You are tasked with designing a wireless communication system that transmit data from a base station to a personal receiver $($possibly some form of a smart watch$)$ at distance of up to $10$ km $.$ The system is required to transmit $\backslash (1\backslash$mathrm$\{$Mbit$\}/\backslash$mathrm$\{$s$\}\backslash )$ data at a center frequency of $3$ GHz with a maximum BER of $\backslash (10^\{-7\}\backslash ).$ The modulation is binary DPSK$,$ and the receiver ratio $\backslash ($ G $/$ T$^\{\backslash$circ$\}\backslash )$ in dB is $\backslash (-30\backslash$mathrm$\{$~dB$\}/\backslash$mathrm$\{$K$\}\backslash ).$ Since the receiver is moving it must have a fade margin of $12\mathrm{.}5$ dB $.$

a$)$ Assuming free$-$space propagation, determine the minimum transmit EIRP required for this system.

b$)$ The minimum height of the receiver is assumed to be $1$ m from the ground. Calculate the required height of the base station transmitter such that the free$-$space propagation can be used.