Measurement of time-variant linear channels

IEEE Transactions on Information Theory

Volumn 52, Issue 11, 2006, Pages 4808-4820

  Pfander, Götz E ^a   Walnut, David F ^b  

^a JACOBS UNIVERSITY BREMEN   (Germany)

^b GEORGE MASON UNIVERSITY   (United States)

Author keywords

Bandlimited Kohn Nirenberg symbols; Channel measurement; Gabor and time frequency analysis; Operator identification; Spreading functions; Underspread operators

Indexed keywords

FOURIER TRANSFORMS; MATHEMATICAL OPERATORS;

CHANNEL MEASUREMENT; KOHN-NIRENBERG SYMBOLS; OPERATOR IDENTIFICATION; SPREADING FUNCTIONS; TIME-FREQUENCY ANALYSIS; UNDERSPREAD OPERATORS;

COMMUNICATION CHANNELS (INFORMATION THEORY);

EID: 33750576200     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.883553     Document Type: Article

References (38)

1. T. Kailath, Sampling models for linear time-variant filters Massachusetts Institute of Technology, Research Laboratory of Electronics, Tech. Rep. 352, 1959.
2. T. Kailath, "Measurements on time-variant communication channels," IEEE Trans. Inf. Theory, vol. 8, pp. 229-236, Sep. 1962.
3. T. Kailath, "Time-variant communication channels," IEEE Trans. Inf. Theory, pp. 233-237, Oct. 1963.
4. D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty. I," Bell Syst. Tech. J., vol. 40, pp. 43-63, 1961.
5. H. Landau and H. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty. II," Bell Syst. Tech. J., vol. 40, pp. 65-84, 1961.
6. H. Landau and H. Pollak, "Prolate spheroidal wave functions, Fourier analysis and uncertainty. III. The dimension of the space of essentially time- and bandlimited signals," Bell Syst. Tech. J., vol. 41, pp. 1295-1336, 1962.
7. W. Kozek and G. Pfander, "Identification of operators with bandlimited symbols," SIAM J. Math. Anal., vol. 37, no. 3, pp. 867-888, 2006.
8. P. Bello, "Measurement of random time-variant linear channels," IEEE Trans. Commun., vol. 15, pp. 469-475, 1969.
9. J. Lawrence, G. Pfander, and D. Walnut, "Linear independence of Gabor systems in finite dimensional vector spaces," J. Fourier Anal. Appl., vol. 11, no. 6, pp. 715-726, 2005.
10. P. Green, "Radar measurements of target scattering properties," in Radar Astronomy. New York: McGraw-Hill, 1968, pp. 1-78.
11. M. Skolnik, Introduction to Radar Systems. New York: McGraw-Hill, 1980.
12. H. Van Trees, Detection, Estimation and Modulation Theory. New York: Wiley, 1971.
13. G. Folland and A. Sitaram, "The uncertainty principle: A mathematical survey," J. Four. Anal. Appl., vol. 3, no. 3, pp. 207-238, 1997.
14. K. Gröchenig, Foundations of Time-Frequency Analysis. Boston, MA: Birkhäuser, 2001, Applied and Numerical Harmonic Analysis.
15. J. Dieudonné, Treatise on Analysis. Vol II Transl.:TRanslated from the French by I. G. MacDonald. New York: Academic Press, 1970, vol. 10-II, Pure and Applied Mathematics.
16. S. Gaal, Linear Analysis and Representation Theory. New York: Springer-Verlag, 1973.
17. B. Fleury and P. Leuthold, "Radiowave propagation in mobile communications: An overview of european research," IEEE Commun. Mag., vol. 34, no. 2, pp. 70-81, 1996.
18. D.-S Yoo, "Channel Characterization and System Design in Wireless Communications," Ph.D., Univ. of Michigan, Ann Arbor, 2002.
19. D. Gabor, "Theory of communication," J. IEE, London, vol. 93, no. 3, pp. 429-457, Nov. 1946.
20. I. Daubechies, "Time-frequency localization operators: A geometric phase space approach," IEEE Trans. Inf. Theory, vol. 34/4, Jul. 1988.
21. C. Heil, J. Ramanathan, and P. Topiwala, "Singular values of compact pseudodifferential operators," J. Funct. Anal., vol. 150, no. 2, pp. 426-452, 1997.
22. H. Feichtinger and W. Kozek, "Quantization of TF-lattice invariant operators on elementary LCA groups," in Gabor Analysis and Algorithms: Theory and Applications, H. Feichtinger and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, pp. 233-266.
23. W. Kozek, "Adaptation of Weyl-Heisenberg frames to underspread environments," in Gabor Analysis and Algorithms: Theory and Applications, H. Feichtinger and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, pp. 323-352.
24. R. Rochberg and K. Tachizawa, "Pseudodifferential operators, Gabor frames, and local trigonometric bases," in Gabor Analysis and Algorithms: Theory and Applications, H. Feichtinger and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, pp. 171-192.
25. D. Labate, "Time-frequency analysis of pseudodifferential operators," Monatsh. Math., vol. 133, no. 2, pp. 143-156, 2001.
26. H. Feichtinger and K. Nowak, "A first survey of Gabor multipliers," in Advances in Gabor Analysis. Boston, MA: Birkhäuser Boston, 2003, Appl. Numer. Harmon. Anal., pp. 99-128.
27. E. Cordero and K. Gröchenig, "Time-frequency analysis of localization operators," J. Funct. Anal., vol. 205, no. 1, pp. 107-131, 2003.
28. C. Heil, "Integral operators, pseudodifferential operators, and Gabor frames," in Advances in Gabor Analysis. Boston, MA: Birkhäuser Boston, 2003, Appl. Numer. Harmon. Anal., pp. 153-169.
29. P. Gibson, M. Lamoureux, and G. Margrave, Representation of Linear Operators by Gabor Multipliers, 2004, to be published.
30. H. Feichtinger, "On a new segal algebra," Monatsh. Math., vol. 92, pp. 269-289, 1981.
31. Y. Katznelson, An Introduction to Harmonic Analysis. New York: Dover, 1976.
32. H. Feichtinger and P. Gröbner, "Banach spaces of distributions defined by decomposition methods. I," Math. Nachr., vol. 123, pp. 97-120, 1985.
33. H. Feichtinger and G. Zimmermann, "A Banach space of test functions for Gabor analysis," in Gabor Analysis and Algorithms: Theory and Applications, H. Feichtinger and T. Strohmer, Eds. Boston, MA: Birkhäuser, 1998, pp. 123-170.
34. G. B. Folland, Real Analysis, 2nd ed. New York: John Wiley & Sons Inc., 1999, Pure and Applied Mathematics (New York).
35. Y. Lyubarskii, "Frames in the Bargmann space of entire functions," Adv. Soviet Math., vol. 429, pp. 107-113, 1992.
36. K. Seip and R. Wallstén, "Density theorems for sampling and interpolation in the Bargmann-Fock space. II," J. Reine Angew. Math., vol. 429, pp. 107-113, 1992.
37. K. Seip, "Density theorems for sampling and interpolation in the Bargmann-Fock space. I," J. Reine Angew. Math., vol. 429, pp. 91-106, 1992.
38. G. Pfander, Two results on the Invertibility of Bi-Infinite Matrices with Applications to Gabor Analysis, 2005, to be published.