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Opportunistic Wireless Energy Harvesting in Cognitive Radio Networks

Seunghyun Lee, Rui Zhang, Kaibin Huang

arXiv:1302.4793v2cs.NIcs.IT

TL;DR

The paper addresses how secondary transmitters can share licensed spectrum while obtaining operating energy from nearby primary transmissions. It develops a stochastic-geometry and Markov-chain framework for transmission probability and outage-constrained throughput, deriving optimal secondary design parameters and extending the analysis to wireless-powered sensor networks.

  • Problem

    The paper studies how to enable low-power secondary transmitters to harvest ambient RF energy while opportunistically accessing primary-network spectrum.

  • Method

    The authors model PTs and STs as independent HPPPs, use Markov chains for battery charging, and analyze throughput and outage constraints to optimize secondary transmit power and density.

  • Results

    The paper derives exact ST transmission probabilities for single- and double-slot charging, bounds for multi-slot charging, and closed-form optimal secondary transmit power and density under outage constraints.

  • Takeaways & Limitations

    The analytical results provide design insights for RF-energy-powered cognitive-radio networks and can also be applied to wireless-powered sensor networks with distributed chargers.

Abstract

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Wireless networks can be self-sustaining by harvesting energy from ambient radio-frequency (RF) signals. Recently, researchers have made progress on designing efficient circuits and devices for RF energy harvesting suitable for low-power wireless applications. Motivated by this and building upon the classic cognitive radio (CR) network model, this paper proposes a novel method for wireless networks coexisting where low-power mobiles in a secondary network, called secondary transmitters (STs), harvest ambient RF energy from transmissions by nearby active transmitters in a primary network, called primary transmitters (PTs), while opportunistically accessing the spectrum licensed to the primary network. We consider a stochastic-geometry model in which PTs and STs are distributed as independent homogeneous Poisson point processes (HPPPs) and communicate with their intended receivers at fixed distances. Each PT is associated with a guard zone to protect its intended receiver from ST's interference, and at the same time delivers RF energy to STs located in its harvesting zone. Based on the proposed model, we analyze the transmission probability of STs and the resulting spatial throughput of the secondary network. The optimal transmission power and density of STs are derived for maximizing the secondary network throughput under the given outage-probability constraints in the two coexisting networks, which reveal key insights to the optimal network design. Finally, we show that our analytical result can be generally applied to a non-CR setup, where distributed wireless power chargers are deployed to power coexisting wireless transmitters in a sensor network.

I. INTRODUCTION

The paper proposes a cognitive-radio architecture in which secondary transmitters harvest RF energy from primary transmissions while opportunistically accessing licensed spectrum. Using stochastic geometry, it analyzes coexistence and extends the framework to wireless-powered sensor networks.

  • I. INTRODUCTION: Secondary transmitters harvest RF energy from active primary transmitters or transmit when sufficiently far from them.The architecture combines opportunistic energy harvesting with opportunistic spectrum access.
  • I. INTRODUCTION: The study derives ST transmission probability and secondary spatial throughput, then optimizes ST transmit power and density under outage constraints.The stated analysis uses stochastic geometry and closed-form optimization results.
  • I. INTRODUCTION: Guard zones protect primary transmissions, while harvesting zones identify STs that can receive usable RF energy.STs inside guard zones cannot transmit, whereas nearby harvesting zones support energy accumulation.
  • I. INTRODUCTION: The analytical framework also applies to wireless-powered sensor networks with distributed wireless power chargers and wireless information transmitters.Unlike the CR setup, the sensor-network scenario does not use guard zones.
  • I. INTRODUCTION: PTs and STs are modeled as independent HPPPs with fixed transmitter–receiver distances and PT access probability.The active PT process is also modeled as an HPPP.

B. Energy-Harvesting Model

The model links RF harvesting, battery charging, opportunistic transmission, and outage-constrained throughput in a slotted CR network. Charging duration determines whether ST transmission probability is obtained exactly or bounded.

  • B. Energy-Harvesting Model: Harvesting zones are determined by RF-harvester sensitivity, with received power above the threshold only within radius rh.Energy received outside harvesting zones is assumed negligible.
  • B. Energy-Harvesting Model: An ST stores harvested energy in a finite battery sized for one slot of transmission at power Ps and transmits when fully charged and outside all guard zones.Its transmission probability is the product of being fully charged and avoiding guard zones.
  • B. Energy-Harvesting Model: The secondary spatial throughput is evaluated using the average transmitting-ST density ptλs under primary and secondary outage constraints.The actual transmitting-ST process is not generally an HPPP because of guard and harvesting zones.
  • B. Energy-Harvesting Model: M denotes the maximum number of harvesting slots needed to fully charge an ST, based on the minimum harvested power at the harvesting-zone edge.M = 1 and M = 2 correspond to single-slot and double-slot charging.
  • B. Energy-Harvesting Model: Finite-state Markov chains give exact transmission probabilities for M = 1 and M = 2, whereas M > 2 yields upper and lower bounds.The multi-slot bounds are based on the double-slot Markov-chain analysis.

A. Single-Slot Charging (M = 1)

The charging analysis models battery evolution with finite-state Markov chains. Single-slot charging has a two-state model, while double-slot charging uses divided harvesting regions and a three-state model.

  • A. Single-Slot Charging (M = 1): For M = 1, the battery level is either 0 or Ps at the beginning of each slot, yielding a two-state Markov chain.The states represent zero and fully charged battery power.
  • A. Single-Slot Charging (M = 1): The single-slot transmission probability is obtained from the steady-state probability of the fully charged state.The fully charged probability is identified with the second stationary-state component.
  • A. Single-Slot Charging (M = 1): For M = 1, transmission probability depends on λp, rh, and rg but not on Ps.Harvesting inside a harvesting zone fully charges the battery within one slot, making the charging probability independent of Ps.
  • B. Double-Slot Charging (M = 2): For M = 2, the harvesting zone is divided into regions corresponding to one-slot and two-slot charging.The regions distinguish harvested power at least Ps from power between 1/2Ps and Ps.
  • B. Double-Slot Charging (M = 2): The double-slot battery model uses three states: zero power, [1/2Ps, Ps), and Ps.Transitions depend on whether the ST lies in the corresponding harvesting regions.
  • B. Double-Slot Charging (M = 2): For M = 2, the transmission probability is obtained from the stationary distribution of the three-state Markov chain.The fully charged-state probability supplies the charging term used in the transmission probability.
  • B. Double-Slot Charging (M = 2): Increasing Ps with fixed Pp and rh shrinks the single-slot charging region, increases two-slot charging frequency, and lowers transmission probability.The stated relation is pt = pfpg, with the fully charged probability decreasing as single-slot charging becomes less frequent.

C. Multi-Slot Charging (M > 2)

For M > 2, the battery cannot generally be represented exactly by a finite-state Markov chain, so the analysis partitions the harvesting zone and derives bounds on ST transmission probability. These bounds are tight for M = 1 or M = 2 but become looser as Ps increases when M > 2.

  • Modeling challenge: For M > 2, the battery power level cannot generally be characterized exactly by a finite-state Markov chain because some state-transition probabilities are unknown.For example, with M = 3, the transition from state 1 to state 2 is not uniquely determined.
  • Bounding analysis: The power harvested in a(X, h2, rh) is alternatively overestimated or underestimated to obtain upper and lower bounds on pt using a corresponding Markov-chain analysis.The overestimation treats the harvested power as 1⁄2Ps, while the underestimation treats it as zero.
  • Zone partition: The harvesting zone is divided into three disjoint regions according to whether harvested power is at least Ps, between 1⁄2Ps and Ps, or below 1⁄2Ps.The regions are b(X, h1), a(X, h1, h2), and a(X, h2, rh), respectively.
  • Transmission-probability bound: Proposition 3.3 bounds the ST transmission probability when Ps > 2ηP_pr^-αh or M > 2.The proposition is obtained after defining mutually exclusive regions and their associated probabilities.

D. Numerical Example

The numerical examples examine how ST transmission probability varies with ST power, PT density, and guard-zone radius, and compare exact or bounded analyses with simulations. Transmission probability decreases with guard-zone radius, while its dependence on PT density is nonmonotonic.

  • ST transmission probability versus Ps: pt is constant for M = 1, decreases with Ps for M = 2, and remains decreasing for M > 2 in simulation.The bounds for M > 2 are tight for M = 1 and M = 2 but become looser as Ps increases; they are considered reasonably accurate for small M.
  • ST transmission probability versus λp: pt first increases with λp at low PT density, then decreases after λp exceeds a threshold.At low λp, charging becomes more frequent; at higher λp, guard zones reduce transmission more strongly.
  • ST transmission probability versus rg: pt decreases as the guard-zone radius rg increases.Larger guard zones reduce the probability that an ST can transmit, with pt = pfpg.
  • Approximation validation: The CDF of exact Is is well approximated by the CDF obtained under Assumption 1.The comparison uses α = 4, η = 0.1, rg = 3, rh = 1, λs = 0.2, λp = 0.01, and Pp = 2.

IV. OUTAGE PROBABILITY

The outage analysis models interference from primary transmitters and active STs, approximating the active-ST process as an HPPP to derive primary and secondary outage expressions. Increasing Ps reduces secondary outage but creates a tradeoff for primary outage, while the approximations rely on Pp ≫ Ps.

  • Interference model: The active ST process Φt is approximated as an HPPP with density ptλs to characterize aggregate interference Is and outage probabilities.Simulations show that the CDF of Is under this approximation can closely match the simulated CDF.
  • Outage characterization: The primary and secondary outage probabilities are derived or approximated for typical receivers under Assumption 1.The secondary analysis conditions on the corresponding active ST being outside all PT guard zones.
  • Model scope: The outage approximations in Lemmas 4.1 and 4.2 are valid only when Pp ≫ Ps.This assumption makes interference from STs inside the primary receiver’s guard zone negligible and supports the approximation used for secondary outage.
  • Effect of ST transmit power: P(s)_out decreases with Ps, whereas P(p)_out is quite insensitive to changes in Ps in the numerical example.Increasing Ps raises received secondary signal power more substantially than aggregate interference, while primary effects involve competing interference and reduced ST activity.

V. NETWORK THROUGHPUT MAXIMIZATION

The paper maximizes secondary spatial throughput over ST transmit power and density under primary and secondary outage constraints, obtaining closed-form solutions under an interference-limited assumption. The optimum reflects a trade-off between RF charging benefits, guard-zone effects, interference, and transmission probability.

  • Optimization formulation: Under σ2 = 0, the maximum secondary throughput, optimal ST transmit power, and optimal ST density are obtained in closed form.The optimization fixes Pp, λp, rg, and rh while optimizing Ps and λs under outage constraints.
  • Solution scope: For M = 1 or M = 2, λ∗s is exact; for M > 2, only upper and lower bounds are available.The general multi-slot charging case relies on bounds for the ST transmission probability.
  • Optimal transmission power: The optimal ST transmission power P∗s decreases as PT density λp increases.The paper attributes this to the increase of µs with λp through the decreasing guard-zone probability pg.
  • Maximum throughput: For ǫp = 0.1, maximum secondary throughput C∗s first increases with λp and then decreases beyond a threshold.When the primary outage constraint prevails, increasing λp eventually requires reducing secondary activity to limit interference.
  • Maximum throughput: For relatively larger ǫp, C∗s increases with λp initially but decreases after a threshold as ptλs is reduced to satisfy the secondary outage constraint.The reported cases are ǫp = 0.2 or 0.3.
  • Optimal ST density: For fixed λp, the optimal active ST density pt(P∗s) is fixed by the outage constraints, while λ∗s is inversely proportional to pt(P∗s).As λp approaches zero, pt approaches zero and λ∗s diverges; sparse PT deployments can therefore require many STs with low activity.

VI. APPLICATION AND EXTENSION

The paper extends its cognitive-radio energy-harvesting analysis to sensor networks powered by distributed wireless power chargers. Wireless power transfer uses a dedicated band separate from information transfer, avoiding interference with wireless information receivers.

  • Extension to sensor networks: Distributed WPCs power WITs over a dedicated band different from the information-transfer band.The extension considers wireless information transmitters and receivers in a sensor network.

A. Transmission Probability

In the sensor-network extension, WITs transmit whenever fully charged because no primary transmitters require guard zones. Consequently, transmission probability generally increases with WPC density.

  • Transmission probability: With rg = 0, pg = 1, so a fully charged WIT can transmit at any time without guard-zone restrictions.The transmission probability is derived from the charging model for the sensor-network setting.
  • Transmission probability: WIT transmission probability pt generally increases with WPC density λp because greater density charges WITs more frequently.This contrasts with the CR case, where guard zones can make transmission probability decrease at high PT density.

B. Network Throughput Maximization

For the sensor network, throughput maximization uses only the WIR outage constraint and inherits a closed-form solution under σ2 = 0. Maximum throughput is independent of WPC density, while required WIT density can decrease as charging becomes more frequent.

  • Optimization formulation: The sensor-network throughput problem applies only the outage constraint for a typical WIR.The optimization is obtained as a simplified version of the CR problem.
  • Closed-form solution: Assuming σ2 = 0, the maximum sensor-network throughput has a closed-form expression based on the CR result.The corresponding corollary gives the maximum network throughput.
  • Throughput and density: Maximum network throughput remains constant regardless of λp because the optimal active-WIT density is determined solely by the WIR outage constraint.Increasing λp can nevertheless reduce the required WIT density because pt generally increases with λp.
  • Scope: The paper concludes that its stochastic-geometry analysis also applies to distributed-WPC sensor networks and similar wireless-powered communication networks.The CR analysis provides the basis for deriving optimal WIT density and transmit power.

APPENDIX A PROOF OF PROPOSITION 3.3

The proof bounds the secondary transmitters’ transmission probability by modeling battery evolution with a Markov chain under maximum and zero harvested power assumptions.

  • Transmission-probability bounds: A 3-state Markov chain represents battery levels 0, [1, 2Ps), and Ps for the upper and lower transmission-probability bounds.The upper bound assumes harvested power in the harvesting region equals 2Ps, while the lower bound assumes it equals 0.
  • Transmission-probability bounds: The upper-bound transition matrix yields a steady-state probability vector, which determines the corresponding bound on pt.The lower bound is obtained analogously from its steady-state distribution, then multiplied by pg.
  • Outage analysis: The outage analysis separates primary and secondary interference expectations because Ip and Is are independent under Assumption 1.Their Laplace transforms are evaluated using the shot-noise result for an HPPP with density λ.

APPENDIX C PROOF OF LEMMA 4.2

The proof converts the primary and secondary outage constraints into two bounds on pt(Ps)λs and identifies their intersection as the optimal operating point.

  • Constraint transformation: The outage constraints are equivalent to pt(Ps)λs ≤ f1(Ps) and pt(Ps)λs ≤ f2(Ps), respectively.The functions f1 and f2 are defined from the outage expressions and system parameters.
  • Optimality characterization: f1(Ps) decreases while f2(Ps) increases as Ps grows, creating an admissible region for feasible (Ps, ptλs) pairs.The admissible region contains operating points satisfying both outage-probability constraints.
  • Optimality characterization: The optimal value of pt(Ps)λs occurs at the intersection pt(Ps)λs = f1(Ps) = f2(Ps).The intersection is found by solving f1(Ps) = f2(Ps); with σ2 > 0, this generally has no closed-form solution.
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