THE ACHIEVABLE ACCURACY IN ESTIMATING THE INSTANTANEOUS PHASE AND FREQUENCY OF A CONSTANT AMPLITUDE SIGNAL

The paper explores the achievable accuracy in estimating the instantan eous phase and frequency of complex constant amplitude signals. It is based on modeling of the signal phase by a polynomial function of time on a finite interval. The phase polynomial is expressed as a linear c ombination of the Legendre basis polynomials. First, we derive the Cra mer-Rao bound (CRB) of the instantaneous phase and frequency of consta nt amplitude polynomial-phase signals. Then we examine some properties of the CRB's and use these properties to estimate the order of magnit ude of the bounds. Finally, we extend the analysis to signals whose ph ase and frequency are continuous but not polynomial. The CRB can be ac hieved asymptotically if the estimation of the phase coefficients is d one by maximum likelihood. Using the maximum likelihood estimates we s how that the achievable accuracy in phase and frequency estimation is determined by the CRB of the polynomial coefficients, and the deviatio n of true phase and frequency from the polynomial approximations.