an evaluation of coverage models for lora

An evaluation of coverage models for LoRa

Main Subject area: Computer Engineering

Author: Felix Paulsson, Issa Bitar

Supervisor: Mikael Wåhlin

JÖNKÖPING 2021 June

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This final thesis has been carried out at the School of Engineering at Jönköping

University within Computer Engineering. The authors are responsible for the presented

opinions, conclusions, and results.

Examiner: Rachid Oucheikh

Supervisor: Mikael Wåhlin

Scope: 15 hp (first-cycle education)

Date: 2021-06-22

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Abstract

LoRaWAN is a wireless network technology based on the LoRa modulation

technology. When planning such a network, it is important to estimate the network’s

coverage, which can be done by calculating path loss. To do this, one can utilize

empirical models of radio wave propagation. Previous research has investigated the

accuracy of such empirical models for LoRa inside cities. However, as the accuracy of

these models is heavily dependent on the exact characteristics of the environment, it is

of interest to validate these results. In addition, the effect of base station elevation on

the models’ accuracy has yet to be researched.

Following the problems stated above, the purpose of this study is to investigate the

accuracy of empirical models of radio wave propagation for LoRa in an urban

environment. More specifically, we investigate the accuracy of the models and the

effect of base station elevation on the models’ accuracy. The latter is the main

contribution of this study.

To perform these investigations, a quantitative experiment was conducted in the city of

Jönköping, Sweden. In the experiment a base station was positioned at elevations of 30,

23, and 15m. The path loss was measured from 20 locations around the base station for

each level of elevation. The measured path loss was then compared to predictions from

three popular empirical models: the Okumura-Hata model, the COST 231-Walfisch-

Ikegami model, and the 3GPP UMa NLOS model. Our analysis showed a clear

underestimation of the path loss for all models.

We conclude that for an environment and setup similar to ours, models underestimate

the path loss by approximately 20dB. They can be improved by adding a constant

correction value, resulting in a mean absolute error of at least 3,7-5,6dB. We also

conclude that the effect of base station elevation varies greatly between different

models. The 3GPP model underestimated the path loss equally for all elevations and

could therefore easily be improved by a constant correction value. This resulted in a

mean absolute error of approximately 4dB for all elevations.

Keywords: LoRa, LoRaWAN, IoT, Empirical models, Path loss, Attenuation,

Coverage

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Table of content

Abstract .......................................................................................... ii

Table of content ............................................................................ iii

1 Introduction ............................................................................. 1

1.1 BACKGROUND .................................................................................................. 1

1.2 PROBLEM STATEMENT ...................................................................................... 1

1.3 PURPOSE AND RESEARCH QUESTIONS ............................................................... 2

1.4 SCOPE AND LIMITATIONS .................................................................................. 2

1.5 DISPOSITION ..................................................................................................... 3

2 Method and implementation .................................................. 4

2.1 RESEARCH DESIGN AND WORK PROCESS ........................................................... 4

2.2 DATA COLLECTION ........................................................................................... 4

2.2.1 Equipment ................................................................................................ 5

2.2.2 Environment ............................................................................................. 6

2.2.3 Test Locations .......................................................................................... 6

2.2.4 Empirical models ..................................................................................... 7

2.3 DATA ANALYSIS ............................................................................................... 7

2.4 VALIDITY AND RELIABILITY ............................................................................. 8

3 Theoretical framework ........................................................... 9

3.1 RADIO WAVE PROPAGATION ............................................................................ 9

3.2 LORA ............................................................................................................... 9

3.2.1 Overview .................................................................................................. 9

3.2.2 LoRa Modulation ................................................................................... 10

3.2.3 Modulation Parameters .......................................................................... 10

3.2.4 LoRaWAN ............................................................................................. 11

3.3 EMPIRICAL MODELS ....................................................................................... 11

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3.3.1 Okumura-Hata Model ............................................................................ 12

3.3.2 COST 231-Walfisch-Ikegami Model ..................................................... 12

3.3.3 3GPP UMa NLOS Model ...................................................................... 14

4 Results ..................................................................................... 15

4.1 COLLECTED DATA .......................................................................................... 15

4.1.1 Base station elevation – 30m ................................................................. 15



4.2 ANALYSIS ....................................................................................................... 17




5 Discussion ............................................................................... 22

5.1 RESULT DISCUSSION ....................................................................................... 22

5.2 METHOD DISCUSSION ..................................................................................... 25

6 Conclusions and further research ........................................ 27

6.1 CONCLUSIONS ................................................................................................ 27

6.1.1 Implications ............................................................................................ 27

6.2 FURTHER RESEARCH ....................................................................................... 27

7 References .............................................................................. 28

8 Appendixes ............................................................................. 30

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1 Introduction

1.1 Background

New types of wireless electronics are being used in urban environments, creating the

concept of “smart cities”, one of the hottest emerging research and business themes of

the 21st century (Boulos & Al-Shorbaji, 2014). A closely related topic is IoT (Internet

of Things), where wireless electronics are embedded in physical objects, such as

wearables, lights, or home appliances, which allows them to be connected to the

Internet. There are several technologies which can be used to connect such devices to

the Internet, for example Wi-Fi, LoRaWAN, and ZigBee.

LoRaWAN is one of the most popular Low Power Wide Area Network (LPWAN)

technologies and provides long-range wireless communication for low-power, low-data

rate applications (Haxhibeqiri, De Poorter, Moerman, & Hoebeke, 2018). Such

networks have recently been installed in several Swedish municipalities. LoRaWAN

consists of nodes (sensors, etc.) and gateways (base stations). Nodes communicate with

gateways, which then connect to the Internet. The wireless communication between the

gateway and the node is enabled by the LoRa modulation technology, which is thought

of as the physical layer of LoRaWAN (LoRa Alliance, 2021).

1.2 Problem statement

When building and planning networks like LoRaWANs, it is important to estimate the

coverage of the gateways to ensure that the nodes of the network have acceptable

reception. This can be done by utilizing empirical models of radio wave propagation.

These are models based on extensive experimental data and statistical analysis

(Faruque, 2015). They predict path loss, which is the attenuation of a signal between

two antennas caused by the environment. The accuracy of these models can vary greatly

depending on the environment in which they are implemented. To achieve an accurate

estimate of a gateway’s coverage, it is therefore important to choose a model that is

created for or adjusted to the specific environment (Stusek, et al., 2020).

Previous research has evaluated several empirical models of radio wave propagation

for LoRaWAN in urban environments. Stusek et al. (2020) evaluated the accuracy of

five empirical models for three popular LPWAN technologies, including LoRaWAN.

To evaluate the models, over 330 samples of signal strength were gathered in total

across two mid-sized cities in the Czech Republic, both covering an area of around

150km2. They also proposed a methodology for fine-tuning the models, improving

relative deviation from the samples by 20-80%. Some models took different factors into

account, such as average building height and street width, but the authors did not

evaluate how this affected the models’ performance. Also, they did not disclose the

gateway location or investigate its effect on the models’ performance.

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El Chall et al. (2019) proposed radio wave propagation models for LoRaWAN in

indoor, urban, and rural environments, derived from several measurement campaigns.

These models were compared with popular empirical propagation models. For the urban

environment, measurements of signal strength were gathered from the city of Beirut

within an area of 60 km2. In total, 2600 samples were gathered from 35 fixed points.

The effect of node elevation was investigated, but not the effect of gateway elevation.

Research has also been conducted to evaluate the general performance of LoRaWAN.

Sanchez-Iborra et al. (2018) evaluated the performance of LoRaWAN by gathering

real-life measurements in three environments: urban, suburban, and rural. The success

rate of data packets sent from a node was investigated for different LoRaWAN physical

level configurations.

1.3 Purpose and research questions

Drawing on the problem statement, it is evident that the choice of empirical model of

radio wave propagation depends on the environment and that the city is an interesting

environment to study. Further, it is evident that knowing the accuracy of such models

is important for planning LoRaWANs. As we are only interested in the radio wave

propagation, not the performance of the LoRaWAN data link or network layer, the

study will focus on LoRa. Consequently, the purpose of this study is:

To investigate the accuracy of empirical models of radio wave propagation for LoRa in

an urban environment.

To fulfill the purpose of the study it will be answered by two research questions. The

first question is related to the accuracy of empirical models of radio wave propagation

for LoRa and hence, the first question of the study is:

[1] How accurate are empirical models of radio wave propagation in estimating the path

loss of LoRa in an urban environment?

In addition to evaluating the accuracy of the models, it is also of interest to investigate

the effect base station elevation has on the accuracy of these models and hence, the

second question of the study is:

[2] How does base station elevation affect the accuracy of empirical models of radio

wave propagation for LoRa in an urban environment?

1.4 Scope and limitations

The study investigates the accuracy of empirical models in the inner city of Jönköping,

Sweden. Only non-line-of-sight (NLOS) cases were tested, as the path between our two

test devices always was obstructed by buildings, etc. As the accuracy of the empirical

models depends on the exact characteristics of the urban environment, the results of this

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study will only be valid for environments with similar characteristics to Jönköping. A

description of the environment of our investigation is available in chapter 2.2.2.

Some empirical models take different factors into account, such as street width and

building height. We investigate their effect on the models’ performance.

Different materials in the environment of radio communications, including materials of

buildings, affect the propagation of radio waves and hence also the accuracy of

predictions by empirical models. However, we do not have access to information of

building materials in Jönköping.

Weather can also affect the results. For example, Bezerra et al. (2019) showed that low

temperatures improved the signal-to-noise ratio and that snow in combination with long

distances negatively impacts the performance of LoRa. However, primarily because of

the limited time span of our investigation, this study will not investigate the accuracy

of the models in different weather conditions. The weather during our investigation in

Jönköping was partly cloudy (no rain or snow) with a temperature of around 15 degrees

Celsius.

LoRa uses different frequency bands in different regions. This study will only

investigate LoRa in the 868MHz band.

1.5 Disposition

In chapter 2, the overall research design and work process is presented, followed by

descriptions of the methods used for data collection and data analysis. The chapter ends

with a statement on the study’s validity and reliability. Chapter 3 begins with an

introduction to radio wave propagation, followed by a description of LoRa. This is

followed by a presentation of the empirical models chosen for the study. Chapter 4

presents the collected data and an analysis of the data for each base station elevation.

Chapter 5 discusses both the results of the study and the methods used. The report ends

with chapter 6, presenting the conclusions of the study, its implications, and a

suggestion for further research.

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2 Method and implementation

This chapter begins with an overview of the research design and the work process. After

that, we present the methods for data collection and data analysis. The chapter ends

with a description of the study’s validity and reliability.

2.1 Research design and work process

To identify existing knowledge on the accuracy of empirical models of radio wave

propagation for LoRa and similar technologies, we performed a literature study. The

literature study provided a theoretical framework, which guided the design of the study

and served as a base for analysis. We then performed a quantitative experimental study

in the city of Jönköping to validate the results of the literature study and to extend the

existing body of knowledge with an investigation on the effects of base station elevation

on the models’ accuracy. Figure 1 presents an overview of the work process for the

thesis.

2.2 Data collection

The collection of data was performed in the experimental study. The experiment was

conducted by comparing the path loss predicted by three popular empirical models to

the path loss calculated from real-life measurements. The real-life measurements were

gathered by placing a LoRa base station at three levels of elevation in the inner city of

Jönköping. For each level of elevation, data packets were sent from 20 fixed test

locations around the base station by a LoRa mobile station. 100 packets were sent from

each test location to account for statistical noise. When receiving each packet, the base

station recorded the packet’s signal strength expressed in decibel-milliwatts (dBm,

decibels with reference to 1 milliwatt), and the signal-to-noise ratio expressed in

decibels. The real path loss was calculated for each sample by adding the transmission

Literature study

Design of experiment

Data collection

Data analysis

Discussion

Figure 1. The work process of the thesis.

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power (dBm), transmitter antenna gain (dB), receiver antenna gain (dB) and subtracting

the measured signal strength (dBm).

Below follows descriptions of the equipment used to gather the real-life measurements,

the data collection of environmental data, the locations chosen for the experiment, and

the data collection for the empirical models.

2.2.1 Equipment

To gather real-life measurements, two test devices were developed. One base station

and one mobile station. The mobile station consisted of an Arduino Uno connected to

a LoRa-shield and an external antenna. The base station featured the same components

as the mobile station, with the addition of a Bluetooth-module to gather the information

about each packet. Images of the test devices are available in Appendix 5 and 6.

The LoRa-shield is a commercial product developed by Pi Supply. It features the LoRa

module RAK811 developed by RAKwireless (Pi Supply, 2021). The RAK811 module

is itself based on the SX1276 LoRa transceiver developed by Semtech (RAKwireless,

2021). The SX1276 has a specified 127dB of RSSI (Received Signal Strength

Indication) dynamic range, a sensitivity of -136dBm, and a maximum ERP (Effective

Radiated Power) of 20dBm (Semtech, 2021). The antennas used for both devices are

omnidirectional antennas with a specified gain of 2dBi (MC Technologies, 2021).

To record the signal strength of a packet, the base station must be able to demodulate

the packet. Therefore, the LoRa modulation was configured to minimize the number of

packets lost. To minimize the packet loss rate, the spreading factor should be

maximized, and the bandwidth should be minimized (Semtech, 2021). Increasing the

ERP also improves the packet loss rate, as it provides a stronger signal, and has an upper

limit of 25dBm in the 868MHz band in Sweden (Swedish Post and Telecom Authority,

2021). Increasing the coding rate can also improve the packet loss rate (Sanchez-Iborra,

Sanchez-Gomez, Ballesta-Viñas, Cano, & Skarmeta, 2018). Table 1 shows the

configuration of the LoRa modulation for the experiment.

Table 1. Configuration of test devices.

Frequency (MHz) 869,5

Bandwidth (kHz) 125

ERP (dBm) 20

Spreading factor 12

Coding rate 4/8

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2.2.2 Environment

The models used for predicting the path loss depend on data of the environment. In this

study, environmental data was manually gathered from Google Maps and Google Earth.

Google Earth was used to measure average height of buildings, while Google Maps was

used to measure distances between the base station and the mobile station, street width,

average building separation, and the angle between the street of the mobile station and

the path to the base station for each test location. The average building height and

separation were calculated from buildings within a 100m radius of each mobile station

location. This is similar to the usual method of measuring location variations in square

areas with sides of 100m to 200m (Ghasemi, Abedi, & Ghasemi, 2016). The collected

data is presented in Appendix 4. A description of the environment in our experiment is

given below.

Our environment is characterized by low-rise buildings with most buildings estimated

to be less than eight stories tall with an average height of about 16m. The streets are on

average 17m wide, with trees planted along most streets. In addition to the fair number

of trees, there are also several parks in the area of investigation. Images of a 3D model

of Jönköping are provided in Appendix 1 and the locations for the mobile station are

displayed in Figure 2. These provide an overview of the environment, with the layout

and structure of buildings, parks, etc.

2.2.3 Test Locations

To be able to test different elevations of the base station, it was mounted outside a

column of windows on the west side of the School of Health and Welfare. Three base

station elevations were tested: 30m, 23m, and 15m above the ground.

For all test locations, the mobile station was kept at a height of 1,5m. The test locations

for the mobile station were evenly spaced to provide a representable set of samples from

the urban part of Jönköping available from the School of Health and Welfare. This

included areas with different building heights, areas with different building separations,

parks, etc. No measurements were taken across the lake Munksjön that divides the city,

as it was deemed to not be representative of an urban environment. The propagation

over such a large body of water greatly deviates from that of an urban environment due

to the lack of obstacles. The test locations for the experiment can be seen in Figure 2.

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2.2.4 Empirical models

To gather predictions from the three empirical models, their mathematical calculation

must be done for each test location. These calculations were performed

programmatically by implementing the models in Python. The models chosen for this

study and their mathematical formulations are presented in chapter 3.3.

2.3 Data analysis

The accuracy of the models is investigated quantitatively by statistically analyzing their

deviation from the path loss calculated from signal strength samples. When analyzing

their accuracy, we perform a short investigation on the effect of the models’ parameters.

The effect of base station elevation on the accuracy of the models is analyzed by

comparing how the measured path loss deviates from the models’ predictions for each

level of base station elevation.

The accuracy is evaluated by analyzing scatterplots of predicted and measured path loss

with respect to distance and calculating the difference in arithmetic mean (DAM) and

the mean absolute error (MAE). The mathematical formulations for the DAM and the

MAE are as follows:

Figure 2. Test locations (Map data ©2021 Google).

⬤ Mobile station locations

⬤ Base station location

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𝐷𝐴𝑀 =∑ 𝑦𝑘 − 𝑥𝑘𝑛𝑘=1

𝑛

𝑀𝐴𝐸 =∑ |𝑦𝑘 − 𝑥𝑘|𝑛𝑘=1

𝑛

In both formulations, 𝑦𝑘 is the predicted path loss, 𝑥𝑘 is the mean measured path loss,

and 𝑛 is the number of received data packets (for each location and base station

elevation). The DAM will indicate if the models generally over- or underestimate the

path loss while the MAE will indicate the average absolute deviation from the real-life

measurements. The MAE will also be calculated with the models’ predictions shifted

by their respective DAM (towards the mean of the measured path loss). This will

indicate the accuracy of the models disregarding the presence of any constant error.

2.4 Validity and reliability

To ensure the validity of the study, relevant related studies and literature were gathered

from the university’s library. The keywords used when searching for literature were a

combination of “LPWAN”, “LoRaWAN”, “LoRa”, “868 MHz”, “Radio wave”, and

“Propagation model”, “Path loss model”, “Attenuation model”, “Coverage model”. The

methods used in this study are in line with identified related studies and have been based

on the literature.

The reliability of the study is strengthened by performing the measurements

systematically and ensuring that the measurement equipment is set up correctly

(keeping distance to the node during measurements, keeping the antennas parallel, etc.).

One factor that could influence the reliability of our results is the potential for some

losses of signal due to practical issues such as imperfect antenna efficiency or small

signal attenuations from the LoRa module to the antenna. However, as we do not have

access to the equipment needed to measure such potential losses, we cannot account for

their potential influence on the results.

Regarding urban environments, cities differ in structure and layout, the materials and

design of buildings, the amount and type of vegetation, etc. These are all factors which

can affect the radio wave propagation. Because of this, and the fact that the set of cities

empirical models are derived from is probably not representable of all cities, they may

perform better in some urban environment than others. Therefore, the experiment

performed in this study will only be valid for urban environments with similar

characteristics as the city of Jönköping. A description of our environment is available

in chapter 2.2.2.

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3 Theoretical framework

This chapter provides an overview of radio wave propagation, followed by a description

of LoRa and its modulation technology. The chapter ends with a presentation and a

description of the empirical models chosen for the study.

3.1 Radio Wave Propagation

In the area of radio wave technology, received signal quality depends on factors such

as transmission environment, radio wave frequency, modulation technology, and

undesirable interfering radio waves (Ghasemi, Abedi, & Ghasemi, 2016).

A transmission environment where a radio wave can take more than one route to the

receiver is called a multipath environment. Cities are a good example of such an

environment. As the radio waves propagate, they can reflect of, scatter of, and penetrate

physical objects. In mobile communications within cities, reflections off buildings and

the ground are often the major propagation mechanism. How these objects interact with

the radio waves depends on their physical properties. Good conductors reflect nearly

all the energy of incident electromagnetic waves at frequencies used for radio

communication. Insulators however, such as glass, brick walls, and concrete, reflect

less of incident radio waves. The energy that is not reflected of a surface instead

penetrates the material. The wave travels inside the material, decaying as it heats it up.

The rate of decay is proportional to the material’s conductivity. For example, a good

insulator such as glass lets electromagnetic waves propagate through it with little loss

(Haslett, 2008).

As radio waves are reflected, they will interfere with each other, both constructively

and destructively. The characteristic of the reflection depends on the smoothness of the

surface, which in turn is dependent on the frequency of the radio wave. Surfaces that

appear rough to electromagnetic waves in the visible spectrum often appear smooth to

radio waves. For rough surfaces, the radio waves are “scattered” more than they are

coherently reflected. The interference patterns created by coherently reflected waves

can lead to great variations in the signal strength over short distances. This effect gets

less noticeable as the roughness of the surface increases (Haslett, 2008).

3.2 LoRa

This chapter features a short overview of LoRa, followed by an explanation of the LoRa

modulation, and the key modulation parameters. The chapter ends with a short overview

of the LoRa-based LPWAN, LoRaWAN.

3.2.1 Overview

LoRa is a modulation technology based on chirp spread spectrum modulation and is

developed by Semtech. It provides long-range wireless communication for low-power,

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low-data rate applications. LoRa operates in the 433-, 868-, and 915MHz ISM bands

and can send data packets with payload sizes varying from 2-255 bytes (Augustin, Yi,

Clausen, & Townsley, 2016).

3.2.2 LoRa Modulation

As LoRa is based on chirp spread spectrum modulation, it encodes information by

linearly increasing or decreasing the frequency over time. The linearity of the chirps, as

the pulses of increasing or decreasing frequency are called, makes frequency offsets

between two devices easy to eliminate, as they are equivalent to timing offsets. The

frequency offset can reach 20% of the bandwidth without affecting decoding

performance, which makes LoRa more robust against the Doppler effect. This

robustness means it is well suited for mobile applications (Augustin, Yi, Clausen, &

Townsley, 2016).

The LoRa modulation is based on symbols. Each LoRa symbol is composed of multiple

chirps covering the whole frequency band (carrier frequency +/- half a bandwidth). To

encode information in the linear frequency variation, the chirps are “interrupted”. It is

the position of these interruptions that encodes the information (Augustin, Yi, Clausen,

& Townsley, 2016). An illustration of a LoRa data packet is presented in Figure 3.

3.2.3 Modulation Parameters

LoRa has three main modulation parameters: bandwidth, spreading factor, and coding

rate. These influence the effective bitrate, the resistance to interference noise, and the

ease of decoding (Augustin, Yi, Clausen, & Townsley, 2016).

The bandwidth specifies the width of the frequency band, with the most popular

bandwidths being 500-, 250-, and 125kHz. A doubling of the bandwidth will double

the effective bitrate, but it will also reduce the decoder sensitivity by approximately

3dB (Augustin, Yi, Clausen, & Townsley, 2016).

Figure 3. Illustration of a LoRa data packet.

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Spreading factor specifies the number of chirps to cover the bandwidth and ranges from

7 to 12. The number of chirps is given by 2𝑆𝐹 , where SF is the spreading factor. Each

increase of the spreading factor increases the decoder sensitivity by approximately 3dB,

but it also almost halves the effective bitrate (Augustin, Yi, Clausen, & Townsley,

2016).

To make the communication more robust against interference, LoRa implements a

forward error correction code. This is controlled via the coding rate, which can assume

the values 4/5, 4/6, 4/7, and 4/8. A higher coding rate (e.g. 4/8) helps reduce the number

of packets lost, but it will also increase the airtime of the packets as more data needs to

be transmitted (Augustin, Yi, Clausen, & Townsley, 2016).

3.2.4 LoRaWAN

LoRaWAN is a LPWAN technology based on the LoRa modulation. It is developed by

the LoRa Alliance, which is an open, non-profit association with member such as IBM,

Cisco, and HP (LoRa Alliance, 2021). LoRaWAN specifies the system architecture and

the communication protocol of the network (network and data link layers respectively),

while using LoRa as the physical layer which defines the modulation technology and

enables long-range communication links. Data packets are sent wirelessly via LoRa

between nodes and gateways. The gateways forward received packets to a network

server via TCP/IP, which handles complex tasks such as filtering redundant packets. In

this way, nodes are not associated with a certain gateway (LoRa Alliance, 2021).

3.3 Empirical models

The following models are investigated in this study:

• Okumura-Hata Model

• COST 231-Walfisch-Ikegami Model

• 3GPP UMa NLOS Model

These were chosen as they were some of the most popular models identified in the

literature study. They were also chosen because they have different levels of complexity

and differ in the number of factors taken into consideration. Their popularity and the

differences in complexity should provide a fair representation of empirical models for

the study.

El Chall et al. (2019) also investigated three models (for the urban environment) and

Stusek et al. (2020) investigated 5 models. The purpose of this study is to investigate

the general accuracy of empirical models, not to find the highest performing model. As

such, we deem an investigation of our three models to provide sufficient representation

of the diversity of empirical models. If our purpose would have been to find the highest

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performing model, then a greater number of models would have been preferable.

Below, we will go through each model and their mathematical formulations.

3.3.1 Okumura-Hata Model

The Okumura-Hata model is derived by Hata from Okumura’s propagation prediction

method and was created to estimate path loss in urban environments for UHF (Ultra

High Frequency) and VHF (Very High Frequency) land mobile radio services (Hata,

1980). It is one of the most popular models identified in the literature study (Haslett,

2008; Faruque, 2015; Ghasemi, Abedi, & Ghasemi, 2016), and it is also the least

complex. The model’s mathematical formulation for a medium-small city is as follows

(Hata, 1980):

𝐿 = 69.55 + 26.16 log10(𝑓) − 13.82 log10(ℎ𝑏) − 𝑎(ℎ𝑚)

+ (44.9 − 6.55 log10(ℎ𝑏)) log10(𝑑)

𝑎(ℎ𝑚) = (1.1 log10(𝑓) − 0.7)ℎ𝑚 − (1.56 log10(𝑓) − 0.8)

In this formulation, 𝐿 is the path loss, 𝑎(ℎ𝑚) is a correction factor for the mobile station

antenna height, 𝑓 is the carrier frequency, ℎ𝑏 is the base station antenna height, ℎ𝑚 is

the mobile station antenna height, and 𝑑 is the distance between the two antennas. The

specified limitations of the model are:

{

150 ≤ 𝑓 ≤ 1500 (𝑀𝐻𝑧)30 ≤ ℎ𝑏 ≤ 200 (𝑚)1 ≤ ℎ𝑚 ≤ 10 (𝑚)1 ≤ 𝑑 ≤ 20 (𝑘𝑚)

3.3.2 COST 231-Walfisch-Ikegami Model

The COST 231-Walfisch-Ikegami (COST-WI) model was created in the EU funded

research project COST 231 as a combination of the previous Walfisch and Ikegami

models. It was created to estimate path loss for applications in urban macro-cells at 900

and 1800 MHz frequency bands (European Commission, 1999).

According to Haslett (2008), the model provides validity even when the base station is

below the surrounding roof height and is more accurate than the Okumura-Hata model

over short distances. However, as stated by Haslett, the Walfisch-Ikegami model

requires more data, which might not be immediately available. The model’s

mathematical formulation for NLOS situations is as follows (European Commission,

1999):

𝐿 = {𝐿0 + 𝐿𝑟𝑡𝑠 + 𝐿𝑚𝑠𝑑 for 𝐿𝑟𝑡𝑠 + 𝐿𝑚𝑠𝑑 > 0𝐿0 for 𝐿𝑟𝑡𝑠 + 𝐿𝑚𝑠𝑑 ≤ 0

𝐿0 = 32.4 + 20 log10(𝑑) + 20 log10(𝑓)

𝐿𝑟𝑡𝑠 = −16.9 − 10 log10(𝑤) + 10 log10(𝑓) + 20 log10(∆ℎ𝑚) + 𝐿𝑜𝑟𝑖

13

∆ℎ𝑚 = ℎ𝑟𝑜𝑜𝑓 − ℎ𝑚

𝐿𝑜𝑟𝑖 = {

−10 + 0.354𝜑 for 0° ≤ 𝜑 ≤ 35°

2.5 + 0.075(𝜑 − 35) for 35° ≤ 𝜑 ≤ 55°4 − 0.114(𝜑 − 55) for 55° ≤ 𝜑 ≤ 90°

𝐿𝑚𝑠𝑑 = 𝐿𝑏𝑠ℎ + 𝑘𝑎 + 𝑘𝑑 log10(𝑑) + 𝑘𝑓 log10(𝑓) − 9 log10(𝑏)

𝐿𝑏𝑠ℎ = {−18 log10(1 + ∆ℎ𝑏) for ℎ𝑏 > ℎ𝑟𝑜𝑜𝑓0 for ℎ𝑏 ≤ ℎ𝑟𝑜𝑜𝑓

∆ℎ𝑏 = ℎ𝑏 − ℎ𝑟𝑜𝑜𝑓

𝑘𝑎 =

{

54 for ℎ𝑏 > ℎ𝑟𝑜𝑜𝑓

54 − 0.8 × ∆ℎ𝑏 for 𝑑 ≥ 0.5 and ℎ𝑏 ≤ ℎ𝑟𝑜𝑜𝑓

54 − 0.8 × ∆ℎ𝑏 ×𝑑

0.5 for 𝑑 < 0.5 and ℎ𝑏 ≤ ℎ𝑟𝑜𝑜𝑓

𝑘𝑑 = {

18 for ℎ𝑏 > ℎ𝑟𝑜𝑜𝑓

18 − 15∆ℎ𝑏ℎ𝑟𝑜𝑜𝑓

for ℎ𝑏 ≤ ℎ𝑟𝑜𝑜𝑓

𝑘𝑓 = −4 + {0.7 (

𝑓

925− 1) for medium-sized cities

1.5 (𝑓

925− 1) for metropolitan centres

As in the last formulation, 𝐿 is the path loss, 𝑓 is the carrier frequency, ℎ𝑏 is the base

station antenna height, ℎ𝑚 is the mobile station antenna height, and 𝑑 is the distance

between the two antennas. There are also four additional parameters:

• height of buildings, ℎ𝑟𝑜𝑜𝑓 (𝑚)

• width of street, 𝑤 (𝑚)

• building separation, 𝑏 (𝑚)

• angle between the street of the mobile station and the direct path to the base

station, 𝜑 (°)

In addition to the extra parameters, the final path loss is constructed of several smaller

functions. Starting from the top, we have 𝐿0, 𝐿𝑟𝑡𝑠, and 𝐿𝑚𝑠𝑑. 𝐿0 is the free space path

loss. 𝐿𝑟𝑡𝑠 is the roof-top-to-street diffraction and scatter loss. It describes “the coupling

of the wave propagating along the multiple-screen path into the street where the mobile

station is located”. Lastly, 𝐿𝑚𝑠𝑑 is the multiple screen diffraction loss.

The function 𝐿𝑟𝑡𝑠 itself contains another function, 𝐿𝑜𝑟𝑖, which describes a correction

factor for the street orientation. 𝐿𝑚𝑠𝑑 also contains other functions: 𝐿𝑏𝑠ℎ, 𝑘𝑎, 𝑘𝑑, and

𝑘𝑓. The function 𝑘𝑎 describes the increase in path loss for base stations below the height

14

of buildings. The functions 𝑘𝑎 and 𝑘𝑑 describe the degree of multi-screen diffraction

loss with respect to distance and frequency, respectively. Descriptions for other parts

of the mathematical formulation, such as for 𝐿𝑏𝑠ℎ, were not provided in the model’s

definition.

The specified limitations of the model are:

{

800 ≤ 𝑓 ≤ 2000 (𝑀𝐻𝑧)4 ≤ ℎ𝑏 ≤ 50 (𝑚)

1 ≤ ℎ𝑚 ≤ 3 (𝑚)

0.02 ≤ 𝑑 ≤ 5 (𝑘𝑚)

3.3.3 3GPP UMa NLOS Model

The 3GPP UMa NLOS model is an empirical model from the 3GPP, which is a

partnership project between seven telecommunications standard development

organizations (3GPP, 2021). It features a complexity that is somewhere between the

Okumura-Hata and the COST-WI models. This exact model was also used by El Chall

et al. (2019) and another model from the 3GPP was used by Stusek et al. (2020). The

model was created for estimating path loss in urban macro-cells in NLOS situations,

and the mathematical formulation is as follows (3GPP, 2010):

𝐿 = 161.04 − 7.1 log10(𝑤) + 7.5 log10(ℎ𝑟𝑜𝑜𝑓)

− (24.37 − 3.7(ℎ𝑟𝑜𝑜𝑓

ℎ𝑏)

2

) log10(ℎ𝑏)

+ (43.42 − 3.1 log10(ℎ𝑏))(log10(𝑑) − 3) + 20 log10(𝑓)

− (3.2(log10(11.75ℎ𝑚))2 − 4.97)

In this formulation, 𝐿 is the path loss, 𝑓 is the carrier frequency, ℎ𝑏 is the base station

antenna height, ℎ𝑚 is the mobile station antenna height, 𝑑 is the distance between the

two antennas, ℎ𝑟𝑜𝑜𝑓 is the average building height, and 𝑤 is the street width. The

specified applicability of the model is:

{

2 ≤ 𝑓 ≤ 6 (𝐺𝐻𝑧)

10 ≤ ℎ𝑏 ≤ 150 (𝑚)

1 ≤ ℎ𝑚 ≤ 10 (𝑚)

10 ≤ 𝑑 ≤ 5000 (𝑚)

5 ≤ ℎ𝑟𝑜𝑜𝑓 ≤ 50 (𝑚)

5 ≤ 𝑤 ≤ 50 (𝑚)

15

4 Results

This chapter presents the results from the experiment and is divided into two parts.

Firstly, a presentation of the collected data, and secondly, an analysis of the collected

data.

4.1 Collected data

This section presents the data collected from the experiment for each level of base

station elevation, starting at 30m.

4.1.1 Base station elevation – 30m

Table 2 shows the mean signal strength, the number of data packets lost, and the

models’ path loss predictions for each location at a base station elevation of 30m.

Table 2. Data from the measurements and the models' path loss predictions for each

mobile station location at a base station elevation of 30m.

Location Mean

signal

strength

(dBm)

Packets

lost

Okumura-

Hata (dB)

COST-WI

(dB)

3GPP

(dB)

1 -111,5 98 121,6 116,9 121,2

2 -115,0 88 120,9 120,2 121,4

3 -114,7 9 116,8 115,4 117,1

4 -115,2 15 117,8 113,6 117,6

5 -110,3 2 119,4 118,6 118,8

6 -105,0 0 114,6 112,1 113,1

7 -113,9 3 111,6 102,8 110,6

8 -114,8 87 114,8 100,7 112,5

9 -103,7 0 106,0 104,7 104,6

10 -111,2 0 113,1 108,2 110,5

11 -110,0 1 111,6 107,7 109,8

12 -100,8 1 94,8 89,6 91,2

13 -102,5 0 100,6 90,8 96,8

14 -109,5 2 108,8 105,3 105,9

15 -106,1 0 115,4 109,6 112,8

16 -100,9 0 109,3 93,4 105,2

17 -115,4 12 116,0 112,8 114,9

18 -110,5 0 121,1 104,1 119,4

19 -114,9 53 121,8 117,7 120,6

20 -113,6 25 120,0 112,3 117,8

16






Location Mean

signal

strength

(dBm)

Packets

lost

Okumura-

Hata (dB)

COST-WI

(dB)

3GPP

(dB)

1 -117,1 34 123,1 122,3 125,0

2 -118,4 93 122,3 127,0 125,4

3 -116,8 41 118,2 120,9 120,8

4 -116,1 68 119,2 119,0 121,3

5 -119,8 83 120,9 124,0 122,5

6 -116,7 32 116,0 117,0 116,7

7 -115,9 13 112,9 107,7 114,2

8 -117,7 88 116,1 105,6 116,1

9 -116,8 31 107,1 110,1 108,2

10 -116,5 81 114,4 112,7 114,0

11 -110,4 9 112,9 112,6 113,3

12 -99,9 0 95,7 94,5 94,6

13 -96,6 0 101,6 95,0 100,1

14 -112,8 41 110,0 109,4 109,2

15 -109,9 0 116,8 113,5 116,1

16 -102,9 0 110,5 97,5 108,5

17 -114,9 5 117,4 117,0 118,3

18 -116,8 49 122,6 108,2 122,9

19 -116,5 24 123,3 122,2 124,2

20 -116,2 74 121,4 116,1 121,2

17




4.2 Analysis

Below, the data from the experiment is analyzed for each level of base station elevation

in order to answer the research questions of the study.


Starting at an elevation of 30m, the measured and predicted path loss is presented in a

scatter plot in Figure 4. The DAM and MAE are presented in Table 5. As visualized by

the scatter plot, at an elevation of 30m all models clearly underestimate the path loss.



Location Mean

signal

strength

(dBm)

Packets

lost

Okumura-

Hata (dB)

COST-WI

(dB)

3GPP

(dB)

1 -121,8 8 125,5 138,9 132,3

2 -122,3 87 124,7 142,4 133,4

3 -122,4 34 120,5 137,2 128,0

4 -122,6 50 121,5 135,4 128,6

5 -124,2 86 123,2 140,5 129,8

6 -125,0 98 118,1 133,7 123,5

7 -121,8 45 114,9 124,2 121,0

8 -119,9 18 118,3 122,3 122,9

9 -119,3 7 109,0 125,2 115,2

10 -123,4 93 116,5 129,9 120,5

11 -119,0 19 114,9 129,1 120,1

12 -106,3 1 97,2 110,1 101,2

13 -104,1 0 103,3 107,5 106,1

14 -120,0 21 112,0 122,0 115,4

15 -119,0 25 119,0 123,6 122,1

16 -111,6 0 112,5 110,1 114,7

17 -120,2 39 119,6 129,6 124,6

18 -121,3 52 125,0 120,8 129,2

19 -121,1 51 125,7 139,4 130,8

20 -122,9 82 123,8 126,3 127,2

18

The measured path loss and the predicted path loss from all models follow a similar

upward trend with respect to distance, but the predicted path loss is shifted downwards

by approximately 20dB, as indicated by the DAM.

As shown in Table 5, the MAE of all models is between 20 and 26dB, identical to the

absolute values of DAM as the mean path loss is higher than the models’ predictions

for all locations. Calculating the MAE for the models with their predictions shifted by

their respective DAM, there is still a mean deviation from the measured path loss of 4

to 5dB. For both the original and the shifted MAE, the Okumura-Hata model had the

least error, followed by the 3GPP- and the COST-WI model.

Comparing the plotted path loss predictions, the models’ different levels of complexity

is clearly visible by their variations independent of the distance. However, the increase

in complexity did not seem to provide better predictions overall, as there is a slight

positive relationship between the complexity and the shifted MAE.

Figure 4. Scatter plot of measured and predicted path loss at a base elevation of

30m.

19


Next, we analyze the data collected for a base station elevation of 23m. Similar to the

previous section, a scatter plot of the measured and predicted path loss is presented in

Figure 5 and the DAM and MAE are provided in Table 6.

Table 5. Difference in arithmetic mean and mean absolute error of models at a base

elevation of 30m.

Okumura-Hata COST-WI 3GPP

DAM (dB) -20,2 -26,2 -21,9

MAE (dB) 20,2 26,2 21,9

MAE (with

predictions

shifted by -DAM)

(dB)

4,2 5,3 4,4


23m.

20

Going from 30 to 23m there is a 3,4dB decibel increase in mean measured path loss. As

indicated by the DAM and visualized by the scatter plot, all models underestimate the

path loss by 22 to 25dB, like the results at 30m. Once again, the mean path loss is higher

than the models’ predictions for all locations, resulting in identical values for the MAE

and the absolute values of DAM.

We now look at the differences in DAM and MAE from 30 to 23m for the different

models. The DAM for the Okumura-Hata model decreased by 2,1dB while the shifted

MAE decreased by 0,5dB, indicating an increased underestimation of the path loss. The

DAM for the COST-WI model increased by 1,4dB and the shifted MAE decreased by

0,5dB, which indicates a decrease in the underestimation of the path loss. Finally, the

DAM for the 3GPP model only increased by 0,1dB while the shifted MAE decreased

by 0,5dB, only indicating a slight overall improvement in accuracy. When comparing

the different models, there is still no apparent advantage to the higher complexity.


Moving on to a base station elevation of 15m, a scatter plot of measured and predicted

path loss is presented in Figure 6 and the DAM and MAE are presented in Table 7. Like

at 30 and 23m, the mean path loss is higher than the models’ predictions for all

locations.

Going from 23 to 15m there is a 6dB increase in mean measured path loss. Looking at

the scatter plot it is apparent that the models’ predictions are diverging, which is also

indicated by the change in DAM and MAE.


elevation of 23m.


DAM (dB) -22,3 -24,8 -21,8

MAE (dB) 22,3 24,8 21,8

MAE (with

predictions

shifted by -DAM)

(dB)

3,7 4,8 3,9

21

The DAM for the Okumura-Hata model continues to decrease, now with a magnitude

of 3,9dB, while the shifted MAE is still at 3,7dB, indicating a further increased

underestimation of path loss. For the COST-WI model, the DAM increased drastically

by 8,8dB while the shifted MAE increased by 0,8dB, indicating a clear overall shift

towards the measured path loss. The DAM for the 3GPP model only decreased by 0,7dB

and the shifted MAE stayed at 3.9dB, indicating a negligible change in accuracy.


15m.


elevation of 15m.


DAM (dB) -26,2 -16,0 -21,1

MAE (dB) 26,2 16,0 21,1

MAE (with

predictions

shifted by -DAM)

(dB)

3,7 5,6 3,9

22

5 Discussion

In this chapter, the results of the study are discussed in relation to our research questions

and purpose. The discussion of the results is followed by a discussion of the methods

used in the study.

5.1 Result discussion

Going back to the research questions of the study, the first research question is as

follows:

[1] How accurate are empirical models of radio wave propagation in estimating the path

loss of LoRa in an urban environment?

The results of the study showed a clear underestimation of the measured path loss for

all base station elevations, mobile station locations, and models. The magnitude of the

mean underestimation was between 16 and 26dB. Accounting for any constant error

and shifting the models’ predictions towards the measured path loss by the DAM, there

was still a mean absolute deviation from the measured path loss by 3,7 to 5,6dB.

Our setup exceeded three of the specified limitations of the models. The Okumura-Hata

model is specified for distances of 1 to 20km and base station elevations of 200 to 30m,

and the 3GPP model is specified for frequencies between 2 and 6GHz. However, all

models’ underestimations were of roughly the same magnitude, and accounting for the

underestimations, they all provided a MAE within 6dB.

Comparing our study to Stusek et al. (2020), they evaluated five empirical models in

the city of Brno, Czech Republic. This included the Okumura-Hata model (and model

derived from it), the COST-WI model, and a different model from the 3GPP for urban

environments. For LoRa, measurements of signal strength were gathered from 303 test

locations approximately one meter above the ground, split between 18 base stations. 10

data packets were sent from each location, totaling 3030 sent packets. They did not

disclose the locations or elevations for the base stations. Neither did they disclose any

details of the environment, nor the environmental data used for the models. To provide

insight into their environment, a 3D map of Brno is available in Appendix 2. Further,

they did not disclose their method for calculating the path loss.

23

Next, we compare our results to those of Stusek et al. (2020). As can be seen in Figure

7b, they calculated a mean deviation (same as DAM) from the measured path loss of

approximately 10 to 35dB for LoRa, with 19dB for the Okumura-Hata model, 30dB for

the COST-WI model, and 16dB for their 3GPP model. These values are in the same

order of magnitude as those obtained in our experiment, but instead show an

overestimation of the path loss. However, looking at their plot of measured and

predicted path loss presented in Figure 7a, their results seem to be biased at greater

distances as the mean signal strength seems to exceed the sensitivity of their test device.

This suggests that their mean deviation would have been much lower had it been

calculated for shorter distances, such as between 100 and 800m, as was tested in our

experiment.

Focusing on the results of Stusek et al. (2020) for the distances tested in our experiment,

their mean deviation from the measured path loss seems much smaller than what was

obtained in our results. The only difference in our experiments impacting this that can

be compared is the difference in the environment. Collecting a small set of

environmental data of Brno through Google Earth suggests an average building height

close to 20m and a street width varying between 12 and 30m. Although this is close to

what was measured for our environment, the city layout of Brno differs from Jönköping,

as shown in Appendix 1 and 2. However, as Stusek et al. do not disclose information

crucial for the models’ performance, such as base station elevation or environmental

data for the models, it is not possible to specify the root of the discrepancy in mean

deviation.

Comparing our study to El Chall et al. (2019), they evaluated three popular empirical

models in the city of Beirut, Lebanon. This included the Okumura-Hata model (and a

model derived from it) and the 3GPP UMa NLOS model. Measurements were collected

from 35 fixed test locations with a height from the ground of 0,2, 1,5, and 3m. For each

test location and mobile station elevation, 25 data packets were sent, totaling 2625

packets. To communicate with the mobile station, they used a single base station

Figure 7. Plots of path loss and mean deviation from Stusek et al. (2020).

a) Path loss for LoRaWAN b) Mean deviation for LoRaWAN, Sigfox,

and NB-IoT

24

mounted on a roof top on a building in the hills of Beirut, with an effective elevation of

200m. They did not disclose the environmental data used for the models, but they did

provide a brief description of the environment. The authors described Beirut as a

“densely populated city” with “a high density of buildings, gardens, roads, and

commercial/industrial facilities”. As there is no 3D map of Beirut available on Google

Earth, we cannot provide any quantitative details. We do however provide an aerial

image of Beirut in Appendix 3, which shows the significantly greater average building

height compared to both the environment of our study and Stusek et al. (2020).

Comparing our results to those of El Chall et al. (2019), they reported mean errors of -

1 to 4dB and a standard deviation of approximately 7dB. The mean error is significantly

(approximately 15dB) lower than our results, indicating a much better overall

estimation of the path loss. The standard deviation cannot be directly compared to our

shifted MAE, but it does indicate a greater spread between the measured and predicted

path loss compared to our results.

Trying to determine the source/sources of the discrepancy between our results and those

of El Chall et al. (2019) is hard, as there are differences in not one, but several of the

variables of the experiments. In their experiment, they measured path loss for distances

between 2 and 9km, we investigated distances between 100 and 800m. They had a base

station elevation of 200m, we tested elevations between 30 and 15m. Their base station

was also mounted on the top of a building, while ours was mounted on the side of a

building (however, from our experience, this should have a negligible effect on the

results). Further, their experiment was performed in an environment with much taller

buildings and a different building layout compared to Jönköping. To be able to

determine the source/sources of the discrepancy, one would need to perform

experiments were only one of these variables were varied at a time, which is outside

the scope of this study.

We finish off with our contribution relating to the first research question. Comparing

our study to the previous research, our study extends the research area with an

investigation of how empirical models perform in a small city with low-rise buildings

and the base station mounted on the side of a building.

Moving on to the second research question, it is as follows:

[2] How does base station elevation affect the accuracy of empirical models of radio

wave propagation for LoRa in an urban environment?

As mentioned for the first research question, the study showed a clear underestimation

of the measured path loss for all base station elevations, mobile station locations, and

models. When looking at the differences in results between each base station elevation

starting at 30m, the DAM of the Okumura-Hata model went from -20,2 to -22,3 to -

25

26,2dB, the COST-WI model went from -26,2 to -24,8 to -16,0dB, and the 3GPP model

went from -21,9 to -21,8 to -21,1dB.

The specified limitation regarding base station elevation is 200 to 30m for the

Okumura-Hata model. As shown by our results, the model’s underestimation

accelerated as the elevation was lowered from 30m. This confirms that the model is not

appropriate at elevations below 30m, as stated in the specified limitations.

For the COST-WI model the opposite effect was observed, the predictions accelerated

towards the measured path loss. This would support the claim of Haslett (2008) that the

model provides better validity than the Okumura-Hata model with the base station

positioned below the average building height. Between 23 and 15m the predicted path

loss increased drastically, as not only the measured path loss increased more than

between 30 and 23m, but so also the predictions in relation to the measured path loss.

This is because, for many of the mobile station locations, the base station was now

below the average building height (approximately 16m), which is a case that is handled

differently by the COST-WI model.

For the 3GPP model, compared to the other models, the overall underestimation of the

path loss was practically constant, only decreasing marginally with the decrease in base

station elevation. It also had a lower shifted MAE compared to the COST-WI model,

even though the COST-WI model is more complex and takes more environmental

factors into considerations.

Even though the DAM varied notably for some models, the shifted MAE stayed

relatively stable, with all models being between 3,7 and 5,6dB. This indicates that the

accuracy of the models could be increase greatly by simple shifting the predicted path

loss by a constant correction value. This is especially true for the 3GPP model, as its

mean deviation from the measured path loss only changed marginally between the shifts

in base station elevation.

5.2 Method discussion

To begin the method discussion, we first go back to the purpose of this study, which

was to investigate the accuracy of empirical models of radio wave propagation for LoRa

in an urban environment.

Regarding the methods used in this study, overall, we believe that they have been

successful in fulfilling the study’s purpose and providing answers to the research

questions. The general performance of some empirical models was demonstrated, and

so also the impact of base station elevation. However, we do not claim that there is

nothing that could be done to increase the validity and reliability of the study.

To begin with, the maximum possible ERP of the LoRa module used in this study was

20dBm while the maximum allowed ERP was 25dBm. Also, for mobile station

26

locations with greater distances to the base station many data packets were lost,

decreasing the effective sample size. As other radio transmitters in the area probably

used the maximum ERP, potentially raising the noise floor, and as a stronger signal is

easier for the LoRa modules to demodulate, an increase in ERP would have decreased

the number of packets lost. This would increase the effective sample size, yielding more

reliable results. Also, access to equipment to investigate potential losses in the test

devices would have made it possible to account for these losses when calculating the

measured path loss, increasing the reliability of the study.

Another factor affecting the results is that the signal strength for a specific location is

heavily dependent on nearby obstructions and objects that could reflect or absorb the

transmitted radio waves, as implied by the theory relating to radio wave propagation.

These objects and obstructions could be things like buildings and trees. By increasing

the number of locations for the mobile station, the effective sample size would increase,

leading to an increased reliability of the study. Related to this, performing the

experiment in other cities with different layouts, shapes of building, etc. would have

provided a more representable sample of urban environments, increasing the validity of

the study and generalizability of the results.

Finally, as the models’ predictions are heavily dependent on the data given to the

models, the results might have been slightly different had the environmental data been

collected in another way. For example, calculating the building height between the base

station and mobile station instead of in the proximity to the mobile station might have

improved the accuracy of the models. However, there were little to no guides for the

collection of data provided with the models or by the literature dealing with empirical

models. A standard for collecting environmental data would make it easier to attribute

differences in the accuracy of models to differences in environments, as the method of

data collection would not vary between experiments.

27

6 Conclusions and further research

This chapter presents the conclusions from the study and provides a suggestion for

further research.

6.1 Conclusions

LoRaWAN is a popular LPWAN technology and is based on the LoRa modulation. It

is important to estimate the coverage of base stations when planning such networks to

provide acceptable reception. Empirical models of radio wave propagation can be used

to estimate the path loss in radio communications, but their accuracy is heavily

dependent on the transmission environment. Previous research has investigated the

accuracy of empirical models for LoRa in some urban environments but has not

investigated the effect base station elevation has on the accuracy.

Regarding the accuracy of empirical models for LoRa in an urban environment, we

conclude that for an environment and setup similar to that of our experiment

(description of environment and setup available in chapter 2.2.2 and 2.2.3 respectively),

the models generally underestimate the path loss by approximately 20dB. However, by

shifting the predictions towards the measured path loss by a constant correction value,

empirical models can achieve a mean absolute error of at least 3,7-5,6dB.

Moving on to the effect of base station elevation, we conclude that there are great

variations in how well different empirical models handle different elevations, especially

for elevations below the average building height. The path loss predictions of the

Okumura-Hata model and the COST-WI model varied notably in relation to the

measured path loss between the different elevations. The 3GPP model however had a

practically constant mean deviation from the measured path loss, easily accounted for

by a constant correction value. This results in a mean absolute error of approximately

4dB for all tested base station elevations.

6.1.1 Implications

The results of the study can help people installing networks like LoRaWANs in

estimating the coverage of base stations to provide acceptable reception considering

different elevations of the base station. This could be private individuals setting up their

own LoRa communications or companies and agencies providing infrastructure for a

great number of IoT devices.

6.2 Further research

One factor that could have influenced our results is the test equipment used in the

experiment. Further research could be conducted to investigate what equipment is most

suitable for generating accurate and reliable measurements of path loss for LoRa.

28

7 References

3GPP. (2010, March 30). 3GPP Portal. Retrieved from

https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.asp

x?specificationId=2493

3GPP. (2021, March 16). About 3GPP. Retrieved from 3GPP's website:

https://www.3gpp.org/about-3gpp

Augustin, A., Yi, J., Clausen, T., & Townsley, W. M. (2016). A Study of LoRa: Long

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Appendix 2 3D map of Brno (Map data ©2021 Google, Landsat / Copernicus Data

SIO, NOAA, U.S. Navy, NGA, GEBCO, IBCAO)

32

Appendix 3 Image of Beirut (Beirut from the air by Magnus Halsnes is licensed

under CC BY-NC 2.0,

https://www.flickr.com/photos/magh/6833218292)

33

Appendix 4 Data for each mobile station location used in the empirical models

Location Distance

(m)

Building

height (m)

Building

separation

(m)

Street

width (m)

Angle (°)

1 750 17 35 17 25

2 715 19 35 16 86

3 550 17 35 12 81

4 585 17 35 14 25

5 650 17 40 17 48

6 475 16 40 17 45

7 390 16 40 13 17

8 480 16 40 22 8

9 270 17 40 14 45

10 430 15 40 20 65

11 390 16 35 17 76

12 130 16 30 17 81

13 190 14 35 17 25

14 325 14 30 17 53

15 500 13 40 17 47

16 335 14 40 25 12

17 520 14 35 12 66

18 725 14 35 17 0

19 760 15 40 17 70

20 675 13 35 17 85

34

Appendix 5 Image of base station

35

Appendix 6 Image of mobile station

an evaluation of coverage models for lora

Documents