Modified Hata Model

 

            Hata’s formula is restricted to a frequency range of 100 to 1500 MHz, distances between 1-20 km and base station effective heights between 30 -200m. Modifications were made to improve accuracy relative to the Okumura curves [1]. Frequency range up to 3000 MHz, and study distance up to 100km are increased by modifications.

             The parameters and restrictions of the Modified Hata used in this part and restriction of the models are shown in    table 1

                                                                          

Parameter

Definition

Range of validity

Lmh

Modified Hata propagation. Median dB

-

hb

Base antenna Height, m

30-300

  hm

Mobile Antenna Height, m

1-10

        U

0 = small/medium, 1= large city

0 or 1

Ur

0 = open area, 0.5 =suburban, 1= urban

0-1

Bl

Percentage of Buildings

3-50

R

Range, km

1-100

f

Frequency, MHz

100-3000

 

Table .1 Parameters and Restrictions of the Modified Hata Model

 

 

The other parameters will be used in Modified Hata’s calculations:

 

Lccir= Lp formula (1) in Hata’s Model

am(Hm)= formula (2) in Hata’s Model

a2(Hm)= formula (3) in Hata’s Model

a4(Hm)= formula (4) in Hata’s Model

Lps= formula (5) in Hata’s Model

Lpo= formula (6) in Hata’s Model

 

To validate Hata’s model in higher frequencies, transition values are defined in the model as follow:


 


 Correction for the earth’s curvature, but propagation not beyond the horizon is written as


 

 


The suburban/urban correction is represented by Ur urbanization parameter as follow:

 

                    So=(1-Ur)[(1-2Ur) Lpo+4UrLps]     

 

Overall height correction ax is derived combining height corrections used in Hata’s Model with frequency transition functions and a small / large city parameters,  

               

                ax=(1-U)am(hm)+U[a2(hm)F1+a4(hm)F2]         

 

 

Another term for contribution of percentage of buildings on loss is considered as

 

                         B0=25log(B1)-30

 

By adding all results , modified Hata formula is written as follow:

 

                  L=-(Lccir+S0+ax+Sks+B0)

 

 

To give an idea about how modification correlates with Okumura’s measurements, comparison of the Modified Hata model with Okumura is shown in figure 1


                                        Figure 1 [1]. Comparison of Modified Hata with Okumura curves

 


In the figure, it is seen that Modified Hata model have about 3 dB deviations from the Okumura curves over the frequency range 100 to 3000 MHz and distance 1-100 km.

The Wireless Simulator Program output as seen in Figure 2 could verify this deviation by taking Hata’s approach for Okumura’s curves.

 


 


                                                                              Figure 2 Comparison of Hata with Modified Hata

 

Study Parameters:

Frequency: 900 MHz,

TX Height (hb)=200m

Mobile Height (hm)=3m

TX Gain:  13 dBi

City Size: Small/Medium

Area Type: Urban

Terrain Parameters:

Average Width: 73.8 m

Average Building Height: 15.84m

Percentage of Buildings: 37%

 

As shown in output of the Wireless Simulator Program in the figure, there is about 4dB difference between Modified Hata and Hata results. This is not expected result when compared with figure 1. Reason for difference could be use of different building percentage in both studies and Hata’s small deviation from Okumura’s result. Although there are ripple difference between Modified Hata and Okumura’s curves, by the sight of computation, it is worth to use Modified Hata’s Formulas as representation of Okumura’s measurements since it represents the curves in wide range.

 

[1] Sounders, Simon.R., “ Antennas and Propagation for Wireless Communication Systems”,Wiley,New York,1999