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This paper addresses the problem of stochastic approximation and data re-use applied to the blind adaptive algorithm for the interference cancellation RAKE CDMA receiver. The improved adaptive algorithm that utilizes step-size adaptation can achieve both faster convergence and higher steady state performance compared to the fixed step-size ones without increasing much more complexity. Moreover, the improved adaptive algorithm that further utilizes solution averaging and data re-use can further improve both convergence speed and steady state performance. Simulations support the resulting significant improvements.