$7.$ Consider a multiple$-$input multiple$-$output $($MIMO$)$ system with $\backslash ($ N$\_\{$t$\}\backslash )$ number of transmitter antennas and $\backslash ($ N$\_\{$r$\}\backslash )$ number of receiver anternnas.

$($a$)$ What are the dimensions of the channel matrix?

$($b$)$ If this MIMO channel is decomposed into virtual parallel channels using singular value decomposition $($SVD$),$ how many parallel channels can we obtain?