Gugrajah_Yuvaan_ Ramesh_2003.pdf

Simulation ofa Load Balancing Routing Protocol Chapter 3
To determine radio propagation, assuming the antennas used are isotropic (radiates
equally in all directions), the ratio of the power radiated by the transmit antenna to
the power available at the receive antenna is known as the path loss. The minimum
loss on any given path occurs between two antennas when there are no intervening
obstructions and ground losses. In such a case, when the receive and transmit
antennas are isotropic, the path loss is known as free space path loss. The power
received (Pr) by an antenna with gain Gr from a transmitter transmitting with power
Pt and having a gain G" when the antennas are separated at a distance d apart is given
by the Friis transmission equation [JanOl]
(3-4)
where A·is the wavelength with the same units as d. Equation 3-1 can be simplified to
where K I is a constant.
Pt
P (d) = K I -
r d 2 (3-5)
The Friis model is valid providing the distance d exceeds the far-field distance or
Fraunhofer distance df where d f = (2D 2 )/'A and D is the largest physical dimension of
the antenna. Since the Friis equation does not hold for d = 0, a received power
reference point, dref is chosen such that d > dref > d f • The reference distance for
practical systems using low-gain antennas in the 1-2 GHz region is usually chosen to
be 1m in an indoor environment and between lOOm or 1km in outdoor environments.
With reference to Figure 3-4, when the distance d between the receive and transmit
antennas is much greater than the product of the height above ground of the receive
(hr) and transmit (hr) antennas, the low angle of incidence of the radio wave allows
the earth to act as a reflector. The reflected signal could be out of phase and the
ground ray destructively interferes with the line-of-sight path. The two-ray ground
reflection model considers both the direct path and the reflected path, resulting in a
3-10