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A blind adaptive multiuser detector for signal demodulation in multipath code-division multiple-access (CDMA) communication channels is proposed. This detector is based on a modified constrained Kalman filtering Algorithm. In order to facilitate the application of a blind linear filter-optimization technique to robust inference suppression, a new canonical representation for Kalman filter is developed first, and then an efficient iterative implementation that provides very fast convergence under this representation is proposed. The proposed algorithm is low in computation complexity, especially suitable for fast optimization of filter vector with short data samples. And also it has a better tracking capability under a dynamic environment where the number of users will change frequently with time. Computer simulation results, along with some analytical convergence results, confirm that the proposed algorithm is effective in multipath fading channels and achieves very satisfactory performance.