Analytic performance evaluation of cumulant-based FIR system identification methods

The covariances of the third- and fourth-order sample cumulants of stationary processes are derived. The resulting expressions are used to obtain the analytical performance of such methods as a function of the coefficients and statistics of the input sequence. The lower bound in the variance is compared for different sets of sample statistics to provide insight about the information carried by each sample statistic. The effect of the presence of noise on the accuracy of the estimates is studied analytically. The results are illustrated graphically with plots of the variance of the estimates as a function of the parameters or the signal-to-noise ratio. Monte Carlo simulations are included for comparison with the predicted analytical performance.<>