Time varying narrowband communications channels : analysis and implementation

An efficient numerical algorithm for the analysis of wireless radio and sonar communications channels in the framework of Hilbert-Schmidt operators is derived. The underlying model is based on the description of the short-time behavior of these channels as a weighted superposition of time and frequency shift operators, where the weight function is called the spreading function of the channel operator. A description of an implementation of the developed algorithm in MatLab completes this technical report.

[1]  A. Quazi,et al.  Underwater acoustic communications , 1982, IEEE Communications Magazine.

[2]  Marc Moonen,et al.  Equalization Techniques for Fading Channels , 2004 .

[3]  Theodore S. Rappaport,et al.  Wireless communications - principles and practice , 1996 .

[4]  Marc Moonen,et al.  Time-domain and frequency-domain per-tone equalization for OFDM over doubly selective channels , 2004, Signal Process..

[5]  Werner Kozek,et al.  Perturbation Stability of Coherent Riesz Systems under Convolution Operators , 2002 .

[6]  Eugenio Hernández,et al.  Band-Limited Wavelets with Subexponential Decay , 1998, Canadian Mathematical Bulletin.

[7]  G. Folland A course in abstract harmonic analysis , 1995 .

[8]  A. Janssen The duality condition for Weyl-Heisenberg frames , 1998 .

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

[10]  Marc Moonen,et al.  Time-varying FIR equalization for doubly selective channels , 2005, IEEE Transactions on Wireless Communications.

[11]  Scott Rickard,et al.  Timefrequency and time-scale representations of doubly spread channels , 2003 .

[12]  Gerald Matz,et al.  A time-frequency calculus for time-varying systems and non-stationary processes with applications , 2000 .

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

[14]  Y. Domar Harmonic analysis based on certain commutative Banach algebras , 1956 .

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

[16]  Phillip A. Bello,et al.  Time-frequency duality , 1964, IEEE Trans. Inf. Theory.

[17]  William C. Jakes Largescale Variations of the Average Signal , 1974 .

[18]  Milica Stojanovic,et al.  Recent advances in high-speed underwater acoustic communications , 1996 .

[19]  D. Middleton,et al.  Channel Modeling and Threshold Signal Processing in Underwater Acoustics: An Analytical Overview , 1987 .

[20]  L. Carleson,et al.  The Collected Works of Arne Beurling , 1989 .

[21]  J. Conway A course in operator theory , 1999 .

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

[23]  Niklas Grip Wavelet and gabor frames and bases : approximation, sampling and applications , 2002 .

[24]  Jitendra K. Tugnait,et al.  Blind identification of time-varying channels using multistep linear predictors , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  Georgios B. Giannakis,et al.  Space-time-Doppler block coding for correlated time-selective fading channels , 2005, IEEE Transactions on Signal Processing.

[26]  Michael Frazier,et al.  Studies in Advanced Mathematics , 2004 .

[27]  Yuriy V. Zakharov,et al.  Multipath-Doppler diversity of OFDM signals in an underwater acoustic channel , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[28]  L. Hörmander The analysis of linear partial differential operators , 1990 .

[29]  Theodore G. Faticoni,et al.  Pure and Applied Mathematics: A Wiley‐Interscience Series of Texts, Monographs and Tracts , 2006 .

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

[31]  H. Feichtinger,et al.  A Banach space of test functions for Gabor analysis , 1998 .

[32]  Georgios B. Giannakis,et al.  Maximum-diversity transmissions over doubly selective wireless channels , 2003, IEEE Transactions on Information Theory.

[33]  J. Lawrence,et al.  Linear Independence of Gabor Systems in Finite Dimensional Vector Spaces , 2005 .

[34]  H. Feichtinger,et al.  Quantization of TF lattice-invariant operators on elementary LCA groups , 1998 .

[35]  Stefan Ericsson,et al.  Efficient wavelet prefilters with optimal time-shifts , 2005, IEEE Transactions on Signal Processing.

[36]  李幼升,et al.  Ph , 1989 .

[37]  H. Reiter Classical Harmonic Analysis and Locally Compact Groups , 1968 .

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

[39]  M. Reed Methods of Modern Mathematical Physics. I: Functional Analysis , 1972 .

[40]  Georgios B. Giannakis,et al.  Orthogonal multiple access over time- and frequency-selective channels , 2003, IEEE Trans. Inf. Theory.

[41]  M. Zatman,et al.  Underwater acoustic MIMO channel capacity , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[42]  Stefan Ericsson,et al.  An Analysis Method for Sampling in Shift-Invariant Spaces , 2005, Int. J. Wavelets Multiresolution Inf. Process..

[43]  R. F. Ormondroyd,et al.  A coherent COFDM modulation system for a time-varying frequency-selective underwater acoustic channel , 1997 .

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

[45]  David Francis Walnut,et al.  Measurement of Time-Variant Linear Channels , 2006, IEEE Transactions on Information Theory.

[46]  Niklas Grip,et al.  A discrete model for the efficient analysis of time-varying narrowband communication channels , 2008, Multidimens. Syst. Signal Process..

[47]  Thomas Strohmer,et al.  Pseudodifferential operators and Banach algebras in mobile communications , 2006 .

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

[49]  T. Strohmer,et al.  Optimal OFDM pulse and lattice design for doubly dispersive channels , 2001, Conference Record of Thirty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.No.01CH37256).

[50]  Georgios B. Giannakis,et al.  Maximum-diversity transmissions over time-selective wireless channels , 2002, 2002 IEEE Wireless Communications and Networking Conference Record. WCNC 2002 (Cat. No.02TH8609).