ANALYSES AND OPTIMIZATION OF LEE PROPAGATION MODEL FOR LORA 868 MHZ NETWORK DEPLOYMENTS IN URBAN AREAS

1 University of Novi Sad, Technical faculty “Mihajlo Pupin” Zrenjanin, 23000 Zrenjanin, Đure Đakovića bb, Republic of Serbia E-mail: dalibor.dobrilovic@uns.ac.rs 2 Panonit, 21000 Novi Sad, 7 Miroslava Antića, Republic of Serbia 3 Technical College of Applied Sciences, 23000 Zrenjanin, Đorđa Stratimirovića 23, Republic of Serbia 4 University of Novi Sad, Faculty of Technical Sciences, 21000 Novi Sad, Trg Dositeja Obradovića 6, Republic of Serbia


INTRODUCTION
In the past decade few technologies such as Wireless Sensor Networks (Nandury & Begum, 2015), Internet of Things (Zanella, Bui, Castellani, Vangelista & Zorzi, 2014), Big Data (Hashem et al., 2016) and Cloud computing (Vögler, Schleicher, Inzinger, Dustdar, & Ranjan, 2016) influenced the shaping of Smart City concept.The term "smart city" defines the new urban environment, one that's designed for performance through information and communication technologies (ICTs) and other forms of physical capital.With the effective management of resources through intelligent management, visionaries hope that cities will drive a higher quality of life for citizens, drive down waste, and improve economic conditions", (Stimmel, 2016).
According to Georgescu and Popescul (2016)  Smart city environments are largely based on wireless technology.According to (Lee, Park, & Seo, 2009), the radio propagation conditions and their statistical characteristics seriously affect the operation of wireless communication systems as well as their performance.So, in preparation for the design of high-performance wireless resource management, it is crucial to understand the characteristics of wireless communication channels.One of the most important characteristics of wireless channels is the channel gain which is determined by three factors: path loss, shadowing, and multipath fading.Path loss represents the decay of signal power dissipated due to radiation on the wireless channels, so it is determined by the channel's physical characteristics of signal propagation and modeled as a function of the distance between the transmitter and receiver.
A number of researches are performed in order to analyze and possibly optimize path loss propagation models in urban, suburban and open space environments.The number of propagation models such as: Okumura-Hata, COST231, Stanford University Interim (SUI), Ericsson 9999, ECC-33, Winner II, Egli, etc; are analyzed for different usage scenarios (Seybold, 2005;Parsons, 2000).Those researches are mainly focused on mobile communications (Alim, Rahman, Hossain, & Al-Nahid, 2010) and WiMAX (Alshami, Arslan, Thompson, & Erdogan, 2011) technologies.Furthermore (Al Salameh et al., 2015) focused his research on mobile communications in urban areas; while Armoogum, Soyjaudah, Mohamudally and Fogarty (2007) focused their research on Digital Television Broadcasting in Mauritius using the same propagation model.Evans, Joslin, Vinson and Foose (1997), dealt with optimization and application of Lee propagation model in the 1900 MHz frequency band.Galvan-Tejada and Duarte-Reynoso (2012) and Galvan-Tejada, Duarte-Reynoso and Flores-Leal (2013) analyzed usability of Lee propagation model in vegetation environments.Rivera et al. (2015) discussed about applicability of Lee propagation model in university campus environments.
There is an evident lack of similar researches for alternate technologies applicable in Smart City environments.This research represents the analyses of usability of Lee propagation model (Lee & Lee, 2000;Lee, 2006;Lee & Lee, 2010;Lee & Lee, 2014) in design, planning and management of wireless networks in urban areas based on LoRa technology for possible Smart City scenarios in small city environments.In addition, the possible optimization of the same model is discussed.
This paper is structured as follows.After the short introduction, Lee propagation model is described.The experiment and results are presented in the following sections.At the end, the conclusion and further work are presented.

LEE PROPAGATION MODEL
The Lee model was originally developed for use at 900MHz and has two modes: area-to-area and point-to-point (Seybold, 2005).This model is used to predict a path loss over flat terrain.If the actual terrain is not flat, e.g., hilly, there will be large prediction errors (Stüber, 2002).Area-to-area model uses reference path loss L 0 for one mile or 1.6 km, slope of path loss curve  in dB and adjustment factor F 0 .Propagation path loss is calculated with formula: Distance between transceiver and receiver d is in km.The reference values for median path losses are given in Table 1.The adjustment factor F 0 is calculated with formula: Where F 1 is base station antenna height correction factor and h b is base station antenna height in meters.
Base station antenna gain correction factor is: G b is base station antenna gain relative to a halfwave dipole [dBd].dBd compares the gain of an antenna to the gain of a reference dipole antenna, while dBi is a measurement that compares the gain of an antenna with respect to an isotropic radiator (a theoretical antenna that disperses incoming energy evenly over the surface of an imaginary sphere.).The difference is 2.15 dB.To convert dBi to dBd or vice versa: the following formula is used: dBd = gain in dBi -2.15 dB.
Further, F 3 or mobile antenna height correction factor is calculated like this: Mobile antenna height correction factor depends on h m or mobile antenna height in meters.Two different formulas are used, one for antenna height above 3 m, and other for antenna heights bellow 3m.
The frequency adjustment factor is: where 2 < n < 3 and f is in MHz (7) Mobile antenna gain correction factor with G m (mobile antenna gain) in dBd is: Another form of formula for Lee propagation is as follows, (Stüber, 2002): Where is power at 1 mile or 1.6 km (reference distance d 0 ); and  is path loss exponent.
Parameters for formula (9) are given in Table 2.
Those parameters are determined with empirical measurements.
Where h b is the base station antenna height expressed in meters, like in the previous case.For  2 or mobile antenna height correction factor following formula is used with h m as mobile antenna height.
Two different formulae are used, one for antenna height above 10 m, and other for antenna heights bellow 3m.
Mobile antenna gain correction factor is:  

RESULTS ANALYSES
Calculations needed for propagation loss are made according to the formula for received power calculation.Received power calculation or link budget may be calculated with (23) and it is based on the authors experience in previous research for ZigBee and 868MHz indoor propagation (Dobrilovic, Odadzic, & Stojanov, 2016) and ZigBee and LoRa outdoor propagation.The link budget is a calculation of all the gains and losses for the link that are added in order to arrive at the mean signal level at the receiver, (Anderson, 2003;Dobrilovic et al., 2016).
P rx is received power (dBm).P tx is transmitter output power (dBm) which represents the timeaverage power of the link transmitter on the transmission channel.The power level is given in dB relative to one milliwatt, dBmW, or dBm; G tx is transmitter antenna gain (dBi) and it depends on the antenna type (mostly its cross section or aperture size) and is obtained from the antenna manufacturer.The antenna type and its gain is one of the link system elements the design engineer can easily change to improve link performance.L tx is transmitter losses (dB) represent losses in transmission line connecting the transmitter as well as the losses in connectors.L pl is propagation loss or path loss (dB) and it is calculated with various propagation models formula.L m represents miscellaneous losses (fading margin, body loss, polarization mismatch, other losses...) (dB) G rx is receiver antenna gain (dBi) and L rx is receiver losses (coax, connectors...) (dB) are the same as G tx and L tx , but on the receiver side.Effective radiated power (dBmW) or ERP is the sum of the transmitter power and transmit antenna gain minus the transmitter losses, (Anderson, 2003).
In this research with usage of LoRA 868 MHz modules based on SX1272 (Libelium, 2017), and accompanied equipment, the P tx is 18 dBm, G tx is 9 dBi and G rx is 4.5 dBi.The P tx and G tx are cumulative included in formula (4).L tx , L rx and L m are very low and therefore disbanded.Also, since the calculations will use formula (1) for prediction of signal strength, and since the Gtx, Grx and Ptx are inserted in formulas (2), ( 4) and ( 8) the formula for path loss calculation that is used in this research is: where L pl is calculated with (1).The calculated predicted signal strengths are given in Figure 2, for urban areas of Philadelphia, Newark, Tokyo and sub-urban, rural and free space areas.On the same figure measurement results from the experiment for 17 locations are shown as blue circles. In of Lee propagation model for LoRa 868 MHz network deployments in urban areas JEMC, VOL. 7, NO. 1, 2017, 55-62 57

Figure 1 :
Figure 1: Locations used in LoRa 868MHz measurements (image is made in Google maps)

Table 1 :
Reference Median Path Loss for Lee's Model

Table 2 :
Reference Median Path Loss for Lee's Model variant 2 Environment p (d o ) The adjustment or correction factor 0 is calculated with formula like in (2):

Table 3 :
The data for measurement locations

Table 4 :
Comparison of Lee propagation model fitting for different environments and measured results Those analyses show that Lee propagation model is accurate enough and that results can be used as a strong base for further research.Further research should be pointed towards a comparison of more measurement results with the Lee model, the comparison of Lee model accuracy with other propagation loss models and finally in the direction of tuning and optimization of Lee model with finding L 0 and γ values for Zrenjanin.