This paper concerns the problem of blind multiuser detection, a special case of the blind source separation problem in which the source signals have finite alphabets. Specifically, we address the problem of identifying and resolving the n/spl times/n unitary matrix ambiguity U that results from whitening the receiver observations, where n is the number of sources. We propose the multidimensional phase-locked loop (MPLL) as a generalization of a scalar decision-directed PLL to vector-valued signals. The MPLL adapts an estimate of U according to the recursion U/spl circ//sub k+1/=U/spl circ//sub k/R/sub k/, where R/sub k/ is an n-dimensional Householder-like rotation depending on only the kth receiver observation. The O(n/sup 2/) complexity of an efficient implementation of the algorithm is extremely low. Nevertheless, simulation results demonstrate good convergence properties and superior steady-state performance when compared with prior techniques. The algorithm is also able to accommodate large alphabets and shaped alphabets.