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Enabling Wireless Power Transfer in Cellular Networks: Architecture, Modeling and Deployment
Kaibin Huang, Vincent K. N. Lau
TL;DR
The paper addresses wireless charging without power cords by proposing a hybrid network that overlays cellular access with power beacons. It models this architecture and derives deployment tradeoffs and outage-related results for microwave power transfer.
Problem
Wireless charging aims to eliminate power cords and chargers, while existing approaches fail to account for ad hoc base-station deployment.
Method
The paper proposes a hybrid network in which power beacons are deployed over an uplink cellular network to charge mobiles via microwave radiation.
Results
The analysis derives tradeoffs among transmission powers and base-station/power-beacon densities, with results covering different mobile energy-storage conditions and a monotone outage-related function.
Takeaways & Limitations
The results provide insight into hybrid-network deployment for wireless mobile charging.
Abstract
from arXiv · showhide
Microwave power transfer (MPT) delivers energy wirelessly from stations called power beacons (PBs) to mobile devices by microwave radiation. This provides mobiles practically infinite battery lives and eliminates the need of power cords and chargers. To enable MPT for mobile charging, this paper proposes a new network architecture that overlays an uplink cellular network with randomly deployed PBs for powering mobiles, called a hybrid network. The deployment of the hybrid network under an outage constraint on data links is investigated based on a stochastic-geometry model where single-antenna base stations (BSs) and PBs form independent homogeneous Poisson point processes (PPPs) and single-antenna mobiles are uniformly distributed in Voronoi cells generated by BSs. In this model, mobiles and PBs fix their transmission power at p and q, respectively; a PB either radiates isotropically, called isotropic MPT, or directs energy towards target mobiles by beamforming, called directed MPT. The model is applied to derive the tradeoffs between the network parameters including p, q, and the BS/PB densities under the outage constraint. First, consider the deployment of the cellular network. It is proved that the outage constraint is satisfied so long as the product the BS density decreases with increasing p following a power law where the exponent is proportional to the path-loss exponent. Next, consider the deployment of the hybrid network assuming infinite energy storage at mobiles. It is shown that for isotropic MPT, the product between q, the PB density, and the BS density raised to a power proportional to the path-loss exponent has to be above a given threshold so that PBs are sufficiently dense; for directed MPT, a similar result is obtained with the aforementioned product increased by the array gain. Last, similar results are derived for the case of mobiles having small energy storage.
I. INTRODUCTION
The paper proposes a hybrid architecture that overlays an uplink cellular network with randomly deployed power beacons for microwave charging. It models this network stochastically and derives deployment tradeoffs under data-link outage constraints for isotropic and directed MPT.
- Architecture and motivation: MPT addresses mobile charging, but practical deployment must overcome propagation loss, create line-of-sight links, and form sharp energy beams.Dense PB deployment shortens transfer distances, while antenna arrays can beam energy toward mobiles.
- Technology context: Large antenna arrays support high MPT efficiency, including a reported 45% efficiency over 36,000 km in a large-scale power-transfer system.The paper contrasts such systems with the dense-PB architecture, where shorter transfer distances make efficient MPT more practical.
- Architecture and motivation: The hybrid network overlays an uplink cellular network with randomly deployed power beacons that wirelessly charge mobiles via microwave radiation.The architecture is designed to eliminate power cords and chargers through wireless mobile charging.
- Stochastic-geometry model: The model represents BSs and PBs as independent homogeneous PPPs and distributes mobiles uniformly within BS-generated Voronoi cells.PBs power uplink transmissions using either isotropic radiation or beamforming toward target mobiles.
- Analysis and scope: The analysis derives tradeoffs among mobile and PB transmission powers and BS/PB densities for isotropic or directed MPT and different mobile energy-storage capacities.These tradeoffs are evaluated under an outage constraint on data links.
- Related technologies: Unlike inductive and magnetic-resonance coupling, MPT does not require transmitter–receiver coil alignment but can suffer severe loss over long distances.The paper positions its hybrid network as a large-scale counterpart to small-scale power-and-information tradeoffs.
B. Modeling the Access and Power-Beacon Networks
The paper models an uplink cellular network and randomly deployed power beacons using stochastic geometry, then derives feasibility regions and deployment tradeoffs under an outage constraint.
- Modeling motivation: Stochastic geometry addresses the tractability limitations of hexagonal-grid models and accommodates ad hoc base-station deployment.
- Transmission modes: Mobiles transmit with fixed power p, and power beacons transmit with fixed power q using either isotropic radiation or directed beamforming.
- Network model: Base stations and power beacons are modeled as independent homogeneous PPPs, while each Voronoi cell contains a uniformly distributed active mobile.
- Cellular deployment: The cellular-network feasibility region characterizes all combinations of p and λb satisfying the outage constraint, with minimum p increasing as λb decreases.
- Hybrid deployment: For hybrid networks with large energy storage, feasibility depends on q, λp, and λb; directed MPT provides an equivalent q increase by the array gain zm.
- Small-storage deployment: With small energy storage, inner bounds are obtained for both MPT modes, and the tradeoffs between λp and λb depend on the data- and MPT-link path-loss exponents.
SUMMARY OF NOTATION
The paper presents notation in Table I and organizes the analysis, numerical results, simulations, and conclusions across successive sections.
- Numerical and simulation results precede the concluding remarks.
- Notation is summarized in Table I.
II. MODELS, METRICS AND CONSTRAINTS
The model combines Poisson-distributed base stations, mobiles, and power beacons with uplink interference, microwave power transfer, and receiver energy storage.
- Access-network model: Base stations form a homogeneous PPP, and nearest-base-station association partitions the plane into Voronoi cells containing uniformly distributed mobiles.
- Access-network model: Active mobiles share their serving base station over time and transmit with fixed power p, while a multiuser detector cancels interference from K nearest interfering mobiles.
- Access-network model: Uplink channels use a no-fading path-loss model with exponent α > 2, and time slots keep channels and point processes fixed within a slot.
- Power-beacon model: Power beacons form an independent homogeneous PPP, and mobiles use dedicated microwave-power receivers for harvesting energy.
- Energy storage: Two energy-storage units support continuous MPT by alternating harvesting and transmitter powering, with roles switched when the powering unit is discharged.
- MPT models: Isotropic MPT uses a short-range propagation model, whereas directed MPT charges each mobile through its nearest power beacon using beamforming.
- MPT models: Directed MPT allows a beacon to serve multiple mobiles simultaneously, scaling its total transmitted raw power by their number and modeling main- and side-lobe responses.
- MPT protocol: Directed MPT requires handshaking in which mobiles request charging and provide pilot symbols so beacons can estimate direction and beam raw power.
C. Metrics and Constraints
The paper measures cellular performance through outage probability and imposes separate constraints for data reliability, received signal power, and power availability. It derives a cellular feasibility region, whose interference-limited case is governed by received-signal-power constraints rather than outage constraints.
- Metrics and Constraints: Pout ≤ϵ defines the cellular-network outage constraint, with 0 < ϵ < 1.
- Metrics and Constraints: Small energy storage can cause fluctuating mobile transmission power because PB locations make received power random.
- Metrics and Constraints: Constraint 3 limits received raw power outage below pt with probability no larger than δ, where 0 < δ < 1.
- Metrics and Constraints: The feasibility region Fc is derived for cellular parameters p and λb, and in interference-limited networks depends only on the BS received-signal-power constraint.
- Metrics and Constraints: Denser BS deployment shortens transmission distances and therefore requires lower mobile transmission power, with the effect increasing for larger α.
- Metrics and Constraints: ϵ(µ) is strictly decreasing in µ, while its closed-form expression and relation with µ are challenging to derive and are evaluated by simulation.
B. Access-Network Deployment with Zero Noise
For zero-noise cellular networks, the paper analyzes outage and received-power feasibility under interference-limited operation. It shows that outage is independent of BS density and transmission power, while throughput still increases with BS density.
- Access-Network Deployment with Zero Noise: Pout is independent of λb in an interference-limited cellular network with zero noise.
- Access-Network Deployment with Zero Noise: Transmission power and BS density do not affect SIR because they scale received signal and interference together.
- Access-Network Deployment with Zero Noise: Outage probability is largely affected by the threshold θ and path-loss exponent α, which determines spatial separation.
- Access-Network Deployment with Zero Noise: Network throughput grows linearly with increasing λb because denser deployments support more active mobiles.
- Access-Network Deployment with Zero Noise: The feasibility region under received-power constraints is independent of the outage constraint and is inner bounded in λb and p.
- Access-Network Deployment with Zero Noise: The zero-noise and nonzero-noise feasibility conditions have the same pλb power-law form and differ only in c.
IV. HYBRID-NETWORK DEPLOYMENT
The hybrid-network analysis derives feasibility regions for isotropic and directed MPT with large energy storage. Required PB density decreases with PB power and BS density, while isotropic and directed transfer benefit from different propagation and beamforming mechanisms.
- Hybrid-Network Deployment: The hybrid feasibility region Fh is derived for isotropic or directed MPT and for different energy-storage regimes.
- Hybrid-Network Deployment: For isotropic MPT, expected received raw power is proportional to PB density λp, PB power q, and duty cycle ω.
- Hybrid-Network Deployment: For directed MPT, one PB transfers significant raw power to each mobile, with sharp beamforming represented by array gain zm.
- Hybrid-Network Deployment: Directed-MPT feasibility is inner bounded when PBs and served mobiles are sufficiently close and a PB supplies enough power through beamforming or high transmission power.
- Hybrid-Network Deployment: For isotropic MPT, required PB density decreases as q and λb increase, diminishes as β approaches 2, and increases with α.
- Hybrid-Network Deployment: For large zmq/σ2, directed-MPT feasibility admits a simplified inner bound, and the zero-noise case follows by replacing σ2/µ with ˜µ.
B. Hybrid-Network Deployment: Mobiles with Small Energy Storage
With small energy storage, the paper enforces instantaneous received-power reliability in addition to the cellular outage constraint. It derives feasibility bounds for isotropic and directed MPT and shows that beamforming reduces the required PB resources.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: Small-storage hybrid deployment must satisfy both the cellular outage constraint and a power-shortage constraint.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: The received-power cumulative distribution has no closed form, so it is upper bounded by considering only the nearest PB.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: Proposition 5 gives the small-storage hybrid feasibility region, with separate inner bounds for isotropic and directional MPT.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: The PB-resource product is proportional to log δ, making the feasibility condition insensitive to changes in δ.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: Beamforming reduces the required PB resource, while the required resource decreases with increasing BS density.
- Hybrid-Network Deployment: Mobiles with Small Energy Storage: The same small-storage results apply to interference-limited cellular networks after replacing σ2/µ with ˜µ.
V. NUMERICAL AND SIMULATION RESULTS
The simulations evaluate cellular and hybrid-network feasibility under different noise, storage, and MPT configurations. They show how BS density, PB density, transmission power, and MPT directionality shape feasible deployment regions.
- At µ = 3.8, the outage probability is ϵ = 0.3, while the interference-limited minimum at µ = 0 is 0.06.
- Cellular-network deployment: The minimum mobile-transmission power decreases linearly in dB as log λb increases, and the feasibility boundaries are parallel across noise conditions.
- Hybrid-network deployment: With directed MPT, mobile-transmission power becomes insensitive to sufficiently large λb, while isotropic-MPT power continues increasing approximately logarithmically with λp.
- Hybrid-network deployment: For large-storage mobiles, the isotropic-MPT feasibility region is obtained analytically, whereas other storage and MPT cases use simulation with inner bounds.
- Hybrid-network deployment: The analytical and simulated inner bounds are generally tight except for isotropic MPT with small energy storage, where no dominant PB supplies most received raw power.
- Hybrid-network deployment: Isotropic MPT enlarges feasibility for relatively small BS densities, whereas directed MPT is advantageous for relatively large BS densities.
VI. CONCLUDING REMARKS
The paper derives first-order deployment tradeoffs for cellular networks overlaid with power beacons. Its results characterize required transmission powers and beacon densities for isotropic and directed MPT, while identifying modeling limits for practical deployment.
- The stochastic-geometry model yields simple first-order tradeoffs among network parameters for realizing MPT in cellular networks.
- Cellular-network deployment: Minimum mobile-transmission power p increases super-linearly as BS density λb decreases under an outage constraint.
- Cellular-network deployment: In an interference-limited network, outage probability is independent of p and λb because noise is absent.
- Hybrid-network deployment: For isotropic MPT with large energy storage, qλpλb^α has to exceed a threshold to satisfy the outage constraint.
- Hybrid-network deployment: Directed MPT effectively increases q by the array gain relative to isotropic MPT, with analogous tradeoffs for small energy storage.
- Limitations and future work: Practical extensions should model array configurations, realistic channels, clustered PB deployments, mobility, and mobile energy-level dynamics.
APPENDIX
The appendix develops analytical expressions for received power and shortage probabilities under isotropic and directed MPT. It uses PPP scaling, Campbell’s theorem, nearest-beacon distances, and probability decompositions to establish the stated results.
- PPP scaling: A spatial scaling function maps a PPP with scaled density to a homogeneous PPP with density λb, enabling tractable analysis of network geometry.
- Received-power analysis: For isotropic MPT, Campbell’s theorem and stationarity yield the expected received raw power expression.
- Received-power analysis: For directed MPT, the expected received power is derived by rewriting the power expression and analyzing the shortest PB-to-mobile distance D.
- Power-shortage analysis: The nearest-PB distance distribution supports a lower bound on no-power-shortage probability when a nearby beacon can provide sufficient received power.
- Power-shortage analysis: The directed-MPT result follows through an analogous derivation after the isotropic-MPT case is established.