William A. Gardner

Gardner completed his M.S. in Electrical Engineering from Stanford University in 1967, attended Massachusetts Institute of Technology while employed as a member of technical staff at Bell Labs from 1967 to 1969, and completed his Ph.D. in Electrical Engineering from University of Massachusetts in 1972, at which time he joined the University of California, Davis as an Assistant Professor.[2]

Gardner performed research and teaching there for nearly 30 years, becoming Professor Emeritus in 2001. In 1982, while at University of California, Gardner founded the R&D firm Statistical Signal Processing, Inc. (SSPI), an engineering research services company serving primarily the national security sector but also the cellular RF communications industry. He served as the president, CEO, and chief scientist of SSPI for 25 years.[2] He also founded several entrepreneurial ventures during the latter 15 years of that period, including Gardner Technologies in 2001 for which he served as IP inventor and chief technology officer for five years.[7]

After completing his Ph.D. dissertation entitled "Representation and Estimation of Cyclostationary Processes," in 1972, Gardner began working on developing a new theory for the class of cyclostationary and polycyclostationary random processes.[1]

In 1985, he wrote his first book, Introduction to Random Processes with Applications to Signals and Systems, which focused on the duality between the stochastic theory based on expectation and the nonstochastic theory based on time averaging, which theory he was developing.[8]

Gardner completed the fundamentals of his nonstochastic theory for stationary processes in 1984 and then reformulated all his research progress to date on cyclostationary stochastic processes within a nonstochastic framework: he developed the novel theory of Fraction-of-Time (FOT) Probability for Poly-Cyclostationary time-series data.[9]

Gardner's 1987 book Statistical Spectral Analysis: A Non-probabilistic Theory presented his FOT theory of both stationary and poly-cyclostationary processes and/or time-series in Part I and Part II, respectively.[10] After publication of this book, recognition of his work, together with the cornucopia of practical applications it spawned, initiated a long period of growth of this new field of study, including approximately 50 research grants and contracts awarded to Gardner over the following 30 years, garnering nearly $25M in awards of research and development funding from approximately 25 government agencies and industrial research laboratories.[11]

Reviewing the Statistical Spectral Analysis, Enders A Robinson wrote "In this work Professor Gardner has made a significant contribution to statistical spectral analysis, one that would please the early pioneers of spectral theory and especially Norbert Wiener."[12] James Massey wrote "I admire the scholarship of this book and its radical departure from the stochastic process bandwagon of the past 40 years."[13]

Gardner won the international IEEE Stephen O. Rice Prize Paper award in communication theory in 1988 and the International EURASIP Best Paper of the Year Award in 1987; both papers treated his theory of cyclostationarity. Gardner and his students went on to further prove the uses of his theory of cyclostationarity in applications in communications and signals intelligence. Together with his doctoral student Chi Kang Chen, he wrote the book of mathematical problem solving, The Random Processes Tutor: A Comprehensive Solutions Manual for Independent Study in 1989.[14]

Gardner, with the assistance of his doctoral student Chad Spooner, also generalized his theory from second-order to higher-order cyclostationarity in the early 1990s, and provided novel insight into the statistical quantity called the cumulant. Later, he worked on cyclostationarity exploitation in the areas of enhanced radio reception for wireless communications and, more extensively, advanced RF signals intelligence. He was the editor and contributing author of the 1994 book, Cyclostationarity in Communications and Signal Processing. Douglas Cochran wrote “this book is a timely contribution that should be a valuable reference for academic and industrial R&D engineers in signal processing and communication systems."[15]

The bulk of Gardner’s primary contributions occur throughout the literature of the latter part of the 20th century starting in the mid-1980s and are individually summed up in Antonio Napolitano’s book Cyclostationary Processes and Time Series, published in 2019.[16] His 2006 review paper, "Cyclostationarity: Half a Century of Research" received the Elsevier Most Cited Paper Award. Gardner provided the original definition and mathematical characterization of almost cyclostationary (ACS) stochastic processes, including poly-CS stochastic processes. He further gave the original definition and mathematical characterization of non-stochastic fraction-of-time (FOT) probabilistic models of CS, ACS, and poly-CS time-series. Gardner also originated the extensions and generalizations of the core theorems and relations comprising the second order and higher-order theories of stationary stochastic processes and stationary non-stochastic time-series to CS, poly-CS, and ACS processes and times-series.[17]

Applications of Gardner’s theory include his discovery and development of the fundamental operational principles of cyclostationarity—Insensitivity to Noise and Interference, and Selectivity/Separability of spectral correlation measurements and the signals themselves—as well as demonstration of applicability to design and analysis of signal processing methods and algorithms for communications, telemetry, and radar systems. This body of work has demonstrated that substantial improvements in system performance can be obtained in various signal processing applications, such as detection, estimation, and classification of signals, by exploiting cyclostationarity—that is, by recognizing and modeling the properties CS and ACS instead of using the stationary-process models which were the standard before Gardner. Major applications include cellular telephone, spectrum sensing--for cognitive radio--and signals intelligence for national security.[18] Gardner in 2016 developed the ad hoc concept of time de-warping into the basic theory of converting irregular cyclostationarity into regular cyclostationarity as a means for rendering the extensive and powerful tools of cyclostationary signal processing technology applicable to natural data exhibiting irregular cyclicity, which pervades essentially all fields of science as well as engineering.[16][1]

Gardner founded Gardner Technologies, Inc. and served as president and chief technical officer until 2006. Through Gardner Technologies, he ventured into more functional wine-packaging with patented wine bottle openers and closures. Upon terminating his brief cellular-telephone-technology venture PureWave Technologies in 2001 and his R&D firm SSPI on its 25th anniversary in 2011.[19]

• 1986 - International Best-Paper-of-the-Year award from the European Association for Signal Processing
• 1987 - Distinguished Engineering Alumnus Award from the University of Massachusetts
• 1988 - International Stephen O. Rice Prize Paper Award in the Field of Communication Theory from the IEEE Communications Society.
• 1991 - Fellow, Institute of Electrical and Electronics Engineers
• 2005 - International DuPont Award for Innovation in Food Packaging Technology
• 2005 - National Frost & Sullivan 2005 Annual Award for Consumer-Product-Design Excellence-in-Technology.
• 2008 – International Most Cited Paper Award for the period 2005 – 2007 from Elsevier

• Introduction to Random Processes with Applications to Signals and Systems (1985); 2nd ed. (1990)
• Statistical Spectral Analysis: A Non-Probabilistic Theory (1987)
• The Random Process Tutor: A Comprehensive Solutions Manual for Independent Study (1990) re-release with errata, (2014)
• Cyclostationarity In Communications and Signal Processing (Editor and Contributor) (1994)