P$3.$ A wireless link between is established between a transmitting and a receiving system,

located at a distance of $10$ km from each other, at a frequency of $5$ GHz$.$ The transmitted

power is PT $=10$W$.$ At the receiving end it is required to have a power of $0\mathrm{.}1$mW

available at the antenna terminals. Assume that for convenience your transmitting and

receiving antennas are identical.

$($a$)$ What is the antennas$$ gain $($in dB$)$ needed for such a link? $($Assume you have

matched the transmitted and received polarization, and that the antenna impedances are

matched to the transmission line impedances to avoid reflections.$)$

$($b$)$ What is the antennas$$ effective aperture?