Cramer-Rao Bounds for A Coupled Mixture of a Polynomial Phase and Sinusoidal FM Signals

This paper introduces a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, motivated by real-world applications, e.g., contactless linear encoders. Specifically, the coupling is introduced to express the sinusoidal FM frequency as a function of the PPSrelated parameters. Given the coupling mixture, it generalizes two existing models: 1) the pure PPS model and 2) the independent mixture model. Performance bounds of parameter estimation for the coupled mixture model are established in terms of the Cramer-Rao bound (CRB). Unlike the pure PPS case, the derived CRB shows its dependence on the PPS-related and sinusoidal FM-related parameters due to the coupling mixture. On the other hand, the derived CRBs for the PPS-related parameters are lower than their counterparts of the independent mixture model, as the sinusoidal FM frequency provides additional information on the PPS parameters.