Hata model

[logistic_guy]

Find the median path loss under the $\displaystyle \text{Hata}$ model assuming $\displaystyle f_c = 900 \ \text{MHz}, h_t = 20 \ \text{m}, h_r = 5 \ \text{m}, \text{and} \ d = 100 \ \text{m}$ for a large urban city, a small urban city, a suburb, and a rural area. Explain qualitatively the path-loss differences for these four environments.

 

[logistic_guy]

$\displaystyle \text{Hata}$ model is given by:

$\displaystyle P_L = 69.55 + 26.16\log_{10}(f_c) - 13.82\log_{10}(h_t) - a(h_r) + (44.9 - 6.55\log_{10}(h_t))\log_{10}(d)$

where $\displaystyle a(h_r) = 3.2(\log_{10}(11.75h_r))^2 - 4.97$ for large cities.

 

[logistic_guy]

Find the median path loss for a large urban city.

$\displaystyle P_L = 69.55 + 26.16\log_{10}(f_c) - 13.82\log_{10}(h_t) - [3.2(\log_{10}(11.75h_r))^2 - 4.97] + (44.9 - 6.55\log_{10}(h_t))\log_{10}(d)$


$\displaystyle = 69.55 + 26.16\log_{10}(900000000) - 13.82\log_{10}(20) - [3.2(\log_{10}(11.75[5]))^2 - 4.97] + (44.9 - 6.55\log_{10}(20))\log_{10}(100) = \textcolor{blue}{353.53 \ \text{dB}}$

 

[logistic_guy]

Find the median path loss for a small urban city.

$\displaystyle P_L = 69.55 + 26.16\log_{10}(f_c) - 13.82\log_{10}(h_t) - [(1.1\log_{10}(f_c) - 0.7)h_r - (1.56\log_{10}(f_c) - 0.8)] + (44.9 - 6.55\log_{10}(h_t))\log_{10}(d)$


$\displaystyle = 69.55 + 26.16\log_{10}(900000000) - 13.82\log_{10}(20) - [(1.1\log_{10}(900000000) - 0.7)5 - (1.56\log_{10}(900000000) - 0.8)] + (44.9 - 6.55\log_{10}(20))\log_{10}(100) = \textcolor{blue}{325.99 \ \text{dB}}$

 

[logistic_guy]

Find the median path loss for a suburb,

$\displaystyle P_{L} = 325.99 - 2\left[\log_{10}\left(\frac{900000000}{28}\right)\right]^2 - 5.4 = \textcolor{blue}{207.88 \ \text{dB}}$

 

[logistic_guy]

Find the median path loss for a rural area.

$\displaystyle P_{L} = 325.99 - 4.78\left[\log_{10}(900000000)\right]^2 + 18.33\log_{10}(900000000) - 35.94 = \textcolor{blue}{70.93 \ \text{dB}}$

 

[logistic_guy]

Explain qualitatively the path-loss differences for these four environments.

If we start from our last result and go upward, we see an increase in the path loss. Why this happens? The path loss increases when multiple reflectors, diffractors, and scatterers are present.