| Cyclostationary processes are stochastic processes whose statistics (mean, autocorrelation, etc.) vary periodically with time. Recent research has demonstrated the utility of exploiting the cyclostationary characteristics of this class of stochastic processes.; An introduction to cyclostationary stochastic processes is developed. This treatment is completed strictly within the realm of stochastic theory and random processes, whereas much of the previously published work has taken the empirically-based approach of statistical theory and random signals. The cyclic spectrum is introduced, as is the related concept of spectral correlation. The application of this theory to common problems in signal processing (filtering, frequency translation, sampling, etc.) is addressed.; The maximum likelihood (ML) estimate of time difference of arrival (TDOA) for a Gaussian cyclostationary process is derived. Direct and continuous realizations of the estimate are presented which can be used for finite observation interval, as the ML estimate assumes an infinite observation period. For a stationary process, the derived ML estimate for cyclostationary processes is shown to be equivalent to the conventional ML estimate for TDOA. The estimate is also compared to a previously published pseudo-ML estimate for cyclostationary processes valid for low signal-to-noise ratios. Practical use of the derived estimate is discussed. A simplification to the derived estimate, resulting in a more feasible implementation, is derived for a special class of signals; as an example, a BPSK process is considered. |
