Mutual information rate of nonstationary statistical signals

The stochastic chirp-stationary (CS) signals are a kind of widely employed nonstationary signal model in communications and radar/sonar systems. However, the measurement of the information for the stochastic CS signals are absent yet. In this paper, the mutual information rate (MIR), which reflects the interdependence of two stochastic signals comprehensively, between two CS signals is proved to be exist. Later, to check the properties of the MIR in different fractional Fourier domains (FrFD), the criteria of the fractional Fourier transform (FrFT) decomposition of a stochastic signal are clarified. The MIR is proved to be an invariant in different FrFDs. In addition, the relationship of the MIR between the input and the output of a fractional filter is built. Based on these properties, two applications are proposed, saying a blind deconvolution algorithm and two methods for determining the frequency of a CS signal. Specifically, the previous application aims at the fractional convolution model. In addition, the second application are based on the measures of interdependence, namely the Pearson correlation function and the MIR, which provide theoretical framework for determining the frequency rate of a CS signal by finite sampling records in practical applications. Finally, the simulations show the applications of the MIR.