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Medium Access Control Protocols for Wireless Sensor Networks with Energy Harvesting
Fabio Iannello, Osvaldo Simeone, Umberto Spagnolini
TL;DR
Battery-oriented MAC design uses network lifetime, but EH-powered WSNs require criteria that address uncertain energy availability despite potentially perpetual operation. This paper analyzes TDMA, FA, and DFA with delivery probability and time efficiency, using analytical models and numerical validation. The results emphasize that both delivery and time efficiency matter when designing EH-WSNs.
Problem
EH-powered WSNs introduce uncertain energy availability and design trade-offs not captured by battery-oriented network-lifetime criteria.
Method
The paper analyzes TDMA, FA, and DFA using delivery probability, time efficiency, analytical models, and numerical simulations.
Results
The numerical results validate the analytical framework and emphasize accounting for both delivery probability and time efficiency in EH-WSN design.
Takeaways & Limitations
EH-WSN MAC design should evaluate the trade-off between successfully delivered measurements and the rate of data collection at the FC.
Abstract
from arXiv · showhide
The design of Medium Access Control (MAC) protocols for wireless sensor networks (WSNs) has been conventionally tackled by assuming battery-powered devices and by adopting the network lifetime as the main performance criterion. While WSNs operated by energy-harvesting (EH) devices are not limited by network lifetime, they pose new design challenges due to the uncertain amount of harvestable energy. Novel design criteria are thus required to capture the trade-offs between the potentially infinite network lifetime and the uncertain energy availability. This paper addresses the analysis and design of WSNs with EH devices by focusing on conventional MAC protocols, namely TDMA, Framed-ALOHA (FA) and Dynamic-FA (DFA), and by accounting for the performance trade-offs and design issues arising due to EH. A novel metric, referred to as delivery probability, is introduced to measure the capability of a MAC protocol to deliver the measure of any sensor in the network to the intended destination (or fusion center, FC). The interplay between delivery efficiency and time efficiency (i.e., the data collection rate at the FC), is investigated analytically using Markov models. Numerical results validate the analysis and emphasize the critical importance of accounting for both delivery probability and time efficiency in the design of EH-WSNs.
I. INTRODUCTION
EH-powered WSNs require system-level MAC design because energy availability is discontinuous and may permit perpetual operation without guaranteeing short-term activity. The paper analyzes TDMA, FA, and DFA using delivery probability and time efficiency to characterize their trade-offs.
- EH can enable perpetual network operation, but temporary energy shortages still limit short-term activity.
- The paper studies single-hop WSNs in which an FC collects sensor data using TDMA, FA, and DFA MAC protocols.
- Delivery probability measures successful sensor reporting to the FC, while time efficiency measures the FC’s data collection rate.
- The analysis uses an analytical framework to assess EH-WSN performance and MAC design trade-offs for the three protocols.
- The paper also addresses backlog estimation for ALOHA-based protocols and validates its analytical results through numerical simulations.
A. Interference Model
The system model treats uplink communication as interference-limited and models sensor energy storage and harvesting as discrete stochastic processes. Sensor participation depends on available energy, while collisions and capture determine successful reception.
- A. Interference Model: Channel gains are constant within an inventory round but vary independently across sensors and rounds through i.i.d. fading.
- A. Interference Model: A sensor is successfully received when its instantaneous SIR exceeds the threshold γth; with γth > 0 dB, at most one colliding sensor can be decoded.
- A. Interference Model: Slots are classified as empty, collided, or successful, with successful reception potentially occurring through the capture effect.
- B. ESD and Energy Consumption Models: The ESD has N + 1 discrete energy levels, with capacity Fε representing the maximum number of transmissions supported by a fully charged device.
- B. ESD and Energy Consumption Models: The energy distribution evolves across inventory rounds according to both the adopted MAC protocol and the energy-harvesting process.
- B. ESD and Energy Consumption Models: Each sensor participates only when it has a new measure and at least ε energy units stored, and a transmission consumes ε energy.
C. Energy Harvesting Model
The model treats harvested energy as discrete, independent across sensors and reporting intervals, with energy available during an interval determined by the store at its start. It evaluates delivery and time efficiency together, capturing both successful reporting and data-collection rate.
- C. Energy Harvesting Model: Harvested energy EH,m(n) is modeled as a discrete random variable, i.i.d. across intervals and sensors.The probability of harvesting iδ energy units is qi, with q0 > 0 and q1 > 0.
- C. Energy Harvesting Model: Because harvesting is slower than an information report interval, a sensor uses only its initial energy Em(n) during that interval.The model assumes TIR(n) is much shorter than Tint, making within-interval harvested energy negligible relative to ε.
- Performance Metrics: Delivery probability measures whether a sensor with a new measure successfully reports it to the fusion center during the current interval.A delivery failure can result from energy shortage or insufficient retransmission opportunities.
- Performance Metrics: Time efficiency measures the probability that a slot is successfully used and captures the data-collection rate at the fusion center.It differs from conventional throughput because the interval duration can be random and is normalized by slots allocated within the interval.
- Performance Metrics: Contention-based MACs trade delivery probability against time efficiency because improving delivery generally requires more slots to reduce collisions.The larger allocation lowers time efficiency, making both metrics necessary for EH-WSN design.
B. MAC Protocols
The paper reviews TDMA, FA, and DFA as conventional MAC protocols for energy-harvesting sensors. Their organization determines how energy availability, collisions, retransmissions, and empty slots affect delivery and time efficiency.
- TDMA: TDMA assigns every sensor an exclusive slot in each fixed-length frame, regardless of whether it has data or sufficient energy.With M slots, each reporting interval has duration MTs.
- TDMA: 33?
- TDMA: TDMA delivery probability is limited only by energy availability and therefore upper-bounds ALOHA-based MACs.Its time efficiency can nevertheless be poor when new-measure probability or harvesting rate is low because many slots are empty.
- DFA: DFA allocates multiple frames and selects each frame length from an estimate of the current backlog size.The ratio ρ controls frame length relative to backlog, while users retransmit after collisions when they retain enough energy.
- FA and DFA: FA is the special case of DFA with one announced frame and no retransmissions within the reporting interval.DFA therefore extends FA by allowing collided packets to try again in later frames.
IV. ANALYSIS OF THE MAC PERFORMANCE METRICS
The performance analysis derives delivery probabilities for TDMA, FA, and DFA under known, sufficiently large backlogs. It combines energy availability with collision or capture success to characterize protocol performance.
- Assumptions: The analysis assumes that the fusion center knows each frame's backlog and that the backlog is large enough for a Poisson approximation.These assumptions make contention probabilities depend primarily on the frame-to-backlog ratio ρ.
- Delivery Probability for TDMA: TDMA delivery probability equals the probability that the sensor has at least ε energy, because the protocol is collision-free.This probability depends on the energy-storage distribution at the beginning of the interval.
- Delivery Probability for FA: FA delivery probability combines the probability of having enough energy with an approximated capture probability under Poisson-distributed interference.The capture probability can be evaluated analytically for some channel-gain distributions or numerically otherwise.
- Delivery Probability for FA: For FA, the Poisson approximation extends the number of possible interfering users because the capture probability rapidly decreases as interference grows.The resulting unconditional capture probability is expressed through the distribution of interfering users and conditional capture probabilities.
3) Delivery Probability for DFA:
DFA analysis tracks conditional capture across retransmission frames while accounting for persistent channel gains and energy depletion. The time-efficiency derivation models new measurements and energy availability jointly, with backlog independence simplifying the result.
- Delivery Probability for DFA: DFA frame-level capture probabilities are computed recursively because collided users retain channel gains across the reporting interval.For later frames, the calculation conditions on previous failed capture events and evaluates the channel-gain density for users in the backlog.
- Delivery Probability for DFA: The large-backlog assumption allows channel-gain correlations among repeated collisions to be neglected because repeated collisions within one interval are unlikely.This simplifies the computation of later-frame capture probabilities.
- Delivery Probability for DFA: DFA delivery probability combines mutually exclusive successful-delivery events across frames with the energy probability required for each retransmission.A user retransmits until its message is successfully delivered, while the required energy increases with the frame index.
- Time Efficiency for TDMA: Under the modeled independence between energy availability and new measurements, TDMA time efficiency equals α times the probability of having at least ε energy.The derivation uses Pr[Mm] = α and independence between Em and Mm.
- Analytical limitation: The exact DFA delivery probability would require averaging over correlated backlog sizes, but the large-backlog assumption removes that dependence.This is an analytical simplification rather than an exact treatment of backlog correlation.
2) Time Efficiency for FA:
FA time efficiency is derived by aggregating successful slot use across possible collision multiplicities, with DFA extending the calculation across multiple frames. Under the large-backlog assumption, FA efficiency becomes independent of the ESD energy distribution.
- FA derivation: FA time efficiency sums the probability of successful use by slots selected by different numbers of simultaneous users.Exactly j users select a slot with probability ρ^j e^-ρ/j!, while successful use contributes jpc(j−1).
- FA properties: Under assumption A.2, FA time efficiency is independent of the ESD energy distribution.The large-backlog model determines slot occupancy without conditioning FA efficiency on stored energy.
- DFA extension: DFA time efficiency weights each frame’s efficiency by its normalized frame length and sums across frames in an interrogation round.The frame length is approximated by its average, Lk ≃ ρE[Bk], under assumption A.2.
- DFA extension: The analysis models DFA sensor-state evolution with a discrete Markov chain, while TDMA and FA follow as special cases with independent ESD evolution.Retransmissions correlate DFA states across interrogation rounds; the large-backlog assumption decouples them for analysis.
A. States of a Sensor
The sensor state combines activity, stored energy, and current frame, enabling a discrete Markov-chain model of energy and transmission evolution. Under stated positivity conditions, the chain is ergodic and yields steady-state distributions for the performance metrics.
- A. States of a Sensor: A sensor state records activity or idleness, stored energy, and the current frame index when active.Active states Akj represent a pending measure with j energy units in frame k; idle states Ij represent j stored units while idle.
- B. Discrete Markov Chain (DMC) Model: The DMC is event-driven, with transitions triggered by harvesting, new measurements, collisions, and successful transmissions rather than fixed time intervals.Harvested energy is associated with idle states because arrivals during the current interrogation round are usable only in the next round.
- A. States of a Sensor: Sensors retransmit across successive frames until delivery, energy shortage, or both; collisions consume energy without successful delivery.Successful transmissions return the sensor to idle states, while collisions can transition it to energy shortage.
- B. Discrete Markov Chain (DMC) Model: When q0 > 0, q1 > 0, and pc,k > 0, the finite DMC is irreducible and aperiodic, hence ergodic with a unique steady-state distribution.The self-transition at I0 establishes aperiodicity, while q1 enables reachability among states.
- B. Discrete Markov Chain (DMC) Model: The steady-state distribution conditioned on the beginning of an interrogation round is used to derive the energy distribution and asymptotic delivery and time efficiencies.The beginning-of-round distribution satisfies φ+ = φ−P and maps to πE, from which GE is obtained.
VI. BACKLOG ESTIMATION
The paper proposes a low-complexity two-step backlog estimator for DFA that combines the ESD energy distribution with observed channel outcomes. It updates future-frame backlog estimates using residual energy availability.
- VI. BACKLOG ESTIMATION: The proposed DFA backlog estimator uses a low-complexity two-step procedure because optimal estimators are generally intractable for many sensors.The FC first estimates the initial backlog from the ESD-energy ccdf, then updates it from channel outcomes and residual ESD energy.
- VI. BACKLOG ESTIMATION: The initial backlog estimate is B̂1 = MαGE(ε), based on the probability that sensors have sufficient energy for transmission.Subsequent estimates use channel observations and the conditional residual-energy distribution.
- VI. BACKLOG ESTIMATION: The FC estimates the next-frame backlog from successful and collided slots, correcting for sensors that are in energy shortage.The update is ĈkGE((k+1)ε|kε), where Ĉk combines estimated collision counts from both slot types.
- VI. BACKLOG ESTIMATION: The estimator accounts for uncertainty in successful slots by using conditional average transmitter counts, with βD,k = 1 when capture is absent.Collided-slot counts use βC,k conditioned on observing a collision.
- VI. BACKLOG ESTIMATION: The algorithm can be applied in any interrogation round by deriving the ESD distribution from the DMC model.The distribution or its ccdf is propagated from an initial distribution through the sensor-state model.
VII. NUMERICAL RESULTS
Numerical results validate the analytical models and show that delivery probability and time efficiency favor different MAC choices. FA and DFA offer tunable trade-offs through ρ, while harvesting rate and capture conditions materially affect performance.
- A. MAC Performance Metrics Trade-offs: TDMA time efficiency decreases with lower harvesting rate because more sensor slots go unused under energy shortage, unlike FA and DFA.Dynamic frame sizing makes FA and DFA comparatively insensitive to harvesting-rate changes in time efficiency.
- VII. NUMERICAL RESULTS: The analytical and simulated results closely match, validating assumptions A.1 and A.2 and the backlog estimation algorithm.The comparisons include simulations with known and estimated backlog.
- A. MAC Performance Metrics Trade-offs: TDMA always outperforms FA and DFA in delivery probability, while DFA surpasses FA at high harvesting rates and performs similarly at low rates.Retransmissions benefit DFA when µH=0.35, but low-energy conditions limit retransmission opportunities for µH∈{0.05, 0.15}.
- A. MAC Performance Metrics Trade-offs: Increasing ρ can raise delivery probability while lowering time efficiency for FA and DFA, exposing a direct performance trade-off.TDMA appears as a single point, whereas FA and DFA provide flexibility through ρ selection.
- A. MAC Performance Metrics Trade-offs: Lower SIR thresholds improve ALOHA-based protocols through increased capture probability, while TDMA is insensitive to the threshold.The comparison varies γth ∈ {0.01, 3, 10} dB at fixed µH = 0.15.
VIII. CONCLUSIONS
The paper examines EH-WSN MAC design through delivery probability and time efficiency, focusing on TDMA, FA, and DFA. Numerical results validate the analytical framework and inform EH-WSN design.
- EH-WSNs require new performance criteria and design solutions because energy harvesting creates challenges beyond battery-powered operation.
- Delivery probability measures whether a MAC protocol delivers any sensor’s measure to the fusion center, while time efficiency measures the FC’s data collection rate.
- The analysis focuses on TDMA, Framed-ALOHA, and Dynamic-FA, while also addressing backlog estimation and frame-length selection.
- Numerical results validate the proposed analytical framework and provide insight into EH-WSN design.
APPENDIX A AVERAGE NUMBER OF SENSOR TRANSMISSIONS PER TIME-SLOT
The appendix derives the average numbers of sensors in successful and collided slots for framed random access. It uses conditional transmission events, Bayes’ rule, and the empty-slot probability.
- The appendix calculates βD,k and βC,k by accounting for the capture effect and an arbitrary ρ.
- Y denotes simultaneous transmissions in a slot, while Uk and Ck denote successful and collided slots in frame k.
- βD,k is obtained by conditioning on the number of simultaneous transmissions and applying Bayes’ rule.
- βC,k is derived from the collided-slot probability after accounting for successful and empty slots.