Cyclostationarity and stochastic resonance in threshold devices

This paper intends to show how the theory of stochastic cyclostationary processes can be used to study stochastic resonance in static nonlinearities. The statistic we use is the covariance function of the output. The covariance is a second-order cumulant and is not dependent on by the mean. Furthermore, this covariance is not averaged in time as is usually done in the stochastic resonance literature. A two-dimensional Fourier transform of the covariance gives the so-called spectral correlation. The spectral correlation depends on the usual harmonic frequency and on another frequency, called cycle frequency. The cyclostationarity of a signal makes the spectral correlation discrete in the cycle frequency. The zero cycle frequency corresponds to the usual "stationary power spectrum" used in the stochastic resonance literature. We thus exploit all the second-order statistical information. We first revisit classical stochastic resonance in threshold devices using the spectral correlation, showing that the effect is seen for nonzero cycle frequencies. The cases of additive and multiplicative noise are detailed. We then study stochastic resonance in threshold devices for communication signals. These signals are usually modeled as stochastic cyclostationary processes. We show that stochastic resonance occurs, and the phenomenon is quantified using the spectral correlation of the output: The amplitude of the spectral correlation at nonzero cycle frequencies presents a maximum as the power of the input noise is increased.