$($a$)$ If the CO wants to send the bit streams $\text{'}1011\text{'},\text{'}0110\text{'}$ and $\text{'}0010\text{'}$ to home $\backslash$#$1,\backslash$#$2$ and $\backslash$#$3$ respectively, draw the transmitted signal waveform at the CO assuming an average signal power of $1$ W $,$ Unipolar NRZ pulse shape and a total bit rate of $\backslash (5\backslash$mathrm$\{$~Gb$\}/\backslash$mathrm$\{$s$\}\backslash ).$

$($b$)$ Calculate the received power $\backslash ($ P$\_\{$r $1\}\backslash )$ at home $\backslash$#$1.$

$($c$)$ Let the thermal noise power at the receiver be $0\mathrm{.}0333$ W $.$ For a bit error ratio$($BER$)$ threshold of $\backslash (10^\{-3\}\backslash ),$ can the signals be successfully recovered at the homes? The dependence of BER on SNR for Unipolar NRZ systems are shown in Figure Q$5.$

$($d$)$ For a BER threshold of $\backslash (10^\{-3\}\backslash ),$ what is the longest distance between home $\backslash$#$1$ and splitter that the FTTH system can support?

$($e$)$ Let the distance between all the homes to the splitter be $5$ km $.$ In this case, how many more homes can this FTTH system support?

$($f$)$ If the splitter has a bandwidth of $15$ GHz $,$ does it change your answer in $($e$)?$

$($g$)$ Propose one change in the system to support more homes than your answer in $($e$).$ Explain your reasoning.