Free Space Propagation Model
The free space propagation model is used to predict received signal strength when the transmitter and receiver have a clear, unobstructed line-of-sight path between them. Satellite communication systems and microwave line-of-sightradio links typically undergo free space propagation
Friis free space equation:
- Pr(d)=Received power;
- Pt =Transmitted power ;
- Gt&Gr =Tx& Rx antenna gain respectively
- λ= wavelength;
- D =Distance;
- L = loss Factor
The gain of an antenna is related to its effective aperture Ae , by
The effective aperture Ae is related to the physical size of the antenna
λ is related to the carrier frequency by
- f = carrier frequency in Hertz;
- wc= carrier frequency in radians per second;
- C= speed of light given in meters/s.
This implies that the received power decays with distance at a rate of 20 dB/decade
An isotropic radiator is an ideal antenna which radiates power with unit gain uniformly in all directions, and is often used to reference antenna gains in wireless systems. The effective isotropic radiated power (EIRP) is defined as
It represents the maximum radiated power available from a transmitter in thedirection of maximum antenna gain, as compared to an isotropic radiator.
The path loss, which represents signal attenuation as a positive quantity measured in dB, is defined as the difference (in dB) between the effective transmitted power and the received power, and may or may not include the effect of the antenna gains.
The path loss for the free space model when antenna gains are included is given by
When antenna gains are excluded, the antennas are assumed to have unity gain, and path loss is given by
The far-field, or Fraunhoferregion, of a transmitting antenna is defined as the region beyond the far fielddistance df, which is related to the largest linear dimension of the transmitter antenna aperture and the carrier wavelength.
The Fraunhofer distance is given by
the Friis equation is not defined for d=0. For this reason, we use a close in distance, do, as a reference point. The power received, Pr(d), is then given by:
Pr(d) = Pr(do)(do/d)2