In this paper, data estimation in the uplink of a synchronous mobile radio system applying CDMA is considered. In mobile radio systems applying CDMA, multipath propagation leads (on the one hand) to intersymbol interference and (on the other hand), together with time variance, to cross interference between the signals of different users regardless of whether the user codes are chosen orthogonal or not. A linear unbiased data estimation algorithm is presented which eliminates both intersymbol interference and cross interference perfectly by jointly detecting the different user signals, thus leading to unbiased estimates of the transmitted data symbols. This algorithm is less complex than MLSE performed, e.g., by the Viterbi algorithm. Furthermore, the complexity does not depend on the kind of the applied linear modulation scheme, which opens a simple way to offer services with different data rates in one system. By theoretical analysis and simulation, the performance of the linear unbiased data estimation algorithm is examined under the assumption that the radio channel impulse responses are known at the receiver. The price to be paid for the interference elimination are SNR degradations, which are calculated for typical mobile radio situations in urban areas. The resulting average uncoded bit error probabilities lead to the conclusion that systems applying the linear unbiased data estimation algorithm are well suited for mobile radio applications.