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Optimization of the capacity of a single-cell code-division multiple-access (CDMA) system, both from the perspective of the maximum number of users that can be served at a required quality of service level and from the information theoretic perspective, has been recently shown to be achieved by the same joint transmit and receive strategies. We propose an alternating minimization based iterative algorithm that updates the transmitters and the corresponding receivers of the users. The algorithm is suitable for online implementation, and the objective function is suitable for extension to multicell networks, both of which are in contrast with the previously proposed algorithms. We show that the algorithm is provably convergent to the optimum signature sequences and the corresponding receivers.