In a frequency hopping communication system, there are five users $($u$1,$ u$2,,$ u$5)$ and five channels $($f$1,$ f$2,$ f$3,$ f$4,$ f$5).$ Assume each user is transmitting one letter $($space is also considered a letter$)$ in each time slot. The information transmitted by each user is as follows. u$1$: The greatest glory in living lies not in never falling u$2$: Getting started is to quit talking and begin doing u$3$: Your time is limited$,$ so don't waste it living someone else's life u$4$: Future belongs to those who believe in the beauty of their dreams u$5$: If you set your goals ridiculously high and it's a failure The frequency hopping sequence of each user is as follow. S$1$ of u$1$: f$1,$ f$2,$ f$3,$ f$4,$ f$5$ S$2$ of u$2$: f$2,$ f$1,$ f$4,$ f$5,$ f$3$ S$3$ of u$3$: f$3,$ f$4,$ f$5,$f$1,$f$2$ S$4$ of u$4$: f$5,$ f$3,$ f$1,$f$2,$f$4$ S$5$ of u$5$: f$4,$ f$5,$ f$2,$f$3,$f$1$Draw an illustration to explain how these letters are transmitted over different channels in different time slots. $[30$pts$]2.$ Given a geosynchronous satellite that is $35,863$ km away from the earth.a$.$ Determine the isotropic free space loss at $4$ GHz$.[10$pts$]$b$.$ Suppose the antenna gains of satellite and ground based antennas are $44$ dB and $48$ dB$,$ respectively, what is the free space path loss? $[10$pts$]$c$.$ Assume the earth station uses a transmission power of $250$ Watt to transmit wireless signals to the satellite, what is the received power at the satellites antenna? $[20$pts$]3.$ A base station $($BS$)$ uses a $900$ MHz transmitter and a vehicle is moving at the speed of $50$ miles per hour. Compute the received carrier frequency, if the vehicle is movinga. Directly toward the BS $[10$pts$].$b$.$ Directly away from the BS$.[10$pts$]$c$.$ In a direction which is $30$ degree to the direction of arrival of the transmitted signal. $[10$pts$]$