$4.$ Recently companies have been touting the $24$GHz unlicensed band for point$-$to$-$point wireless bridge links between rural base stations and the wired core network. A typical design has $33$dBi antennas for both transmission and reception, transmit power of $20$dBm and a receiver sensitivity requirement of $-50$ dBm or greater for a $1$Gbps data rate.

$($a$)$ What is the path loss budget?

$($b$)$ What is the maximum distance for the link assuming an ideal Free Space line of sight model?