Improving the Convergence Period of Adaptive Data Rate in a Long Range Wide Area Network for the Internet of Things Devices

: A Long-Range Wide Area Network (LoRaWAN) is one of the most efﬁcient technologies and is widely adopted for the Internet of Things (IoT) applications. The IoT consists of massive End Devices (EDs) deployed over large geographical areas, forming a large environment. LoRaWAN uses an Adaptive Data Rate (ADR), targeting static EDs. However, the ADR is affected when the channel conditions between ED and Gateway (GW) are unstable due to shadowing, fading, and mobility. Such a condition causes massive packet loss, which increases the convergence time of the ADR. Therefore, we address the convergence time issue and propose a novel ADR at the network side to lower packet losses. The proposed ADR is evaluated through extensive simulation. The results show an enhanced convergence time compared to the state-of-the-art ADR method by reducing the packet losses and retransmission under dynamic mobile LoRaWAN network.


Introduction
Low Power Wide Area Networks (LPWANs) are one of the widely adopted technologies for the Internet of Things (IoT). They offer long-range and multi-year battery life with low cost solutions. Among LPWANs technologies, Narrowband (NB)-IoT, Sigfox, and Long-Range Wide Area Network (LoRaWAN) are the leading and widely adopted for static and mobile-IoT applications. Compared to NB-IoT and Sigfox, LoRaWAN offers low-cost and adaptive solutions, where the key advantages of LoRaWAN are shown in Table 1. The basic LoRaWAN network design is comprised of End Devices (EDs), a Gateway (GW), and a Network Server (NS), as highlighted in Figure 1. The EDs in the LoRaWAN network interact with the environment and form the most significant part of a LoRaWAN. The GW forms a bridge between the ED and the NS. At the same time, the NS is responsible for Downlink (DL) notifications (acknowledgements) and controls the Spreading Factor (SF) and Transmit Power (TP) of ED through the Adaptive Data Rate (ADR) using Media Access Control (MAC) commands. LoRaWAN comprises three kinds of devices (Class A, B, and C) to serve diverse applications. Class A devices are energy-constrained and always initiate a packet in the Uplink (UL) direction using different SFs (i.e., 7 to 12). After each UL, every ED opens a Receive Window (RX1) to get a DL Acknowledgement (ACK) using the same SF and channel. If ED misses an ACK in RX1, it opens another RX2 with SF 12 using a dedicated channel 869.525 MHz. Class B end devices use beacons to interact with the GW [4]. Finally, class C end devices are not energy-efficient than class A and B because class C end devices always listen to the channel.

Network server Gateway
End devices Internet cloud In a LoRaWAN network, resources (e.g., SF and TP) are managed using an adaptive method called the ADR [5]. The ADR method is implemented both at ED-and NS-sides. EDside ADR is responsible for regaining connectivity for the ED during the communication by stepping up one SF at a time. While the NS-side ADR controls both parameters, the SF and TP can efficiently maintain the battery life of the ED. However, the underlying ADR of LoRaWAN is suggested for the static EDs [6] and performs inefficiently when the EDs are mobile due to the variation in the signal strength caused by the ED movement, resulting in low Packet Delivery Ratio (PDR) and convergence time issues. This situation occurs when EDs try to retransmit a lost packet, leading to massive interference. To address the packet loss and convergence time issues, we propose an NS-side ADR and claim to make the following contributions:

1.
In the proposed work, NS-side ADR uses Gaussian-filter to smooth the SNR and receives power and allocates the resource (e.g., SF and TP) based on these parameters, resulting in a low packet loss regarding sensitivity at the GW.

2.
The proposed NS-side ADR significantly increases PDR and decreases convergence time by adapting itself to the variable channels condition and allocating a suitable SF and TP. 3.
The proposed NS-side ADR method can efficiently reduce energy consumption by lowering the impact of retransmission because retransmission of a packet with high parameters (e.g., SF and TP) can negatively influence the energy consumption due to high Time-On-Air (ToA).
The remaining of this paper is structured as follows: Section 2 emphasizes current state-of-the-art approaches to allocating resources to EDs. Section 3 describes the network model utilized in this paper. Section 4 presents the proposed solution. Section 5 outlines the simulation analysis of the proposed method with the state-of-the-art techniques, while Section 6 concludes this paper.

Related Works
This section highlights the existing enhancements made to the ADR, which either enhanced the PDR or the convergence time.

Performance Improvement of the ADR
To improve typical ADR efficiency, the authors in [7] averaged the Signal-to-noise ratio (SNR) of the last P packets (i.e., P = 20) received at the NS and then took the Standard Deviation of the resultant value. Their proposed method effectively determines the SF and TP based on the computed value using Standard Deviation. Therefore, the results of their approach indicate improved ADR performance in terms of energy consumption. However, the proposed work in [7] does not consider the convergence time, which is dependent on the channel conditions [8]. A similar approach termed ADR+ was presented in [9] by averaging the SNR of P packets at the NS. Their simulation results based on OMNET++ showed improved Packet Delivery Ratio (PDR) and energy consumption outcomes. However, the ADR+ [9] failed to consider the shadowing and interference impact. Another ADR under the mobility environment was presented in [10] using the trilateration method. Their proposed work assumed a pre-defined trajectory. The authors evaluated their proposed method with ADR and showed improved performance in ToA and energy depletion. The ADR of LoRaWAN uses a fixed SF 12 during the deployment. Therefore, it suffers a massive packet loss due to interference. The authors proposed an Improved ADR (IADR) [11] to address the initial SF 12 problem in ADR. IADR aimed to assign all SFs concerning the received signal strength between the ED and GW during the network deployment. The IADR method [11] when compared to the ADR, improved the PDR. The performance results of the proposed scheme with the ADR show an improved packet delivery ratio. The authors also highlight the convergence time issue in their work. However, it failed to present a solution and resolve the convergence time issue.
The network server-based Best Equal LoRa (BE-LoRa) was proposed in [12] to optimize the energy consumption by efficiently allocating SF and TP based on optimum SINR. Their proposed method reduced energy consumption up to 36% and PDR by 17.44% compared to the typical ADR of LoRaWAN. Furthermore, another optimal energy allocation mechanism was proposed in [13] based on the ED sensing capabilities, and it showed improved energy consumption results compared to the typical ADR. The energy consumption ED can be further enhanced by utilizing a reinforcement learning method [14]. The primary aim of [14] is to allocate the best SF and TP to reduce the energy consumption and increase the PDR. Their method showed enhanced results in terms of energy consumption and PDR.

Performance Improvement of the Convergence Time of ADR
The convergence time issue is highlighted in [3,5,11] and resolved by the authors in [15,16]. Initially, the convergence time issue of the ADR was highlighted in [5] using various channel conditions. The authors in [5] showed through results that the ADR has the issue of convergence time due to poor adaptation of the SF and TP parameters under different underlying link conditions. In particular, their results revealed that ADR_ACK_DELAY (set to 32 packets at the ED-side ADR) was mainly responsible for causing the convergence time (unconfirmed mode). However, authors in [3] claimed that ADR in unconfirmed mode does not have a convergence time issue. Furthermore, their simulation results in [3] reported that the convergence time is caused by the number of EDs and UL intervals. However, authors in [3,5] failed to propose a convergence time solution.
Recently, it was realized in [15] that convergence time is a prime issue in the ADR, which reduces the PDR and needed immediate attention. Therefore, authors in [15] proposed enhanced ADR (EADR) both at ED-and NS-sides. The NS-side ADR handles their ED-side method by taking the PDR of the packets since the last changed data rate. The NS-side ADR is simple, which reduces the P packet to five (i.e., P = 5 was set) to find a suitable SF and TP. Their proposed method results show enhanced convergence time along with low energy consumption. However, the authors in [15] only considered a static environment. The convergence time issue was resolved in mobility environments in [16]. Therefore, the authors in [16] proposed two NS-side ADRs (exponentiation moving average and Gaussian-filer-based). The underlying propagation model does not change in a static environment, and the packets received at the NS with similar SNR. However, in a mobility scenario, packets are received with different SNR. Therefore, exponentiation moving average and Gaussian-filer-based approaches significantly enhanced the PDR and convergence time. Furthermore, a summary of these existing schemes is highlighted in Table 2.

2018-[7]
NS SF and TP To improve the energy consumption 2018- [9] NS SF and TP To improve the energy consumption and PDR 2019- [10] NS SF and TP To lower the time-on-air and improve PDR 2020- [11] ED SF To improve the PDR 2021- [12] NS SF and TP To enhance the energy consumption 2021- [13] NS SF To enhance the energy consumption 2021- [14] NS SF and TP To enhance the energy consumption 2018- [5] NS SF and TP Analysis of convergence period only 2020- [3] ED SF To improve PDR and energy consumption 2020- [15] ED and NS SF and TP To reduce the convergence period 2020- [16] ED and NS SF and TP Convergence, PDR, and energy consumption Proposed ADR NS SF and TP Convergence, PDR, and energy consumption This paper proposes an NS-side ADR, which efficiently allocate resources (i.e., SF and TP) to EDs based on the Gaussian filter in conjunction with the received power. The proposed ADR method efficiently enhances the convergence period, PDR, and energy consumption by reducing the packet retransmission and packet loss ratios.

Network Model
This paper assumes class A end devices using the confirmed mode of communication under mobility conditions. EDs in the confirmed mode always expect a DL message (ACK) from the NS in the two receive windows. These EDs follow European region frequency with three default channels and duty cycle of 1% and 10% for UL and DL, respectively.
In the rest of this section, we highlight link measurement and link performance models of the LoRaWAN.

Model for the Link-Measurement
The link measurement model considers propagation loss, fading, and shodowing models, as shown in Equation (1) [17].
Equation (1) can be used to calculate the received power (P rx ) at the GW, where G ED and G GW represent the antenna gains for the ED and GW, respectively, PL is the path loss model, and ξ is the shadowing term.

Log-Distance Path Loss Model
Macrocell propagation loss model (log-distance) for urban and suburban scenarios containing buildings of approximately uniform height is presented in [18]. (2) where d represents the distance in a kilometer, h represents the height of the GW antenna in meters (usually measured from rooftop level), and f is the frequency in MHz.
In this work, we utilize frequency 868 MHz; therefore, for the GW antenna height (i.e., 15 m assumed), the PL [dB] is [19] PL [dB] = 120.5 + 37.6 × log 10 (d). ( After the PL [dB] is computed, log-normally distributed shadowing with a standard deviation of 10 dB can be added [17]. Log-normally distributed shadowing is used when there is a shadowing consequence; otherwise, it is zero.

Model for Link Performance
The model for the link performance is based on the probability of correct reception of a packet at lower complexity, given the earlier calculated link measurement, the amount of interference, and other system-level consequences.

Receiver Sensitivity
Successful packet reception at the GW is mainly based on the receiver sensitivity of the GW for the corresponding SF. Table 3 presents the ED (S e ) and GW (S g ) sensitivities for each SF, where the sensitivity of each SF increases, and the GW achieves a better sensitivity than EDs and, therefore, can decode weaker signals. A packet can be detected and successfully received by the GW if its P rx is above the sensitivity level. The Receiver Sensitivity (RS) is significantly dependent on the choice of SF and ED uses to transmit a packet, which is given by where −174 is the thermal noise computed in dBm for 1 Hz of bandwidth (BW), NF represents the Noise Factor (i.e., margin) at GW (which is set to 6 dB in this work) [16], SNR is the signal to noise ratio for a given SF, as mentioned in Table 3, where it can be seen that higher values of SF allow for better sensitivity. In LoRaWAN, EDs use ALOHA to access the channel, which causes a collision when multiple EDs select the same channel for a packet transmission simultaneously. Collision in LoRaWAN is classified as when two packets collide over the same channel using the Intra-SF (collision at the GW occurs between the two packets when transmitted with the same SF and channel) or Inter-SF (collision at the GW occurs between the two packets when transmitted with different SF and same channel) interferences [17,22]. In this work, we consider both interferences impact on the dynamic LoRaWAN network, which is based on the model presented in [17,23,24]. According to the interference models presented in [17,23,24], a packet received at the GW using SF (i,j) is successful, if the cumulative interference power (γ) is higher than β (i,j) (a threshold value, as shown in Equation (5)).

Proposed ADR Scheme
This section presents the proposed algorithms, running at the NS-side, as highlighted in Figure 2 and Algorithms 1 and 2. These algorithms are discussed in the remaining part of this section. Note that the working of the ED-side algorithm remains the same. Further, the symbols used in the proposed ADR are highlighted in Table 4.

Algorithm 1: The Network Server Proposed ADR to Smooth the Received Power (P rx ) and Signal-to-Noise-Ratio (SNR)
Input : Equations (6)-(10), P = 20 Output : Smooth Received Power and Signal-to-Noise-Ratio if (ADRACKReq == enabled) then // NS waits for 20 packets for j ← 0 to P do if (P rx > G LPF and P rx < G HPF ) then insert P rx into a list (P_List) end if (SNR > G LPF and SNR < G HPF ) then insert SNR into a list (SNR_list) end end P rx = Sum / number of items in the P_List SNR m = Sum/ number of items in the SNR_list return P rx and SNR m end Table 4. Symbols used in the Proposed ADR.

Symbol Description
ADRACKReq MAC command used by the ED to request NS for ACK (0 = disabled; 1 = enabled) G LPF Gaussian low pass filter (G LPF = µ − σ) G HPF Gaussian high pass filter (G HPF = µ + σ) P rx Received power at the NS associated with each packet x Mean of the P rx P_List A list containing P rx values after filtering using Gaussian filter SNR_list A list containing SNR values after filtering using Gaussian filter SNR req Minimum SNR value required of each SF, as mentioned in Table 3 S g GW sensitivity value, as mentioned in Table 3  steps A number of times the ADR will be executed LinkADRReq MAC command containing SF and TP sent to ED by the NS

The Proposed ADR to Smooth the Received Power (P rx ) and SNR
The proposed ADR to smooth SNR is executed when it receives P packets from a corresponding ED with ADRACKReq being enabled. To smooth the SNR, the proposed ADR computes the Sum, Mean (x), Standard Deviation (σ), Low Pass Filter (G LPF ), and High Pass Filter (G HPF ) using Equations (6)-(10), respectively, as under: wherein Equation (8), x i represents a number of UL packets received at the NS, P is the total number of packets (i.e., 20) required to execute the proposed algorithm. The primary purpose of Algorithm 1 is to smooth the received power (P rx ) and SNR values associated with each UL packet received by the NS. To smooth the signal variation (i.e., in P rx ) caused due to mobility during the ED movement, the proposed ADR compares the computed P rx to Gaussian filters (i.e., G LPF and G HPF ). The resultant values containing P rx are recorded in a list (P list ). Next, to smooth the SNR values, these are compared to G LPF and G HPF (these are computed for SNR values separately) and saved in a list SNR list . Finally, smoothed P rx and SNR (SNR m ) are computed. These are further utilized in Algorithm 2.

The Network Server Proposed ADR Method
The proposed ADR in Algorithm 2 utilizes the default ADR settings, such as computing the SNR req , SNR margin , and steps. Based on the smoothed P rx and SNRm values, the proposed ADR finds a suitable SF concerning the GW sensitivity values (S g ) to lower the chances of packet loss arriving at GW under the sensitivity. Then by using steps, the proposed ADR finds the best possible TP for the concerned ED. If steps has zero value, it shows the ADR is already using the best value of TP. When steps is higher than zero, it shows that the current TP is not optimized (i.e., consumes more energy). Therefore, the proposed ADR decreases the TP by 2 (until it reaches the minimum limit) to optimize energy consumption (i.e., lower energy consumption). On the other hand, when steps is lower than zero, the proposed ADR increases the TP by 2 (until it reaches the maxim value). When both parameters (i.e., SF and TP) are found, these are communicated to the concerned ED using a MAC command LinkADRReq.

Performance Analysis of the Proposed ADR
This section describes the performance evaluation of the proposed ADR in comparison with ADR. The performance is evaluated in terms of PDR, convergence time, and energy consumption under a mobility environment using a confirmed communication mode. The performance evaluation is done using NS-3 [25].

Application Scenario
In this work, we consider a pet-tracking IoT-enabled application with various requirements, such as packet length, reliability, and mobility [26][27][28]. Every ED in the simulation transmits 48 packets/day with a packet size of 50 bytes.

Simulation Environment
We consider class A EDs (N) uniformly distributed around a single GW within a 5-km radius. The GW and ED antenna heights are set to 15 and 1.5 m, respectively. The rest of the simulation parameters are presented in Table 5. In this work, the Packet Delivery Ratio (PDR) is defined as when ED receives a DL ACK from the NS in one of the eight transmission attempts [30]. Figure 3 shows the PDR of the proposed ADR and the ADR for different number of ED under mobility conditions. The PDR trend shown in Figure 3 decreases with an increasing number of EDs. When the number of EDs increase, the UL traffic is increased, which cause a bottleneck at the GW, resulting in packet loss due to interference and packets arriving under sensitivity in the case of ADR. However, in the proposed ADR, the SF and TP are adapted based on the smoothed signal strength and P rx , resulting in improved PDR.

Convergence Time
The convergence time in LoRaWAN is defined as the time taken by ED to reach a steady SF, TP, and PDR. The convergence time occurs after the initial deployment phase, and it can last for hours or even days and is mainly dependent on the number of EDs and uplink period [5,11,15,16]. At the ED-side ADR, this convergence time is mainly based on both ADR_ACK_LI MIT and ADR_ACK_DELAY [5,15]. This time is affected by the arbitrary uplink history used at the NS (20 packets) on the NS-side. Before adopting SF or TP, the NS-side ADR must wait for the 20 packets from each ED at the NS. This waiting time increases the convergence time, and this increases the massive packet loss.
In Figure 4, ADR suffers from high convergence time because it cannot adapt itself to the variable channel condition. The new parameters (i.e., SF and TP) identified by the ADR could not successfully deliver a packet to the GW due to the underlying propagation environment caused by end device mobility. Therefore, NS cannot identify a suitable SF, resulting in massive packet loss at GW due to arriving under the sensitivity. In addition, the uplink traffic is increased from the end devices involved in the communication due to the packet loss. As a result, this increased uplink traffic causes a bottleneck at the GW, resulting in a large number of packet losses due to interference. Therefore, during the 24 h of simulation time, ADR failed to converge to a stable PDR due to end device mobility, which causes interference.   However, in the proposed ADR for the N = 400 and N = 1000, the convergence time is 9 and 19 h, respectively. The primary reason behind this low convergence time is that the proposed ADR at the NS side manages to smooth the signal strength and identify the best possible configuration containing both SF and TP. In addition, the proposed ADR considers the P rx value, which helps to identify a suitable SF for the ED, thus decreasing the chances of packet loss arriving under the SF sensitivity thresholds.

Energy Consumption
The energy consumption is determined by dividing the overall energy spent by EDs during the simulation period by the number of packets successfully received [31,32]. We used the energy consumer module from [33] and the Semtech SX1272/73 datasheet with a 3.3 V supply voltage [21] in this paper. Figure 5 shows that energy consumption increases for both the proposed ADR and the ADR when the number of EDs increases. This is because both proposed ADR and ADR utilize SF = 12 during the initial network deployment, which causes significant interference due to high ToA. In addition, the energy consumption of the ADR is relatively higher than the proposed ADR due to the number of retransmission. When a packet is lost in the confirmed mode, it is retransmitted up to 7 times. This retransmission causes significant energy consumption in the case of ADR. Therefore, we believe that this high energy consumption in ADR is caused due to the high SF, TP, ToA, and retransmission [31]. However, in the proposed ADR, the energy consumption is low because it assigns a suitable SF and TP using the Gaussian filter and P rx . This appropriate SF and TP adaptation leads to better PDR, resulting in lowering the number of retransmissions. Therefore, the proposed ADR's energy consumption is lower than ADR, outperforming the ADR.  Figure 6 shows the fraction of the PDR and Packet Loss Ratio (PLR) caused by interference (PLR-I), receiver saturation (PLR-R), under the sensitivity (PLR-S), and transmission of ACK (PLR-T). PLR-I occurs when two or more packets overlap each using the same or different SFs over the same channel. Here, the impact of PLR-I for the proposed ADR and ADR is almost identical. However, the proposed ADR PLR-I is a little lower. PLR-R occurs when all the available reception paths at the GW are busy (there are 8 parallel reception paths at the GW for the default 3 channels). PLR-R for both of the proposed and ADR is primarily similar. PLR-R and PLR-I are subject to UL traffic. When UL traffic increases, both PLR-R and PLR-I increase due to congestion at the GW. However, a significant improvement in the case of PLR-S (it occurs when packets arrive at the GW under the required sensitivity) for the proposed ADR is observed, as shown in Figure 6a. This is because the proposed ADR allocates the SF based on the P rx , which reduces the chances of packets arriving at the GW under the sensitivity. On the other hand, the PLR-S impact is high in ADR, as shown in Figure 6b. This is because ADR cannot allocate a suitable SF, which increases the chances of packets arriving at the GW under the sensitivity. Therefore, PLR-S is significant in the ADR. Another reason for the packet loss in the LoRaWAN network is the PLR-T. PLR-T occurs when GW is busy transmitting ACK packet to ED; simultaneously, a packet arriving at the GW is discarded. Thus, PLR-T impact is almost identical in both cases. Figure 7 shows the improvement of the proposed ADR with the ADR. The enhancement shown in Figure 7 represents the average improvement in percentage for energy, PDR, and PLRs. Thus, the proposed ADR has significantly improved the performance, particularly in energy consumption (i.e., 16% improvement) and PDR (i.e., 18% improvement). In PLRs, the proposed ADR enhances the performance by 5%, 39%, 3%, and 2% for the PLR-I, PLR-S, PLR-R, and PLR-T, respectively.

Conclusions
In a LoRaWAN network, resources (e.g., SF and TP) are managed using an adaptive method called the Adaptive Data Rate (ADR). The NS-side ADR of the LoRaWAN network controls both the SF and TP parameters to maintain the ED's battery life efficiently. On the other hand, ED-side ADR only increments SF to keep the complexity of ED as low as possible. However, the ADR is inefficient when the EDs are mobile due to the variation in the signal strength caused by the ED movement. Therefore, we proposed an ADR at the NSside based on the Gaussian filter and the received power, which efficiently assigned both SF and TP. The simulation results showed that the proposed ADR is efficient at reducing convergence time and energy consumption. We also observed that the proposed ADR efficiently enhances the packet delivery ratio by reducing packet losses. Furthermore, since the proposed ADR works at the NS side, it can be easily integrated at the NS as part of routine maintenance. Therefore, we believe that the proposed ADR can be adopted for mobile IoT end devices, which require low convergence time and a high packet delivery ratio with low energy consumption. In the future, we can reduce the interference impact by employing an ADR at both the ED-and NS-sides.