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Wireless Energy Harvesting in a Cognitive Relay Network
Yuanwei Liu, S. Ali Mousavifar, Yansha Deng, Cyril Leung, Maged Elkashlan
TL;DR
The paper addresses wireless energy harvesting in underlay cognitive relay networks with multiple primary users and develops analyses of outage and throughput under practical interference and power constraints. It finds that interference from many primary transmitters can outweigh harvested-energy benefits, while transmitter placement near the secondary source and away from relay and destination improves outage performance.
Problem
Wireless energy harvesting must be analyzed in underlay cognitive relay networks where secondary transmission is constrained by power and interference limits.
Method
The paper proposes a harvesting protocol and derives exact outage and throughput expressions, plus asymptotic analyses as the number of primary transceivers grows.
Results
Interference from primary transmitters outweighs harvested-energy benefits when their number is large, while outage improves when transmitters are near SS and sufficiently far from SR and SD.
Takeaways & Limitations
Primary-transmitter placement and population size are important design factors because harvesting gains can be offset by interference at the secondary relay and destination.
Abstract
from arXiv · showhide
Wireless energy harvesting is regarded as a promising energy supply alternative for energy-constrained wireless networks. In this paper, a new wireless energy harvesting protocol is proposed for an underlay cognitive relay network with multiple primary user (PU) transceivers. In this protocol, the secondary nodes can harvest energy from the primary network (PN) while sharing the licensed spectrum of the PN. In order to assess the impact of different system parameters on the proposed network, we first derive an exact expression for the outage probability for the secondary network (SN) subject to three important power constraints: 1) the maximum transmit power at the secondary source (SS) and at the secondary relay (SR), 2) the peak interference power permitted at each PU receiver, and 3) the interference power from each PU transmitter to the SR and to the secondary destination (SD). To obtain practical design insights into the impact of different parameters on successful data transmission of the SN, we derive throughput expressions for both the delay-sensitive and the delay-tolerant transmission modes. We also derive asymptotic closed-form expressions for the outage probability and the delay-sensitive throughput and an asymptotic analytical expression for the delay-tolerant throughput as the number of PU transceivers goes to infinity. The results show that the outage probability improves when PU transmitters are located near SS and sufficiently far from SR and SD. Our results also show that when the number of PU transmitters is large, the detrimental effect of interference from PU transmitters outweighs the benefits of energy harvested from the PU transmitters.
I. INTRODUCTION
The paper proposes wireless energy harvesting for a decode-and-forward cognitive relay network with multiple primary-user transceivers. It derives exact and asymptotic performance expressions while examining the tradeoff between harvested energy and interference.
- Motivation and protocol: The protocol lets energy-constrained secondary source and relay nodes harvest RF energy from multiple primary transmitters while sharing licensed spectrum.The study targets a decode-and-forward cognitive relay network and evaluates how energy harvesting and primary-user interference affect secondary-network performance.
- Analytical framework: The exact outage analysis incorporates maximum transmit-power limits, peak interference limits at primary receivers, and interference from primary transmitters at the relay and destination.These constraints jointly capture harvested-energy availability, spectrum-sharing protection, and interference affecting secondary reception.
- Analytical framework: The paper derives throughput expressions for both delay-sensitive and delay-tolerant transmission modes.It also develops asymptotic expressions for outage probability and both throughput modes as the number of primary transceivers grows large.
- Main findings: An optimal number of primary transceivers can minimize outage probability and maximize secondary-network throughput.The result reflects the competing effects of increased harvested energy and increased primary-transmitter interference.
- Main findings: When many primary transmitters are present, interference at the secondary network outweighs the benefits of additional harvested energy.The paper identifies this tradeoff as central to designing energy-harvesting underlay cognitive relay networks.
B. Notation and Organization
The network uses an underlay cognitive relay architecture in which energy-constrained SS and SR harvest RF energy and transmit over shared PU spectrum under interference and fading assumptions.
- Network model: The primary network contains M PU transmitters and N PU receivers, while SS communicates with SD through energy-constrained SR without a direct SS–SD link.PU transmitters and receivers are modeled as clustered, and PU receivers use multi-user detectors to cancel interference among PU transmitters.
- Channel assumptions: Channel gains among secondary, primary, and interference links are modeled as exponentially distributed under quasi-static Rayleigh fading.The model uses path-loss-dependent exponential parameters and identical distributions for corresponding PU-transmitter and PU-receiver links.
- Modeling assumptions: The model treats PU-transmitter interference at SR and SD as dominant over noise and excludes shadow fading for analytical tractability.The relay and destination SIRs depend on shared random quantities, making them dependent random variables.
- EH-IT protocol: SS and SR harvest RF energy for αT, then transmit during the remaining (1−α)T; the protocol sets β = 1/2 for the two information-transmission phases.The harvested energy is stored, and SS-to-SR and SR-to-SD transmissions occupy β(1−α)T and (1−β)(1−α)T, respectively.
- Power constraints: SS and SR transmit under maximum harvested-energy limits and peak interference constraints that keep interference at each PU receiver below PI.The analysis also assumes harvested power exceeds the activation threshold and that energy-processing costs are negligible relative to transmission energy.
III. EXACT PERFORMANCE ANALYSIS
This section derives outage-probability and throughput expressions for the proposed secondary-network energy-harvesting protocol to assess parameter impacts on performance.
- Performance analysis: The analysis derives expressions for outage probability and both delay-sensitive and delay-tolerant throughput.These expressions are intended to provide practical design insight into how system parameters affect secondary-network performance.
A. Outage Probability
The outage analysis defines failure through the two relay hops, derives distributions for aggregate interference and harvested-energy variables, and states an exact outage expression.
- Outage definition: The network is in outage when either hop’s equivalent SIR falls below the threshold γth.ΓR and ΓD denote the SIR random variables at SR and SD, respectively.
- Distribution analysis: Each Zp variable is a sum of N independent exponential random variables with a chi-square distribution, while Yq distributions are also derived.The corresponding PDF and CDF expressions use gamma and incomplete gamma functions.
- Model assumptions: The model assumes clustered PU transmitters and receivers relative to their distances from the secondary nodes.This assumption supports the use of common distribution parameters for corresponding PU links.
- Exact result: Theorem 1 gives the exact outage probability for the secondary network under the proposed energy-harvesting protocol.The expression is assembled from terms JR,I, JR,II, JD,I, and JD,II defined in Appendix A.
1) Delay-sensitive Transmission:
The paper defines throughput for fixed-rate delay-sensitive transmission and ergodic-capacity-based delay-tolerant transmission, then studies large-system tradeoffs as PU populations grow.
- Delay-tolerant Transmission: Delay-tolerant throughput allows rates up to the ergodic capacity determined by the minimum of the two hop SIRs.Its evaluation uses the CDF of Γth, which is identified with the outage probability.
- Large-system analysis: As N increases, additional harvested energy competes with increased interference at SR and SD, potentially producing optimal M and N values for outage and throughput.Increasing M also increases the number of PU receivers at which SS and SR may impose interference.
- Large-system analysis: The large-system derivation uses asymptotic distributions for aggregate variables and rewrites the SR and SD SIRs before obtaining outage expressions.The analysis invokes convergence in distribution and asymptotic normality for relevant sums and maxima.
A. Outage probability
The section gives the asymptotic outage probability of the cognitive relay network in closed form as the number of transceivers tends to infinity. It obtains the result by evaluating the relay and destination terms from distribution expressions and substituting them into the outage decomposition.
- The asymptotic outage expression uses the relay and destination terms as separate factors because their corresponding variables are independent.
- Theorem 2 gives the outage probability in closed form as the number of transceivers goes to infinity.
- The relay term is obtained from the CDF and PDF expressions for X1 and Y1, followed by further algebraic simplification.
- The destination term follows by substituting the corresponding parameters into the relay-term expression.
- Substituting the derived relay and destination terms into the asymptotic outage decomposition yields the closed-form probability.
B. Throughput
The section derives asymptotic throughput expressions for delay-sensitive and delay-tolerant transmission. These expressions use the asymptotic outage probability and its associated threshold CDF.
- The section derives both delay-sensitive and delay-tolerant throughput expressions.
- The asymptotic outage expression from (23) is used to evaluate the delay-sensitive throughput.
- The threshold CDF is evaluated from the asymptotic outage probability in (23).
V. NUMERICAL RESULTS
The numerical results examine outage probability and throughput under interference, primary-transmitter power, primary-network size, and energy-harvesting time allocation. They show tradeoffs between harvested energy and interference, with performance depending strongly on power constraints, node placement, and transmission mode.
- Impact of PI: Increasing PI lowers outage probability and raises throughput by permitting SS and SR to transmit at higher power.As PI approaches infinity, the maximum transmit powers depend only on harvested energies.
- Impact of PP Utx: Higher PP Utx degrades outage probability and throughput because interference at SR and SD outweighs the additional harvested energy.The outage probability improves when PU transmitters move nearer SS and farther from SR and SD.
- Transmission modes: Delay-tolerant throughput is higher than delay-sensitive throughput.Delay-tolerant transmission can use a flexible rate because its data can tolerate delays.
- Analysis validation: The exact and asymptotic analyses agree as the number of PU transceivers becomes large, and Monte Carlo results validate the analytical derivation.The asymptotic curves converge to the exact curves as M increases.
- Impact of M: Throughput increases and then decreases with M, approaching zero around M ∼100 because interference from PU transmitters becomes excessive.The outage probability likewise decreases and then increases, with an optimal M minimizing outage probability.
- Impact of α: Throughput increases and then decreases with α because energy-harvesting and information-transmission durations trade off.Small α provides insufficient harvested energy, whereas large α leaves too little time for information transmission; optimal α can differ by transmission mode.
VI. CONCLUSIONS
The paper proposes and analyzes wireless energy harvesting for a decode-and-forward cognitive relay network with multiple primary users. It derives exact and asymptotic outage and throughput expressions, showing that interference eventually outweighs harvesting benefits as the primary-network size grows.
- Contributions: The paper derives exact outage and throughput expressions for delay-sensitive and delay-tolerant transmission, plus asymptotic expressions as the number of primary users grows.The asymptotic results include closed forms for outage probability and delay-sensitive throughput and an asymptotic expression for delay-tolerant throughput.
- Conclusion: For sufficiently many primary users, interference from the primary network outweighs the benefits of harvested energy.
APPENDIX A
The appendix derives the outage probability by conditioning dependent random variables to obtain products of independent conditional probabilities, then averaging the resulting terms.
- Conditional decomposition: Conditioning on Z2 factorizes the joint success probability into independent relay and destination conditional probabilities.The relay and destination probabilities are then derived separately.
- Relay analysis: The relay probability accounts for the three power constraints through separate cases based on whether ρZ1 is below PI Y1.The resulting terms are conditioned on additional variables to simplify their dependence.
- Destination analysis: The destination terms are likewise decomposed using conditioning, allowing joint probabilities to be written as products of marginal probabilities.The appendix conditions destination terms on Z2 and Z3 before averaging.
- Final evaluation: The outage probability is evaluated by substituting the appendix-derived terms into the paper's exact outage expression.