Modified Cramér-Rao Bounds for Continuous-Phase Modulated Signals

We consider the estimation of signal amplitude, time offset, and the parameters of a polynomial-phase signal from a continuous-phase modulated (CPM) signal that contains both unknown data symbols and known pilot symbols. Transformation of the polynomial-phase signal into an orthogonal basis allows us to derive the modified Cramér-Rao bounds (MCRB) for the problem of vector-parameter estimation in closed form. Numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences. Since our bounds are easy to evaluate, they can aid the design of pilot and burst configuration for CPM systems.