Problem $5$

For a two$-$users CDMA system, assume that user $1$ has spreading code $s_1=(1,1,1,1)$ and for user $2s_2=(1,-1,1,-1).$ Now, assume that users $1$ and $2$ transmit information bits $b_1=\{1,-1,-1,1\}$ and $b_2=\{1,1,-1,1\}.$

$($a$)$ What will the signal transmitted by users $1$ and $2$ be$?$

$($b$)$ If both users transmit simultaneously, what would the signal at the receiver be$?$

$($c$)$ Assuming that the receiver knows the spreading codes of both users, how can the receiver determine the transmitted information bits by users $1$ and $2?$