Free-Space Path Loss (FSPL) in Wireless Links

Free Space means a propagation medium for electromagnetic (EM) signal such as space, air, or vacuum; whereas Free-Space path loss (FSPL) means the attenuation of EM energy as it propagates through free space. Mathematical modelling of FSPL assumes that following conditions are being met by the transmission medium:

• Medium is free of any obstruction that might resist the propagation of electromagnetic energy.
• EM signal travels along line-of-sight (LOS) path between transmitting and receiving antenna.

Next, let’s develop mathematical equation to calculate FSPL between a transmitting and receiving antenna. Note that mathematical model of FSPL includes two effects:

1. The reduction of power density of EM signal as it spreads in all directions from the source of EM energy.
2. The efficiency of receiving antenna in receiving the incoming EM signal.

For the first effect, lets suppose that we have an isotropic radiator that radiates EM energy uniformly in all directions, which creates spheres around the source having constant power densities on the surfaces. And this constant surface power density for a particular sphere is inversely proportional to the surface area of sphere, which means that power density is also inversely proportional to the distance between the source and surface (that is equal to the radius of the sphere). This relationship is termed as inverse square law and can be expressed as:

S= Power density at a distance d, in W/m²

P_t = transmitted power in Watts

d = distance between transmitting and receiving antenna in meters

Next, the efficiency of the receiving antenna in receiving EM energy depends upon the frequency of the signal:

P_r = Received Power in W/m²

c = speed of light in m/s

f = frequency of EM signal in Hz

Now, FSPL is expressed as a ratio of P_t and P_r :

Now, converting above equation to dB format:

Where in last equation, frequency is expressed in GHz, distance is expressed in km and FSPL in dB.