The Geometry of Coherence and Its Application to Cyclostationary Time Series

The consequences of cyclostationary structure in a random process have traditionally been described in terms of the correlation or coherence of pairs of particular time and frequency shifted versions of the process. However, cyclostationarity, and more generally almost cyclostationarity, are manifest in the mutual coherence of subspaces spanned by sets of time and frequency shifted versions of the process. The generalized coherence framework allows any finite collection of pertinent samples of the cyclic autocorrelation function estimates formed from the measured signal data to be combined into a detection statistic. This paper develops the subspace coherence theory of almost cyclostationary processes as a guide to constructing such detectors in both the time and spectral domains.