Performance of the decorrelating multiuser detector in a correlated fading environment

We analyze the performance of the decorrelating multiuser detector for a code-division multiple-access system in a correlated Rayleigh fading environment in terms of the bit error probability (BEP) of an user. The fading gains are independent among the users but correlated among the receive diversity branches. The branches are combined using maximal ratio combining, which requires channel estimation. The channel is estimated by means of pilot symbols, and both maximum likelihood criterion and maximum aposteriori probability criterion are considered. A closed-form expression for the BEP is obtained using a characteristic function approach. Numerical results for the case of exponentially correlated branches and equicorrelated signature waveforms show that (1) the signature cross-correlation has a stronger effect on the performance than the branch correlation, (2) the BEP steadily decreases with increase in the number of branches, and increases with increase in the number of users, rapidly tending to reach saturation as the number of users becomes large.