# Network Size Estimation in DtS-IoT: A LoRaWAN Approach for Satellite Constellations

Pablo Ilabaca, Diego Maldonado, Juan Fraire, Samuel Montejo-Sánchez, Sandra Céspedes

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Pablo Ilabaca, Diego Maldonado, Juan Fraire, Samuel Montejo-Sánchez, Sandra Céspedes. Network Size Estimation in DtS-IoT: A LoRaWAN Approach for Satellite Constellations. ICC 2025 - IEEE International Conference on Communications, Jun 2025, Montreal, France. pp.5506-5511, 10.1109/ICC52391.2025.11162046 . hal-05357368

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# Network Size Estimation in DtS-IoT: A LoRaWAN Approach for Satellite Constellations

Pablo Ilabaca*, Diego Maldonado†, Juan A. Fraire†‡, Samuel Montejo-Sánchez§, Sandra Céspedes*

* Department of Computer Science and Software Eng., Concordia University, Montreal, Canada

† Inria, INSA Lyon, CITI, UR3720, 69621 Villeurbanne, France

‡ Universidad Nacional de Córdoba - CONICET, Córdoba 5000, Argentina

§ Instituto Universitario de Investigación y Desarrollo Tecnológico, Universidad Tecnológica Metropolitana, Santiago, Chile

**Abstract**—Low Earth Orbit (LEO) constellations are pivotal for the global connectivity of Internet of Things (IoT) networks. They facilitate Direct-to-Satellite (DtS) communications for ground nodes and address the absence of terrestrial infrastructure in remote regions. Although LoRa-based solutions provide low-cost connectivity to constrained devices in DtS-IoT networks, scalability remains a significant challenge due to heavy channel congestion associated with large-scale deployments. The LoRa Optimistic Collision Information-based (L-OCI) mechanism has been designed to estimate efficiently the network size of a LoRa-based DtS-IoT deployment. It enables a passing satellite to gauge the potential congestion in the served region by estimating the number of active ground nodes within its coverage area. However, this mechanism was devised to operate assuming a single LEO satellite. This paper introduces the constellation L-OCI (CL-OCI), a new methodology for network size estimation designed for LEO satellite constellations. We thoroughly tested CL-OCI using FLoRaSat, a discrete-event satellite constellation simulator with realistic orbital DtS-IoT scenarios. Results indicate a substantial improvement in scalability, doubling the maximum number of nodes CL-OCI can estimate, and a seven-fold reduction in energy wasted due to collided transmissions compared to the baseline single-satellite L-OCI.

**Index Terms**—Direct-to-Satellite, Internet of Things, Low Earth Orbit, LoRa, LoRaWAN, Network size estimation, Medium Access Control.

## I. INTRODUCTION

The Internet of Things (IoT) and Massive Machine-Type Communications are rapidly going out of the reach of terrestrial infrastructure. With applications ranging from healthcare to environmental phenomena monitoring, billions of new connected devices are expected to be deployed in the upcoming years [1]. Satellite technology is an appropriate approach to the ubiquitous coverage needed to achieve a truly global IoT for these devices. However, the high costs of commercially developed solutions restrict access to satellite technology for multiple stakeholders [2].

The Direct-to-Satellite IoT (DtS-IoT) paradigm is a promising alternative for the large-scale coverage of many remotely deployed IoT devices [3], [4]. With this architecture, small energy-constrained devices (nodes) communicate directly with a satellite or a constellation of satellites. Low-Earth Orbit (LEO) constellations have the lowest deployment costs, propagation delays, and link budget due to their low-altitude orbits, which make them ideal candidates for DtS-IoT. Iridium, Astro-

cast, Globalstar, and Lacuna Space are examples of companies providing global DtS-IoT services using LEO constellations.

Regarding low-cost technology options, LoRaWAN is identified as a simple and low-power solution among the leading Low-Power Wide-Area Network (LPWAN) technologies [5]. Although designed for urban and rural terrestrial areas, LoRaWAN can be adapted for use in DtS-IoT networks [6]. Research papers, such as [3], [7], [8], support using LoRa/LoRaWAN for DtS-IoT. Furthermore, several commercial ventures, such as Lacuna Space, operate their DtS-IoT solutions over LoRaWAN.

However, scalability remains one of the main challenges in DtS-IoT when thousands of nodes are served by a single satellite at a given time, thus unavoidably leading to packet collisions [6]. These collisions hinder the network's performance and undermine DtS-IoT applications when the link is saturated [9]. From the node point of view, this scalability challenge is further accentuated by the limited satellite visibility period of LEO orbits. Addressing packet collisions and enhancing overall network performance creates a need for intelligent and more sophisticated Medium Access Control (MAC) protocols that cope with dense scenarios and improve scalability [10], [11].

In this line, the authors in [12] propose a MAC protocol that enhances network throughput by adjusting node transmission probability based on the number of nodes within a satellite's coverage. Determining the size of a node population is essential for attaining scalability and energy efficiency in certain access control protocols [12], [13]. Furthermore, knowing the number of devices contending to access the DtS-IoT LEO satellite will help ensure the quality of service for their respective applications [14]. Estimating the number of active nodes is challenging due to the remote and isolated deployment. In [14], the Optimistic Collision Information-based estimator (OCI) was presented offering low estimation error and the lowest computational costs when compared with existing network size estimators for LEO DtS-IoT, making it an ideal candidate for heavily constrained devices such as CubeSats. In [6], the OCI estimator was implemented using the LoRa/LoRaWAN protocol. Results show that LoRa/LoRaWAN-based OCI (L-OCI) maintains low Root Mean Square Error (RMSE) and power efficiency for network sizes up to 500 nodes. However, L-OCI only considers a single satellite and does not account
for ground track shifts due to Earth's rotation, limiting its applicability in constellations.

This work introduces a novel mechanism for implementing the L-OCI estimator in realistic satellite constellations, accounting for ground-track shifts due to Earth's rotation. The proposed Constellation L-OCI (CL-OCI) extends the estimator's scalability to accommodate larger network sizes, addressing the limitations of previous implementations and enhancing its applicability in more complex and expansive satellite network scenarios.

The remainder of this paper is organized as follows. Section II briefly reviews network size estimation techniques in satellite IoT environments. Section III presents the system model, the proposed CL-OCI extension, and energy consumption implications. Section IV presents the simulation scenarios and discusses the results. Section V concludes the paper.

## II. NETWORK SIZE ESTIMATION TECHNIQUES IN SATELLITE IoT

The problem of estimating the number of ground nodes the satellite serves is known as network size estimation. Many solutions rely on a network size estimation mechanism to allocate resources at different layers of the stack of protocols. For example, in [12] and [13], the authors propose MAC protocols that incorporate the network size information to control node transmission probability according to the estimated number of nodes within the satellite's coverage area, substantially improving network throughput when compared to a blind transmission probability. Nevertheless, estimating the number of active nodes in a given area is challenging because IoT nodes are often deployed in remote and isolated environments.

In [14], the OCI estimator was shown to have better precision regarding RMSE and, simultaneously, to be less computationally demanding than the state-of-the-art estimators with which it was compared in a simulated satellite IoT network. The low computational requirements make OCI a low-cost option for resource-constrained infrastructure such as CubeSats and other nanosatellites. In [6], the L-OCI estimator was proposed to adapt OCI to LoRa technology. The following sections describe OCI and L-OCI in more detail.

### A. OCI

The OCI estimator is based on the number of slots where collisions, successful receptions, or absence of signal (idle) were detected in Frame Slotted ALOHA (FSA) [14]. It is common in current literature to assume that terrestrial nodes use Aloha protocols to access the channel in LoRa-based DtS-IoT networks [15]–[17], specifically Slotted Aloha and FSA [4]. In these latter protocols, terrestrial nodes transmit at the beginning of a time slot. Multiple lightweight techniques for synchronizing terrestrial nodes and satellites exist in the literature [18]–[20]. The OCI estimator consists of two stages: training and operation.

a) Training phase: First, nodes of a population of known size $n_k$ transmit small dummy frames in randomly chosen slots of an FSA frame of length $w$ slots. At the end of each frame, a “naive” estimate is calculated as $\phi = s + 2c$, where $s$ and $c$ represent the number of successfully decoded messages and collisions detected. In these experiments, the value of $n_k$ gradually increases until it reaches $N$, the maximum number of nodes expected to be estimated during the operation phase. Then, OCI employs a polynomial fitting technique to map the “naive” estimation curve to the real number of nodes in the simulation $n_k$. The polynomial coefficients obtained from the fit are stored, concluding the training phase.

b) Operation phase: During the operation phase, an unknown number of nodes transmit in randomly chosen slots of the FSA frame. The coefficients stored previously are used to calculate the OCI estimation at the end of each frame.

### B. L-OCI

Although effective, the OCI estimator is limited by several assumptions. It assumes that the beacon is always successfully decoded by all ground nodes and that these nodes remain synchronized with the satellite, which overlooks potential errors in DtS-IoT networks. Moreover, the model presumes a stable group of nodes within the CubeSat's coverage for the entire frame duration, whereas, in reality, node coverage can change rapidly. Some nodes may receive the beacon but move out of range before transmitting, while others may enter coverage after the beacon transmission. The model also focuses solely on collisions as the cause of data loss, ignoring other factors such as the capture effect and weak signal strength. These limitations led to the development of the L-OCI model.

Due to the issues above, modifications to OCI are presented in [6] to adapt the estimator following LoRa technology, enabling its applicability in more realistic DtS-IoT scenarios. First, a Time Division Multiple Access (TDMA)-based protocol is added to the LoRaWAN MAC layer. The work in [6] is also based on LoRaWAN modifications to enable collision detection. For temporal synchronization, LoRaSync [21] is utilized, which extends LoRaWAN Class B to adopt a beaconing system to allow nodes to schedule uplink transmissions in time slots within the beacon period.

The beacon period comprises three distinct parts. First, the satellite broadcasts a beacon, advertising the start time of contention and the duration of the uplink slots. This is followed by the Beacon Window period, divided into $w$ uplink slots, each with a duration equal to a message's maximum Time on Air (ToA). Finally, the Beacon Period concludes with a Beacon Guard interval to provide the gateway sufficient time to decode the last transmissions before starting the next Beacon Period with the corresponding beacon transmission.

Although there are many parameters in LoRa, in [6], the authors studied the optimal combinations of Spreading Factor (SF), Bandwidth (BW), and Frame Length (BCN) for various network sizes, solving a Multi-objective Optimization Problem. A specific combination of SF and BW results in a determined ToA, which, together with BCN, yields a precise
<figure><img src="image_2.png" /><figcaption>Fig. 1. Two satellite footprints drawn side by side illustrating the ground track shift phenomenon</figcaption></figure>

Beacon Window time $T_W$. Consequently, these parameters influence the number of slots per frame, $w$. The results in terms of RMSE and energy consumption are presented in [6]. In particular, for the combination $w = 167$ [slots], $SF = 10$, $BW = 125$ [kHz], and $BCN = 91$ [s], an estimation with an RMSE error of fewer than 10 nodes is achieved for populations of up to 500 nodes. This limitation is because the “naive” estimate, based on the OCI estimation, converges to $2w$ when the channel is saturated and all messages collide within the frame. One of the objectives of the proposed CL-OCI extension is to overcome this limitation of 500 nodes.

### C. Open Challenges

Both OCI and L-OCI consider only a single satellite with its coverage centered on the cluster of nodes and the development of a single Beacon Period per repetition. Consequently, orbital phenomena that could affect the L-OCI estimation are ignored, such as only a portion of the cluster being within the satellite's coverage or the ground track of a satellite in the same constellation not necessarily passing through the same point centered on the cluster.

A satellite's ground track will naturally deviate due to Earth's rotation unless its orbit is carefully designed to maintain it [22]. Consequently, each satellite in an aligned constellation “sees” a different part of Earth's surface despite being in the same orbital plane.

In the following sections, our discussion focuses on solving the estimation of a constellation of satellites during a single pass of the constellation over the node deployment area, considering the ground track shift experienced by each satellite relative to the first one. This implies that if the first satellite is considered centered over the cluster, as in [6], each subsequent satellite will cover an equal or smaller portion of that same cluster, as illustrated in Fig. 1.

## III. CONSTELLATION L-OCI (CL-OCI)

Constellation L-OCI (CL-OCI) aims to overcome the limitations of previous OCI techniques and adapt them to a realistic constellation environment, considering ground track

shifts. Additionally, this adaptation seeks to extend L-OCI's estimation limit capacity beyond 500 nodes with the implemented set of parameters, while maintaining low hardware and cost requirements.

The general concept of this mechanism is to transmit a $G$ index to the ground nodes via the downlink beacon. Afterward, the nodes compete during the beacon period with a probability of $1/G$. The estimation process is similar to that used in L-OCI: each satellite performs its calculations and then transmits the results to a ground station located on the Earth's surface.

On the ground station side, the coordinates of the satellites at the moment of transmitting the downlink beacon are known. These coordinates are used to calculate the projection of each satellite's coverage on the ground and the portion of this coverage that overlaps with the reference satellite. The reference satellite is positioned at the center of the node deployment area.

By determining the degree of overlap, estimating the portion of the node cluster covered at any given time is possible. In this manner, each satellite estimates the entire cluster by observing a subset of nodes during the contention process. The size of this subset depends on the known $G$ and the calculated overlap with the reference. The average of these individual satellite estimates provides the constellation-wide estimation.

### A. Scenario Model

a) **Topology:** The studied scenario involves a Discontinuous LEO satellite constellation [23] (DisLEO) comprising $Q$ CubeSat satellites in a Low Earth Orbit (LEO), serving as gateways to terrestrial nodes under the DtS-IoT scheme at an altitude of approximately 600 kilometers and an orbital inclination of 98 degrees. CubeSats are assumed to possess attitude and orbit control designed for small satellites [24], [25]. All satellites are deployed in the same orbital plane. Most large satellite constellations operate in multiple orbit planes to ensure global coverage. However, smaller constellations may operate in a single orbital plane, depending on their specific mission requirements. Indeed, our estimator is specifically designed for low-cost DtS-IoT CubeSat applications operating in a single orbital plane, simplifying mission design and reducing costs for smaller constellations. For example, both systems, Astrocast [26] and Fossa [27] are small DtS-IoT constellations that initially operate in a single plane and later expand into multiple planes if needed. Future work considers multiple orbit planes and larger satellite constellations.

A cluster of $N$ nodes is deployed uniformly in an arbitrary circular region on the Earth's surface, matching the satellites' coverage area according to the parameters $w = 167$, $SF = 10$, $BW = 125$, $BCN = 91$, which gives a range of approximately 1100 km [6]. The first satellite in the constellation is positioned above the cluster, so its ground projection coincides with the center of the node deployment cluster. The satellites are spaced with a mean anomaly separation of -36 degrees in FLoRaSat. Whether nodes are static or mobile is not essential; nodes are assumed to stay inside the deployment region, and their mobility inside of it doesn't affect CL-OCI's operation.
b) Operation: The Q satellites periodically broadcast a beacon, marking a Beacon Period's beginning. Nodes that successfully decode this beacon randomly choose a slot with uniform probability. Given the DisLEO constellation, satellites only receive transmissions from nodes that received their corresponding beacon. As in [6], it is assumed that the first satellite in the constellation starts with its coverage area centered on the cluster. The terrestrial nodes activate their radios only when a satellite is visible and transmit a single dummy message during each Beacon Window in which they contend.

## B. Grouping Approach

CL-OCI involves dividing the cluster of nodes into G groups, so each satellite in the constellation must estimate at most N/G nodes. The division into groups is achieved by transmitting the index G in the beacon of the first satellite, after which the nodes calculate $g_n$, an integer between 1 and G, upon receiving the beacon. Once $g_n$ is calculated, node n will contend in the Beacon Window if $g_n = 1$, otherwise in the $g_n$-th Beacon Window, and then successively in the $g_n+G$-th. It is common in recent literature to assume the IoT devices use a predictor of the satellite orbit [28]. Given techniques for estimating visibility time [16], [29], [30] and the nodes' knowledge of the satellites' trajectory, each node should only turn on its radio when appropriate.

This grouping approach reduces the number of transmissions and, thus, the related energy costs. The energy implications are as follows:

a) Energy Model: The subsystem of the ground nodes that consumes the most energy is the radio [31]. The energy consumed by the radio in the process of a complete pass of the constellation is defined as:

$$E_{pass} = \sum_{i=1}^{Q} E_{i}^{sat} + \sum_{n=1}^{N} E_{n}^{node}, \quad (1)$$

where $E_{pass}$ is the total energy consumed in the interaction between nodes and the gateway, defined as the sum of the energy consumed by each satellite $E_i^{sat}$ and each node $E_n^{node}$. The subsequent downlink of the received LoRa frames from each satellite to the ground station is ignored. The energy consumed by each satellite and node during this estimation phase is defined as follows:

$$\begin{aligned} E_{i}^{sat} &= P_{tx}^{sat} T_{BP} + P_{rx}^{sat} T_{W}, \\ E_{n}^{node} &= \frac{Q}{G} (P_{rx}^{node} T_{BP} + P_{tx}^{node} T_{M}), \end{aligned} \quad (2)$$

where $P_{tx}^{sat}$ ($P_{tx}^{node}$) and $P_{rx}^{sat}$ ($P_{rx}^{node}$) are the power consumed on a satellite (node) during transmission and reception, respectively; $T_{BP}$ is the duration of the LoRa packet the satellite sent to initiate the Beacon Period, $T_{W}$ is the duration of the Beacon Window contention period and $T_{M}$ is the duration of a node's transmission message. Finally, $\frac{Q}{G}$ determines the probability of a node receiving the Beacon from one of the Q satellites and consequently sending a message to it. So, the energy consumption decreases with an increase in G for a constant

Q. However, G cannot be increased indefinitely. Determining an optimal G value and the trade-off with estimation accuracy is discussed in Section IV.

## C. Ground Track Shift

To address the ground shift perceived by each satellite, we use the portion of the cluster under its coverage when it transmits a beacon. The first satellite of the constellation is centered over the cluster, as shown in Fig. 2, and its coordinates are taken as a reference.

Each satellite passes with its ground track shifted by a certain number of kilometers, covering only a portion of what the reference satellite covered. We define this portion as $O_{i,b}$, the percentage overlap of the satellite coverage projection i when transmitting the beacon b. Given that the Beacon Periods, during which satellites perform their estimations, are finite and sequential, $O_{i,b}$ is expressed as $O_b$. Each satellite is responsible for initiating a specific subset of these beacon periods, meaning that the total set of beacon periods during a constellation pass, B, is distributed among all satellites in the constellation. For example, satellite 1 may handle beacon periods 1 through 4, while satellite 2 is responsible for beacon periods 5 through 7, continuing in this manner until beacon B. There is a maximum distance between satellites beyond which the ground track shift is significant enough for the overlap to be zero, which limits the number of satellites Q worth considering during the simulation.

Each satellite performs an estimation $\Theta_b$, corresponding to the OCI estimation of a satellite during the b-th beacon period. Then, considering the overlap proportion, the estimation is weighted as follows:

$$\phi_b = \frac{\Theta_b}{O_b} G. \quad (3)$$

Finally, the estimates from different satellites are sent to a ground station, which proceeds to calculate the average to produce the estimate of the whole constellation:

$$\Phi = \sum_{b=1}^{B} \frac{\phi_b}{B}, \quad (4)$$

where B indicates the number of estimations made by the constellation.

## D. Performance Metrics

The following performance metrics evaluate CL-OCI performance for a satellite constellation environment.

**RMSE:** A sufficiently large number of iterations, K, of the experiments executed to achieve a 95% confidence interval. The Root Mean-Squared Error is then calculated as follows:

$$\epsilon_{rsme} = \sqrt{\sum_{k=1}^{K} \frac{(\Phi_k - n_k)^2}{K}}. \quad (5)$$

**Energy cost:** The energy cost to obtain the estimate is calculated as the sum of attempted transmissions during Beacon Windows periods and multiplied by the power consumption
of a transmission equal to the maximum allowed according to Semtech's specifications: 25.12 mW [32]. Results are normalized and expressed as energy cost in milliwatts per node.

## IV. EVALUATION

We evaluate CL-OCI's performance by recreating a DtS-IoT scenario where a cluster of nodes is deployed over the Brazil, Bolivia, and Paraguay regions, as shown in Fig. 2. A constellation of nanosatellites orbits over this region, transmitting beacons periodically and receiving node transmissions during the uplink period.

<figure><img src="image_3.png" /><figcaption>Fig. 2. FLoRaSat UI of a simulated scenario with 50 nodes</figcaption></figure>

The FLoRaSat [33] simulator is used for simulations. This event-driven open-source end-to-end simulation tool leverages OMNeT++ and is specialized in simulating DtS-IoT networks. The experiments contemplate varying values of the network size *N* and the group division index *G*. *N* varies, starting at 500 nodes and growing up to 1000 with steps of 100. The *G* index starts from *G* equal to 2 up to 10 with steps of 2. For each configuration, 21 iterations are performed. Given the orbital parameters of the simulations, starting from the sixth satellite, the ground track deviates because it cannot estimate the node cluster. For this reason, *Q* = 5 is considered for all experiments.

As the ground track deviates and the percentage of overlap with the reference satellite coverage area decreases, the estimates' error becomes greater. Given this, the results are shown considering an overlap threshold that filters the estimates of satellites presenting an overlap percentage lower than the threshold when transmitting their beacons.

Fig. 3 shows the experiments' average RMSE and energy cost results. Results for *G* = 1 are those from the single-satellite L-OCI, which are shown to contrast the adaptation's contribution to the multi-satellite case in CL-OCI. As seen in the figure, increasing *G* reduces the energy cost proportionally to *G*, *G* = 10 having the lowest energy cost in milliwatts per node. This is a direct benefit of requiring lower node participation in terms of transmissions to calculate an estimate. An increase in cluster size *N* leads to higher congestion, which, in turn, results in an increased RMSE for the estimation. In general, the RMSE decreases for the different values of *G* in comparison to *G* = 1 if the threshold is set to 100%, i.e., only the estimate of the reference satellite is integrated into the OCI estimate as done in [6]. This latter witnesses the scalability of

<figure><img src="image_4.png" /><figcaption>Fig. 3. RMSE vs. Energy cost of estimates for different values of G, N, and overlapping threshold</figcaption></figure>

CL-OCI with this new mechanism. *G* = 6, *G* = 8, and *G* = 10 show slightly worse RMSE for *N* = 600 in comparison to *G* = 1. Increasing *G* increases the RMSE progressively. This is because the multiplications to consider the overlap in 3 amplify the associated error, which makes larger values of *G* more sensitive to estimation errors. The overlap threshold shows that considering estimates from more satellites in the global estimate benefits *G* = 1 and *G* = 2 up to a certain point from which the error increases. However, for values of *G* superior to or equal to 4, the RMSE increases when estimates with a lower overlap percentage are integrated. This is because the estimation error is high and amplified by the multiplication of equation 3. Given these results, calculating the OCI estimation from separate satellite estimates provides better accuracy than integrating the estimates from multiple satellites for *G* values of 4 or higher.

These results show that the more pronounced the energy constraints, the more suitable the utilization of a higher *G* value. In [14], the MAC protocol Slotted Aloha Game (SA GAME) was tested using OCI estimates as input, demonstrating that errors up to 300 nodes in terms of RMSE did not significantly affect the throughput of SA GAME. This implies that increasing *G* results in a lower energy cost while maintaining adequate RMSE values.

## V. CONCLUSIONS

This work introduced CL-OCI, a network size estimator tailored for multi-satellite DtS-IoT constellations. By addressing the non-uniformity and ground track shifts inherent in satellite constellations, CL-OCI enhanced the scalability and accuracy. Our approach effectively segments terrestrial nodes into *G* groups, allowing each satellite to estimate a fraction of the total network, thereby reducing energy consumption and maintaining accuracy.

Simulation results demonstrated that increasing the group index, *G*, leads to proportional energy savings while achieving acceptable RMSE values, which are critical for integration
with MAC protocols like SA Game. Specifically, CL-OCI doubles the number of nodes it can accurately estimate and reduces the energy wasted due to collided transmissions by seven-fold compared to single-satellite L-OCI. The results validate the scalability and efficiency of CL-OCI, making it a viable solution for large-scale DtS-IoT deployments using satellite constellations.

Future work will focus on further optimizing the group di-
vision strategy and exploring integrating inter-satellite links to
enhance the robustness and flexibility of CL-OCI in dynamic
and dense IoT environments.

ACKNOWLEDGMENT

This research received support from Mitacs through the
Mitacs Globalink Research Award - project IT34052, from the
ANID FONDECYT Regular Project No. 1241977, from ANID
Basal Project AFB240002, from NSERC Canada Discovery
Grant RGPIN-2024-05730, and from the French National
Research Agency (ANR) under the project ANR-22-CE25-
0014-01.

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