The problem of blind adaptive channel estimation in code-division multiple access (CDMA) systems is considered. Motivated by the iterative power method, which is used in numerical analysis for estimating singular values and singular vectors, we develop recursive least squares (RLS) and least mean squares (LMS) subspace-based adaptive algorithms in order to identify the impulse response of the multipath channel. The schemes proposed in this paper use only the spreading code of the user of interest and the received data and are therefore blind. Both versions (RLS and LMS) exhibit rapid convergence combined with low computational complexity. With the help of simulations, we demonstrate the improved performance of our methods as compared with the already-existing techniques in the literature.