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Wirelessly Powered Backscatter Communication Networks: Modeling, Coverage and Capacity
Kaifeng Han, Kaibin Huang
TL;DR
The paper addresses how to power and connect massive embedded IoT devices without relying on difficult-to-maintain batteries. It proposes and models WP-BC networks using Poisson cluster processes and stochastic geometry, deriving coverage and capacity results that characterize duty-cycle, reflection-coefficient, and beacon-density effects. The analysis finds concave dependence on backscatter parameters and identifies operating trends for capacity and coverage.
Problem
Powering billions of embedded IoT devices is difficult because batteries increase form factors and make recharging or replacement costly or infeasible.
Method
The paper models WP-BC networks as Poisson cluster processes and applies stochastic geometry to derive success-probability and transmission-capacity expressions incorporating location-dependent power, circuit power, duty cycle, and reflection coefficient.
Results
Success probability is concave in the backscatter parameters, with observed optima near β = 0.6 and D = 0.3 − 0.35; capacity grows linearly with PB density at low density before saturating at high density.
Takeaways & Limitations
WP-BC design can be guided by optimizing duty cycle and reflection coefficient while accounting for clustered topology, energy constraints, and interference-limited capacity.
Abstract
from arXiv · showhide
Future Internet-of-Things (IoT) will connect billions of small computing devices embedded in the environment and support their device-to-device (D2D) communication. Powering this massive number of embedded devices is a key challenge of designing IoT since batteries increase the devices' form factors and their recharging/replacement is difficult. To tackle this challenge, we propose a novel network architecture that integrates wireless power transfer and backscatter communication, called wirelessly powered backscatter communication (WP-BC) networks. In this architecture, power beacons (PBs) are deployed for wirelessly powering devices; their ad-hoc communication relies on backscattering and modulating incident continuous waves from PBs, which consumes orders-of-magnitude less power than traditional radios. Thereby, the dense deployment of low-complexity PBs with high transmission power can power a large-scale IoT. In this paper, a WP-BC network is modeled as a random Poisson cluster process in the horizontal plane where PBs are Poisson distributed and active ad-hoc pairs of backscatter communication nodes with fixed separation distances form random clusters centered at PBs. Furthermore, by harvesting energy from and backscattering radio frequency (RF) waves transmitted by PBs, the transmission power of each node depends on the distance from the associated PB. Applying stochastic geometry, the network coverage probability and transmission capacity are derived and optimized as functions of the backscatter duty cycle and reflection coefficient as well as the PB density. The effects of the parameters on network performance are characterized.
I. INTRODUCTION
The paper proposes WP-BC networks, where power beacons energize dense backscatter D2D links, and models their clustered spatial structure to analyze coverage and capacity. It incorporates location-dependent harvested power and backscatter operation into a stochastic-geometry framework.
- Motivation and architecture: WP-BC networks integrate wireless power transfer from power beacons with low-power backscatter communication for large-scale passive IoT deployment.Nodes transmit by reflecting and modulating carrier signals sent by power beacons.
- Motivation and architecture: Backscatter transmitters reflect and modulate incident RF signals while harvesting energy, avoiding energy-hungry components and consuming orders-of-magnitude less power than conventional radios.The reflection coefficient controls antenna impedance mismatch and the reflected signal.
- Network model: The network is modeled as a Poisson cluster process with Poisson-distributed power beacons and random transmitting-node clusters centered at beacon locations.Clusters use either the Matern or Thomas model, with isotropic node directions and cluster-specific distance distributions.
- Network model: Each transmitting node is paired with a unit-distance receiver in an isotropic direction, producing a random spatial process of distributed D2D links.The resulting transmitting-node density is λ_p c̄.
- Backscatter operation: Time slots are divided into mini-slots, and each node randomly selects one mini-slot for backscatter transmission, giving duty cycle D = 1/M.This creates separate backscatter and waiting phases, with durations 1/M and (1 − 1/M), respectively.
- Power and channel model: A power beacon beams a continuous wave to its cluster, and a node’s harvested and backscattered power depends on its distance from the serving beacon.The received WPT power follows ηg|X_0 − Y_0|^-α1, while the backscattered signal includes reflection coefficient β and Rayleigh fading.
B. Backscatter Communication Model
During the backscatter phase, nodes modulate information by varying antenna impedance and reflect part of the incident continuous wave. During the waiting phase, they stop transmitting and harvest energy, transmitting only when the circuit-power constraint is satisfied.
- Backscatter operation: Nodes modulate information bits by adapting their antenna-impedance mismatch during the backscatter phase.The reflected signal uses the incident continuous wave as its carrier.
- Backscatter operation: The reflection coefficient β determines backscattered power βP_X, while the remaining fraction is consumed by the circuit or harvested.This partitions incident power between communication and node operation.
- Backscatter operation: During the waiting phase, nodes withhold transmission and perform only energy harvesting.The slot therefore alternates between transmission and energy accumulation.
- Transmission condition: A node transmits or remains silent according to whether its circuit-power constraint is satisfied.The model explicitly represents this on/off transmission behavior.
C. Performance Metrics
The WP-BC network is evaluated using success probability and transmission capacity. These metrics capture reliable communication over a typical backscatter D2D link and the density of reliable active links.
- C. Performance Metrics: Success probability Ps is the probability that transmission over a typical backscatter D2D link succeeds.Success requires the received SIR to exceed the fixed threshold θ under the interference-limited model.
- C. Performance Metrics: Transmission capacity C measures the spatial density of reliable active backscatter D2D links.
III. INTERFERENCE AND SIGNAL DISTRIBUTIONS
The analysis derives interference and signal-power distributions for a typical backscatter node, then uses them to characterize network coverage and capacity.
- III. INTERFERENCE AND SIGNAL DISTRIBUTIONS: Interference and typical-node signal-power distributions provide the basis for characterizing WP-BC network coverage and capacity.
A. Interference Characteristic Functionals
The interference analysis derives characteristic functionals by conditioning on a typical link and separating interference within the typical cluster from interference across other clusters.
- A. Interference Characteristic Functionals: The interference power I is decomposed into intra-cluster interference Ia and inter-cluster interference Ib.The first component concerns the typical cluster, while the second concerns other clusters and the cluster centered at the associated power beacon.
- A. Interference Characteristic Functionals: The characteristic functionals Ca(s) and Cb(s) are derived separately for the two interference components.Together they form the overall interference characteristic functional C(s).
- A. Interference Characteristic Functionals: Slivnyak’s Theorem and Campbell’s Theorem are used to obtain the intra- and inter-cluster interference expressions.The derivations condition on the typical backscatter and receiving nodes and evaluate expectations over clusters.
B. Signal Distribution
The signal-distribution analysis identifies a circuit-power threshold that determines whether a backscatter node can transmit. It then characterizes transmission power, outage probability, and parameter effects.
- B. Signal Distribution: A PB-to-node separation threshold determines whether the node’s transmission power is zero under the circuit-power constraint.Beyond the threshold, the node experiences circuit power outage.
- B. Signal Distribution: The typical node transmits with Pt = βηg|X0 − Y0|^-α1 within the threshold and Pt = 0 otherwise.
- B. Signal Distribution: The transmission-power distribution has support {0} ∪ [βPc/(1−βD), ∞], with corresponding outage probability and complementary CDF expressions.
- B. Signal Distribution: Increasing βD decreases the separation threshold, while increasing Pc increases it; conditioned on transmission, the power CCDF increases with β and is independent of D.The outage probability decreases as the threshold d0 increases.
IV. NETWORK COVERAGE AND CAPACITY
This section characterizes coverage and capacity in the WP-BC network using results derived earlier.
- Coverage and capacity are characterized for the WP-BC network.
- The characterization uses results derived in the preceding section.
- The section addresses both network performance metrics within the WP-BC model.
A. Network Coverage
Network coverage requires both sufficient harvested power under the circuit constraint and an SIR above the threshold. Its success probability depends on transmission probability, duty cycle, and reflection coefficient, with intermediate parameter values preferred.
- A. Network Coverage: Ps combines the probability of satisfying the circuit-power constraint with the conditional probability that receive SIR exceeds θ.The expression is Ps = Pr(PthX0 ≥ θI | Pt ≠ 0) Pr(Pt ≠ 0).
- A. Network Coverage: Theorem 1 bounds the network success probability using the interference characteristic functional and power outage probability.
- A. Network Coverage: Success probability increases linearly with the transmission probability of a backscatter node, (1 − p0).
- A. Network Coverage: Ps is maximized over duty cycle D and reflection coefficient β because extreme values increase interference, waiting, or weaken received signal.Large D creates dense interferers, small D lengthens waiting, large β strengthens interference, and small β weakens the received signal.
B. Network Capacity
In the close-to-full-coverage regime, transmission capacity is approximated by the density of transmitting nodes and depends on PB density, duty cycle, and reflection coefficient. The capacity results apply only within reliability-preserving parameter ranges.
- B. Network Capacity: In close-to-full coverage, Ps ≈ 1 − p0 and transmission capacity reduces to the density of transmitting nodes.
- B. Network Capacity: Theorem 2 approximates network transmission capacity for both Matern and Thomas cluster processes.
- B. Network Capacity: Transmission capacity is proportional to the density of backscatter nodes in the considered regime.
- B. Network Capacity: Capacity decreases with β in the almost-full-coverage regime and scales as (1 − Dβ) because larger β reduces harvested energy and transmitting-node density.
- B. Network Capacity: Increasing D raises backscatter-node density but lowers transmission probability through reduced harvested energy, so capacity can be optimized over D.
- B. Network Capacity: The capacity results hold only when D and β lie within ranges that ensure link reliability.An inner bound for the admissible (β, D) region can be derived by requiring a positive conditional success probability close to one.
V. SIMULATION RESULTS
Simulations compare analytical and empirical coverage and capacity across backscatter parameters, PB density, reflection coefficient, and cluster sizes. The results support tight analytical bounds and reveal concave or saturating performance trends.
- V. SIMULATION RESULTS: The simulations use η = 40 dBm (10 W), Pc = 7 dBm, θ = −5 dB, α1 = α2 = 3, β = 0.6, and D = 0.4.
- V. SIMULATION RESULTS: The baseline uses λp = 0.2 /m2, expected cluster size c̄ = 3, 1 m D2D links, and a Thomas process with σ2 = 4.
- V. SIMULATION RESULTS: Theorem 1 lower bounds closely match simulated success-probability curves, which are concave in duty cycle and reflection coefficient.
- V. SIMULATION RESULTS: Optimal simulated values are approximately β = 0.6 and D = 0.3 − 0.35 across the tested cluster sizes c̄ ∈ {3, 4, 5}.
- V. SIMULATION RESULTS: Capacity grows linearly with PB density at low density, saturates at high density, and decreases with β when β ≥ 0.6.At high PB density the network becomes dense and interference limited.
VI. CONCLUSION
The paper proposes WP-BC networks for dense backscatter communication powered by power beacons and uses stochastic geometry to quantify coverage and capacity. It relates network performance to backscatter duty cycle and reflection coefficient.
- WP-BC networks use power beacons to enable dense backscatter communication networks through wireless power transfer.
- A Poisson cluster process models the large-scale WP-BC network topology.
- Stochastic geometry derives success probability and transmission capacity to quantify network coverage and capacity.
- Figure 4 examines network capacity against power-beacon density and reflection coefficient for expected cluster sizes c̄ ∈{3, 4, 5}.