Comparison of cyclic moments-based estimators of the parameters of random amplitude polynomial phase signals

It has been suggested that the accuracy of the cyclic moments-based estimator of the frequency of a random amplitude sinusoid in additive noise may be increased by using the squared observations rather than the raw observations. This paper extends this idea to random amplitude polynomial phase signals of arbitrary order. The covariance matrix of the cyclic moments-based estimators is derived for the cases where either the observations or the squared observations are used. It is found that, for first and second order phases, the use of the squared observations results in more accurate phase parameter estimates in a wide range of conditions. For higher order phases the use of the squared observations is more accurate only under restrictive conditions.