$(4)[20$ points$]$ A satellite transponder supports multiple earth stations based on the time division multiple access $($TDMA$)$ scheme. The system parameters are provided as following. Note that system parameters are simplified for your easy calculation even without the calculator $($not practical values$).$

$-$ Bit rate $($BPSK$)$: $100$ bits$/$second

$-$ Frame length: $156$ seconds

$-$ Preamble per each data burst $($for each earth station$)$: $200$ bits

$-$ Guard time after each data burst $($for each earth station$)$: $1$ second

We consider two scenarios where both scenarios use three frames, that is$,156[$seconds$/$frame$]\backslash (\backslash$times $3\backslash )[$frames$]\backslash (=468\backslash )$ seconds in total $.$

Scenario$-($a$)$ Supporting four earth stations $($ESs$)$: ES$-1,$ ES$-2,$ ES$-3$ and ES$-4$ in the first frame. Then supporting another four: ES$-5,$ ES$-6,$ ES$-7$ and ES$-8$ in the second frame. Finally, supporting ES$-9,$ ES$-10,$ ES$-11$ and ES$-12$ in the third frame.

Scenario$-($b$)$ Supporting all $12$ ESs: ES$-1,$ ES$-2,...,$ ES$-11,$ ES$-12$ in each frame during three frames.

In each scenario, describe the capacity of one earth station $($ES$)$ in terms of the effective data rate with the unit $[$bits$/$second$].$

Which scenario is better than the other, if both are feasible? Describe the reason for that.