In this problem, we evaluate the bit error rate (BER)

Chapter 11, Problem 11.41

(choose chapter or problem)

In this problem, we evaluate the bit error rate (BER) performance of the CDJVIA communications system introduced in 11.3.8. In our experiments, we \Vill make the follo,ving additional assumptions. In practical systems, code vectors are generated pseudorandomly. We \Vill assume the code vectors are random. For each transmitted data vector X , the code vector of user i \vill be Si = 1 [ ] I ~ S i1 S i 2 S in , \Vhere the components S ij are iid random variables such that Psi. 1(1) = Psij(-l) = 1/ 2. Note that the factor 1 / fa is used so that each code vector Si has length 1: II Si 11 2 = s~si = 1. Each user transmits at 6dB SNR. For convenience, assume Pi = p = 4 and a 2 =1. (a) Use MATLAB to simulate a CD Mi\. system 'vith processing gain n, = 16. For each experimental trial, generate a random set of code vectors {Si}, data vector X , and noise vector N . F ind the l\/IL estimate x* and count the number of bit errors; i.e., the number of positions in which : : ei =J.:. xi. use the relative frequency of bit errors as an estimate of the probability of bit error. Consider k = 2, 4, 8, 16 users. For each value of k, perform enough trials so that bit errors are generated on 100 independent trials. Explain \vhy your simulations take so long. (b) For a simpler detector known as the matched filter, when Y = y , the detector decision for user i is where sgn (x) = 1 if x > 0, sgn(x) -1 if x < 0, and otherwise sgn (x) 0. Compare the bit error rate of the matched filter and the maximum likelihood detectors. Note that the matched filter is also called a single user detector since it can detect the bits of user i \Vi thou t the kno\v ledge of the code vectors of the other users.