Derive the relation for the maximum coverage distance in mobile environment

7. Derive the relation for the maximum coverage distance in mobile environment.

The structure of a mobile environment is shown in below figure

Consider a cell site antenna of height ‘h1’ and a mobile antenna of height ‘h2’ is moving away from cell site. The maximum distance up to which, the mobile antenna receives the signal is the maximum coverage distance.

Let the maximum coverage distance is ‘d’. So when mobile antenna moving away from the cell site we can observe two waves of propagation, i.e., direct wave and reflected wave.

Direct wave is the direct propagation from cell site to mobile antenna, without any deviation and the distance travelled by this wave is considered to be (d2), a range ‘φ’ with surface angle φ is known as elevation angle.

Reflected wave is the wave propagated from cell site to surface and then surface to mobile antenna, let the distance travelled by it is ‘d1’ angle done by it with surface is ‘θ’.

Based on direct path and ground reflected path the received power ‘Pr’ is given by

P0 = Transmitted Power,

d = Maximum coverage distance,

av = Reflection coefficient.

Δφ = The phase difference between direct path and reflected path

λ=Wave length.

Second

ΔG = 20 log (he/h1) …………(5)

Where, h1= Height of the cell antenna

he = Effective antenna height

= (h1 + h2) and

ΔG is the gain in decibels obtained from two different antenna heights at the cell site.

Hence, equation (5) represents, equation for the system gain.