The Kalman filter as the optimal linear minimum mean-squared error multiuser CDMA detector

In this paper, it is shown that a first-order linear state-space model applies to the asynchronous code-division multiple-access (CDMA) channel, and thus the Kalman filler produces symbol estimates with the minimum mean-squared error (MMSE) among all linear filters, in long- or short-code systems for a given detection delay. This result may be used as a benchmark against which to compare the performance of-other linear detectors in asynchronous channels. It also reveals that a time-varying recursive biter with a fixed and finite complexity implements the tired-lag linear MMSE (LMMSE) detector, which hitherto has been assumed to require a processing window (and hence complexity) that grows with time.