Currently, code-division multiple access (CDMA) technique continues to be a dominant air-interface technology for personal wireless communication systems. Mobile communication systems based on CDMA is always subject to multiple access interference (MAI) problem due to the difficulty in maintaining orthogonality of CDMA signals in a mobile environment. MAI which limits the system capacity of the CDMA systems and leads to strict power control requirements to alleviate the near-far problem can be solved by multiuser detection (MUD) technique through exploiting the information of signals from other interfering users. Meanwhile, MUD and power control problem are the root-finding procedure for solving systems of linear algebraic equations. It is well known that the iterative method is used for solving a set of linear equations corresponding to linear interference cancellation, one of MUD structures. In this thesis, the preconditioned iterative symmetric successive overrelaxation (SSOR) method as well as a new evolutionary computation technique particle swarm optimization (PSO) linear interference cancellation technique are suggested to solve MAI with simplified computational complexity. Finally, a preconditioned power control algorithm is introduced for realistic CDMA systems to solve the near-far problem with drastically fast convergence speed. Simulation results show that the SSOR preconditioner is a powerful tool for solving the problem of MUD and power control in CDMA systems and PSO is a great approach for MUD as well.