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Several issues on the problems of the adaptive array beamforming and code-division multiple access (CDMA) multiuser detection are investigated in this dissertation. Recently, based on the decomposition of observation vector space into two orthogonal eigenspace, the eigenspace-based (ESB) and the generalized eigenspace-based (GEIB) array signal processing techniques have been widely discussed due to their superior performance over conventional techniques. At first, the purpose of this dissertation is mainly to present robust and efficient algorithms for further enhancing the performance of ESB and GEIB techniques under imperfect and practical operation environments. We also propose a method of corrected steering angles to combat the supersensitivity of eigenanalysis interference canceler (EIC) to source number overestimation and steering angle errors. We analyze the performance of several ESB multiuser detectors, including conventional direct-form detector and generalized sidelobe canceler (GSC) for synchronous CDMA system with and without desired user code mismatch. We also present a way of resolving spreading code mismatch in blind multiuser detection with subspace-based technique. Furthermore, the structure of GSC can be utilized to deal with the case of the desired user's SNR < 0 dB. Next, algorithm for adaptive H¡Û filter has demonstrated the advantage of reduction of sensitivity to modeling error (due to finite tap number) and suitability for arbitrary ambient noise over recursive least squares (RLS) algorithm. However, the computational burden of the H¡Û algorithm is enormous. In order to reduce the computational complexity, subweight partition scheme is employed to an H¡Û-based algorithm. The computation burden of the conventional adaptive H¡Û algorithm can be mitigated with slight performance degradation. The H¡Û-based algorithm is then further extended to the adaptive beamformer and blind multiuser detector. Finally, we present new diversity techniques for multiuser detection under multipath fading channels in asynchronous CDMA systems. The enhanced capacity of diversity for multipath channels can be achieved by appropriately utilizing the constraint matrix and the response vector in multiple constraint minimum variance (MCMV) algorithm. Moreover, the proposed techniques offer gratifying multiple access interference (MAI) suppression. We also incorporate the signal subspace-based projection into MCMV detector, so that the noise enhancement in the MCMV criterion can be reduced.