On the performance of source separation with constant modulus signals

Cramér-Rao bounds (CRBs) are developed for narrow band source separation, when the sources are constrained to have constant modulus (CM). The bounds are appropriate for multi path CM sources, in blind, semi-blind, or fully known cases. Source separation bounds are contrasted for calibrated and uncalibrated arrays. It is shown that, from the CRB perspective, calibration adds no additional information. Closed-form CRBs are given for a single source, and two-source examples are also presented. Optimality of the analytical constant modulus algorithm (ACMA) for blind CM-source separation is demonstrated, achieving the appropriate constrained CRBs over a wide SNR range in challenging multipath scenarios.