JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 1, JUNE, 2010
MACROCELL PATH LOSS MODEL FOR TROPICAL SAVANNAH
Adenike Folaponmile
Computer Engineering Department, Kaduna Polytechnic, Kaduna
E mail: nikkyfola04@yahoo.com
Abstract
Propagation models are used extensively in network planning, particularly for conducting feasibility studies and during initial deployment. This work sets out to determine the propagation model that is best suitable for Nigerian regions and by extrapolation to other tropical areas with similar geographic climate and terrain. This is done by comparing some existing prediction models which have wide acceptability and is currently in use for mobile radio propagation with measurement results. From the results, necessary adjustments to these models are proposed for use in mobile communications system design in tropical areas such as Nigeria.
Keywords: Macrocell, propagation, prediction, path loss
Introduction
Macrocells is described by Sanjay (2008) as cells that are generally large, providing coverage range on the order of kilometers, and are used for outdoor communications. Several empirical path loss models have been determined for macrocells. Two of such models are HataOkumura’s model and Lee’s model. Since terrain and landuse information vary widely from country to country, it becomes imperative to determine how best certain propagation models are applicable in particular coverage areas.
This work was conducted in three major cities within Kaduna state, northern Nigeria. Measurements were taking in open, suburban and urban areas. It was done using base stations belonging to Zain Nigeria Ltd., one of the major GSM companies in Nigeria. The results of the measurements were used to validate propagation prediction models proposed by Okumura – Hata and Lee in order to determine the necessary adjustments to these models for use in mobile communications system design in tropical areas such as Nigeria.
Mobile radio propagation models
Propagation models are used extensively in network planning, particularly for conducting feasibility studies and during initial deployment (Kurniawan, 1997). There are various propagation prediction models for mobile radio communications systems. Such as LongRice model, OkumuraHata’s model, Lee’s model, Durin’s model, Walfisch and Bertoni’s model etc
In this work, particular attention is given to prediction models by OkumuraHata and Lee. This is because these models have been widely accepted and as such will be used to evaluate the propagation measurements results.
OkumuraHata model
The OkumuraHata’s model was first described by Okumura and then modified by Hata. This model is based on propagation measurements conducted in Kanto (near Tokyo), Japan. (Hata, 1980). The initial model by Okumura presents signal strength prediction curves over distance in a quasismooth urban area. Form these prediction curves, Hata developed a mathematical formulation for simple computational applications. Therefore, this model is called OkumuraHata’s model.
In using this model, radio transmission parameters such as frequency, base station antenna height, mobile station antenna height, terrain etc must be taking into consideration.
OkumuraHata model is given as:
= A + B log (d) for urban areas
Lp(dB) = A + B log (d)  C for suburban areas (1)
= A + B log (d)  D for open areas
Where:
A = 69.55 + 26.16log (fc) – 13.82log (hb) – a (hm)
B = 44.9 – 6.55log (hb)
C = 5.4 + 2 [log (fc /28)]
D = 40.94 + 4.78 [log (fc)] 2 – 19.33log (fc)
and
= [1.1log (fc) – 0.7] hm – 1.56 log (fc)0.8 for medium / small city (2)
a (hm) = 8.28[log (1.54 hm)] 2 – 1.1 for large city and fc ≤ 400 MHz
= 3.2 [log (11.75 hm)] 2 – 4.97 for large city and fc ≥ 400 MHz
For specification range of:
Carrier frequency: 150MHz ≤ fc ≤ 1000MHz
Base station height: 30m ≤ hb ≤ 200m
Mobile station height: 1m≤ hm ≤ 10m
Distance between mobile and base station: 1Km≤ d ≤ 20Km
Lee’s model
Lee’s model was based on empirical data obtained in various areas in the United States and later in
Europe, Korea and Japan. (Lee, 2006). Lee’s prediction model is divided into two categories. These are: area –toarea prediction model and pointtopoint prediction model which is derived from, and is an improvement on the areatoarea model.
The received signal strength in dBm is expressed as:
(3)
Two parameters are initially required to characterize the model: µΩo (the power at a 1.6Km point of interception) and the path loss exponent β. these two parameters are determined from the empirical measurements and listed in table (1). Subsequently, the following nominal conditions are set when employing Lee’s model:
do = distance of 1.6Km
Carrier frequency: fc = 900MHz
Base station height: 30m
Mobile station height: 3.0m
Base station antenna gain: 6 dB above dipole gain
Mobile station antenna gain: 0 dB above dipole gain
The following parameters must also be set:
f the actual frequency
d distance between mobile station and base station antennas
αo correction factor
The parameter αo is basically used to account for different BS and MS antenna heights, transmit power and antenna gain. If the actual conditions differ from the nominal ones, then αo is computed as:
αo = α1 α2 α3 α4 α5 (4)
Where:
(5)
(6)
(7)
(8)
(9)
The values of n in (3) and ζ in (6) are based on empirical data and recommended to take the following values:
n = 2.0 for fc < 450MHz and in suburban / open area
= 3.0 for fc > MHz and in urban area
ζ = 2.0 for MS antenna height >10m
= 3.0 for MS antenna height < 3m
Finally, the path loss Lp is given as:
Lp = Pt – µΩo dBm (10)
For scenarios listed in Table (1), the path loss obtained from Lee’s model can be reduced to:
= 85 + 20 log(r /1.6Km) +10n log (f /900MHz) – αo Free space
= 89 + 43.5 log(r/1.6Km) +10n log (f /900MHz) – αo Open area
Lp (dBm) = 101.7 + 38.41 log(r/1.6Km) + 10n log (f /900MHz) – αo Suburban (11)
= 101 +36.81log(r/1.6Km) + 10n log (f /900MHz) – αo Philadelphia
= 104 + 43.1log(r/1.6Km) + 10n log (f /900MHz) – αo New York
= 124 + 30.520 log(r/1.6Km) + 10n log (f /900MHz) – αo Tokyo
Where r is in Km and f is in MHz.
Table 1: Parameters for Lee’s path loss model
Terrain 
µΩo 
β 
Free Space 
45 
2 
Open Area 
49 
4.35 
Suburban 
61.7 
3.84 
Philadelphia 
70 
3.68 
New York 
64 
4.31 
Tokyo 
84 
3.05 
Experimental setup and parameter
Propagation measurements were conducted in three different sites. The sites are located in Kaduna metropolis, Mando and Kafancha road all in Kaduna State in northern Nigeria. These sites represents three different terrain namely, urban, suburban and open area respectively. The measurements were taking at different times and on different days and the mean used to compute the path loss.
Taking the measurements, the received signal level (RSL) was recorded as a function of distance away from the base station with the aid of Geographic Positioning System (GPS), Altimeter, Tems phone and Computer laptop. The GPS was used to accurately establish the measurement location, the Altimeter was used to measure the ground height, the Tems phone captured the signal strength and was recorded on the computer laptop.
The measurements were taken while in a slowly moving van away from the base station. The measurements locations were concentrated mainly within a region from 200 to 2km from the BS at an incremental rate of 200m.
Table 2: Experimental parameter
Parameter 
Kaduna metropolis 
Mando 
Kafancha 
Frequency 
900 MHz 
900MHz 
900 MHz 
Transmit power 
45 dBm 
48 dBm 
54 dBm 
Transmit antenna gain 
17 dBi 
17.8 dBi 
18.2 dBi 
Transmit antenna height 
35 m 
48 m 
60 m 
Receive Antenna height 
3 m 
2m 
2m 
Data analysis
The measurements data were analyzed with the use of least square (LS) regression using SPSS 10, Matlab 7.0 and Microsoft Excel. The respective path loss for each terrain was determined using the experimental parameters used for this measurement as presented in table (2). The mean error and standard deviation were generated from the LS regression using SPSS 10.
Comparison with measurements
The corresponding error statistics in terms of the mean prediction error and the Standard deviation (SD) of the prediction error are shown in tables (35) for all three environments. The prediction errors are calculated as the difference between the measurement and prediction.
Figure (1) compares the path loss obtained in an urban environment. It clearly shows that, both Hata and Lee’s model under predict the path loss with Lee’s model, grossly under predicting the path loss. Hata’s model gave a closer prediction to the measurement with a mean error of 5.265dB and SD of 1.114. Lee’s model gave a mean error of 36.124dB and SD of 2.209.
Figure 1: Comparison of empirical models with measurements from a typical urban environment.
Table 3: Error statistics of model predictions for rural area

HATA 
LEE 
MEAN ERROR 
5.265 
36.124 
SD 
1.114 
2.209 
The regions covered in Mando are typical of a suburban environment. The results are shown in figure (2) and from the results, it can be seen that both Hata and Lee’s model under predict the path loss with Lee’s model, grossly under predicting the path loss. Hata’s model gave a closer prediction to the measurement with a mean error of 9.55dB and SD of 0.441. Lee’s model gave a mean error of 32.9dB and SD of 2.051.
Figure 2: Comparison of empirical models with measurements from a typical suburban environment.
Table 4: Error statistics of model predictions for suburban

HATA 
LEE 
MEAN ERROR 
9.505 
32.9 
SD 
0.441 
2.051 
Figure (3) compares the path loss obtained in an open area. It clearly shows that, both Hata and Lee’s model under predict the path loss with Lee’s model, grossly under predicting the path loss. Hata’s model gave a closer prediction to the measurement with a mean error of 12.367dB and SD of 1.332. Lee’s model gave a mean error of 51.449dB and SD of 3.583.
Figure 3: Comparison of empirical models with measurements from a typical open area.
Table 5: Error statistics of model predictions for open area

HATA 
LEE 
MEAN ERROR 
12.367 
51.449 
SD 
1.332 
3.583 
Conclusion
Measurements taken in Kaduna, Mando and Kafancha representative of Urban, suburban and open area respectively, were compared against predictions made by two empirical propagation models. Lee’s model show large mean path loss error, generally, grossly under predicting the path loss. Hata’s model showed closer agreement with measurement results with lower mean path loss errors.
Hata’s model shows that it performed best in urban environment giving the least error of 5.265dB and showing the closest curve to the measured result. It is therefore recommended that Hata’s model is suitable for use in the tropical savannah and that an additional loss factor of 5.265dB be added to correction factor for urban environment, 9.55dB for suburban environment and 12.37dB for open area for use in mobile communications system design in tropical areas such as Nigeria.
References
Hata, M, “Empirical formula for Propagation Loss in Mobile Radio Services”, IEEE Transaction on Vehicular Technology, Vol VT29, no 3, pp 317325, 1980.
Kurniawan A, “Prediction of Mobile Radio Propagation by Regression Analysis of
Signal Measurements”, Magazine of Electrical Engineering, Indonesia, Vol. 3, no 1, pp 1121, May 2007.
Lee C.Y.,Wireless and Cellular Telecommunications, McGraw Hill Singapore, 2006, pp 373382.
Parsons J.D., ‘The Mobile Radio Propagation Channel’, Second Edition, John Wiley & Sons Ltd., 2000
Sanjay S., Wireless and Cellular Communications, S.K. Kataria and Sons, New Delhi, 2006, pp 3033.