination link is below γ.This expression is obtained by evaluating the minimum-link condition at a predefined threshold.
- Achievable throughput: Achievable throughput accounts for effective information-transmission time and is given separately for TS and PS protocols.The two protocols therefore use different throughput expressions because their information-transmission times differ.
- Achievable throughput: Unlike conventional relaying with fixed relay power, energy-harvesting throughput depends on the received information and interference powers in addition to fading.The relay transmission power is random because it depends on replenished harvested energy.
C. Impact of Interference Power Distribution
The section uses majorization and Schur-convexity to order capacity under different interference-power distributions with equal aggregate interference power. Equal-strength interferers give the worst capacity, while a single interferer gives the best case.
- Majorization framework: Majorization provides the comparison framework for interference distributions while holding total received interference power equal.The analysis assumes nonnegative, non-increasing interference-power components and applies Schur-convexity to capacity.
- Capacity ordering: Ergodic capacity and achievable throughput are Schur-convex with respect to the ordered interference-power vector µ.The vector components satisfy µ1 ≥ µ2 ≥ ··· ≥ µM ≥ 0.
- Capacity ordering: The worst capacity occurs when the received interfering signals have equal strength at the relay.This is the capacity ordering implied by the Schur-convex result.
- Capacity ordering: The best capacity occurs when only one interferer affects the relay.This comparison is made among interference distributions with the same aggregate interference power.
IV. OUTAGE CAPACITY
The outage-capacity section derives closed-form outage probability, outage capacity, and achievable throughput for dual-hop interference-aided energy-harvesting DF relaying. It also analyzes how interference-power distributions affect outage performance using majorization theory.
- Analytical derivation: Exact closed-form expressions are derived for outage probability, outage capacity, and achievable throughput in the dual-hop energy-harvesting DF system.The derivation includes generalized incomplete Gamma functions.
- Outage probability: Outage probability is the probability that instantaneous output SNR falls below a predefined threshold γth.If the source-relay SINR is below γth, the destination declares an outage because the decoded data is not transmitted.
- Outage probability: The destination outage probability combines source-relay decoding failure with relay-destination failure after successful source-relay decoding.An indicator variable distinguishes the event γSR > γth.
- System model: The received destination SNR depends on relay-destination channel gain and on the information and interference powers harvested at the relay.This differs from conventional DF relaying, where constant relay power leaves the destination SNR dependent only on relay-destination channel gain.
- Analytical derivation: Simplified outage-probability expressions are provided for i.i.d. interference and for the single-interferer case.The general result is obtained through the PDF of Z ≜ (γh + IR)1C and subsequent integration.
B. Outage Capacity and Achievable Throughput
This section defines outage capacity as a constant rate maintained at a specified outage probability over slowly varying fading blocks. It also distinguishes TS and PS throughput through their effective information-transmission times.
- Outage capacity: Outage capacity is the maximum constant rate maintainable over fading blocks at a specified outage probability.It is defined for slowly varying channels whose instantaneous SNR remains constant over many symbols.
- Outage capacity: A factor of 1/2 appears because source-destination communication through the relay uses two transmission phases.This factor applies to the cooperative communication rate expression.
- Achievable throughput: Achievable throughput depends on the effective information-transmission time rather than only the outage-capacity rate.Separate expressions are specified for TS and PS protocols.
C. Impact of Interference Power Distribution
The energy-harvesting decode-and-forward relaying system is Schur-convex with respect to the interference-power vector, and its outage capacity and achievable throughput inherit this property. The analysis provides engineering guidance for relay positioning, although detailed application-specific positioning is beyond the paper’s scope.
- The energy-harvesting decode-and-forward relaying system is Schur-convex with respect to the interference-power vector µ.Here, µ is ordered as µ1 ≥ µ2 ≥ · · · ≥ µM ≥ 0.
- The outage capacity Cout and achievable throughput Tout are also Schur-convex with respect to µ.
- Equal aggregate interference power at different relay locations can correspond to different interference-power distributions.The analysis considers relays on the same interference-power contour but with different power distributions.
- The analysis can identify the best relay positioning and provides engineering insights for energy-harvesting relay-system design.
- Detailed application of the positioning analysis depends on the specific problem and is beyond the paper’s scope.The authors identify such applications as possible future extensions.
V. NUMERICAL RESULTS AND DISCUSSIONS
The numerical results examine how energy-harvesting ratios, SNR, SIR, protocol choice, and interference distributions affect throughput in the proposed relaying system. Throughput is concave in the harvesting ratio, PS is preferable at high SNR whereas TS is preferable at low SNR, and concentrated interference yields the best capacity while equal-power interference yields the worst.
- Harvesting-ratio effects: Throughput initially increases with the TS harvesting ratio α, reaches an optimum, and then decreases to zero as α approaches one.More harvesting improves second-hop capacity, but eventually excessive harvesting wastes information and reduces decoding.
- Interference and SNR: For fixed received average SNR, increasing CCI power can deteriorate performance while reducing the optimal TS harvesting ratio α.The experiments compare throughput against first-hop average SNR under different average SIR values.
- Harvesting-ratio effects: Throughput under PS is likewise concave in θ because increasing harvested power improves the second hop but leaves less power for information decoding.The analytical results match the simulation results for the PS expressions.
- Protocol comparison: At high SNR, PS outperforms TS in optimal Terg and Tout, whereas at relatively low SNR TS outperforms PS for optimal Tout with little difference in optimal Terg.At high SNR, PS preserves decodability with an optimal split, while TS incurs information loss during harvesting; at low SNR, splitting causes more relay decoding errors.
- Interference distributions: With equal aggregate interference power, throughput is ordered by interference concentration: Terg(µ1) ≥ Terg(µ2) ≥ Terg(µ3) and Tout(µ1) ≥ Tout(µ2) ≥ Tout(µ3).The worst case occurs when interfering signals have equal received power; the best case occurs with one interferer.
VI. CONCLUSION
The paper proposes interference-aided RF energy harvesting for decode-and-forward relaying, comparing TS and PS protocols through capacity and throughput analysis. PS outperforms TS at high SNR, whereas TS is better at relatively low SNR; capacity is worst with equal-strength interferers and best with one interferer.
- System and protocols: The relay harvests energy from received information and co-channel interference signals, then forwards the correctly decoded signal using that harvested energy.The proposed system uses TS and PS protocols, unlike conventional decode-and-forward relaying with constant relay transmit power.
- Capacity analysis: Analytical expressions for ergodic and outage capacities were derived to determine the system’s achievable throughputs.
- Protocol comparison: PS is superior to TS at high SNR in achievable throughput, while TS outperforms PS at relatively low SNR.
- Interference distribution: With equal aggregate interference power at the relay, capacity is worst when interfering signals have equal strength and best when only one interferer affects the relay.