Statistical tests for presence of cyclostationarity

The presence of kth-order cyclostationarity is defined in terms of nonvanishing cyclic-cumulants or polyspectra. Relying upon the asymptotic normality and consistency of kth-order cyclic statistics, asymptotically optimal χ² tests are developed to detect the presence of cycles in the kth-order cyclic cumulants or polyspectra, without assuming any specific distribution on the data. Constant false alarm rate tests are derived in both time- and frequency-domain and yield consistent estimates of possible cycles present in the kth-order cyclic statistics. Explicit algorithms for k⩽4 are discussed. Existing approaches are rather empirical and deal only with k⩽2 case. Simulation results are presented to confirm the performance of the given tests