Consider that a $100-$kbit$\frac{s}{s}$ data stream is to be transmitted on a voice$-$grade telephone circuit $($with a bandwidth of $3$ kHz $).$ Is it possible to approach error$-$free transmission with an SNR of $10$ dB $?$ Justify your answer. If it is not possible, suggest system modifications that might be made. $[20$ POINTS$]$

Consider a telephone modem operating at $28\mathrm{.}8$ kbits that uses trellis$-$coded QAM modulation. $[20$ POINTS$]$

a$.$ Calculate the bandwidth efficiency of such a modem, assuming that the usable channel bandwidth is $3429$ Hz $.$

b$.$ Assuming AWGN and an available $\frac{E_b}{N_0}=10dB,$ calculate the theoretically available capacity in the $3429$ Hz bandwidth.

c$.$ What is the required $\frac{E_b}{N_0}$ that will enable a $3429$ Hz bandwidth to have a capacity of $28\mathrm{.}8$ kbits$/$s$?$

How many loop filters are there in a typical digital communication system used for synchronization? List ALL of them. $[20$ POINTS$]$

Spread$-$spectrum techniques can be used to meet government regulations regarding flux $($power$)$ density radiating the surface of the earth. If a satellite at synchronous altitude $(36,000km)$ transmits $4$kbit$\frac{s}{s}$ data using $100$ W of EIRP, what spreading bandwidth is required to maintain a flux density on the earth's surface no greater than $151dB\frac{W}{m^2}$ in any $4$ kHz band? $[20$ POINTS$]$

In the allocation of the communications resource, state the basic ways of distributing communications resource in a digital communication system? $[20$ POINTS$]$