Given an LTE network with $10$MHz spectrum, if $64$ QAM is used,

a$)$ Estimate the peak down link throughput without consideration of Multi$-$Input Multi$-$Output $($MIMO$)$ and include all $14$ OFDM symbols in a subframe.

b$)$ If $4$x$4$ MIMO is used in down link, what would be the peak DL throughput?

c$)$ If in average the first $3$ OFDM symbols in each subframe are reserved for carrying the control signals $($as was indicated in the footnotes of slide $16$ in Lecture Outlines$),$ what would be the peak DL throughput to transport the user traffic?