Convergence analysis of LMS multiuser CDMA detectors

The convergence behaviour of the LMS CDMA multiuser detector is of great interest both in practice and in theory. The sampling rate for the tap-input of a LMS detector may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally-spaced (FS) detection, respectively. It is shown in this paper that CS and FS detectors with the same time-span exhibit identical convergence behaviour, if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of transient behaviour, and the influence of the initial tap weight vector on convergence speed, are highlighted. Specifically, initialization within the signal subspace or to the origin leads to very much faster convergence compared to initialization in the noise subspace