**Subject :**Wireless Communication

## Clarke's Model for Flat Fading

**Clarke model**

- The model assumes a fixed transmitter with a vertically polarized antenna.
- The field incident on the mobile antenna is assumed to be comprised of N azimuthal plane waves with arbitrary carrier phases, arbitrary azimuthal angles of arrival, and each wave having equal average amplitude.
- The equal average amplitude assumption is based on the fact that in the absence of a direct line-of-sight path, the scattered components arriving at a receiver will experience similar attenuation over small-scale distances.
- Figure shows a diagram of plane waves incident on a mobile traveling at a velocity v, in the x-direction.

For the nth wave arriving at an angle α_{n} to the x-axis, the Doppler shift in Hertz is given by

λ is the wavelength of the incident wave

- The vertically polarized plane waves arriving at the mobile have E and H field components given by

where E_{0} is the real amplitude of local average E-field,C_{n}is a real random variable representing the amplitude of individual waves, η is the intrinsic impedance of free space (377Ω), and f_{c}is the carrier frequency.

- The random phase of the n th arriving component θ
_{n}is given by

- The amplitudes of the E-and H-field are normalized such that the ensemble average of the C
_{n}'s is given by