Cyclostationarity: half a century of research

The importance of the concept of cyclostationarity in design and analysis of signal detectors, synchronizers, and extractors in communication systems is briefly discussed, and the central role of spectral correlation, in the characterization of random processes that are cyclostationary in the wide sense, is explained. A spectral correlation function that is a generalization of the power spectral density function is described, and a corresponding generalization of the Wiener-Khinchine relation and several other fundamental spectral correlation relations also are described. Explicit formulas for the spectral correlation function for various types of analog-modulated signals are derived. This includes pulse and carrier amplitude modulation, quadrature amplitude carrier modulation, and phase and frequency carrier modulation. To illustrate the differing spectral correlation characteristics of different modulation types, the magnitudes of the spectral correlation functions are graphed or described in graphical terms as the heights of surfaces above a bifrequency plane.

Spectral Correlation of Modulated Signals: Part I--Analog Modulation

https://faculty.engineering.ucdavis.edu/gardner/wp-content/uploads/sites/146/2013/02/The_Spectral_Correlation_Theory_of_Cyclostationary_Time-Series.pdf

The spectral correlation theory of cyclostationary time-series

https://www.dtc.umn.edu/s/resources/bib05eurasip.pdf

Bibliography on cyclostationarity

Full-duplex data communication over a multi-input/multi-output linear time-invariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both near- and far-end crosstalk and independent additive noise. The MMSE equalizer is completely specified in terms of the channel and crosstalk transfer functions by using a generalization of previous work due to Salz (1985). Conditions are given under which the equalizer can completely eliminate both near- and far-end crosstalk and intersymbol interference. The MMSE transmitter filter, subject to a transmitted power constraint, is specified when the channel and crosstalk transfer functions are bandlimited to the Nyquist frequency. Also considered is the design of MMSE transmitter and receiver filters when the data signals are arbitrary wide-sense stationary continuous or discrete-time signals, corresponding to the situation where the crosstalk is not phase-synchronous with the desired signal. >

/pdf/suppression-of-near-and-far-end-crosstalk-by-linear-pre-and-5gfua9exy3.pdf

Suppression of near- and far-end crosstalk by linear pre- and post-filtering

This paper considers the cyclostationary nature of digital signals when determining crosstalk interference between such signals in multipair cable. This approach is necessary as the interference is only relevant at the decision instants in the receivers of the disturbed systems and any time variation of this interference with respect to the sampling instants changes the effect of this interference; previous studies in the area have ignored the cyclostationary nature of the digital signal. Expressions for the time-varying mean and variance of far-end and near-end crosstalk (FEXT and NEXT) have been derived. These expressions demonstrate the inherently smaller time variation of the NEXT interference when compared to the FEXT interference. An interesting result is that the calculation of the time-averaged value of the variance of FEXT and NEXT interference still requires the use of the cyclostationary properties of the digital signal. The results of this paper are extended and applied to various examples of the engineering of digital line systems in multipair cable in Part II of this paper.

The Cyclostationary Nature of Crosstalk Interference from Digital Signals in Multipair Cable--Part I: Fundamentals

In this paper, the results of Part I are applied to the engineering of primary-level digital line systems in multipair cable operating in either a nonsynchronous or a synchronous network. It is shown that the erstwhile incorrect assumption that crosstalk interference from digital line systems is wide sense stationary, and not cyclostationary, leads to an overestimation of system margin of less than 1 dB. It is also shown that the change from a nonsynchronous to a synchronous network leads to a reduction in system margin which is difficult to quantify exactly, but it is typically less than 2.5 dB for FEXT and 1.5 dB for NEXT. The paper concludes with a consideration of the cyclostationary nature of block,encoded digital signals such as 4B3T, MS43, etc., and extends some of the results of Part I.

J. Campbell

Papers

The Cyclostationary Nature of Crosstalk Interference from Digital Signals in Multipair Cable--Part I: Fundamentals

The Cyclostationary Nature of Crosstalk Interference from Digital Signals in Multipair Cable--Part II: Applications and Further Results