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Abstract-The capacity of conventional wireless communications systems based upon Direct-Sequence Code Division Multiple Access (DS-CDMA) schemes, is mainly limited by Multiple Access Interference (MAI). Therefore, methods aimed at reducing MAI are mandatory solutions to increase the capacity of such systems. Smart Antennas are a promising technology for improving the performance of high capacity mobile communications systems, because they are expected to be able to increase the Signal to Interference plus Noise power Ratio (SINR) of the received signals by dynamically adapting the equivalent array beam pattern in order to track the movements of the users within the cell. In this paper we propose a novel blind adaptive beamforming algorithm tailored for the up-link of multi-code multi-rate DS-CDMA wireless communications systems. Our proposal is based upon a modified Constant Modulus (CM) criterion, whose fundamental feature is the capability to overcome the main drawback of the classic CM algorithm, which lies in its difficulty of ensuring the convergence toward the desired user. The proposed algorithm exploits user-specific information intrinsically known at the receiver, which is the code uniquely associated to each user, without requiring the knowledge of the spatiotemporal propagation channel nor any specific training sequence. Within this paper we present a broadband solution, designed to temporally re-align uncorrelated clusters of multipaths, as well as spatially recombine correlated multipaths belonging to the same cluster. Computer simulations show that our proposed technique can effectively exploit path diversity and multipath correlation, also in the presence of Doppler effect and time-variable propagation conditions.