Suppose two users in a Direct Sequence-CDMA system have signatures (that is, sequences of chips) given by (1 -1 1 -1) and (1 1 -1 -1), respectively.
(a) Evaluate the correlation between the two signatures.
(b) Sketch the baseband signals for the two users when user 1 sends the bits 011, and user 2 sends the bits 101. Add the signals for the first bit only, and show that the output of the correlator for user 1 is -4, corresponding to a 0, and the output of the correlator for user 2 is 4, corresponding to a 1.
(c) Suppose now that user 2 is assigned the signature (1 -1 1 1). Adding the signals as in part (b), what is the output of the correlator for user 1 for the first bit? Explain the effect of changing the signature in terms of the likelihood of making an error when additional noise and interference is present.