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Wide-sense stationary discrete-time random processes: Analyses in the discrete-Fresnel and discrete-frequency domains
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DOI：10.1016/j.jfranklin.2024.107310.png)
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Abstract
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This article investigates the expectation and autocorrelation functions of random processes in the discrete-Fresnel and the discrete-frequency domains, originating from wide-sense stationary (WSS) random processes in the discrete-time domain. Through mathematical deduction, it is demonstrated that WSS random processes in the discrete-time domain exhibit the same expectation and autocorrelation functions as transformed to the discrete-Fresnel domain. In contrast, this property is not observed in the discrete-frequency domain. White, pink, and brown random processes are considered to illustrate these behaviors in the discrete-Fresnel and discrete-frequency domains. Furthermore, this study numerically compares data communication systems based on single-carrier with cyclic prefix, orthogonal chirp-division multiplexing, and orthogonal frequency-division multiplexing schemes, which are respectively designed in the discrete-time, discrete-Fresnel, and discrete-frequency domains. The numerical results show that orthogonal chirp-division multiplexing and single-carrier with cyclic prefix schemes achieve comparable communication performance under any additive noise modeled by a wide-sense stationary random process, regardless of the chosen linear equalization or the absence of it.
Keywords:
Discrete-frequency domain
Discrete-Fresnel domain
Random process
Wide-sense stationarity
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