Answer: Doppler Shift:-There is always a relative motion between the cell-site transmitter and the mobile receiver. As a result Doppler effect occurs in the shift of the received carrier frequency. Doppler spectrum is the spectrum of the fluctuations of the received signal strength.

Multipath fading provides the distributions of the amplitude of a radio signal a signal strength will be  a pre-defined threshold value that is, the duration of fade, and it crosses a threshold value that is frequency of transitions or fading rate. Doppler effect results in the inaccurate operation of the system. Proper compensation technique needs to be implemented to minimise this effect. A study of Doppler spectrum is important to design the coding and interleaver schemes for efficient performance.

Thus multipath propagation, speed of mobile unit, speed of reflecting objects, and Doppler shift are the main causes of fading. Multipath propagation can result in positive or negative Doppler shift. As mobile unit moves around, the resulting multipath reception of waves reflected from different objects can also result in a positive or negative Doppler shift. The Rayleigh distribution is often used to model the received enve-lope of such a signal in a statistical time-varying way. Rayleigh fading is also called multipath fading in the mobile radio environment. Speed of reflecting objects can induce their own Doppler shift in the reflected wave.

Doppler frequency or Doppler shift is given by

$\mathrm{f_d= \dfrac{1}{\lambda _c} V_m \ \cos \theta }........(1)$

where$\mathrm{\lambda _c}$ is the wavelength of the carrier signal, $\mathrm{V_m}$is the relative velocity of the mobile, the angle $\mathrm{\theta}$ is between the motion of the mobile and direction of arrival of the scattered waves and $\mathrm{V_m\ \cos \theta}$ represents the velocity component of the motion of the mobile in the direction of the incoming signal. The maximum Doppler frequency will be obtained when the mobile unit is moving in line with the direction of the recened signal. that is, o$\mathrm{\theta = 0^0 \ or \ \cos \theta =1}$ That from Eq. (1), the maximum Doppler frequency is given by

$\mathrm{f_{dm}=\dfrac{V_m}{\lambda _c}=\dfrac{V_m f_c}{c}}..........(2)$

where $f_c$ is the frequency of transmission in $\text{Hz}$, $\mathrm{V_m}$ is the speed of the mobile and$c$ is speed of light in same units. When a pure sinusoidal carrier signal having frequency $f_c$ is transmitted, the received signal spectrum, called the Doppler spectrum.This simply means that Doppler shift will be positive or negative depending on whether the mobile receiver is moving toward or away from the base station transmitter.