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The paper deals with the design of a receiver for synchronous multi-carrier direct-sequence code division multiple access (MC-DS-CDMA) systems, in time-varying frequency selective fading channels. We consider a structure operating in two steps; after channel compensation and time alignment along each carrier, the resulting signals are combined and define the input of the blind adaptive multiuser detector. Our contribution is twofold. First, we propose a generalization of the blind least mean squares (LMS) algorithm on the basis of multiple delayed input signal vectors, which has the advantage of improving the convergence features in a high multiple access interference (MAI) environment and time-varying fading scenario. In addition, we carry out a comparative study between the proposed algorithm and previously published blind LMS and blind Kalman filter algorithms. Simulation results show that the proposed algorithm can trade-off performance with complexity. In other words, it can have a better performance than the existing blind LMS algorithm and less computational complexity than the blind Kalman filter algorithm.