1 Introduction

Internet-of-Things (IoT) is expanding at a fast rate to provide connections for billions of devices [31]. The IoT technology has been changing social behavior through disruptive technologies in new verticals and applications, such as Smart farms/agriculture, home/building automation, and healthcare, to cite only a few examples of intelligent environment IoT verticals [23, 40, 43]. In this context, the everyday environment will soon have a large number of IoT devices per square meter [4]. For instance, both academia and industry estimate that the Internet would have approximately 500 billion IoT devices connected until 2030 [41]. Also, the number of 5G-connected IoT devices will reach 4.1 billion by 2024 [13]. IoT applications have different energy consumption requirements, coverage, Quality of Service (QoS), and massive Machine-Type Communication [9].

IoT applications could rely on different network technology for data dissemination. Specifically, short-range network technologies (e.g., WiFi and Bluetooth) provide coverage area limited to a few meters and are positively affected by interferences. However, short-range networks need highly-dense deployment to achieve an expanded coverage area, increasing Capital expenditure (CAPEX) and Operational expenditure (OPEX). On the other hand, traditional cellular networks operating on licensed frequency bands can provide extended coverage from tens of hundreds of meters, supporting thousands of devices with high throughput. However, modulation complexity, along with medium access schemes, are highly energy demanding characteristics. To support the IoT growth, innovative long-range technologies, such as Low Power Wide Area Network (LPWAN) [21], is attracting attention from both academic and industry researchers. That is because of their promising capabilities in broad area connectivity and their operations on unlicensed frequency bands with the appropriate data rate, power consumption, and throughput tailored for many IoT applications [29].

Long-Range Wide-Area Network (LoRaWAN) technology is considered the most adopted LPWAN technology, promising ubiquitous connectivity for many IoT applications while keeping a simple network structure and management [26, 42]. In particular, LoRaWAN was developed by LoRa Alliance[5], i.e., a non-profit association, which defined the higher layers and network architecture on top of the LoRa physical layer [14, 26]. The LoRa physical layer is a proprietary spread spectrum modulation based on the robust Chirp Spread Spectrum (CSS) by Semtech [24]. The LoRaWAN Alliance has more than 500 associated members, higher than 140 LoRaWAN deployments, and more than 130 Network Operators in different countries [44]. LoRaWAN provides extended coverage to operate in unlicensed and pure implementation frequency ranges with low cost, low energy consumption, and flexible transmission rate. Moreover, LoRaWAN must potentially support a large and varying number of IoT devices sending data to the application server through the same Gateway. This significant demand causes a network overload and creates the called hotspot problem, which results in signal interference and affects QoS due to packet loss caused by collisions [34]. For instance, a LoRaWAN gateway will be unable to correctly decode simultaneous signals sent by IoT devices using the same Spreading Factor (SF) on the same Carrier Frequency (CF).

[An efficient adaptive resource allocation mechanism must adjust on-the-fly the LoRaWAN radio-related parameters, such as SF and CF, to reduce the packet loss caused by interference based on current network conditions.] However, resource allocation holds several possibilities for configuring such parameters. In this way, a mathematical model developed through Mixed Integer Linear Programming (MILP) has great importance in formulating and presenting the optimal solution to maximize performance because it can optimize parameter settings. [Therefore, an adaptive resource allocation based on a heuristic method is required to make computationally-efficient decisions in LoRaWAN and to generate results close to an optimal solution.] State-of-the-art solutions that have focused on resource allocation have investigated the SF allocation [7], SF and Coding Rate (CR) allocation [36], and increasing the data flow [37]. However, none of the previous works considers the device requirements for an efficient resource allocation on-the-fly adjusting the configuration of radio related parameters to minimize channel utilization while minimizing collisions.

In this article, we introduce an extensive analysis of our proposed heuristiC fOr adaptive REsource alloCaTion on LoRaWAN for IoT applications (CORRECT) [30] to evaluate the impact of the radio configuration parameters in massive IoT scenarios in terms of QoS. We describe the CORRECT mechanism’s operation, which dynamically adjusts the LoRaWAN parameters to reduce interference and packet collision, minimize the channel utilization, and increase the number of delivered packets. The heuristic chooses the settings based on the signal strength and distance between the device and the gateway to provide the tradeoff between increasing the transmission range and reducing the delay, energy, and interference. Furthermore, we describe a MILP called Optimization Model for LoRaWAN Resource AlloCation for IoT ApplicatiOns (MARCO) to compare the proposed heuristic with an optimal resource allocation solution. This article extends the previous work described in [30]. Its main research contributions include an extensive review of related works, a more detailed description of the mechanism, and an extensive evaluation of the impact of a resource allocation mechanism for LoRaWAN under a different network scenario. Specifically, using the CORRECT heuristic instead of the ADR heuristic, we obtained an improvement of up to 18% in PDR. For other heuristics, this difference is even more significant. The heuristic CORRECT yields up 18.70% higher throughput than Explora-AT; this difference increases even more than other heuristics.

The rest of the paper is organized as follows. Section 2 presents the state-of-the-art results which have explored resource allocation in LoRaWAN. Section 3 introduces the proposed heuristic model, called CORRECT. Section 4 explores the simulation model developed to evaluate CORRECT and present the results obtained. Finally, Section 5 concludes the work and introduces future research directions.

2 Related Works

This section presents the most recent works which focus on resource allocation for LoRaWAN. In each work, we discuss their advantages and disadvantages. Amichi et al. [7] formulated a nonlinear optimization of mixed integers considering the harmful effects of interference between SFs. The focus of the authors is to obtain a fair throughput and reduce energy consumption. Nevertheless, this model does not consider optimizing the choice of CFs and reduces energy consumption according to the SF choice.

El-Aasser et al. [18] proposed two SF allocation heuristics, which adjust the SF service radius, i.e., the maximum distance that an SF can be assigned to an End-Device (ED), ensuring the correct demodulation by the gateway. However, setting SF based only on distance is not recommended because it depends on the device’s signal strength. In the same approach, Caillouet et al. [11] designed an optimization model for LoRaWAN that optimizes SF allocation to minimize collisions and maximize the number of served nodes. The optimization is modeled as an Integer Linear Programming (ILP) that considers a Rayleigh channel. Nevertheless, this model does not consider channel allocation and the choice of SF to reduce energy consumption. Analytical models have made progress in the last few years, e.g., Sandovalet al. [37] presented two Markov chains to model the Transmission Cycle (TC) and energy consumption. Based on these models, the optimal solution finds TC that increases throughput while keeping power consumption below a threshold. Moreover, the authors present a solution for calculating a global network configuration that maximizes the throughput obtained analytically [36]. Such a proposal formulates a Markov Decision Process (MDP), in which the optimal update policy allows the system to maximize the accumulated network throughput in a short time interval.

The literature presents some strategies for resource allocation. Farhad et al. [20] proposed two resource allocation schemes to enhance the packet success ratio by lowering the impact of interference. The first scheme, called the channel-adaptive SF recovery algorithm, increments or decrements the SF based on the ED packets’ re-transmission, indicating the network’s channel status. The second approach allocates SF to EDs based on ED sensitivity during the initial deployment. However, this work does not perform an intelligent configuration of CF, where, based on the presented interference model, it would cause significant losses due to the packet collisions on the same channel. Moreover, Khaled et al. [2] proposed a heuristic for data rate fairness among nodes within a LoRaWAN. In the first phase, it derives a fair data rate distribution along with all the devices in the LoRaWAN, which aims to address the unfair LoRaWAN characteristic when EDs are very close to the gateway or use lower SFs. The second phase performs transmission power allocation that seeks to mitigate the effect that harms the network. The second phase performs transmission power allocation that aims to mitigate the effect that harms the network. However, although the approach shows improvements in the Packet Delivery Ratio (PDR), this algorithm does not consider the CF allocation, which presents promising results in solving the problem of capture effect in network packets.

Zorbas et al. [46] proposed a resource allocation mechanism to improve the LoRaWAN potential by employing multiple communication parameters. They modeled the average success probability per set as a density function, analyzing intra-SF and inter-SF collisions. Each ED has different communication settings based on such a model in terms of Bandwidth (BW) and SF. In this sense, this work tries to assign most EDs on a given BW and SF to increase the packet delivery probability for each BW and the distance between the ED and a given gateway. However, the authors considered only the SF collisions without considering the interference when two packets have the same CF and SF. The algorithm does not cover all the packet loss possibilities. In a similar context, Babaki et al. [8] presented a solution to enhance the default resource allocation algorithm, i.e., ADR, by dynamically designating the radio-related parameters, SF and TP, by applying the Ordering Weight Average (OWA) operator. This work aims to increase the network noise resilience and PDR in dense IoT scenarios recognizing the OWA decision-make nature and the Packet Loss Ratio (PLR) metric. However, this approach does not consider the packet collision as a fundamental problem affecting the network packet loss and achieving an optimal CF configuration on the devices.

Cuomo et al. [15] proposed two resource allocation solutions named ExploraSF and Explora-AT, which aim to optimize LoRaWAN execution by configuring the SF values for each ED based on the signal strength. Explora-SF attempts to equally allocate ED in the Gateway’s (GW) radio area to all SF, limited by their Received Signal Strength Indicator (RSSI) values and appropriate thresholds. On the other hand, Explora-AT propagates impartial allotments of the ToA among the end nodes in the network, prioritizing the lower SFs to reduce collision probability. In this way, a higher signal strength leads to lower SF for a given ED, where it considers a limited number of ED in each SF based on ToA. Nevertheless, both Explora-SF and Explora-AT do not consider the CF allocation to further reduce packet loss when the packets have the same SF and CF configuration. From another perspective, Dawaliby et al. [16] presented a Software-defined Network-based solution for network slicing to optimize and manage a LoRaWAN. Each Gateway has multiple virtual slices, which must find the correct configurations of SF and transmission power that simultaneously increase the QoS and minimize cost energy consumption and package loss rate. However, this work adds a processing overhead to perform slicing over LoRaWAN, which reduces the network resources available and does not consider the CF (i.e., channels) in decision making. Moreover, the authors did not analyze the computational cost of applying the proposed solution. Additionally, they did not evaluate important evaluation metrics for IoT applications.

Table 1 summarizes the main characteristics of the resource allocation mechanisms analyzed based on optimization goal, energy-efficiency, RSSI-awareness, and LoRaWAN radio parameters considered. Such characteristics significantly improve the system performance in terms of maximizing the QoS level by minimizing collisions. Based on our state-of-the-art analysis, we conclude that a resource allocation mechanism’s adjustment of radio-related parameters shows promise for configuring such parameters. In this way, an optimization model is essential in formulating and achieving the optimal solution to maximize performance, whereas only a few works [7, 11, 36, 37] introduced an optimization model. Some studies [2, 7, 8, 15, 16, 20, 37] considered energy-efficiency by adjusting the radio-related parameters. Moreover, it is essential to estimate the signal strength based on the distance between the ED and the gateway to provide the tradeoff between increasing the transmission range and reducing the delay, energy, and interference. However, only a few works [2, 15, 20, 46] estimate the RSSI to adjust the radio-related parameters. Finally, none of the existing works efficiently combines SF and CF adjustment to improve the scalability, reliability, and energy-efficiency. To the best of our knowledge, only one study [30] has considered a heuristic and an optimization model for resource allocation that configures radio-related parameters to minimize channel utilization, minimizing collisions while considering RSSI based on the ED’s position.

Table 1 Summary of analyzed resource allocation mechanisms for LoRaWAN
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2.1 Research Contributions of this Work

We summarize the main research contributions of this work as follows:

  • A MILP model optimally allocates the SF and CF LoRaWAN radio parameters through a MARCO channel optimization.

  • A heuristic to efficiently on-the-fly configure the SF and CF parameters named CORRECT.

  • An extensive evaluation of the impact of a resource allocation mechanism for LoRaWAN under a dense IoT scenario.

3 Adaptive Resource Allocation for LoRaWAN

In this section, we propose the optimal solution for resource allocation based on MILP, called MARCO. First, we describe a global view of network modeling. Next, we present the MARCO model to use as a benchmark resource allocation. Finally, we propose a heuristic to adaptively choose radio parameters based on the signal strength and distance between the device and the gateway, called CORRECT.

3.1 Network and System Model

For LoRaWAN modeling purposes, we consider two device types: ed ∈ ED = {1,2,...,n} and gw ∈ GW = {1,2,...,m}. Each ED has an identification i ∈ [1,n], and a tuple edi = (xi,yi,zi,txi) to represent its geographical coordinates and the transmission power txi. In contrast, the tuple gwj = (xj,yj,zj) represents the geographical coordinates of a given gateway with an identification j ∈ [1,m]. In this context, we consider a set of gwj deployed in the monitored area, which is deployed based on a positioning algorithm to improve the application performance and reduce the deployed and maintained costs [28]. Each gwj has a circular coverage area A with a radio range Rj, where there is a set of edi deployed around the gwj.

[LoRaWAN defines three classes of EDs at upper-layer protocols, namely A, B, and C [12].] These classes allow bidirectional communication to support different application requirements. In this article, we considered only Class A devices, which behave by opening a window to wait for messages (downlink) only at the end of its transmission (uplink) because it is the highest energy-efficient class.

In the LoRaWAN architecture, there is a single-hop communication between the edi and gwj over several channels, forming a star network topology [27]. Each edi broadcasts messages for neighbor gwj, which forwards the message to the application server through an existing IP network. LoRaWAN communication is bi-directional, although the uplink communication from edi to the network server is strongly favored as expected in many IoT applications. The network server implements the resource allocation mechanism, such as CORRECT, to return the configuration of radio-related parameters, i.e., SF and CF, to each edi through the downlink communication, Figure 1 shows. Based on this architecture, LoRaWAN provides connectivity to edi deployed over a vast area by employing a control access mechanism with less complexity at the cost of low throughput [33].

Figure 1
figure 1

LoRaWAN architecture overview.

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We consider that each gwj could simultaneously decode signals in all SF and CF because LoRaWAN offers different possibilities to orthogonalize the transmissions, i.e., multiple edi use the same channel over other SF simultaneously without interference. However, an efficient resource allocation for the uplink transmission is still challenging due to a higher probability of having multiple edi transmitting on the same SF and CF on dense LoRaWAN, as expected in future IoT scenarios. In this way, a dense LoRaWAN suffers higher packet loss caused by interference.

Efficient resource allocation for LoRaWAN provides flexibility to adjust a set of radio parameters. In this context, LoRaWAN supports different configurable radio-related parameters to provide a tradeoff between increasing the transmission range and reducing delay, energy, and interference. For instance, each packet can be transmitted with a different SF value (\(SF=\{sf_{k}|(k \in \mathbb {N}) \land (7\leqslant k \leqslant 12)\}\)), which defines how many chirps are sent per second by the data carrier. Higher sfk values increase the sensitivity and radio range at the cost of growing Time on Air (ToA) and energy consumption to transmit a packet. In comparison, packet transmission with higher sfk values takes much longer to send packets at lower rates, resulting in more collisions.

SF is a crucial parameter to increase QoS. For instance, ToA increases from 659ms to 1318ms for the packet transmitted with a payload of 20 bytes sent with sf12 instead of sf11, respectively, which increases the collisions by keeping the channel busy during a more extended time. [Furthermore, the packet transmitted using sf11 consumes ten times more energy compared with using sf7 [17].] Besides, SF’s have a semi-orthogonal design, enabling them to separated into the receptor and avoiding collisions whether they conform to the interference model. Therefore, simultaneous transmissions must select different SFs and channels to avoid collisions.

\(CF=\{cf_{f}|(f \in \mathbb {F}) \land (1\leqslant f \leqslant 8)\}\) is the center frequency for LoRaWAN communication, spread out on different frequency channels by implementing pseudo-random channel hopping [18]. The cff values depend on local frequency regulations, where LoRaWAN gateways typically support eight channels, while the ED usually supports at least 16 channels [18, 35]. It is worth pointing out that the number of channels could be designed to minimize the collision probability. We consider the European frequency plan with eight available channels for the uplink transmission. Furthermore, regional authorities regulate the maximum duty-cycle parameter defined as the maximum percentage of time an end-device can occupy a channel. For instance, if an end-device has a duty-cycle of 1% in the European band, the devices must remain for 100-times the last transmission duration before transmitting it again in the same channel [6]. We consider the European frequency plan with eight available channels for the uplink transmission and a duty-cycle of 1% for this article.

We consider the Long-distance propagation model LPl(d), as shown in Eq. 1, which has good representation in a large number of indoor and outdoor LoRaWAN environments [19]. The LPl(d0) means the path loss at the reference distance d0, γ denotes the loss exponent, and d denotes the Euclidean distance between a given edi and gwj, which is subjected to d ≤ Rj. The model parameters are derived from a regression or fitting curve over the measured data and depend on the environment. In this article, we consider γ as 2.32 and LPl(d0) as 128.95, which are based on the measures done in Oulu’s city (Finland) [32].

$$ L_{Pl}(d)[d B]=10 \gamma \log_{10}\left( d / d_{0}\right)+L_{Pl}(d_{0}) $$
(1)

[The total received power (Prx, j, i) is used to measure the signal strength of a packet received by a gwj from the edi. ] It is computed based on the sum of the device transmission power Di ⋅ tx with the antenna gain GL, subtracting the propagation loss PL(d), as shown in Eq. 2.

$$ \small P_{rx, j, i} = D_{i} \cdot tx + GL -L_{Pl}(d) $$
(2)

[We define the tuple M = (xi,yi,zi,d, Prx, j) to have the ED coordinates (xi,yi,zi), Euclidean distance d between a given edi and gwj, and power received Prx, j. Specifically, the device power Prx, j, i is used to decide the minimal sfk value to allow the communication between a given edi and gwj, because gwj needs to receive a packet with receiver power Prx, j, i higher than the sensibility value for a given SF value [39]. Table 2 shows the sensitivity \(S_{sf_{k}}\) value for each sfk for a bandwidth of 125 kHz. Therefore, we assign an ED for each sfk value by guaranteeing that the selected sfk value provides the packet reception at gwj with enough power Prx, j, i.]

Table 2 Sensitivity value for each sfk for bandwidth 125 kHz
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A LoRaWAN packet consists of a combination of non-modulated and modulated chirps. The non-modulated defines the preamble and the Start Frame Delimiter (SFD), while the modulated defines the payload and Cyclic Redundancy Check (CRC). In this way, the time required to transmit a frame over the air (i.e., ToA) depends on the Preamble length (Tpream) and the load duration (Tload), shown in Eq. 3.

$$ ToA = T_{\textit{pream}} + T_{\textit{load}} $$
(3)

The Tpream is computed by the sum of the preamble size (Npream) with the mandatory preamble, i.e., 4.25, multiplying with the symbol duration (Tsimb), as detailed in Eq. 4.

$$ T_{\textit{pream}} = (N_{\textit{pream}} + 4.25) \cdot T_{\textit{simb}^{k}} \\ $$
(4)

The Tsimb is computed based on Seller et al. [38], as shown in Eq. 5. As a result, a higher SF requires a longer Tsimb, considering a constant BW.

$$ T_{\textit{simb}^{k}} = \frac{2^{\textit{sf}_{k}}}{BW}, \forall \textit{sf}_{k} \in SF \\ $$
(5)

The Tload is computed based on the load size (Nload) multiplied by \(T_{\textit {simb}^{k}}\), as shown in Eq. 6.

$$ T_{\textit{load}} = N_{\textit{load}} \cdot T_{\textit{simb}^{k}} \\ $$
(6)

We computed Nload based on Eq. 7, where PL denotes the packet size, IH means the implicit header, DE represents the data rate optimization. Specifically, IH is 0 if the header is enabled, one otherwise. The implicit header reduces the packet size using predefined CR and the receiving check digit CRC, settings, where the frame header would include these values without it. The DE value is set to 1 if the data rate optimization DE is enabled.

$$ \begin{array}{@{}rcl@{}} N_{load} &=& 8 + max(ceil\left[\frac{(8PL-4sf_{k}+28 + 16CRC-20IH)}{4(sf_{k}-2DE)}\right]\\ &&\cdot (CodingRate +4),0) \end{array} $$
(7)

We compute the Coding Rate value based on Eq. 8.

$$ CodingRate = \frac{4}{4+CR} , CR \in [1, 4] $$
(8)

Table 3 describes the main symbols used in this article.

Table 3 Main symbols used in our model
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3.2 MARCO

Resource allocation holds several possibilities for configuring SF and CF radio parameters. In this way, MARCO considers a mixed-integer linear optimization formulation to define the ideal configurations of the SF and CF parameters to minimize the channel utilization, which reduces the number of collisions. In general, MARCO take into account a MILP to define the ideal settings of SF and CF parameter, as it considers variables that are not integers. The results of MARCO can be used as a benchmark to those achieved by other heuristics because MARCO represents the best SF and CF parameters configurations.

To optimally allocate the EDs in each sfk, we assign more ED in some specific sfk to provide the tradeoff between minimizing channel utilization and reducing the interference, delay, and power consumption. This definition is because the lowest sfk value (i.e., SF equals 7) supports significantly more devices with lower interference than other SFs, which is explained by the relation between the transmission rate and SF [45]. Moreover, increasing the sfk value results in longer transmission times, increasing the collisions while keeping the channel busy for a more extended period [45].

In this context, initially we obtain ToA for each sfk based on Eq.3–8, which is denoted as \(T_{\textit {sf}_{7}}\), \(T_{\textit {sf}_{8}}\), \(T_{\textit {sf}_{9}}\), \(T_{\textit {sf}_{10}}\), \(T_{\textit {sf}_{11}}\), \(T_{\textit {sf}_{12}}\). Based on the \(T_{\textit {sf}_{k}}\) values, it is possible to define the maximum number of ED for each sfk, which is fundamental to the optimization process. In this sense, we need to estimate the overall ToA in the channel (TToA) as follows:

$$ T_{ToA} = \sum\limits_{\textit{sf}_{k} \in \textit{SF} } T_{\textit{sf}_{k}} $$
(9)

We compute the ratio between the ToA for each sfk (\(\textit {Ratio}_{\textit {sf}_{k}}\)) by dividing the sum of ToA to normalize the values, as shown in Eq. 10. It aims to obtain the fraction of each ToA concerning the total in the system.

$$ \textit{Ratio}_{\textit{sf}_{k}} = \frac{T_{\textit{sf}_{k}}}{\textit{T}_{ToA}} , \quad \forall \textit{sf}_{k} \in SF $$
(10)

We inverted the \(\textit {Ratio}_{\textit {sf}_{k}}\) value according to Eq. 11 because of higher ToA means worse network performance.

$$ \textit{WeightedSum} = {\sum}_{\textit{sf}_{k} \in \textit{SF}} \frac{1}{\textit{Ratio}_{\textit{sf}_{k}}} $$
(11)

We divide the normalized value for each SF (\(\textit {Ratio}_{\textit {sf}_{k}}\)) with the sum of it (WeightedSum), resulting in the ratio of ED for each sfK, as shown in Eq. 12. Hence, we define the ED ratio to be assigned for each sfK value based on ToA, which gives priority to have more ED in the lowest sfk value.

$$ Priori_{\textit{sf}} = \frac{\textit{Ratio}_{\textit{sf}_{k}}}{\textit{WeightedSum}} , \quad \forall \textit{sf}_{k} \in \textit{SF} $$
(12)

Finally, we compute the exact number of EDs each sfk (Quantsf), determined based on Eq. 13.

$$ Quant_{\textit{sf}}= Priori_{\textit{sf}}\times n, \quad \forall \textit{sf}_{k} \in \textit{SF} $$
(13)

Besides, the following variables are defined to guarantee the optimal settings of SF and CF parameters:

  • 𝜗i, sf, cf ∈{0.1}: binary variable, where a value of 1 means that edi with sfk in the cff was chosen by the model, 0 otherwise;

  • δi, sf ∈{0.1}: a binary variable, where 1 denotes that edi has enough power for transmitting the packet with the selected sfk value, 0 otherwise;

  • λ: average transmission rate, measured in packets/second.

The MILP model aims to minimize the channel utilization U and collisions by configuring the SF and CF parameters. MARCO uses the LoRaWAN channel with the lowest possible cost based on the time needed to transmit a frame Tsfk and the average transmission rate λ, as shown in Eq. 14. Specifically, MARCO computes the channel cost by \(\left (T_{\textit {sf}_{k}}\times \lambda \right )\), while the variable 𝜗i, sf, cf decides which sfk and cff values a given edi will use.

[The constraint, defined by Eq. 15, guarantees that the selected sfk and cff values (δd, sf) provide packet transmissions with enough power. This behavior is because the gwj needs to receive a packet with receiver power Prx, j, i higher than the sensibility \(S_{sf_{k}}\) for a given sfk value [39].] We consider the sensitivity \(S_{sf_{k}}\) values introduced in Table 2. The restriction introduced by Eq. 16 ensures that resource allocation has been made appropriately for all EDs, and the number of EDs is defined previously. The constraint defined by Eq. 17 establishes the ratio of ED to be assigned for each sfK value based on ToA, which gave priority to have more ED in the lowest sfk value. Finally, the restrictions introduced by Eqs. 18 and 19 perform channel allocation, considering the reduction of packet collisions on the same SF and CF.

$$ \min_{U} \displaystyle\quad U = {\sum}_{i\ \in\ L} {\sum}_{\textit{sf}_{k}\ \in\ \textit{SF}}{\sum}_{\textit{cf}_{f}\ \in\ \textit{CF}} \vartheta_{\textit{i,sf,cf}}\times \left( T_{\textit{sf}_{k}}\times \lambda \right) $$
(14)

subject to:

$$ {\sum}_{\textit{sf}_{k}\ \in\ \textit{SF}} {\sum}_{\textit{cf}_{f}\ \in\ \textit{CF}} \vartheta_{\textit{i,sf,cf}} \times \delta_{\textit{d,sf}} = 1 , \quad \forall i\ \in\ n $$
(15)
$$ {\sum}_{i\ \in\ L}{\sum}_{\textit{sf}_{k}\ \in\ \textit{SF}}{\sum}_{\textit{cf}_{f}\ \in\ \textit{CF}} \vartheta_{\textit{d,sf,cf}}\ =\ n $$
(16)
$$ {\sum}_{\textit{cf}_{f}\ \in\ \textit{CF}} {\sum}_{i\ \in\ L} \vartheta_{\textit{d,sf,cf}} \times \delta_{\textit{d,sf}}\ =\ n\times \ Priori_{\textit{sf}}, \forall \textit{sf}_{k} \in \textit{SF} $$
(17)
$$ \begin{array}{@{}rcl@{}} {\sum}_{i\ \in\ L} (\vartheta_{\textit{d,sf,cf}} - \vartheta_{\textit{d,sf,cf-c}})\ &\leqslant& 1,\quad \forall \textit{sf}_{k}\ \in\ \textit{SF}, \\ \forall \textit{cf}_{f}\ \in\ \textit{CF}, \forall c\ &\in& \{1..(cf_{f}-1)\} \end{array} $$
(18)
$$ \begin{array}{@{}rcl@{}} {\sum}_{d\ \in\ L} (\vartheta_{\textit{d,sf,cf}} - \vartheta_{\textit{d,sf,cf+c}})\ &\leqslant& 1,\quad \forall \textit{sf}_{k}\ \in\ \textit{SF}, \\ \forall \textit{cf}_{f}\ \in\ \textit{CF}, \forall c\ &\in& \{1\cdots(8-cf_{f})\} \end{array} $$
(19)

3.3 CORRECT

This subsection presents CORRECT, a resource allocation heuristic to efficiently adjust on-the-fly SF and CF to minimize the channel utilization while reducing the interference. Unlike an optimization model, this approach uses mathematical approximations to allocate EDs in the available SF and CF, with a lower computational cost. This procedure makes it possible to implement the algorithm internally to the reduced system of an ED. [The complexity of the CORRECT heuristic is analyzed as follows. In worst case the complexity of CORRECT is O(n ∗|SF|∗ (|CF| + (|CF|− 1))). Given the cardinality of the set SF (|SF|) and the set CF (|CF|) equal to 6 and 8, respectively, the number of CFs and SFs can be considered constant values. Hence, the CORRECT heuristic algorithm’s complexity is then O(n), where it depends only on the number of EDs n.] In its operation, the CORRECT heuristic receives as input the number of EDs n. Based on Algorithm 1, CORRECT adjusts the SF and CF configurations for each ED in a LoRaWAN network.

Initially, we compute the sum of ToA for each SF (TToA) based on Eq. 9 to estimate the overall ToA in the channel. Moreover, CORRECT computes the fraction each SF ToA has to TToA (\(\textit {Ratio}_{\textit {sf}_{k}}\)) based on Eq. 10. Next, CORRECT inverted the \(\textit {Ratio}_{\textit {sf}_{k}}\) value according to Eq. 11 because a higher ToA means worse network performance. Then, CORRECT computes the ratio of IoT devices from a LoRaWAN for each sfk, as shown Eq. 12, by dividing the normalized value for each SF, \(\textit {Ratio}_{\textit {sf}_{k}}\), with the sum of it, WeightedSum. Finally, based on the fraction of devices per sfk obtained, we calculate Quantsf based on Eq. 13, which defines the exact number of EDs on each SF.

In this way, the CORRECT heuristic analyzes if the ED power is enough to transmit based on the sensitivity \(S_{sf_{k}}\) (Line 9). [In this context, we need to estimate the received power Prx, j, i in the gateway gwj based on Eq. 2 and compare it with the current SF sensitivity \(S_{sf_{k}}\) based on Table 2.] After that, it checks if the number of EDs assigned to the current SF (\(\sum ed_{i} \in \{sf_{k}\}\)) did not exceed the number of devices allowed for such sfk (Quantsf), as shown in Line 10, and assigns the current SF to the device edi. This analysis helps ensure that most EDs are distributed in the smaller sfk, reducing ToA and consequently decreasing collisions. In addition, it checks if the number of EDs assigned to the current CF (\(\sum ed_{i} \in \{cf_{f}\}\)) did not exceed the number of devices allowed for such cff (\(\frac {Quant_{{sf_{k}}}}{CF}\)), as shown in Line 13, and assigns the current CF to the device edi. Finally, the CORRECT heuristic checks if devices remain without CF configuration, comparing the number of EDs assigned to the current SF (\(\sum ed_{i} \in \{sf_{k}\}\)) and the sum of the number of devices allocated in each cff (\({\sum }_{\textit {cf}_{f}\ \in \ \textit {CF}}\sum ed_{i} \in \{cf_{f}\}\)), and in case there are EDs without configuration, we configure each one edi in a cff. This step helps reduce the channel overhead, thereby reducing packet collision.

figure a

4 Evaluation

This section presents an evaluation of the CORRECT heuristic using various simulation tests and performance metrics. We describe the simulation environment and the performance metrics used. Specifically, we analyzed the performance of CORRECT and four other resource allocation heuristics with different numbers of EDs using performance metrics such as PDR, the number of interfered packets, throughput, and transmission delay. Moreover, we analyzed the MARCO model as a benchmark performance for the heuristics we have evaluated.

4.1 Simulation Environment

We implemented the MARCO optimization model using the Optimization Programming Language (OPL) and the IBM CPLEX solver 12.6 on a computer equipped with an Intel (R) Xeon (R) Silver 4112 CPU @ 2.60GHz, 64 GB of RAM running the Ubuntu operating system server. The CPLEX resolution time limit was set to 1h, but all scenarios considered the convergence of MILP before reaching the limit. For example, MARCO converged in 34 minutes, on average, for the scenario with 3000 devices. Besides, we performed several simulation experiments using NS-3 [22], an open-source discrete-event network simulator, targeted primarily for research and educational use to evaluate the effectiveness of the evaluated resource allocation heuristics. [We deployed one gateway at the center of a two-dimensional scenario with 6x6 km, with a radius of Rj of 2.5 km, which consists of the most challenging scenario due to the higher load of packet interference and packet loss compared with a multi-gateway scenario. Moreover, different numbers of EDs are deployed around the gateway, from 500 to 10000, as expected in massive IoT deployments.] Table 4 summarizes the main simulation parameters.

Table 4 Main simulation parameters
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[We conducted 33 simulations with different randomly generated seeds by the simulator’s default pseudo-random number generator (MRG32k3a). The results obtained show the values with a confidence interval of 95%. Each simulation evaluates the performance of different resource allocation solutions for LoRaWAN, namely ADR, Min_ToA, Explora-SF, Explora-AT, CORRECT, and MARCO optimization model.] Precisely, the ADR heuristic adjusts SF and the transmission power based on the distance and physical obstacles in the transmission, which is the implementation provided by The Things Network [1]. The Minimum Airtime heuristic (Min_ToA) is a standard assignment used by an ED to assign a fixed SF so that packets have the minimum ToA time,i.e., sf7. The EXPLoRa-SF heuristic distributes the number of EDs equally among the available SF to reduce packet collision [15]. The Explora-AT heuristic distributes the IoT devices along with the SF according to a priority in the lower SFs based on the ToA related to each SF [15]. Finally, MARCO and CORRECT both adjust the SF and CF values[30].

4.2 Performance Metrics

We considered four metrics to evaluate the heuristic for resource allocation of LoRaWAN, namely, PDR, number of interfered packets, network throughput, and transmission delay. PDR∈ [0,1] is an effective way to analyze network deployment as a whole, i.e., in an optimal network deployment with a minimum number of collisions and losses, e.g., the value is close to 1 [10]. PDR is computed from the total number of received packets and the total number of transmitted packets over the network.

We define Interference as soon as packets overlap each other in the receptor using the same SF and CF, configuring the called capture effect, i.e., the intra-SF collision. [The inter-SF collision is configured when two packets overlap, using different SF and the same CF. In these two contexts, the Interference causes a low Signal-to-Interference-plus-Noise Ratio (SINR).] [Based on the interference model proposed in [25], the SINR anticipated in a gwj is computed by Eq. 20.] Where \(Tx_{packet_{0}}\) is the referenced packet transmission power, σ2 is the variation between the measured path loss LPl(d) and an expected path loss ELPl(d), and \({\sum }_{packet=1}^{N_{Packets}} Tx_{packet}\) is the accumulative transmission power of the interfered packets. Besides, considering the SINR matrix (21), the element \(T_{sf_{i}, sf_{j}}\) is the margin (in dB units) to consider a packet lost due to interference. For example, suppose the computed SINR of a packet transmitted in sf7 and a packet transmitted in sf8 is below -24 dB. In that case, it is configured double packet loss due to collisions, which worsens the system’s performance.

$$ \text{SINR}=\frac{Tx_{packet_{0}}}{\sigma^{2}+{\sum}_{packet=1}^{N_{Packets}} Tx_{packet}} $$
(20)
(21)

We also consider the Network Throughput as the capacity of all the EDs to send any amount of data to the GW over time. In this work, the throughput is measured in Kbps, and we consider the simulation time as the measuring range. Finally, Delay is computed as the time spent between sending the packet from the physical layer of the IoT device through the radio channel until the GW’s physical layer successfully receives it.

4.3 Results

SF is the leading radio parameter that can be adjusted to influence the radio range, ToA, collisions, and energy consumption. In this sense, Figure 2 represents a snapshot of the SF distribution for the different evaluated models or heuristics when 7500 EDs are deployed around a GW, wherein the behavior is quite similar to other numbers of EDs deployed around a GW. By analyzing the results, we can conclude that both MARCO and CORRECT have similar SF distribution, showing that there is a similar SF allocation caused by the use of Priorisf defined in Eq. 12, as Fig. 2a and b show. CORRECT defines ED ratio to be assigned for each SF value based on ToA, which gives priority to have more EDs in the lowest SF values. For instance,CORRECT assigned 47% of ED to sf7, 25.8% to sf8, and so on. CORRECT also assigns the SF value by guaranteeing that the selected SF value provides packet reception at the gateway with enough RSSI. Min_ToA assigns all ED in the lowest SF, i.e., sf7, as Fig. 2f shows, so that maximum data rate with minimum ToA can be achieved. ADR assigns many EDs in the lowest SF, i.e., sf7, and Fig. 2e shows. Therefore, the amount of SF is similar for Min_ToA and ADR, due to the extensive GW coverage range, changing a small portion, which is in sf8. The SF configuration Min_ToA leads to 3.8% of EDs which are out of the range of the gateway. EXPLoRa-SF uniformly distributes EDs among the available SF values to reduce packet collision, as Fig. 2d shows. Finally, EXPLoRa-AT computes a fairness ToA distribution to normalize the ToA for all SF configuration, as Fig. 2c shows. Thus EXPLoRa-AT prioritizes the lower SFs to reduce the total network ToA.

Figure 2
figure 2

SF value for each ED according to each resource allocation mechanism for a scenario with 10000 EDs.

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Figure 3 shows PDR for different numbers of EDs on the network for CORRECT, MARCO, ADR, Min_ToA, EXPLoRa-SF, and EXPLoRa-AT resource allocation. In this way, simulating a real scenario considering an imperfect SF orthogonality, occurs a higher number of packet loss due to collisions [11]. This problem can be seen by the higher drop in performance in all algorithms with device densification. The CORRECT heuristic provides results remarkably close to the best solution available (i.e., MARCO optimization model). Specifically, CORRECT reduced the PDR by 3.5% in the worst case compared to MARCO. This result occurs because CORRECT heuristic efficiently adjusts SF and CF parameters. Specifically, CORRECT assigns the SF value by guaranteeing that the selected SF value provides packet reception at the GW with enough received power. Moreover, it defines the number of devices assigned for each SF value based on ToA, which gives priority enables more ED in the lowest SF values. We also observe that CORRECT performs 4.3%, 14%, 13%, and 18%, better in terms of PDR compared to EXPLoRa-AT, EXPLoRa-SF, Min_ToA, and ADR, respectively. The Min_ToA and ADR have a poor PDR performance because both set most EDs in the sf7. This behavior leads to high chances of packet collisions and a low transmission range, resulting in packet losses, especially in networks with high EDs. For instance, the GW will be unable to correctly decode the simultaneous signals sent by the different EDs using the same SF on the same channel. On the other hand, by uniformly distributing EDs in each SF, EXPLoRa-SF assigns many ED in higher SFs. This issue leads to packet collisions probability mainly in sf11 and sf12 because EXPLoRa-SF occupies the channel longer [11]. Finally, EXPLoRa-AT reduces packet collisions by balancing the ToA of packets in each SF and decreases packet losses when using lower SF values. EXPLoRa-AT also assigns the SF based on ToA, but EXPLoRa-AT has PDR results 4.3% lower compared to CORRECT because the latter avoids collisions with an efficient CF allocation. Therefore, the PDR results confirm the CORRECT resource allocation heuristic benefits to using the channel with a higher delivery probability, even considering an imperfect SF orthogonality, because CORRECT efficiently adjusts the SF and CF values.

Figure 3
figure 3

PDR according to number of EDs for each resource allocation mechanisms.

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Figure 4 shows the overall throughput (in Kbps) for different numbers of EDs on the network for the evaluated resource allocation models. By analyzing the results, we observe that the throughput increases when the number of EDs increases, regardless of the resource allocation mechanism. This behavior is because the throughput is the sum of the throughput of each ED in the network. However, the packets lost due to collisions considering an imperfect SF orthogonality affects all mechanisms [25]. In the densest scenario, with 10.000 devices, the higher number of packets lost impairs the performance. Moreover, in all algorithms, throughput stabilizes and tends to stop growing after a certain point. This behavior is due to the network’s duty cycle limitation limiting the rate of data exchanged on the channel in high device deployments [3]. [Let us analyze the scenario with higher packet losses, i.e., 10.000 EDs deployed around the GW; we note that the CORRECT heuristic yield result 5.35% closer compared to MARCO, with 556.3 and 586.09 Kbps, respectively. Explora-AT also assigns the SF based on ToA, leading to Throughput results of 23% compared to CORRECT because CORRECT avoids collisions due to the efficient allocation of CF. EXPLoRa-SF yields similar results compared to ADR, i.e., 198.70 Kbps, which is 179.96% worse than CORRECT. This behavior occurs because EXPLoRa-SF has many EDs transmitting in higher SFs, which occupy the channel longer, while Min_ToA and ADR allocate most EDs in the sf7.. The SF allocation performed by Min_ToA leads to worse Throughput results, i.e., 117.12 Kbps, which is 374.98% worse compared to CORRECT because of the high number of collisions. Specifically, using the CORRECT heuristic instead of the ADR heuristic, up to 18% improvement in PDR is obtained. The heuristic CORRECT yields up 23% lower throughput compared with the Explora-AT. ]

Figure 4
figure 4

Overall network throughput according to number of EDs for each resource allocation mechanisms.

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Figure 5 shows the number of interference packets, i.e., collisions, for different numbers of EDs on the network for the evaluated resource allocation models. It is essential to highlight that we defined interference as soon as packets overlap each other in the same CF receptor with the same SF and differents SFs regarding the SINR threshold based on matrix (21). In this context, interference has a high probability of packet loss, worsening the system’s performance. By analyzing the results, it is possible to conclude that the number of packet collisions for the CORRECT heuristic is close to the MARCO model, being 4.74% higher as it has more collisions due to the packets with the same frequency. This behavior occurs because, in some scenarios, CORRECT has a more significant difference in the number of EDs per CF than MARCO. The similar performance of the CORRECT heuristic compared to the MARCO optimization model is because the CORRECT heuristic efficiently adjusts the SF and CF parameters. In contrast, the number of packet collisions for CORRECT is about 5.34% lower than EXPLoRa-AT, 16.24% lower than EXPLoRa-SF, 14.92% lower than ADR, and 19.24% lower than Min_ToA. Specifically, in a scenario with 10.000 EDs deployed around the GW, Explora-SF, ADR, and Min_ToA methods experienced 97381, 110058, 108351, and 114142 packet collisions, respectively, while CORRECT has approximately 92180 packets collisions. EXPLoRa-AT also assigns the SF based on ToA. Explora-AT has PDR results 5.34% lower than CORRECT because the latter avoids collision with an efficient CF allocation. This behavior occurs because ADR and Min_ToA methods assign many EDs in the same SF. Thus, the GW cannot correctly decode the simultaneous signals sent by the different devices using the same SF on the same CF. Finally, the EXPLoRa-SF method equally distributes the number of EDs along with the available SF. Thus there are many EDs with higher SFs, which increase the packet collisions mainly in SFs 11 and 12; once it occupies the channel longer, the collision probability increases [11].

Figure 5
figure 5

Number of interfered packets according to number of EDs for each resource allocation mechanisms.

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Figure 6 shows the delay results for different numbers of EDs for the evaluated models or heuristics. As expected, ADR and Min_ToA delivered the packets with the lowest delay values because they assign the lowest SF values for all EDs, resulting in shorter transmission times. For instance, the ToA increases from 659 ms to 1318 ms for a packets transmitted with sf12 instead of sf11, respectively [17]. It is worth mentioning that MARCO and CORRECT have similar delay performance results because the CORRECT heuristic can efficiently adjust the SF and CF values to provide identical performance results compared to MARCO. On the other hand, EXPLoRa-SF delivered packets with the highest delay performance, which is explained by the fact that it mainly considers high SF values, resulting in longer ToA than lower SF. EXPLoRa-AT has a similar SF distribution to MARCO and CORRECT, leading to a similar ToA. However, once the packets are lost due to collisions, the network performance in terms of QoS is affected. Moreover, as the definition, the delay metric only computes the correctly received packets by the GW transmitted from the EDs. Therefore, the packets configured in higher SFs, as of sf10, sf11, or sf12, suffer more collisions because it occupies the channel longer. The collision probability increases [11], causing the average delay to be affected mainly by lower SF packets as the scenario densifies. Consequently, all the algorithms have mostly considered packets received from lower SFs such as sf7 and sf8, making larger deployments, such as 10,000 EDs, even delay behavior.

We found that CORRECT demonstrated an efficient performance in delivering high PDR values from our performance evaluation analysis. Consequently, a high throughput due to SF and CF’s smart allocation reduces most packets interference even in a semi-orthogonal SF scenario. It considers duty cycle limitations, as shown in interference results, while offering a lower delay. Table 5 summarizes the average performance results from all deployment formats for the evaluated resource allocation mechanisms.

Figure 6
figure 6

Delay per device according to number of EDs for each resource allocation mechanisms.

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Table 5 Performance comparison among evaluated resource allocation mechanisms
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5 Conclusion

Resource allocation is a crucial aspect of LoRaWAN, especially as scalability grows. This article evaluates a heuristic for resource allocation for LoRaWAN, called CORRECT. The evaluated heuristic adjusts the LoRaWAN SF and CF parameters to reduce the channel utilization, packet collisions and, consequently, maximize the number of packets delivered. The results obtained through simulations have shown that the CORRECT heuristic provides results close to optimal obtained by the MARCO model to use the channel, improving the allocation of LoRaWAN parameters to reduce collisions and improve the performance of the system as a whole. Specifically, using the CORRECT heuristic instead of the ADR heuristic, an improvement of up to 18% in PDR is obtained. For other heuristics, this difference is even more significant. As for the network throughput, the heuristic CORRECT heuristic yields up 18.70% improvement compared to the EXPLoRa-AT; this difference increases even more when compared with other heuristics. In the future, we plan to develop a machine learning model that considers SF, ToA, and CF to improve resource allocation.