Clarke's Model for Flat Fading
- 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 αn 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 E0 is the real amplitude of local average E-field,Cnis a real random variable representing the amplitude of individual waves, η is the intrinsic impedance of free space (377Ω), and fcis the carrier frequency.
- The random phase of the n th arriving component θnis 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