Time-Frequency Foundations of Communications

In the tradition of Gabor's 1946 landmark paper [1], we advocate a time-frequency (TF) approach to communications. TF methods for communications have been proposed very early (see the box History). While several tutorial papers and book chapters on the topic are available (see, e.g., [2]-[4] and references therein), the goal of this paper is to present the fundamental aspects in a coherent and easily accessible manner. Specifically, we establish the role of TF methods in communications across a range of subject areas including TF dispersive channels, orthogonal frequency division multiplexing (OFDM), information-theoretic limits, and system identification and channel estimation. Furthermore, we present fundamental results that are stated in the literature for the continuous-time case in simple linear algebra terms.

[1]  P. Bello.  Characterization of Randomly Time-Variant Linear Channels , 1963 .

[2]  Gerald Matz,et al.  Fundamentals of Time-Varying Communication Channels , 2011 .

[3]  Akbar M. Sayeed,et al.  Joint multipath-Doppler diversity in mobile wireless communications , 1999, IEEE Trans. Commun..

[4]  Thomas Strohmer,et al.  High-Resolution Radar via Compressed Sensing , 2008, IEEE Transactions on Signal Processing.

[5]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[6]  T. Strohmer,et al.  Gabor Analysis and Algorithms: Theory and Applications , 1997 .

[7]  Markku Renfors,et al.  Filter Banks for Next Generation Multicarrier Wireless Communications , 2010, EURASIP J. Adv. Signal Process..

[8]  Shlomo Shamai,et al.  Fading Channels: Information-Theoretic and Communication Aspects , 1998, IEEE Trans. Inf. Theory.

[9]  D. Slepian,et al.  On bandwidth , 1976, Proceedings of the IEEE.

[10]  Georgios B. Giannakis,et al.  Modelling and equalization of rapidly fading channels , 1996 .

[11]  W. Marsden.  I and J , 2012 .

[12]  L. Freitag,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE JOURNAL OF OCEANIC ENGINEERING 1 Peer-Reviewed Technical Communication Multicarrier Communication Over Un , 2022 .

[13]  Georgios B. Giannakis,et al.  Wireless multicarrier communications , 2000, IEEE Signal Process. Mag..

[14]  Robert Bregovic,et al.  Multirate Systems and Filter Banks , 2002 .

[15]  P. Bello,et al.  Measurement of random time-variant linear channels , 1969, IEEE Trans. Inf. Theory.

[16]  Werner Kozek,et al.  Identification of Operators with Bandlimited Symbols , 2005, SIAM J. Math. Anal..

[17]  Gerald Matz,et al.  Nonstationary spectral analysis based on time-frequency operator symbols and underspread approximations , 2006, IEEE Transactions on Information Theory.

[18]  Helmut Boelcskei.  Efficient design of pulse-shaping filters for OFDM systems , 1999, Optics & Photonics.

[19]  Antonio Ruiz,et al.  Frequency domain data transmission using reduced computational complexity algorithms , 1980, ICASSP.

[20]  Luís Díez del Río,et al.  Analysis of the cyclic short-term variation of indoor power line channels , 2006, IEEE Journal on Selected Areas in Communications.

[21]  Andreas F. Molisch,et al.  On the systematic measurement errors of correlative mobile radio channel sounders , 2002, IEEE Trans. Commun..

[22]  N. Thomas Gaarder,et al.  Scattering function estimation , 1968, IEEE Trans. Inf. Theory.

[23]  Prashant Parikh.  A Theory of Communication , 2010 .

[24]  Patrick Flandrin,et al.  Time-Frequency/Time-Scale Analysis , 1998 .

[25]  T. Kailath,et al.  Measurements on time-variant communication channels , 1962, IRE Trans. Inf. Theory.

[26]  Robert Spayde Kennedy,et al.  Fading dispersive communication channels , 1969 .

[27]  Philip Schniter,et al.  Max-SINR ISI/ICI-Shaping Multicarrier Communication Over the Doubly Dispersive Channel , 2007, IEEE Transactions on Signal Processing.

[28]  Andreas F. Molisch,et al.  Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels , 1998, IEEE J. Sel. Areas Commun..

[29]  Jason Wexler,et al.  Discrete Gabor expansions , 1990, Signal Process..

[30]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

[31]  M. Melamed.  Detection , 2021, SETI: Astronomy as a Contact Sport.

[32]  Lajos Hanzo,et al.  Coherent versus Non-coherent and Cooperative Turbo Transceivers , 2010 .

[33]  Fredrik Tufvesson,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. INVITED PAPER Vehicular Channel Characterization and Its Implications for Wireless System Design and Performan , 2022 .

[34]  R. Chang.  Synthesis of band-limited orthogonal signals for multichannel data transmission , 1966 .

[35]  Manfred Martin Hartmann,et al.  Analysis, Optimization, and Implementation of Low-Interference Wireless Multicarrier Systems , 2007, IEEE Transactions on Wireless Communications.

[36]  I. Daubechies,et al.  Gabor Time-Frequency Lattices and the Wexler-Raz Identity , 1994 .

[37]  Shlomo Shamai,et al.  Information Theory of Underspread WSSUS Channels , 2011 .

[38]  F. Hlawatsch,et al.  Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory , 1998 .

[39]  Uwe Ladebusch,et al.  Terrestrial DVB (DVB-T): A Broadcast Technology for Stationary Portable and Mobile Use , 2006, Proceedings of the IEEE.

[40]  O. Christensen.  An introduction to frames and Riesz bases , 2002 .

[41]  Helmut Bölcskei,et al.  Identification of Sparse Linear Operators , 2012, IEEE Transactions on Information Theory.

[42]  D. A. Bell,et al.  Information Theory and Reliable Communication , 1969 .

[43]  Cornel Ioana,et al.  Time-scale and dispersive processing for wideband time-varying channels , 2011 .

[44]  A. Janssen.  Duality and Biorthogonality for Weyl-Heisenberg Frames , 1994 .

[45]  Erik Haas,et al.  Aeronautical channel modeling , 2002, IEEE Trans. Veh. Technol..

[46]  Gerald Matz,et al.  Wireless Communications Over Rapidly Time-Varying Channels , 2011 .