The problem of channel estimation in code-division multiple-access systems is considered. Using only the spreading code of the user of interest, a technique is proposed to identify the impulse response of the multipath channel from the received data sequence. While existing blind methods suffer from high computational complexity (due to large SVDs) and sensitivity to accurate knowledge of the noise subspace rank, the proposed method overcomes both problems. By employing a computationally simple matrix power that requires no a-priori knowledge of the noise subspace rank, we obtain efficient estimates of the noise subspace. The impulse response is then directly identified through a small sized (order of the channel) SVD or a least squares optimization. Both approaches (SVD and least squares) are also extended to accommodate for synchronization with respect to the user of interest. Extensive simulations demonstrate robustness of the proposed scheme and performance comparable to existing SVD techniques but at a lower computational cost.