$3.$ Consider the following modulation scheme.

Where $\backslash (\backslash$mathrm$\{$d$\}\_\{3\}\backslash$mathrm$\{$~d$\}\_\{2\}\backslash$mathrm$\{$~d$\}\_\{1\}\backslash$mathrm$\{$~d$\}\_\{0\}\backslash )$ is the binary symbol representation varying from $0000$ to $1111$ and $\backslash (\backslash$phi$\_\{$i$\}=\backslash$mathrm$\{$i$\}^\{*\}(\backslash$pi $/8)\backslash )$

a$)$ Draw the constellation diagram for this system indicating the $16$ I$/$Q constellation points and the angle of each point.

b$)$ What type of modulation is used in this system $($e$.$g$.4-$ASK, $8-$PSK$,$ FSK$,$ etc..$)?$

c$)$ Assuming a channel bandwidth of $1$ MHz $.$ Calculate the maximum channel capacity $($Shannon Capacity$)($Mbps$)$ assuming a target SER of $1$E$-6$ and the minimum SNR required achieving the target SER for the above modulation scheme $($see fig. below$).$

d$)$ Based on Shannon Capacity, what is the required SNR to achieve a max capacity of $12$ Mbps $?$