# Hata-Okumura Model

The Hata-Okumura model is a simple empirical approach for macro-cellular areas with vertical polarization. This model features a very short computation time.

The Hata-Okumura model is based on the evaluation of intensive measurements at frequencies between 200 MHz and 2 GHz with vertical polarization. The equations derived from the measurement data require only the following four parameters:

frequency $f$ ,

the distance between transmitter and receiver $d$ ,

antenna height of the transmitter ${h}_{t}$ ,

antenna height of the receiver ${h}_{r}$ .

Figure 1 shows the definition of the effective antenna height:

Because of the calibration with measurement data the Hata-Okumura model is restricted to the following ranges for the different parameters:

(1)
(2)
(3)
(4)

The basic transmission loss in urban areas is then computed according to the following formulas. There is an equation for the basic loss and different correction terms according to different propagation environments (dense urban, suburban and open):

(5) $L=69.55+26.16\text{log}\left(f}{\text{MHz}}\right)-13.82\text{log}\left({h}_{eff}}{\text{m}}\right)-\frac{c\left({h}_{r}\right)}{\text{dB}}+\left[44.9-6.55\mathrm{log}\left({h}_{eff}}{\text{m}}\right)\right]\mathrm{log}\left(\frac{d}{\text{km}}\right)$

where for suburban areas

(6) $c\text{(}{h}_{\text{r}}\right)=\left(1.1\mathrm{log}\left(\frac{f}{\text{MHz}}\right)-0.7\right)\frac{{h}_{\text{r}}}{\text{m}}-\left(1.56\mathrm{log}\left(\frac{f}{\text{MHz}}\right)-0.8\right)$

For urban areas ( ):

(7) $c\left({h}_{r}\right)=8.29{\left[\mathrm{log}\left(1.54\frac{{h}_{r}}{\text{m}}\right)\right]}^{2}-1.1$

For urban areas ( ):

(8) $c\left({h}_{r}\right)=3.2{\left[\mathrm{log}\left(11.75\frac{{h}_{r}}{\text{m}}\right)\right]}^{2}-4.97$

In addition to the formulas for the urban case, there are some modifications for rural (village) and open areas (acre). This leads to the following equations:

(9) ${L}_{rural}=\frac{L}{\text{dB}}-2{\left[\mathrm{log}\left(\frac{f/28}{\text{MHz}}\right)\right]}^{2}-5.4$
(10) ${L}_{open}=\frac{L}{\text{dB}}-4.78{\left[\mathrm{log}\left(\frac{f}{\text{MHz}}\right)\right]}^{2}+18.33\mathrm{log}\left(\frac{f}{\text{MHz}}\right)-40.94$

These formulas describe the wave propagation assuming a flat terrain because the terrain profile between the transmitter and the receiver is not taken into account. If there is, for example, a hill between the transmitter and receiver, the results will not be affected. In addition, local effects around the receiver are neglected (for example, reflection or shadowing).

COST 231 has extended the Hata-Okumura model to the frequency band between 1500 MHz and 2000 MHz by analyzing Okumura's propagation curves in the upper-frequency band. This combination is denoted as the “COST-Hata-Model”1:

(11) $\begin{array}{c}L=46.3+33.9×\mathrm{log}\left(\frac{f}{\text{MHz}}\right)-13.82×\mathrm{log}\left(\frac{{h}_{eff}}{\text{m}}\right)-\frac{c\left({h}_{r}\right)}{\text{dB}}\\ +\left(44.9-6.55×\mathrm{log}\left(\frac{{h}_{eff}}{\text{m}}\right)\right)×\mathrm{log}\left(\frac{d}{\text{km}}\right)+\frac{{C}_{m}}{\text{dB}}\end{array}$

where for medium-sized cities and suburban centers and metropolitan centers.

1 E. Damosso, ed., Digital Mobile Radio: COST 231 View on the Evolution towards 3rd Generation Systems. Bruxelles: Final Report of the COST 231 Project, published by the European Commission, 1998.