Mumbai University > Electronics and Telecommunication > Sem 7 > Mobile Communication

Marks: 5M

Year: Dec 2014

1.Consider a mobile moving at constant velocity v along a path segment having length d between points x and y while it receives signal from remote source s as illustrated in figure below.

The difference in path length traveled by the wave from source s to the mobile at points x and y is ∆l = d cos⁡θ = u∆t cos⁡θ where ∆t is time required to travel from x to y and θis assumed to be same at points x and y since source is assumed to be very far away.

2.The phase change in received signal due to difference in path length is therefore

$$∆φ = \frac{2π∆l}{δ} = \frac{2πv∆t}{δ} cos⁡θ$$

Doppler’s shift is nothing bur apparent change in frequency, which is given as $f_d$

$$f_d = \frac{1}{2π} \frac{∆φ}{∆t} = \frac{u}{δ} cos⁡θ$$

Above equation relates Doppler’s shift to mobile velocity and spatial angle between direction of motion of mobile and direction of arrival of wave.

3.From above equations it can be seen that if mobile is moving towards the direction of arrival of wave the Doppler shift is positive that is the apparent received frequency is increased.

4.And if the mobile is moving away from direction of arrival of wave then the Doppler shift is negative that is apparent received frequency is decreased. The multipath component of cw signal which arrive from different directions contribute to Doppler spreading of received signal thus increasing the signal bandwidth.