We consider the estimation of channel parameters for code-division multiple access (CDMA) communication systems operating over channels with either single or multiple propagation paths, The multiuser channel estimation problem is decomposed into a series of single user problems through a subspace-based approach, By exploiting the eigenstructure of the received signal's sample correlation matrix, the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters, The channel estimate is formed by projecting a given user's spreading waveform into the estimated noise subspace and then either maximizing the likelihood or minimizing the Euclidean norm of this projection, Both of these approaches yield algorithms which are near-far resistant and do not require a preamble.