On the kurtosis of digitally modulated signals with timing offsets

Beside being a renowned parameter in signal classification, the kurtosis of a source signal is an indicator of the separation difficulty in blind signal separation and deconvolution. Whereas the maximum kurtosis is unbounded, the lower bound on the minimum kurtosis is -2. This means that the family of sub-Gaussian signals, to which most modulated communication signals belong, have an inherent limit in their suitability for blind techniques. Furthermore, the kurtosis of a composite signal has bounds which depend on the kurtoses of the constituent signals. Exact expressions for the kurtoses for a number of digital modulation formats are derived, and the influence of sampling-time accuracy to the kurtosis of the sampled signal is investigated