A wireless communication link needs to be established between a transmitter and a receiver separated by a distance of $40$ km$.$ The available transmission power at the source is $5$ kW$,$ and the system operates at a frequency of $18$ GHz$.$ At each repeater, the transmission power is reduced by $4$ dB relative to the source power. The signal transmission bandwidth is $15$ MHz$,$ and both the transmitter and receiver antennas, as well as the repeaters, have a gain of $45$ dBi. How many repeaters are necessary to maintain communication across the link