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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×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 Uˆk+1=UˆkRk, where Rk is an n-dimensional Householder-like rotation depending on only the kth receiver observation. The O(n2) 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.