For the CDMA communications system of Pro bl em 11. 3. 8,

Chapter 11, Problem 11.35

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For the CDMA communications system of Pro bl em 11. 3. 8, a detection str ategy known as decorrelation applies a transformation to Y to generate 'vhere N = (S'S)- 1S'N is still a G~ussian noise vector with expected value E[N] = 0 . Decorrelation separate_s the signals in that the ith component of Y is 'vhich is the same as a single-user receiver output of the binary communication system of Example 11.6. For equally likely inputs Xi= 1 and Xi= -1, Example 11.6 showed that the optimal (minimum probability of bit error) decision rule based on the receiver output Yi is xi = sgn (Yi). Although this technique requires the code vectors Si, . .. , S k to be linearly independent, the number of hypotheses that must be tested is greatly reduced in comparison to the optimal ML detector introduced in 11.3.8. In the case of linearly independent code vectors, is the decorrelator optimal? That is, does it achieve the same bit error rate (BER) as the optimal ML detector?