The Kalman filter as the optimum MMSE multiuser CDMA detector

Abstract

It is shown that t h e Kalman filter implements t h e exact linear MMSE filter i n an asynchronous multiuser CDMA system, given a n y detection delay. T h e Kalman filter is a finite-order recursive filter as opposed to the well-known tapped-delay line (TDL) MMSE filter, which must grow in length with increasing time a n d is therefore not practically implementable. Our result is useful as a baseline for comparison with o t h e r linear detectors, and m a y lead to adaptive detectors with (soft) feedback.