Nonparametric Detection of Complex-Valued Cyclostationary Signals

In wireless communication, radar, surveillance, and active sensing systems it is necessary to detect transmitted signals in noise. Employed signals are man-made and consequently have many statistical and structural properties that can be used to aid the detection. Such properties are present even if the transmitted data itself would be random or unknown. One such key property is cyclostationarity which means that some signal statistics such as autocorrelation function are periodic. Typically these signals are observed in demanding signal environments where the standard assumption on Additive White Gaussian Noise (AWGN) may not be true. Signal detection has to be performed reliably in the face of interference and in challenging propagation environments characterized by shadowing and fading effects as well as heavy-tailed noise distributions. In this chapter, a robust computationally efficient nonparametric detector of second order cyclostationary statistics based on the spatial sign function is presented. Nonparametric approach leads to improved robustness against heavy-tailed noise and in cases when the noise statistics are not fully specified. Asymptotic distribution of the spatial sign cyclic correlation estimator under the null hypothesis is established. Tests using constraint on false alarm rate constraint are derived for single detector and decentralized detector employing multiple distributed sensors. A theoretical justification for spatial sign based detection of cyclostationary signals is provided. A sequential test for reducing the average detection time and detecting rapid changes is presented. Simulation examples on identifying idle radio spectrum are provided. Simulation example shows the reliable and statistically robust performance of the proposed nonparametric detector both in heavy-tailed and Gaussian noise environments.