i$.$Suppose that in a WiFi system using a subchannel width of $312\mathrm{.}5$ kHz and a cyclic prefix of $0\mathrm{.}4$s there are $180$ subchannels carrying user data. If $64$QAM is used, show that the total bit rate is $300$ Mbit s$1.$

$4$ marks

ii$.$If a cyclic prefix of $1\mathrm{.}6$s were used in the above example, what would the bit rate be$?$

$2$ marks

iii.In a few sentences $($with no calculations$),$ explain why changing the cyclic prefix has affected the bit rate in the way shown in your answers to $($i$)$ and $($ii$)$

$2$ marks