Cyclostationary processes are an important class of nonstationary processes. We consider nonparametric estimation of the cyclic cross spectrum. A smoothed periodogram-based estimator is studied and its asymptotic behavior characterized, extending univariate work to the multivariate case. Application to cyclic coherence measurements is discussed. The results are useful in a variety of multisensor cyclostationary signal processing scenarios such as time delay and bearing estimation.

We generalize Parzen's (1961) analysis of "asymptotically stationary" processes to mixtures of deterministic, stationary, nonstationary, and generally complex time series. Under certain mixing conditions expressed in terms of joint cumulant summability, we show that time averages of such mixtures converge in the mean-square sense to their ensemble averages. We additionally show that sample averages of arbitrary orders are jointly complex normal and provide their covariance expressions. These conclusions provide us with statistical tools that treat random and deterministic signals on a common framework and are helpful in defining generalized moments and cumulants of mixed processes. As an important consequence, we develop consistent and asymptotically normal estimators for time-varying, and cyclic-moments and cumulants of kth-order cyclostationary processes and provide computable variance expressions. Some examples are considered to illustrate the salient features of the analysis.>

Extraction of almost periodic signals from their noisy observations is accomplished by exploiting cyclostationarity. The additive noise is allowed to be generally cyclostationary with unknown distribution. Consistency of the proposed estimators is proved and their asymptotic properties are presented. Further, adaptive algorithms are employed for tracking possible time-variations in the parameters of the almost periodic signal. Finally, the proposed methods are tested via simulations.>

Second- and higher-order almost cyclostationary processes are random signals with almost periodically time-varying statistics. The class includes stationary and cyclostationary processes as well as many real-life signals of interest. Cyclic and time-varying cumulants and polyspectra are defined for discrete-time real kth-order cyclostationary processes, and their interrelationships are explored. Smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal. Asymptotic covariance expressions are derived along with their computable forms. Higher than second-order cyclic cumulants and polyspectra convey time-varying phase information and are theoretically insensitive to any stationary (for nonzero cycles) as well as additive cyclostationary Gaussian noise (for all cycles).>

By viewing discrete-time amplitude-modulated signals and processes with missing observations as cyclostationary signals, nonparametric, mean-square-sense consistent, and asymptotically normal single record estimators are developed for their kth-order cumulants and polyspectra, along with the asymptotic covariances. The proposed estimation schemes use cyclic cumulants and polyspectra, and are theoretically insensitive to any additive stationary noise. In addition, schemes of order k>or=3 convey complete phase information and are insensitive to additive cyclostationary Gaussian noise of unknown covariance. The conventional approaches cannot recover mixed-phase linear processes, are susceptible to additive noise, and are a special case of the proposed schemes. Simulations demonstrate superior performance of the proposed algorithms.>

Identification of known order (almost) periodically time-varying autoregressive moving average (ARMA) models is addressed using cyclic cumulants of output only, or, input/output data. Several approaches are presented under different modeling assumptions and their relative merits are discussed. Both linear and nonlinear algorithms are derived in time- and cyclic-domains and optimality issues are considered. All the algorithms utilize consistent single record estimators, are phase sensitive and are shown to be insensitive to any stationary noise as well as additive (perhaps nonstationary) Gaussian noise of unknown covariance.>

Viewing noise cancellation as an input/output identification problem, designs are developed using third-order statistics which are insensitive to corruption of the reference signal by additive Gaussian noise of unknown covariance. As a by-product of designing linear noise cancelers, a parametric time-delay estimation approach is readily available. Higher-order statistics can also be employed to design nonlinear cancelers of the discrete Volterra type, which maximize the output signal-to-noise ratio. Both the linear only and the linear-quadratic designs are derived in batch and adaptive form, the latter being implemented using recursive least-squares approaches. Simulation examples are given to illustrate the new cancelers and to compare them with conventional approaches.>