STATISTICAL CHARACTERIZATION OF SAMPLE 4TH-ORDER CUMULANTS OF A NOISYCOMPLEX SINUSOIDAL PROCESS

The paper deals with the statistical characterization of sample estima tes of the fourth-order cumulants of a random process consisting of mu ltiple complex sinusoids and additive colored Gaussian noise, In parti cular, it presents necessary and sufficient conditions for strong cons istency of the sample cumulants of arbitrary orders, and derives expre ssions for the asymptotic covariance of the sample estimates of the fo urth-order cumulants. It is shown that the fourth-order cumulant C-4y( tau(1), ..., tau(4)) can be written as a function of a single argument tau = <tau(3)> + tau(4) - tau(1) - tau(2) which implies large flexibi lity in estimating the cumulant, It is recommended that the estimate b e based upon lags such that tau(1) is distant from tau(2) and tau(3) i s distant from tau(4), andlor as a linear combination of such terms, T he asymptotic variance of a cunulant-based frequency estimator is show n to have the form c(2) . SNR(-2) + c(3) . SNR(-3) + c(4) . SNR(-4), w here the coefficient c(2) may possibly vanish. The theory is illustrat ed via numerical examples, The results of this paper will be useful in analyzing the performance of various cunulant-based frequency estimat ion algorithms.