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Passive RF Sensing for People Counting with Dense IoT Networks
Federica Fieramosca, Vittorio Rampa, Michele D'Amico
TL;DR
Estimating people counts from ambient RF signals requires a way to model how multiple bodies affect propagation and to determine how many targets a network can distinguish. The paper introduces C-MAM and derives resolvability bounds; its simulations report resolution of up to 14–15 targets in specified dense-network settings.
Problem
Estimating people counts from RF measurements is challenging because body-wave interactions must be modeled and large-scale sensing involves high-dimensional inverse problems.
Source: §1 · p. 1Method
The paper introduces C-MAM for cumulative multi-body attenuation and derives resolvability bounds from network geometry and electromagnetic properties.
Source: §1.2 · p. 2Results
With 60 antennas at 5.8 GHz, environments of 49–100 m2 support accurate resolution of up to N = 14–15 targets.
Source: §5.1 · p. 4Takeaways & Limitations
The bounds provide a tool for pre-deployment assessment of RF sensing performance across network layouts and signal conditions.
Source: §1.2 · p. 2, §6 · p. 6A target influences a link only when at least 50% of its elliptical footprint lies within that link’s Fresnel zone.
Source: §4 · p. 3
Abstract
from arXiv · showhide
Radio Frequency (RF) convergence, the joint use of radio signals for both communication and sensing, is gaining increasing attention in research and industry, mostly for its potential in Internet of Things (IoT) applications. By using RF signals of opportunity, such as those generate by the wireless networks, RF sensing exploits the effects of human bodies on the electromagnetic waves to detect both people presence and their movements without requiring wearable devices. In this paper, we address the problem of estimating the number of people in a monitored area covered by several RF nodes of a wireless network: to this aim, we propose a composite diffraction-based model, namely C-MAM, to capture the cumulative RF attenuation induced by multiple human bodies. Building on this model, we derive the analytical resolvability bounds that quantify the maximum number of distinguishable individuals based on the layout geometry and other physical characteristics of the wireless network. These bounds allow for the pre-deployment assessment of RF sensing performance under different scenarios.
1 Introduction
RF sensing uses ambient wireless signals to detect people, but modeling human-body interactions and solving large-scale inverse problems remain challenges. This paper presents C-MAM and derives resolvability bounds for dense RF networks.
1 Introduction
- RF sensing uses ambient signals to detect, locate, and track people, while sensing methods face challenges modeling body-wave interactions and solving high-dimensional inverse problems [6].The paper situates RF sensing within ISAC, where wireless nodes serve as virtual sensors for communication and sensing.Source: §1 · p. 1
1.1 RF Sensing Scenario: Infrastructural Snapshot
- The infrastructural-snapshot scenario estimates the number of people at time t and characterizes their motion and physical traits from a dense deployment of RF nodes.Targets are described by footprint position, orientation, height, and lateral body size.Source: §1.1 · pp. 1–2
1.2 Contributions
- C-MAM models cumulative attenuation from multiple bodies while accounting for occlusion and interference within Fresnel’s zones, using classical diffraction theory.The model is introduced as a physically based EM model for dense RF sensing.Source: §1.2 · p. 2
- The paper derives resolvable-target bounds for dense RF networks from link geometry, Fresnel-zone overlap, signal frequency, and subject size.The bounds use stochastic geometry to guide system design and deployment; the paper points to for related single-target pre-deployment strategies.Source: §1.2 · p. 2
2 System model
The system represents a monitored area as a graph of RF nodes and active links. Nodes collect neighbor-link measurements over time, which are aggregated into network-wide sensing data under simplifying assumptions about node height and the free-space reference.
2 System model
- The monitored area is represented by a graph G = (V, L), where RF nodes are vertices and active links between distinct nodes are edges.The number of active links is bounded by L ≤ |V|(|V| − 1).Source: §2 · p. 2
- Nodes sequentially receive beacon signals from neighbors and collect EM measurements that are aggregated into a network-wide sensing matrix.Each node’s vector records its local EM signature; the resulting matrix encodes the network’s global EM state under the targets’ influence.Source: §2 · p. 2
- For geometric simplicity, the model places all nodes on a horizontal plane at a constant height and measures attenuation relative to the no-people free-space scenario.The node-height assumption sets z_u = 0 for every node.Source: §2 · p. 2
3 EM Modeling of Multi-Body Attenuation
The section develops attenuation models from a single target to multiple bodies, then motivates C-MAM as a way to address implausible additive estimates in dense settings. Resolvability also depends on whether targets are covered by links and have sufficiently distinct Fresnel-zone signatures.
3 EM Modeling of Multi-Body Attenuation
- A single-target model uses scalar diffraction theory to model a human body as a 2D absorbing sheet that perturbs the field between two RF nodes.The received field is compared with the free-space field, and the corresponding attenuation is expressed in dB.Source: §3 · p. 2
- The Multi-body Additive Model (MAM) extends the single-target case by summing attenuation contributions from all targets.In dense scenes, this summation can produce physically implausible estimates when multiple targets occlude the same region.Source: §3 · p. 2
- C-MAM addresses dense-scene overestimation by limiting target contributions to those within a link’s first Fresnel zone and preventing further additions when a target fully obstructs that zone.These assumptions prevent additive contributions in shadowed regions.Source: §3 · pp. 2–3
- Figure 2 defines resolvability conditions: targets need sufficiently distinct Fresnel-zone coverage, and a target outside every zone is unresolved because no link fully covers it.The distinctness condition is expressed as Jaccard distance δ_n,m > τ.Source: Figure 2 · p. 3
4 Limits on resolvable subjects in dense graphs
The section derives a diffraction-based upper bound on the number of targets a dense RF network can resolve, using Fresnel-zone coverage and link-pattern distinctness. The bound depends on network layout and RF parameters and is presented as a model-based tool for assessing system capability.
4 Limits on resolvable subjects in dense graphs
- A target influences a link when at least 50% of its elliptical footprint lies within that link’s Fresnel zone; these indicators form its covering-link set.The covering-link set is evaluated across all links.Source: §4 · p. 3
- The bound estimates the maximum resolvable targets by requiring distinct link-occlusion patterns (C1) and at least one covering link per target (C2).C1 compares target link sets using a tolerance threshold τ; typical values are 0.2–0.4.Source: §4 · p. 3
- A correction fractionally discounts targets with identical or highly similar Fresnel-zone coverage because they cannot be individually distinguished.Source: §4 · p. 3
- The upper bound depends on link count, node geometry, and carrier frequency through Fresnel-zone size, and is valid under dense connectivity.The stated dense-connectivity regime has L ≃ |V|(|V| − 1).Source: §4 · p. 3
- The bound supports model-based capability assessment without training data or ML tools and serves as a benchmark for data-driven counting strategies.Source: §4 · p. 3
5 Experimental Validation and Results
The section evaluates theoretical accuracy bounds through simulations and tests C-MAM predictions against indoor RF measurements. Across these analyses, results assess counting accuracy under different network configurations and subject conditions.
5 Experimental Validation and Results
- The evaluation combines theoretical bounds, synthetic attenuation samples from MAM and C-MAM, and measurements from a real-world indoor deployment in the 2.4 GHz band.The simulation study varied room size, antenna count, subject dimensions, operating frequency, and Jaccard threshold.Source: §5 · p. 4, §5.1 · p. 4
5.1 Simulation-Based Analysis
- With 60 antennas at 5.8 GHz, 49–100 m² environments support accurate resolution of up to 14–15 targets; fewer nodes or wider spacing reduce this to 6–10.Accuracy also improves with larger subject width, lower Jaccard thresholds, and higher frequency, particularly as target count increases.Source: §5.1 · p. 4, Figure 4 · p. 5
5.2 Experimental Validation
- The indoor campaign measured RSSI across two 2.4 GHz IEEE 802.15.4 networks, and aggregated attenuation vectors were used as inputs to an RNN trained on C-MAM simulations.The 38-antenna deployment had 342 active links; measured accuracy was evaluated for up to seven real subjects and compared with model predictions.Source: §5.2 · pp. 4–5
- C-MAM predictions closely follow measured accuracy, while MAM consistently overestimates performance; C-MAM is more conservative in overlapping Fresnel zones.For 20 nodes, C-MAM slightly underestimates accuracy when N < 4; for 38 nodes, it tends to slightly overestimate accuracy when N > 5.Source: §5.2 · p. 5, Figure 5 · p. 6
6 Conclusion
The paper presents C-MAM for estimating people counts in dense IoT RF networks and derives resolvability limits from network and subject properties. It reports experimental validation and identifies extensions to sparse or heterogeneous networks and moving subjects as future work.
6 Conclusion
- C-MAM models cumulative attenuation from multiple bodies, including electromagnetic interactions, while resolvability limits link distinguishable-target counts to network geometry and subject properties.The bounds support pre-deployment evaluation of accuracy and the maximum number of resolvable individuals.Source: §6 · p. 6
- Experimental received-signal-strength measurements in a controlled indoor setup validated the theoretical predictions and supported the model’s predictive capability.Source: §6 · p. 6
- Future work will extend the framework to sparse and heterogeneous networks, improve robustness for moving subjects, and address dynamic environments.The paper also mentions tracking movement using, for instance, Bayesian methods.Source: §6 · p. 6