Bibliography on cyclostationarity

Abstract

The present bibliography represents a comprehensive list of references on cyclostationarity and its applications. An attempt has been made to make this bibliography complete by listing most of the existing references up to the year 2005 and by providing a detailed classification group.

Introduction

Cyclostationary processes are those signals whose statistics vary almost periodically, and they are present in numerous physical and man-made processes: ultrasonic imaging of materials and biological tissues, medicine (EEG, ECG, circadian rhythm), solid state and plasma physics, radio-astronomy, mechanics (vibration and noise analysis for condition-based monitoring of rotating machineries: engines, turbines), radar, sonar, telemetry, and communications systems, modeling and performance evaluation of the noise figure in electronic and optic devices, etc. In communication systems, operations like sampling, modulation, mixing, multiplexing, coding, and scanning create an information bearing signal with periodic or almost periodic characteristics; in ultrasonic imaging, regular scatterer spacings induce a quasi-periodicity on ultrasonic pulse echo scans; in electronics, noise at the output of a nonlinear electronic device is excited by periodic signals (noise currents in MOSFET vary periodically with the oscillating waveform) and many circuits present time-varying operating points (mixers, oscillators, samplers, and switched filters); in climatology, presence of rhythmic or seasonal behavior in nature results in repetitive climatological data; in rotating machinery vibration signals produced by IC engines have cyclic nature. In short, cyclostationary signals are frequently encountered in a broad range of applications and since exploitation of the periodic features present in cyclostationary signals generally leads to algorithms with substantially improved performance relative to the case when the processed signals are viewed as stationary, cyclostationary signals appear as the most suited framework for modeling and processing such periodically correlated processes. In literature, cyclostationary processes are named in multiple different ways such as periodically correlated, periodically nonstationary, periodically nonstationary or cyclic correlated processes.

Historically, it appears that Bennett (1958) [77] observed for the first time the presence of cyclostationary signals in the design of synchronization algorithms for communications systems. Shortly after (1959–1980), several mathematicians from the former Soviet Union (Gladyshev, Gudzenko, Dragan, etc.) introduced key concepts for representation of cyclostationary processes [345], [346], [347], [348], [349], [350], [556], [557], [558], [559], [585], [586]. More specifically, in 1959 Gudzenko [586], presented a study on non-parametric spectral estimation of cyclostationary processes. Later in 1961 and 1963, Gladyshev [556], [559], worked on spectral analysis recognizing relation between periodically correlated processes and stationary vector sequences, and he also introduced the concept of almost periodically correlated processes. In 1963, Nedoma [1005] presented cycloergodicity for cyclostationary processes with single period and later in 1983, Boyles and Gardner [145] extended it to general cyclostationary processes with multiple periods. After Bennett's first usage of cyclostationarity in communication context, Franks (1969) [424] devoted a relatively detailed section of his book to cyclostationarity in communication. Then, in 1969 Hurd's thesis [663] appeared as a very good introduction to continuous time cyclostationary processes. In 1975, Gardner and Franks [449] studied benefits of series representation of cyclostationary processes especially in the context of optimum filtering. First comprehensive treatment of cyclostationarity in communication and signal processing appeared in Gardner's book [452] in 1985. In 1987, Gardner presented his nonprobabilistic statistical theory of cyclostationarity in [461]. In parallel, Giannakis and Dandawate [295], [297], [547], approached cyclostationarity within the framework of stochastic processes. In 1992, Spooner [1272] considered the theory of higher-order cyclostationarity.

As the theory of cyclostationary developed, lots of related works appeared in many different areas such as climatology in Hurd [676], hydrology in Kacimov [763], medicine and biology in Finelli [413], oceanology in Dragan [352], economics in Pagano [1047], mechanics in Sherman [1241] and many fields in communication and signal processing like crosstalk in Campbell [173] and parameter estimation in Gardner [461]. Also, the last decade marked a renewed interest in cyclostationarity through the pioneering works of Tong [1324], [1327], Tugnait [1361], Ding [333] and Giannakis [547], which generated an intensive research activity in the area of blind estimation and equalization of communications channels.

In short, after the early treatment, mainly two research groups have contributed significantly in USA to the theory and applications of cyclostationary signal processing in the engineering community, namely the research centers of Professors W. Gardner and G.B. Giannakis. Basically, Gardner builds the theory of CS signals within a “nonprobabilistic” approach, referred to as the fraction-of-time (FOT) approach [461]. In contrast to the FOT-approach, Giannakis assumes a probabilistic approach, namely the framework of stochastic processes [295], [297], [547]. Fundamental research contributions in the area of cyclostationary signal processing were also reported by Izzo and Napolitano [713], [714], [715], [716], [717], [718], [719], [720], [721], [722], [723], [724], [725], [726], [727], [728], [729], [730], [731], [732], [733], [734].¹

The authors hope that this bibliography on cyclostationarity will help the researchers, especially the ones from the signal processing and communications communities, to find new research problems and interesting practical applications. To the best knowledge of the authors, this bibliography appears to be the most complete source of references on cyclostationary processes. The authors have also tried to fit the presented references in a classification group and to design a detailed classification group. Despite authors’ huge efforts to include all the existing references that deal with cyclostationarity, a number of references might have not been included. We would like to apologize in advance to all the researchers whose works have not been cited in this bibliography.

Classification