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A detector based on a network of Kalman filters (NKF) has recently been proposed for joint multiple access interference (MAI) and intersymbol interference (ISI) compensation in DS-CDMA systems (Sayadi, B. and Marcos, S., ISSSTA'02, vol.2, p.511-15, 2002; ICASSP'03, vol.5, p.37-40, 2003; Sayadi, Ph.D. thesis, Paris Sud University, 2003). It is based on a symbol state space representation of the DS-CDMA system. The NKF-based detector presents an exponential complexity in terms of the Kalman filters (QK, where Q is the number of points in the symbol constellation and K is the number of active users in the system). We propose to linearize the number of Kalman filters used in the structure by combining a hybrid SIC/PIC structure and a reduced NKF based on a reduced state space representation of the DS-CDMA system. The proposed structure involves two steps. The first, called forward step, decodes the users in a serial approach using a SIC structure. The second, called backward step, is based on a hybrid SIC/PIC structure in order to produce better estimates of the transmitted symbols. The new resulting structure based on a reduced forward-backward NKF detector employs 2(K-1)Q Kalman filters. It exhibits better performance than the well known existing SIC-RAKE receiver, especially in channels with a large delay spread.