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The problem of blind user spatial signature estimation using the parallel factor (PARAFAC) analysis model is addressed in the context of applications to wireless communications. A time-varying user power loading in the uplink mode is proposed to enable identifiability and the application of PARAFAC analysis. Identifiability issues are carefully studied and two blind spatial signature estimation algorithms are developed. The first technique is based on the PARAFAC fitting trilinear alternating least squares (TALS) regression procedure, while the second one makes use of the joint approximate diagonalization algorithm. These techniques do not require any knowledge of the propagation channel and/or sensor array manifold and are applicable to a more general class of scenarios than earlier blind approaches to spatial signature estimation.