Optimal adaptive multiuser detection in unknown multipath channels

An optimal multiuser detector in the weighted least squares (WLS) sense is derived. This detector, which includes the maximum likelihood multiuser detector as a special case, consists of two parts: a bank of linear fractionally chip spaced minimum mean squared error (MMSE) filters, and a nonlinear WLS metric minimizer. It is shown that the symbol spaced samples at the output of the MMSE filter bank provide a set of sufficient statistics for WLS detection. The relationship between the taps of a centralized decision feedback detector and the MMSE filter bank is derived. It is proven that all the necessary parameters for implementing the WLS detector can be realized by adaptively training a centralized decision feedback detector. Therefore, the WLS detector achieves optimal joint synchronization and data detection even in the presence of colored noise, such as narrowband interference, without any a priori knowledge of the users' signatures, multipath channel taps or statistics of the colored noise. Significant features of the WLS detector are that: (1) the WLS detector is a generalization of the maximum likelihood multiuser detector that employs a bank of matched filters; (2) it is implemented adaptively; and (3) it has structural flexibility in terms of implementation complexity.