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Energy-Neutral Coverage Optimization by Joint Deployment and Scheduling in Ambient IoT Devices with Directional Sensing
David E. Ruíz-Guirola, Samuel Montejo-Sánchez, Richard Demo Souza, Onel L. A. López
TL;DR
The paper studies how to jointly deploy and schedule directional-sensing A-IoT devices under energy-harvesting constraints. It compares LP, RL, and hybrid LP+RL strategies, finding that RL-based policies achieve the strongest coverage while LP initialization substantially speeds convergence.
Problem
Existing coverage and deployment methods do not jointly account for energy harvesting, directional FoV constraints, and sensing schedules in A-IoT settings.
Method
The paper formulates long-term energy-neutral coverage maximization and compares LP, grid-initialized centralized RL, and hybrid LP+RL deployment and scheduling frameworks.
Results
RL and hybrid LP+RL consistently outperform grid and LP methods, achieving up to 2x higher mean effective coverage in low and medium EH regimes.
Takeaways & Limitations
Hybrid LP+RL is the most robust practical solution across the considered duty-cycle regimes and accelerates offline optimization through structured initialization.
Abstract
from arXiv · showhide
Ambient IoT (A-IoT) devices rely on energy harvesting and duty cycling to sustain operation, thereby fundamentally changing collaborative sensing compared with traditional always-ON sensor networks. In this paper, we study the joint deployment and sensing scheduling of A-IoT devices equipped with directional sensing. We explore four solution strategies: (i) a grid deployment with static duty cycling, (ii) a centralized policy-gradient reinforcement learning (RL) approach that begins with a grid deployment and learns energy-aware device relocation and duty-cycling policies, (iii) a mixed-integer linear programming (LP) approach that couples static deployment design with duty-cycle allocation, and (iv) a hybrid LP+RL that combines optimization-based initialization with learning-based refinement. Using representative A-IoT use cases, we evaluate coverage as a function of device density, field-of-view, and maximum feasible duty cycle, determined by harvested energy and device consumption. Numerical results indicate that the proposed LP+RL and RL policies consistently outperform both the grid baseline and the LP-based method, achieving up to 2x higher mean effective coverage in low and medium energy harvesting (EH) regimes. In contrast, the standalone LP method remains limited by its conservative static duty cycle allocation under tight EH constraints. Moreover, the structured initialization of the LP+RL method substantially accelerates convergence, reducing the total offline optimization time by up to 10x compared to the standalone RL.
I. Introduction
The paper addresses coverage optimization for energy-harvesting A-IoT devices whose directional sensing and intermittent energy availability challenge conventional deployment and scheduling methods. It jointly considers deployment and sensing schedules, comparing LP, RL, and hybrid LP+RL frameworks across coverage conditions.
- Existing approaches largely assume continuously active or battery-powered sensors with isotropic sensing, omitting EH constraints, FoV heterogeneity, and sensing schedules.
- The paper jointly optimizes device placement and temporal sensing schedules under intermittent energy availability for representative A-IoT use cases.
- Three energy-aware frameworks are compared: LP, grid-initialized RL, and hybrid LP+RL using LP initialization to accelerate learning.
- The hybrid method converges faster than standalone RL, with the paper analyzing computational complexity and runtime.
- RL, especially hybrid LP+RL, provides the best coverage across device densities, FoVs, and feasible duty-cycle regimes, particularly under low and medium energy budgets.
II. System model
The system models collaborative event sensing by energy-harvesting devices with directional FoVs and distance-dependent detection reliability. Detection requires an active device, sufficient proximity, and an orientation that includes the event.
- A base station coordinates energy-harvesting A-IoT devices deployed over a monitored region, with each device having an energy buffer and directional sensing modality.
- The event-driven model activates devices through duty cycling, and unsuccessful detection occurs when no device detects the event in its occurrence TTI.
- An event is detectable only when a device is active, within sensing radius rmax, and oriented so the event lies inside its FoV Θ.
- The FoV is an angular sector Θ = [θmin, θmax] with width ∆θ = θmax − θmin; events outside that sector cannot be detected.
- Conditioned on being inside the FoV, sensing reliability decays with distance up to maximum range rmax.
B. Energy consumption and harvesting model
The energy model tracks finite battery dynamics, slot-level sensing and transmission consumption, and stochastic harvesting. Energy-neutral operation bounds each device’s feasible duty cycle by harvested energy relative to activity costs.
- Each device has a finite-capacity battery with stored energy Bj(t) ∈ [0, Emax].
- Active sensing and reporting consume fixed amounts Esense and ETx, while inactive sensing-related consumption is zero.
- A sensing or reporting operation cannot execute when battery energy is below Esense + ETx.
- Harvesting follows an i.i.d. binary process delivering either a fixed EH quantum or zero energy per slot.
- Under energy-neutral operation, the long-term average consumed energy cannot exceed harvested energy, defining the maximum feasible duty cycle fj.
III. Problem formulation
The formulation maximizes long-term spatial coverage by jointly selecting deployment, FoV orientations, and a state-dependent duty-cycling policy under battery and energy-availability constraints. Coverage is based on sensing probability over the monitored region and varies with active devices.
- The optimization seeks device locations, FoV orientations, and duty-cycling decisions that maximize reliable event detection throughout the region of interest.
- The device state includes positions, duty-cycling actions, and battery levels that evolve according to energy-harvesting and consumption dynamics.
- A device’s sensing contribution is zero when it sleeps or when a point lies outside its effective sensing region.
- The per-TTI coverage metric is a spatial average sensing probability over the region, rather than binary point coverage.
- The policy π maps observed states to duty-cycling actions and FoV orientations, while the objective maximizes time-average coverage subject to battery dynamics and energy availability.
IV. Deployment policy
The deployment policy frames joint device placement and sensing decisions as a maximum-coverage problem under energy constraints, using grid initialization for heuristic and learning-based methods.
- Maximum coverage is NP-hard even with fixed batteries and a single time interval when at most K < N devices may be active.
- Grid initialization provides both a static-duty-cycle baseline and an initial state that learning can refine through device relocation and sensing schedules.
- Position updates during training are virtual actions, while final learned locations are fixed and sensing policies run during operation.
- The centralized controller therefore needs no real-time physical relocation feedback after deployment.
A. Grid + static duty cycling
The paper compares fixed grid scheduling, centralized RL, and LP-based deployment with duty-cycle allocation, highlighting their different adaptability and computational structures.
- A. Grid + static duty cycling: Grid devices use a periodic active-sleep pattern satisfying average EH budgets but not adapting to instantaneous battery state or transient coverage gaps.
- A. Grid + static duty cycling: The regular-grid baseline uses a fixed deployment and pre-designed duty cycling, whereas RL can refine positions, orientations, and schedules.
- B. RL-based Proposal: The centralized RL policy starts from grid deployment and learns stochastic relocation, FoV, and duty-cycling decisions through policy gradients.
- B. RL-based Proposal: The RL reward penalizes excessive activation while promoting high coverage availability, with µ controlling the trade-off between coverage and energy efficiency.
- C. Convex Approach and Greedy Deployment: The LP approach discretizes the region and candidate configurations, then uses coverage variables and energy-budget constraints to formulate static deployment selection.
- C. Convex Approach and Greedy Deployment: The relaxed LP solution prioritizes candidates by marginal coverage gain per unit cost, selecting feasible configurations until the budget is exhausted.
- C. Convex Approach and Greedy Deployment: Duty-cycle allocation orders selected devices by coverage weights αj and activates them up to EH-limited duty cycles under the average active-device budget Kavg.
D. Hybrid LP + RL Proposal
The hybrid LP+RL method uses an interpretable LP deployment as initialization and RL to refine positions and sensing decisions under nonlinear coverage and energy interactions.
- The LP stage first selects static sensor locations and orientations, providing an interpretable starting point for the subsequent RL stage.
- RL refines deployment and sensing decisions to improve long-term effective coverage despite energy-harvesting uncertainties.
- After offline training, device locations remain fixed and the learned sensing and duty-cycling policy is applied during operation.
- The hybrid combines structured LP initialization with RL modeling of coverage overlap, directional sensing, and time-varying energy availability.
E. Complexity Analysis
The grid benchmark has negligible optimization cost, whereas LP and RL require substantially more computation; hybrid initialization can reduce time to convergence despite added per-episode cost.
- O(N) is the maximum offline complexity of the grid benchmark because deployment is fixed and duty cycling is pre-defined.
- O(PM) constructs the LP coverage matrix, while greedy maximum coverage contributes O(NPM) and duty-cycle sorting contributes O(N log N).
- O(Nep N) characterizes the practical RL training cost, which increases with the number of episodes required for convergence.
- Hybrid LP+RL can reach convergence in less total time than standalone RL despite its higher per-episode computational cost.
V. Results Analysis
The evaluation uses representative A-IoT operating regimes defined by energy-neutral duty-cycle limits, with performance measured across sensing configurations and repeated Monte Carlo runs.
- Evaluation setup: Three operating regimes use maximum feasible duty cycles fj,max ∈ {10−3, 10−2, 10−1}, selected from representative A-IoT use-case KPI ranges.The regimes are chosen according to the energy budget required to remain operational.
- Energy model: Energy-neutrality relates average available energy to active sensing and reporting energy, with Eactj = Esense + ETx.The duty-cycle regimes are derived from this energy-neutral operating condition.
- Evaluation setup: Performance is evaluated for an illustrative deployment with N devices over 150 independent Monte Carlo runs.Each device performs energy harvesting with λHj = 0.1.
- Evaluation setup: The simulations consider FoV values of 60◦, 180◦, and 360◦, a maximum sensing range of rmax = 3 m, and event duration tev = 1 s.Energy buffers begin empty, and the area is discretized at 1 cm resolution.
A. Coverage Performance
Coverage is evaluated across deployment density, directional FoV, duty-cycle limits, event windows, and temporal behavior. The LP+RL hybrid generally provides the strongest and most balanced coverage, while standalone LP is constrained under tight energy budgets.
- Coverage performance: Fig. 2 varies device density, FoV, and maximum energy-neutral duty cycle to compare mean effective coverage per TTI across four methods and an upper bound.Columns represent FoV values of 60◦, 180◦, and 360◦; rows represent duty-cycle limits of 10−3, 10−2, and 10−1.
- Coverage performance: For fmax = 10−3, LP yields the lowest effective coverage, whereas LP+RL performs best as device density increases; RL outperforms the grid benchmark.The LP+RL, RL, grid, and LP methods are compared against a duty-cycle-aware upper bound.
- Coverage performance: At fmax = 10−2 and 10−1, LP+RL remains best across FoVs, followed by RL and the grid benchmark, while LP remains below the hybrid.LP+RL stays closest to the upper bound in these regimes.
- Density requirements: For FoV 180◦, Fig. 3 reports the minimum device density needed for coverage targets across three duty-cycle regimes and event windows of 1 s, 100 ms, and 10 ms.Longer event windows substantially relax coverage requirements, especially at medium and high duty cycles.
- Density requirements: With fmax = 10−3 and tev = 10 ms, practical schemes achieve roughly 1%–5% effective coverage, while the upper bound reaches about 10%.The combination of a very small feasible duty cycle and short observation window leaves limited opportunity for collaborative sensing.
- Temporal and spatial behavior: For N = 100 and FoV = 60◦, LP+RL produces the most uniformly distributed spatial coverage and the fewest persistent blind regions among the compared methods.Fig. 4 shows deployments and coverage-probability heatmaps for fmax = 0.01 and fmax = 0.1.
- Temporal and spatial behavior: In a 200 ms window with fmax = 10−1, LP+RL attains the highest instantaneous effective coverage, followed by RL, while grid and LP remain lower.RL and LP+RL generate periodic peaks associated with coordinated sensing opportunities and sleep phases.
- Temporal and spatial behavior: Periodic peaks in RL and LP+RL indicate coordinated high-coverage sensing opportunities, whereas static grid and LP schedules produce flatter, smaller peaks.The flatter trajectories are less effective at exploiting the available energy budget for high-coverage opportunities.
C. Sensitivity Analysis
The LP+RL hybrid achieves higher and more stable effective coverage than standalone RL across reward-weight settings, while RL is more sensitive to reward tuning.
- 0.69–0.71 coverage: LP+RL consistently exceeds RL’s 0.62–0.64 across the tested reward-weight range.The comparison uses N = 100, FoV = 60◦, and fmax = 0.1.
- The hybrid’s coverage remains concentrated around 0.69–0.71, whereas RL remains between 0.62 and 0.64 under the specified settings.Error bars represent standard deviation across runs.
- RL coverage tends to decrease and its error bars increase as the reward weight µ grows.Increasing µ prioritizes coverage relative to energy-budget adherence, which can produce less balanced deployment and scheduling decisions.
- LP+RL coverage varies only mildly with µ, indicating reduced sensitivity to reward-weight selection.The structured LP initialization places learning near a spatially aligned operating point and reduces dependence on exact reward tuning.
D. Convergence Analysis
The hybrid LP+RL method converges substantially faster than standalone RL despite higher per-episode computational cost, reducing total offline optimization time by nearly an order of magnitude.
- tGrid = 0.091 s, tLP = 1.845 s, tRL = 21.508 s, and tLP+RL = 2.373 s average total runtime per scenario.These runtimes are implementation- and platform-dependent indicative empirical costs.
- The LP+RL method reduces total offline optimization time by nearly one order of magnitude compared with standalone RL.Its structured LP initialization reduces the exploration required during learning, although the hybrid is more computationally expensive per episode.
- The conclusion reports that structured LP initialization reduces offline optimization time by up to 89% compared with standalone RL.The hybrid is described as the most robust practical solution across the considered duty-cycle regimes and FoV settings.