Figure depicts the direct (line-of-sight) and indirect (reflected) paths of a radio link operating over a plane

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Figure depicts the direct (line-of-sight) and indirect (reflected) paths of a radio link operating over a plane earth. The heights of the transmitting antenna at the base station and the receiving antenna of a mobile unit are hb and hm respectively. Assume the following:

The reflection coefficient of the ground is – 1.

The distance d between the two antennas is large enough to make the phase difference Φ between the reflected and direct paths small compared to 1 radian, so that we may set sin Φ  Φ.

Hence, show that the received power P. is given by the approximation where Pt, is the transmitted power, and Gb and Gm are the power gains of the transmitting base and mobile antennas, respectively. Compare this result with the Friis free-space equation.

P,G,G P, - m d? hь d- 1589

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