The Cramer-Rao lower bound for signals with constant amplitude and polynomial phase

The authors derive the Cramer-Rao lower bound (CRLB) for complex signals with constant amplitude and polynomial phase, measured in additive Gaussian white noise. The exact bound requires numerical inversion of an ill-conditioned matrix, while its O(N ^-1) approximation is free of matrix inversion. The approximation is tested for several typical parameter values and is found to be excellent in most cases. The formulas derived are of practical value in several radar applications, such as electronic intelligence systems (ELINT) for special pulse-compression radars, and motion estimation from Doppler measurements. Consequently, it is of interest to analyze the best possible performance of potential estimators of the phase coefficients, as a function of signal parameters, the signal-to-noise ratio, the sampling rate, and the number of measurements. This analysis is carried out