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Average Age of Information in Wireless Powered Sensor Networks
Ioannis Krikidis
TL;DR
WPT sensor networks need a way to assess the freshness of received updates, an aspect conventional metrics may not capture. This paper analyzes a simple capacitor-powered sensor that transmits when fully charged, deriving average-AoI expressions and optimizing capacitor size with a one-dimensional search.
Problem
Many WPT studies focus on complex network structures or conventional metrics that do not capture timeliness, while AoI-based WPT design remains a new research area.
Source: §I · p. 1Method
The sensor harvests RF energy into a capacitor and, once fully charged, sends an update using all stored energy under a greedy policy.
Source: §I · p. 1, §II · p. 2Results
The paper derives closed-form average-AoI expressions dependent on capacitor size and computes the optimal size through a one-dimensional optimization.
Source: §V · pp. 3–4Takeaways & Limitations
The capacitor-size tradeoff and resulting theoretical analysis provide performance bounds that can guide practical WPT implementations.
Source: §I · p. 1The analysis concerns a simplistic system model, so its results are presented as guidelines and performance bounds for practical implementations.
Source: §I · p. 1
Abstract
from arXiv · showhide
In this letter, we deal with the age of information (AoI) for a sensor network with wireless power transfer (WPT) capabilities. Specifically, we study a simple network topology, where a sensor node harvests energy from radio frequency signals (transmitted by a dedicated energy source) to transmit real-time status updates. The sensor node generates an update when its capacitor/battery becomes fully charged and transmits by using all the available energy without further energy management. The average AoI performance of the considered greedy policy is derived in closed form and is a function of the capacitor's size. The optimal value of the capacitor that maximizes the freshness of the information, corresponds to a simple optimization problem requiring a one-dimensional search. The derived theoretical results provide useful performance bounds for practical WPT networks.
I. INTRODUCTION
Many WPT studies use complex topologies or conventional metrics that do not capture timeliness, while AoI-focused WPT design remains a new research area. This letter analyzes a simple sensor link and derives average-AoI expressions dependent on capacitor size.
I. INTRODUCTION
- Existing WPT work often studies complex network structures or uses conventional metrics that do not capture the timeliness needs of sensing and actuation.AoI measures the time elapsed since generation of the freshest status update received at the destination.Source: §I · p. 1
- AoI optimization for WPT networks is described as a new research area; one cited two-way system derived closed-form average uplink AoI, and few other relevant works were identified.The cited system has a master node transfer energy and information to a slave node, which uses harvested energy for its uplink.Source: §I · p. 1
- The paper derives closed-form average AoI for a WPT sensor link and finds the capacitor size can be optimized through a one-dimensional search.The system uses a greedy policy: the sensor transmits when its capacitor is charged, using all stored energy.Source: §I · p. 1
- The studied topology has an energy transmitter broadcast to a sensor, which communicates with an information receiver by discharging its capacitor.The capacitor size creates a tradeoff: smaller capacitors recharge sooner, while larger ones provide more transmit power and improve successful decoding.Source: §I · p. 1, Figure 1 · p. 1
II. SYSTEM MODEL
The model has a dedicated energy transmitter, a capacitor-equipped sensor, and an information receiver. The sensor transmits after charging, while the model specifies wireless-link assumptions, update timing, and AoI measurement.
II. SYSTEM MODEL
- When its finite capacitor is fully charged, the sensor generates a status update and transmits using all stored energy under a greedy online policy.Energy and communication use orthogonal channels; the sensor may also harvest energy during transmission using a suitable capacitor architecture.Source: §II · p. 2
- The model assumes Rayleigh block fading, independent across slots, and additive white Gaussian noise on all wireless links.A linear WPT model is used, which the paper says provides useful lower bounds for harvested energy under nonlinear models.Source: §II · p. 2
- After the capacitor fills, the sensor transmits in the next slot; successful decoding resets the receiver's AoI to one.The packet uses spectral efficiency r, and transmission takes one time slot.Source: §II · p. 2
- The receiver's AoI is measured as the elapsed time since generation of the freshest update it has received.The model defines RF-to-DC conversion efficiency η and treats harvested energy from AWGN as negligible.Source: §II · p. 2
- The time between consecutive received updates is the sum of recharge intervals across the transmissions needed until successful decoding.X_k is the received-update interarrival time, T_k is the interval between capacitor recharges, and M counts transmission attempts until success.Source: §II · p. 2, Figure 2 · p. 2
III. ANALYSIS OF THE AVERAGE AGE OF INFORMATION
The section derives average AoI from recharge and successful-update interarrival moments and the area under the AoI curve. It also gives high-power limits and formulates capacitor-size optimization.
III. ANALYSIS OF THE AVERAGE AGE OF INFORMATION
- The propositions provide first- and second-order moments for capacitor recharge intervals and successful-update interarrival times at the receiver.The S-IR link success probability enters the interarrival-time result.Source: §III · p. 2
- Average AoI is obtained from the AoI area accumulated across update intervals and normalized by elapsed time.The time average tends to the ensemble average as N → ∞.Source: §III · pp. 2–3
- Theorem 1 states the average AoI for the considered sensor network; the paper says it follows by using Propositions 1 and 2 and substituting (11) into (9).Source: §III · p. 3
- For fixed B, average AoI converges to 1/π as P → ∞; when B and P grow with B/P = θ, it converges to 1 + 3(λθ/η) + (λθ/η)^2.Source: §III · p. 3
- The capacitor size B is selected by minimizing average AoI for given transmit power, with the optimum solved numerically rather than in closed form.Source: §III · p. 3
IV. NUMERICAL RESULTS
The results show that capacitor size creates a trade-off between charging time and transmission energy, with an optimal size that depends on transmit power. Minimum AoI also depends on power, spectral efficiency, and distance, and the analysis agrees with simulations.
IV. NUMERICAL RESULTS
- Higher transmit power and/or shorter distance reduces average AoI by charging the capacitor faster and shortening energy-harvesting idle time.The optimal capacitor size differs across transmit-power values.Source: §IV · p. 3, Figure 3 · p. 3
- Capacitor size trades faster transmission against longer charging time, and its AoI-minimizing value varies with transmit power.High B requires more charging slots; low B provides less transmission energy.Source: §IV · p. 3, Figure 3 · p. 3
- The theoretical results match the simulations, which use σ2 = −50 dBm, η = 0.5, and r = 0.05 BPCU.The sensor is 20 meters from both the energy transmitter and information receiver; the pathloss exponent is α = 2.2.Source: §IV · p. 3
- Higher spectral efficiency and/or distance increases minimum average AoI, which converges to a floor of 1/π as P → ∞.The minimum is evaluated at B∗.Source: §IV · p. 3, Figure 4 · p. 3
V. CONCLUSION
The paper analyzes average AoI for a wireless-powered sensor that discharges a capacitor charged by a dedicated energy source. It derives closed-form expressions and numerically selects the AoI-optimal capacitor size through a one-dimensional optimization.
V. CONCLUSION
- The sensor sends updates to the destination by discharging a capacitor charged by a dedicated energy source.The average AoI is the performance measure considered.Source: §V · pp. 3–4
- Closed-form average-AoI expressions show that performance depends strongly on capacitor size.The optimal capacitor value is computed numerically through a one-dimensional optimization problem.Source: §V · p. 4
- A one-dimensional optimization problem determines the capacitor value that maximizes information freshness.The paper computes the optimal value numerically.Source: §V · p. 4
APPENDIX A PROBABILITY OF CAPACITOR CHARGING IN K
Appendix A uses independent exponential random variables to calculate the probability that the capacitor charges over K consecutive slots. It then averages over transmission attempts to obtain interarrival-time moments for successful updates.
APPENDIX A PROBABILITY OF CAPACITOR CHARGING IN K
- The charging calculation uses K independent, identically distributed exponential random variables with rate parameter λ.Their exponential density is fX(x) = λ exp(−λx).Source: Appendix A · p. 4
- The appendix averages over the number of transmissions until successful decoding to derive first- and second-order moments of successful-update interarrival time.The success probability for the S-IR link is denoted by π.Source: Appendix A · p. 4
- The probability that the capacitor charges in K consecutive time slots is Π(β/λ, K).Source: Appendix A · p. 4
APPENDIX B PROOF OF PROPOSITION 1
Appendix B computes the average time between capacitor recharges using the charging probability derived in Appendix A. It also sets up the second-order moment of recharge time.
APPENDIX B PROOF OF PROPOSITION 1
- The average time between capacitor recharges is computed using Π(β/λ, k), defined in Appendix A.The result also relies on [14, Eq. 1.212].Source: Appendix B · p. 4
- The proof proceeds to derive the second-order moment of the time between consecutive capacitor recharges.Source: Appendix B · p. 4
APPENDIX C PROOF OF PROPOSITION 2
The proof defines the number of transmissions through successful decoding and relates equation (20) to expressions (15) and (16).
APPENDIX C PROOF OF PROPOSITION 2
- k is the positive-integer number of transmissions until successful decoding at the IR.If k transmissions occur, the first k − 1 are unsuccessful.Source: Appendix C · p. 4
- Equation (20) is based on expressions (15) and (16).Source: Appendix C · p. 4