$1)$ Using DSSS and assuming a data sequence $10010101,$ show graphically the operations in the transmitter and receiver. The locally generated random numbers are $10010110100101001010110010110110.$

What is the length of the spreading code?

What is the relationship between the bit rate of the data sequence before and after it has been encoded using DSSS$?$

$2)$ Consider two user transmitters $($A$,$ B$)$ and a receiving user $($C$)$ using CDMA data d$1=-1,$ d$0=1,$ and a chipping code of $8$ bits. Using a Hadamard matrix:

what should be the $8-$bit CDMA users$$ transmitter codes to prevent interference between them? Show that the selected transmitter codes are orthogonal.

what should be the output of the transmitters $($A$,$ B$)($combined bit values on the channel$)$ and the receiver user $($C$)?$ Assume that only user A needs to be decoded at the receiver.

$3)$ Assume a communication system with Bss $=800$ KHz using the FHSS technique. Compute the bandwidth B of the given system considering a total # of hops of $128.$

$4)$ DSSS using BPSK: Assume the data d$($t$)=-1+1-1+1$ and the spreading code c$($t$)=-1-1+1+1-1+1-1-1-1+1-1-1.$ Draw the corresponding BPSK signal sd$($t$)$ and the spread spectrum signal s$($t$).$