Currently, code-division multiple access (CDMA) techniques are being applied to third generation systems. In wireless CDMA systems, the orthogonality of CDMA signals cannot be maintained in a fading channel so that all mobiles will interfere with each other. In order to improve system capacity and the quality of communication service, CDMA systems utilize multiple access interference cancellation techniques known as multiuser detectors. Power control is another essential technique to reduce co-channel interference.On the other hand, MUD problem and power control problem are the root-finding procedure for solving systems of linear algebraic equations. The traditional classification of solution methods as being either direct or iterative is an oversimplification and the computational complexity is dramatically increases as the linear equations increase. To alleviate the computational complexity, preconditioning techniques was introduced. Preconditioning techniques include the diagonal precondition, the SOR precondition, the SSOR precondition, the incomplete Cholesky precondition, sparse approximate inverses, polynomial precondition, algebraic multilevel precondition etc. In this thesis, the symmetric successive overrelaxation (SSOR) preconditioning techniques are study at the CDMA systems.In this thesis, we first introduce the SSOR preconditioning scheme, which is applied to the Bi-CG, Bi-CGSTAB, Bi-CGSTAB2, GPBi-CG, TFQMR and GMRES methods for solving a set of linear equations corresponding to linear interference cancellation structures of the CDMA systems. The performance of the detectors is investigated and it is found that our proposed the SSOR preconditioned iteration methods have better performance compared with the decorrelating and the LMMSE detector. Especially for the SSOR preconditioned GPBi-CG and GMRES approaches can provide significantly faster convergence.The convergence speed of power control algorithm is critically in determining its practical application especially when the propagation and traffic condition are rapidlychanging. In order to improve the convergence speed of power control algorithm, a new centralized power control algorithm is proposed based on the SSOR preconditioning technique using one Krylov subspace iteration method called GPBi-CG to solve the power allocation problem in this thesis. The simulation results show that, by comparing terms of the Normalized Euclidean Distance, average relative power, average SIR and the outage probability, our proposed C-SSOR GPBi-CG algorithm converges asymptotically faster than the DCPC and CSOPC.Therefore, the SSOR preconditioner is a powerful tool for solving the problem of Linear Interference Cancellation and power control in CDMA systems.