The Algebra of Coherence and the Detection of Almost Cyclostationary Processes

Detecting a cyclostationary signal in stationary interference relies on exploiting the correlation between suitably time-shifted and frequency shifted replicates of the measured time-series data. Recent perspectives have framed this process in terms of estimating the coherence between subspaces associated with these shift and modulation operations. In the case of almost cyclostationary signals, which manifest two or more non-commensurate cyclic frequencies, detection entails quantification of the extent to which a subspace is simultaneously coherent with two or more other subspaces. This paper discusses detection of almost cyclostationary signals from this point of view and introduces an "algebra of coherence"suitable for codifying the process of this kind of quantification. The utility of this framework in designing effective detection statistics for almost cyclostationary signals is demonstrated.