Order Statistics of the Normalized Spectral Distribution for Detecting Weak Signals in White Noise

This paper further develops the topic of the authors' previous research. In particular, order statistics of the discrete normalized spectral distribution of the additive white Gaussian noise are investigated to detect a deterministic useful signal in a noise mixture using information features. An additional relationship is established between the discrete spectral distribution of the single-window realization statistics of the white noise. Another novel result consists in exact formulas for calculating the mean and variance of normalized order statistics. Based on the analytical expressions derived, a new formula for calculating the spectral complexity is proposed and the already known one is refined. The theoretical results are verified by statistical simulation.