Multiple-access interference plus noise-constrained least mean square (MNCLMS) algorithm for CDMA systems

Since multiuser code-division multiple-access (CDMA) communications systems suffer significantly from multiple-access interference (MAI) and from classical white Gaussian noise, it is therefore necessary to consider their impact on the performance of these systems. It is well known that the learning speed of any adaptive filtering algorithm is increased by adding a constraint to it. In this paper, a constrained least-mean-square (LMS) algorithm, which incorporates the knowledge of the number of users, spreading sequence length, and additive noise variance, is developed subject to the new combined constraint comprising the MAI and noise variance for a synchronous downlink direct-sequence CDMA system. The novelty of this constraint resides in the fact that the MAI variance was never used as a constraint. In our approach, a Robbins-Monro algorithm is used to minimize the conventional mean-square-error criterion subject to the variance of the new constraint (MAI plus noise). This constrained optimization technique results in an (MAI plus noise)-constrained LMS (MNCLMS) algorithm. The MNCLMS algorithm is a type of variable step-size LMS algorithm where the step-size rule arises naturally from the constraints on MAI and noise variance. Convergence and tracking analysis of the proposed algorithm are carried out in the presence of MAI. Finally, a number of simulations are conducted to compare the performance of the MNCLMS algorithm with other adaptive algorithms.