Coherence

David Ramírez is Associate Professor of Electrical Engineering at the Universidad Carlos III de Madrid (UC3M). Before joining UC3M, he was Research Associate and Assistant Professor at the Universität Paderborn, Germany, and Visiting Researcher at University of Newcastle, Australia, University College London, and Colorado State University, Fort Collins. His research interests are in the area of statistical signal processing, as it applies to wireless communication and bio-medicine. He has participated in many national and international research projects related to the these topics. Prof. Ramírez has co-authored more than 75 publications in refereed journals and international conferences/workshops. Prof. Ramírez received the 2012 IEEE Signal Processing Society Young Author Best Paper Award and a Certificate of Merit awarded by the IEEE Signal Processing Society “for outstanding editorial board service for the IEEE Transactions on Signal Processing” in 2020. He is a Senior Member of IEEE.Ignacio Santamaría is a Professor of Electrical Engineering at the Universidad de Cantabria, Santander, Spain. His research interests lie at the intersection of statistical signal processing, machine learning, and information theory, with special emphasis on applications to wireless communication systems and multi-sensor signal processing for radar and sonar.  He has been involved in numerous national and international research projects on these topics, with more than 200 publications co-authored in refereed journals and international conference proceedings. He has been a visiting researcher at the University of Florida,  University of Texas at Austin, and Colorado State University, Fort Collins. He has served as a member of the IEEE Machine Learning for Signal Processing and Signal Processing Theory and Methods Technical Committees, and as a steering committee member of the IEEE Data Science Initiative. He served as Associate Editor and Senior AreaEditor of the IEEE Transactions on Signal Processing. Prof. Santamaría was general Co-Chair of the 2012 IEEE Workshop on Machine Learning for Signal Processing (MLSP 2012). He was a co-recipient of the 2008 EEEfCOM Innovation Award, and co-author of a paper that received the 2012 IEEE Signal Processing Society Young Author Best Paper Award. He is a Senior Member of IEEE.Louis Scharf is Research Professor of Mathematics and Emeritus Professor of Electrical and Computer Engineering at Colorado State University, Fort Collins, CO. He holds a courtesy appointment in Statistics. His research interests are in statistical signal processing and machine learning as these disciplines apply to space-time adaptive processing for communication, radar, sonar, and remote sensing; to modal analysis for electric power system monitoring; to spectrum analysis for nonstationary times series modeling and hyperspectral imaging; and to image processing for group-invariant classification and registration. He has made original contributions to matched and adaptive subspace detection; to group-invariant signal processing; to spectrum analysis; and to reduced-rank signal processing. Prof. Scharf has co-authored the books, L.L. Scharf, "Statistical Signal Processing: Detection, Estimation, and Time Series Analysis," Addison-Wesley, 1991, and P.J. Schreier and L.L. Scharf, "Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals," Cambridge University Press, 2010. His co-authored book, L.L. Scharf and R.T. Behrens, A First Course in Electrical and Computer Engineering," Addison-Wesley, Reading, MA, 1990, was re-published by Connexions in 2008. Professor Scharf has received several awards for his contributions to statistical signal processing, including the Technical Achievement and Society Awards from the IEEE Signal Processing Society; the Donald W. Tufts Award for Underwater Acoustic Signal Processing, a Diamond Award for Academic Excellence from the University of Washington, and the 2016 IEEE Jack S. Kilby Medal for Signal Processing. In 2021 he received the Education Award from the IEEE Signal Processing Society. Professor Scharf is a Life Fellow of IEEE.

• Introduction.- Historical perspective, motivating problems, and preview of what is to come.- Least Squares and related.- Classical correlations and coherence.- Coherence in the multivariate normal (MVN) model.- Classical tests for correlation.- One-channel matched subspace detectors.- Adaptive subspace detectors.- Two channel matched subspace detectors.- Detection of spatially-correlated time series.- Coherence and the detection of cyclostationarity.- Partial coherence for testing causality.- Subspace averaging.- Coherence and performance bounds.- Variations on coherence.- Conclusion.