Blind unitary source separation using a multidimensional phase-locked loop

Blind source separation cannot generally be performed using second-order statistics alone because of a unitary matrix ambiguity. We present the multidimensional phase-locked loop (MPLL) as a blind algorithm for resolving this ambiguity. The MPLL is a multidimensional generalization of the scalar decision-directed PLL for resolving phase rotations in scalar digital communication systems, and as such is applicable only to discrete-alphabet sources. We compare the MPLL to other known unitary source separation algorithms, and find that the MPLL compares favorably in terms of both performance and complexity.