$($a$)$ Find the equivalent parallel channel model for a MIMO channel with channel gain matrix $([0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}2],[0\mathrm{.}2,0\mathrm{.}1,0\mathrm{.}2],[0\mathrm{.}2,0\mathrm{.}2,0\mathrm{.}1]).$

$($b$)$ Find the capacity and optimal power allocation for the MIMO channel in the previous part, assuming SNR $=10dB$ and bandwidth as $1$ Hz $.$