Free-Space Path Loss of Wireless Communication Channel

Free-Space Path Loss of  Wireless Communication Channel

4G Communications

Consider a signal transmitted through free space to a receiver located at distance d from the transmitter. Assume there are no obstructions between the transmitter and receiver and the signal propagates along a straight line between the two. The channel model associated with this transmission is called a line-of-sight (LOS) channel, and the corresponding received signal is called the LOS signal or ray. Free-space path loss introduces a complex scale factor, resulting in the received signal

where  

square root of(G1) is the product of the transmit and receive antenna field radiation patterns in the LOS direction. The phase shift exp(-j 2πd/λ) is due to the distance d the wave travels. The power in the transmitted signal s(t) is Pt, so the ratio of received to transmitted power from previous equation is 

Thus, the received signal power falls off inversely proportional to the square of the distance d between the transmit and receive antennas. for other signal propagation models, the received signal power falls off more quickly relative to this distance. The received signal power is also proportional to the square of the signal wavelength, so as the carrier frequency increases, the received power decreases. This dependence of received power on the signal wavelength λ is due to the effective area of the receive antenna. However, directional antennas can be designed so that receive power is an increasing function of frequency for highly directional links. The received power can be expressed in dBm as 

Free-space path loss is defined as the path loss of the free-space model:

The free-space path gain is thus

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