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Question#1

Find the median path loss under the Hata model assuming

fc = 900 MHz, ht = 20m, hr = 5 m and d = 100m for a large urban city, a small urban city, a suburb, and a rural area. Explain qualitatively the path loss differences for these 4 environments.

Solution for Question#1

In this question, we are given the following parameters:

-f c = 900 MHz

-ht = 20m

-hr = 5 m

- d = 100m- Large urban city :

The standard formula for empirical path loss in urban areas under the Hata model is (equation#1)

PL,urban (d ) dB = 69 .55+26 .16 log10( f c)-13 . 82 log10(ht )-a(hr )+(44 .9-6 .55 log10(ht )) log10(d ).

But a (hr ) is a correction factor for the mobile antenna height based on the

size of the coverage area. So, for large urban city

a (hr )= 3 . 2( log10(11.75hr ))2 - 4 .97 dB.

Substitute a (hr ) and the given parameters in equation#1 will give:

PL,urban(d ) = 69.55+234.24-17.98—10.01+4.97+89.8-17.4

PL,L arg e Urban City= 353.52 dB

Small urban city :

The use equation#1 But a (hr ) is given by

a (hr )=(1.1 log10( f c) - . 7 )hr - (1 .56 log10( f c ) - . 8)dB,

Substitute a (hr ) and the given parameters in equation#1 will give:

PL,urban(d )= 69.55+234.24-17.98-45.75+13.17+89.9-17.04

PL,Small Urban City= 325.99 dB

Suburb :We use

PL,suburban (d )= PL,small urban city(d ) - 2 [ log10( f c /28)]2 - 5 . 4

We have

- PL,Small Urban City= 325.99 dB

- f c = 900 MHz

Then we will get

PL,suburban (d )= 325.99-112.71-5.4

PL,suburban (d )= 207.88 dB

Rural area :We use

PL,Rural (d )= PL,Small Urban City ( d ) - 4 .78 [ log10( f c ) ]2 + 18 .33 log10( f c ) - K,

We have

- PL,Small Urban City= 325.99 dB

- = 900 MHz

- K ranges from 35.94 (countryside) to 40.94 (desert)

In the case of K=35.94 (countryside), we will have

=325.99-383.25+164.13-35.94

=70.93 dB

In the case of K=40.94 (desert), we will have

= 325.99-383.25+164.13-40.94

= 65.93 dB

Since reflection, diffraction and scattering are the three basic propagation mechanisms which impact propagation in a wireless or mobile communication system, and then path loss is affected by these three propagation mechanisms. So, from our results shown above path loss is higher in lager urban city where many reflectors, diffractors and scatterers are appear and low in rural area where there are few reflectors, diffractors and scatterers. Consequently, path loss state (value) depends on the number of reflectors, diffractors and scatterers in the area where the path loss to be measured.