Statistical analysis of polynomial phase signal parameter estimates based on structured auto-regressive modeling

A statistical analysis of the polynomial phase signal parameter estimates achieved when using the structured auto-regressive approach is presented. The estimates are consistent for high SNR or large number of samples, N. An expression for the covariance of the estimates is given. Numerical examples confirm that the theoretical covariance apply well to empirical data for a wide range of SNR and N. The performance of the estimator depends on the filter length, n, and the sampling strategy which may be non-uniform. The optimal choice of n for evenly sampled cisoids is given as a function of N. The variance is inversely proportional to SNR² for small SNR, and to SNR for medium and high SNR