Overview of Propagation Models for Mobile Communication


In this world we are all connected by Wireless Communication. We all know how mobile communication plays an important role in our day-to-day life. There are various propagation models for mobile communication. Explosive growth of mobile communication continues, it is very valuable to have the capability of determining optimum base-station locations ,obtaining suitable data rates and estimating their coverage ,without conducting a series of propagation measurement, which are very expensive and time consuming. It is therefore important to develop effective propagation models for mobile communication.
Propagation or Path loss models are basically used to predict coverage area, frequency assignment and interference, which are the main concerns in cellular network planning.
The path loss values compared with existing model for rural, suburban and urban areas. The propagation model tuning must optimize the model parameters in order to achieve minimal error between predicted and measured signal strength.
PATH LOSS:
Ratio of the transmitted power to the received power is the Path Loss between a pair of antennas, usually expressed in decibels(dB). All the possible loss elements associated with interaction between propagating wave and objects in between transmitter and receptor antenna are included in Path Loss of antenna.
            In  mobile channels Path Loss applies to the power averaged over several fading cycles. This pathloss is difficult to measure  directly as various losses and gains in the radio system also have to be considered.
To define pathloss very properly the losses and gain in the system must be considered.
[1]

The power PR appearing at the receiver input terminals of the antenna can be expressed as
PR = PTGTGR/LTLLR
Where,
PR= received power
PT= transmit power
GT= transmitting antenna gain
GR= receiving antenna gain
L= Path Loss
LT=transmitting feeder loss
LR=received feeder loss.

EIRP(effective isotropic radiated power) = PTGT/LT
PTI = effective isotropic transmitting power
PRI = effective isotropic receiving power
PRI = PR LR/ GR
The advantage of expressing the powers in terms of EIRP is that the path loss L, can then be expressed independently of system parameters by defining it as the ratio between the transmitted and the received EIRP, or the loss that would be experienced in an idealized system where the feeder losses, were zero and the antennas were isotropic radiators( GT,R =1, LT,R =1 ).
Main goal of propagation model is to predict the Path Loss as accurately as we possible.
L= PTI /PRI = PTGTGR/PRLTLR
The maximum range of the system occurs when the received power drops below a level which provides just acceptable communication quality. This level is often known as the receiver sensitivity. The value of L for which this power level is received is the maximum acceptable path loss. It is usual to express the path loss in decibels, so that
LdB=10 log (PTI / PRI)[1]
PROPAGATION MODELS:
To predict the propagation loss for mobile let us go through some Path Loss model. Path loss models are very important in wireless cellular systems.
[1]


FREE SPACE MODEL:                                                                                                  
 In this model pathloss L[1] defines the loss during propagation from transmitter to receiver. This model is diverse on frequency and distance where Frequency f is calculated in MHz and distance d is in Km. It can be calculated as
                                             L = 32.45 + 20log ( d) + 20log (f)  
·       HATA-OKUMUA MODEL:
 To make the traditional okumura’s model easier for computer implantation Hata’s model delivered from okumura and has fit okumura’s curves with analytical expression , because of this computer implementation of this hata-okumura model is straightforward. The formula for the median path loss in urban areas is given by

L( urban) = 69.55 + 26.16logf -13.S2loghte-ahre + (44.9 -6.55 loghte) log d

frequency (in MHz), which varies from 150 -1500 (MHz),
hte and hre are the effective heights of the base station and the mobile antennas (meters) respectively
d is the distance from the base station to the mobile antenna
a(hre) is the correction factor for the effective antenna height of the mobile unit, which is a function of the size of the area of coverage.

For small to medium-sized cities, the mobile-antenna correction factor is given by
a(hre) = (1.1 logf -0.7)hre -(1.56 logf -O.8)

For a large city, it is given by
a(hre)= { 8.29(log(1.54 hre))2 -1.1  , f < 300MHz
 3.2(log(l1.75hre))2 -4.97  , f >= 300MHz
             To obtain the path loss in a suburban area, the standard Hata formula is
L50 (dB) = L50(urban )-2[log(f/28)]2 -5.4
The path loss in open rural areas is expressed through
L50(dB) = L50 (urban) -4.78(log f)2 -18.33 logf -40.98
Today, the Hata implementation of the Okumura's model can be found in almost every RF propagation.
·       COST – 231 HATA MODEL:
COST -231 Hata model is widely used for predicting path loss in mobile wireless system. This model was devised as an extension to the Hata-Okumura model. The model is designed to be used in the frequency band from 500 MHz to 2000 MHz. This model also contains corrections for urban, suburban and rural (flat) environmental conditions.
The basic equation for path loss in dB is [4]:
L50 (dB) = 46.3 + 33.9logf - 13.82loghb +cm – ahm + (44.9 - 6.55loghb)logd
where, f: frequency (MHz)
             d: distance from the base station to the mobile antenna in (km)
             hb is the base station antenna height above ground level in metres.
The parameter cm is defined as 0dB for suburban or open environments and 3dB for urban environments. The parameter ahm is defined for urban environments as [6]:
ahm = 3.2(log(11.75hr))2 - 4.97 ,f > 400Mhz
For suburban or rural (flat) environments, the parameter is defined as:
ahm = (1.1logf - 0.7)hr - (1·56logf-0.8)
where, hr: mobile antenna height above ground level.
This model is quite suitable for large-cell mobile systems, but the model requires that the base station antenna to be higher than all adjacent rooftop.
·       STANFORD UNIVERSITY INTERIM (SUI) MODEL:
            IEEE 802.16 is a series of wireless broadband standards written by the Institute of Electrical and Electronics Engineers (IEEE). The working group proposed the standards for the frequency band below 11 GHz containing the channel model developed by the Stanford University, namely the SUI models. This prediction model also came from the extension of Hata model with frequency larger than 1900 MHz. The correction parameters are allowed to extend this model up to 3.5 GHz band. In the United States of America, this model is defined for the Multipoint Microwave Distribution System (MMDS) for the frequency band from 2.S GHz to 2.7 GHz.
The base station antenna height of SUI model can be used between 10 m to 80 m. Receiver antenna height varies from 2 m to 10m. The cell radius varies between 0.1 km to 8 km. The SUI model describes three types of terrain, they are terrain A, terrain B and terrain C. Terrain A can be used for hilly areas with moderate or very dense vegetation. This terrain presents the highest path loss. In this blog, we consider terrain A as a dense populated urban area. Terrain B is characterized for the hilly terrains with rare vegetation, or flat terrains with moderate or heavy tree densities. This is the intermediate path loss scheme. We consider this model for suburban environment. Terrain C is suitable for flat terrains or rural with light vegetation, here path loss is minimum.

The basic path loss expression of The SUI model with correction factors is presented as [7]:
  L = A + 10γlog(d/d0) + Xf + Xh + s  for  d> d0
 Where, d: distance between base station and mobile antenna in (metres)
d0: 100m
Xf : correction for frequency above 2GHz in (MHz)
Xh : correction for receiving antenna height
s: correction for shadowing in dB
γ: path loss exponent
The random variables in the formula are taken through a statistical procedure. The log normally distributed factor s is between 8.2 dB and 10.6 dB for shadow fading because of trees and other clutter on a propagations path. The parameter A is defined as:
A = 20 log( 4πd0/lambda )
and the path loss exponent  γ is given by:
 γ = a – bhb + (c/hb)
where, the parameter hb is the base station antenna height in meters and ranges between 10 m and 80 m. The constants a, b, and c depend upon the types of terrain, that are given in Table 2[1].
The frequency correction factor Xf and the correction for receiver antenna height Xh for the model are expressed in:
            Xf = 6.0 log(f/ 2000)
Xh = -10.8 log(hr/2000)  for terrain type A and B
Xh = -20.0 log(hr/2000)  for terrain type C
 where, f is the operating frequency in MHz, and hr is the receiver antenna height in metres.
For the above correction factors this model is extensively used for the path loss prediction of all three types of terrain in rural(C), urban(A) and suburban(B) environments.
Sr. No.
Model Parameter
Terrain A
Terrain B
Terrain C
1
a
4.6
4
3.6
2
b
(m^-1)
0.0075
0.0065
0.005
3
C(m)
12.6
17.1
20

·       ECC-33 MODEL:
The original Okumura model’s experimental data were gathered in the suburbs of Tokyo[6] . The authors in the research papers refer to urban areas subdivided into 'large city' and 'medium city' categories. They also give correction factors for 'suburban' and 'open' areas. Use of ‘medium city model’ is recommended for European cities. Although the Hata-Okumura model is widely used for UHF bands, its accuracy is questionable for higher frequencies. The COST-231 model was extended to use up to 2 GHz but it was proposed for mobile systems having omnidirectional receiver antennas sited less than 3 m above ground level.
A different approach was considered, which extrapolated the original measurements by Okumura and modified its assumptions so that it more closely represents a wireless system. This path loss model is referred as the ECC-33 model.
The path loss is defined as:
L = Afs + Abm – Gb - Gr
where, Afs , Abm , Gb and Gr are the free space attenuation, the basic median path loss, the Base station height gain factor and the receiver height gain factor respectively.
 They are individually defined as the following:
Afs = 92.4 + 20 log d + 20 log f
Abm = 20.41 + 9.83logd + 7.89logf +9.56[logf]2
Gb  = log(hb/200)(13.958 + 5.8log(d))2
For medium city environment ,
Gr = [42.57 + 13.7logf][log(hr)-0.585]
and for large city  Gr = 0.759 hr - 1.862
where, f is the frequency in GHz
d is the distance between base station and mobile antenna in km
hb is the base station antenna height in metres and
hr is the mobile antenna height in metres
 The medium city model is more appropriate for European cities whereas the large city environment should only be used for cities having tall buildings like sky scrapers. It is interesting to note that the predictions produced by the ECC-33 model do not lie on straight lines when plotted against distance having a log scale.
·        STANDARD MACRO-CELL MODEL:
            This model is an empirical model based on the modified Hata model. Before going into the details of the model, lets first understand what is macro cell. The cell is the area in which a bandwidth of frequency is being used for mobile communication. Macro  cell is a widest range of cell sizes. (around 35 km wide) and it provides high power transmission. As the number of users per area increases, macro cell is further get divided into microcells(2 km wide), picocells(up to 200 m wide) and femtocells(10 m). 
Standard Macro-cell Model is used for macro cells and it is usually used in rural areas where number of users per area are less or along the highways where continuous handoff is unnecessary. In this model, three main factors are taken into consideration.
1.      Effective base station height
2.      Diffraction loss
3.      Effects of clutter
To measure the diffraction loss, the Epstein-Peterson, Bullington, Deygout or Japanese Atlas knife edge techniques are used.
The formula for the path loss in this model is given as[2],



Where,
[3]
The propagation model can be further tuned by modifying the k factors. For improved near and far performance, dual slope attenuation can be introduced by specifying both near and far values for  k1 and k2.

·       LOG DISTANCE PROPAGATION MODEL:
            This model is based on the theory that, the average received signal power decreases logarithmically with distance (d) between the transmitter and the receiver.
This can be mathematically expressed as,


            Where,
[3]
Here, n gives the idea of size of obstructions. Larger the n, a greater number of obstructions are present in the path hence the decrease in average received power is faster as distance become larger.
Also, the reference distance  varies  according to the propagation environment. In large coverage cellular systems, 1 km reference distances are commonly used and in microcellular systems, much smaller distances (such as 100 m or 1 m) are used. The reference distance should always be in the far field of the antenna so that near-field effects do not alter the reference path loss.

·       BERTONI-WALFISCH PROPAGATION MODEL:
            This model is a semi-empirical model. It is applicable for propagation through buildings in urban environments. This model is known for its simplicity and validity. This model works on some assumptions, they are:
·       Heights of buildings are to be uniformly distributed.
·       Separation between buildings are equal.
Then, the model considers the multiple diffraction past these rows of buildings.
 Path Loss formula for Bertoni-Walfisch propagation Model is given as,
           

Where,
·      

[3]

We have discussed different propagation models up till now in the blog. Selection of propagation model changes according to the geographical area in which it has to be applied or implemented. This can be illustrated by some following experiments performed at different locations.
Ø  Dar es Salaam names city which is located  in Tanzania is chosen for comparison of different propagation model. For presenting urban area, Posta (NIC) were selected ,for suburban part Kizuiani were chosen and for rural part Kimbiji was selected.  Experimental meausrements are taken in these 3 areas for 2G/3G system. Experimental measurements of radio propagation characteristics are made in urban, suburban and rural areas for a 2G/3G system working at 900/1800/2100 MHz frequencies.
Comparison of error standard deviation is shown in the below table.
Sr. No.
Error Standard Deviation
Hata
ECC
SUI
Ericsson
COST 231
1
Urban
17.68
25.98
15.92
25.84
12.98
2
Suburban
28.47
14.50
37.67
31.91
18.88
3
Rural
37.89
NA
10.99
43.94
11.22


From above table we can observe that no model is perfectly suitable for all the three regions. From above table, COST 231 has minimum error standard deviation i.e. 12.98 for urban area among all the models. Similarly ECC has least value i.e. 14.50 for suburban area and SUI has least value i.e. 10.99 for rural area. But COST 231 Hata model has the least average error standard deviation for the three environments. i.e. each model works differently for particular area.
Here are some graphs showing the relation between pathloss and the distance for different models in urban, suburban and rural areas respectively.





Fig. Comparison of path loss models with the measurement from urban area

Fig. Comparison of path loss models with the measurement from suburban area

Fig. Comparison of path loss models with the measurement from rural area.
From these graphs also we can observed that each propagation model works differently in different areas with different efficiencies.
Ø  Another two experiments were done on the same city called Nablus which  is in Palestine[3].
For the first experiment, cusing digital maps city was classified into buildings, low tree, buildings, agriculture, seasonal water bodies. Parameters  for network designing such as coverage, capacity and quality of service were considered for the network design for the city For cell planning, radio cell planning tool is used to predict the radio coverage by means of propagation models, for a particular area.
From the simulation result, they selected Algorithm 9999 model which is dependent on the Ericsson mand Okumura – Hata model  as best suited  .
For the second experiment done on the same city, geographical structure like buldings, mountains were considered. By applying different empirical propagation models such as Bertoni-Walfisch, Hata, Haret, standard macrocell model, log distance propagation model, COST231 Walfisch- Ikegami , different parameters such as mean error, standard deviation etc. are calculated.
Comparsion of these models on the basis of above mentioned parameter is shown in the following table.

Sr. No.
Empirical Propagation Model
Mean Error (dB)
Standard Deviation
Root Mean Square Error
1
Hata
12.598
12.96
18.075
2
Haret
10.348
12.98
16.6
3
COST 231 Walfisch-Ikegami
10.58
12.99
16.76
4
Bertoni- Walfisch
1.426
13
13.07

From the above table it is seen that Bertoni- Walfisch model has least mean error and root mean square error. So this was the best model for the city in this experiment.

Statistics & Result about the different Propagation Models and their comparison:
STANDARD MACROCELL MODEL TUNING:
As it is a emperical model the tuning of the model can be done by various methods after the tuning of the Standard Macrocell Model the coefficients ,K1 and K2 are changed .The tuning of trhe model was done by the LMSE on the path loss equation .
Pl(dB)=k1+k2log(d)+k3(Hms)+k4log(Hms)+k5log(Heff)+k6log(Heff)log(d)+k7(diffin)+Closs
The pathloss in the Standard Macro cell Model before tuning and after tuning is represented in the figure.


Parameters
Before Tuning
After Tuning
K1
135
139.41
K2
38
30
K3
-2.55
K4
0
K5
-13.82
K6
-6.55
K7
0.7













fig. Path loss comparison of Standard Macrocell model before and after tuning

 BERTONI-WALFISCH MODEL TUNING:
Also Bertoni-Walfisch model is a empirical model the tuning of the model can be done by various methods after the tuning of the Bertoni-Walfisch Model the coefficients
Pl(dB)=78.5+A+23log(d)-18log(ht-hb)+21log(f)
The Path loss before tuning and after tuning is given in the graph given below.
Before Tuning
After Tuning
89.5
78.5
38
23
2
21













                        fig. Path loss comparison of Bertoni-Walfisch model before after before tuning

Mean Error comparison between tuned Bertoni-Walfisch model with known Models
BS#
Tuned Bertoni-Walfisch
Bertoni-Walfisch
Hata
Walfisch-Ikegami

Haret
Standard Macrocell Model
BS1
0
1.426
12.59
10.58
10.34
10.91
BS2
6.978
10.728
17.82
16.5
10.32
18.536
BS3
2.367
9.633
9.737
10.106
8.636
12.067
BS4
3.254
6.941
14.72
11.697
10.96
14.510
BS5
10.041
12.32
23.11
18.936
15.76
21.774
BS6
3.342
11.576
10.789
11.083
9.707
13.565
BS7
5.88
8.991
16.424
14.322
13.567
16.797
BS8
16.813
16.311
27.21
25.255
24.377
25.971
Avg Mean Error
6.64
9.55
16.55
14.80
12.96
16.76














Ref #[3] Allam Mousa, Y. D. (2012). Optimizing Outdoor Propagation Model based on Measurements for Multiple RF Cell


 Standard Deviation comparison between tuned Bertoni-Walfisch model with known Models
BS#
Tuned Bertoni-Walfisch
Bertoni-Walfisch
Hata
Walfisch-Ikegami

Haret
Standard Macrocell Model
BS1
11.294
13
12.96
12.99
12.98
11.792
BS2
9.544
13.52
12.73
13.52
12.879
10.807
BS3
7.956
8.941
8.861
8.94
12.358
8.396
BS4
9.2
11.362
11.163
11.362
11.362
10.157
BS5
9.09
10.987
10.567
10.987
10.644
9.621
BS6
5.127
6.027
5.944
6.026
5.924
5.496
BS7
8.039
9.286
9.220
9.286
9.229
8.556
BS8
7.559
8.538
8.489
8.538
8.496
7.987
Avg Mean Error
8.47
10.20
9.99
10.20
10.48
9.10

Ref #[3] Allam Mousa, Y. D. (2012). Optimizing Outdoor Propagation Model based on Measurements for Multiple RF Cell

 Path Loss Comparison Between :
·       Hata Model
·       Bertoni-Walfisch model before tuning
·       Haret Model
·       Malfisch-Ikegami model
·       Standard Macrocell model
·       Bertoni-Walfisch model after tuning

                                                    fig. Path loss comparison of different models
Conclusion:
In this blog we have discussed various propagation model namely Bertoni-Walfisch, Standard macrocell model, Log distance propagation model, Hata okumura model, Ecc-33 model, Stanford university interim (SUI) model, Cost 231 Hata model. The statistics and the data collected from the various resources confirms that according to the urban, suburban, rural area terrain the various models can be implemented. Although, when it comes to generalization of which model is most dominating, no model outperforms all other model in all conditions. Each model differs widely in approach of complexity and accuracy. Most cellular operator use version of Hata model for conducting propagation characterization. Also the survey which was carried out in the nabukus city of palestine. After the tuning of  Bertoni-Walfiesch model, it really stood up.

Refrences: 

            [1] Michael S. Mollel, Dr. Michael Kisangiri, “An Overview of Various Propagation Model for Mobile Communication”, Nelson Mandela African Institution of Science and Technology (NM-AIST), School of Computational and Communication Science and Engineering Arusha, Tanzania.
[2].Tarapiah, S. a. (2016, July). Mobile Network Planning Process Case Study - 3G network. Computer and Information Science, 9, 115. doi:10.5539/cis.v9n3p115.
[3] Allam Mousa, Y. D. (2012). Optimizing Outdoor Propagation Model based on Measurements for Multiple RF Cell. International Journal of Computer Applications (0975 – 8887) , Volume 60– No.5, 6.
[4] C. Action, "231," Digital Mobile Radio Towards Future Generation Systems, Final Report". European Cooperation in the Field of Scientific and Technical Research, EUR, vol. 18957, 1999.
[5]Y. Okumura, E. Ohmori, T. Kawano, and K. Fukuda, "Field strength and its variability in VHF and UHF land-mobile radio service," Rev. Elec. Commun. Lab, vol. 16, pp. 825-73, 1968.
[6] H. R. Anderson, Fixed Broadband WirelessSystem Design: John Wiley & Sons, 2003. V.
[7 ] Abhayawardhana, 1. Wassell, D. Crosby, M. Sellars, and M. Brown, "Comparison of empirical propagation path loss models for fixed wireless access systems," in Vehicular Technology Conference, 2005. VTC 2005-Spring. 2005 IEEE 6lst, 2005, pp. 73-77. S



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