Wireless multicarrier digital transmission via frames: Capacity analysis and optimization design

Abstract

By treating information transmission as tiling over the time-frequency plane, we propose a digital signal transmission scheme employing overcomplete frames as modulation pulses. The new scheme can achieve a signaling rate larger than the Nyquist rate. We first analyze the capacity performance of the frame transmission scheme over additive white Gaussian noise (AWGN) channels. It proves that the proposed scheme can achieve the Shannon capacity asymptotically. Next, we design the Gabor frame system parameters in time-frequency dispersive channels. It is shown that the pulses shape and the time-frequency separation should be matched to the channel dispersion parameters to achieve the minimum energy perturbation. Numerical results are presented to verify the theoretical findings.

Key words： overcomplete; frame; Nyquist rate; signaling efficiency; capacity

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 60975041, 61071067, and 61033004).

References

1 Akansu A N, Duhamel P, Lin X, de Courville M. Orthogonal transmultiplexers in communication: A review. IEEE Transactions on Signal Processing, 1998, 46(4): 979-995

2 Weinstein S B, Ebert P M. Data transmission by frequency division multiplexing using the discrete Fourier transform. IEEE Transactions on Communication Technology, 1971, 19(5): 628-634

3 Kozek W, Molisch A F. Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels. IEEE Journal on Selected Areas in Communications, 1998, 16(8): 1579-1589

4 Haas R, Belfiore J C. A time-frequency well-localized pulse for multiple carrier transmission. Wireless Personal Communications, 1997, 5(1): 1-18

5 Strohmer T, Beaver S. Optimal OFDM design for time-frequency dispersive channels. IEEE Transactions on Communications, 2003, 51(7): 1111-1122

6 Daubechies I. Ten Lectures on Wavelets. Philadelphia: SIAM, 1992

7 Bölcskei H, Duhamel P, Hleiss R. Orthogonalization of OFDM/OQAM pulse shaping filters using the discrete Zak transform. Signal Processing, 2003, 83(7): 1379-1391

8 Jung P, Wunder G. The WSSUS pulse design problem in multicarrier transmission. IEEE Transactions on Communications, 2007, 55(10): 1918-1928

9 Matz G, Schafhuber D, Grochenig K, Hartmann M, Hlawatsch F. Analysis optimization, and implementation of low interference wireless multicarrier systems. IEEE Transactions on Wireless Communications, 2007, 6(5): 1921-1931

10 Heath R W Jr, Strohmer T, Paulraj A J. On quasi-orthogonal signatures for CDMA systems. IEEE Transactions on Information Theory, 2006, 52(3): 1217-1226

11 Goyal V K, Kovacevic J. Generalized multiple description coding with correlating transforms. IEEE Transactions on Information Theory, 2001, 47(6): 2199-2224

12 Goyal V K, Kovacevic J, Kelner J A. Quantized frame expansions with erasures. Applied and Computational Harmonic Analysis, 2001, 10(3): 203-233

13 Hochwald B M, Marzetta T L, Richardson T J, Sweldens W, Urbanke R. Systematic design of unitary space-time constellations. IEEE Transactions on Information Theory, 2000, 46(6): 1962-1973

14 Heath R W Jr, Bölcskei H, Paulraj A J. Space-time signaling and frame theory. In: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing. 2001, 4: 2445-2448

15 Heath R W Jr, Paulraj A J.Linear dispersion codes for MIMO systems based on frame theory. IEEE Transactions on Signal Processing, 2002, 50(10): 2429-2441

16 Han F M, Zhang X D. Wireless multicarrier digital transmission via Weyl-Heisenberg frames over time-frequency dispersive channels. IEEE Transactions on Communications, 2009, 57(6): 1721-1733

17 Shannon C E.A mathematical theory of communication. The Bell System Technical Journal, 1948, 27: 379-423, 623-656

18 Nyquist H. Certain topics in telegraph transmission theory. AIEE Transactions, 1928, 47: 617-644

19 Shannon C E. Communication in the presence of noise. Proceedings of the IRE, 1949, 37(1): 10-21

20 Silverstein J W, Bai Z D. On the empirical distribution of eigenvalues of a class of large dimensional random matrices. Journal of Multivariate Analysis, 1995, 54(2): 175-192

21 Cover T M, Thomas J A. Elements of Information Theory. New York: Wiley, 1991

22 Gallager R G. Information Theory and Reliable Communication. New York: Wiley, 1968

23 Bello P A. Characterization of randomly time-variant linear channels. IEEE Transactions on Communications Systems, 1963, 11(4): 360-393

24 Daubechies I. The wavelet transform, time-frequency localization and signal analysis. IEEE Transactions on Information Theory, 1990, 36(5): 961-1005

25 Feichtinger H G, Strohmer T. Gabor Analysis and Algorithms: Theory and Applications. Boston: Birkhauser, 1998

26 Le Floch B, Alard M, Berrou C. Coded orthogonal frequency division multiplex. Proceedings of the IEEE, 1995, 83(6): 982-996

27 Schafhuber D, Matz G, Hlawatsch F. Pulse-shaping OFDM/BFDM systems for time-varying channels: ISI/ICI analysis, optimal pulse design, and efficient implementation. In: Proceedings of the 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications. 2002, 3: 1012-1016

28 Liu K, Kadous T, Sayeed A M. Orthogonal time-frequency signaling over doubly dispersive channels. IEEE Transactions on Information Theory, 2004, 50(11): 2583-2603

29 Cohen L. Time-Frequency Analysis. New York: Prentice-hall, 1995

30 Strohmer T. Approximation of dual Gabor frames, windows decay, and wireless communications. Applied and Computational Harmonic Analysis, 2001, 11(2): 243-262

31 Lyubarskii Y. Frames in the Bargmann space of entire functions. In: Levin B Y, ed. Entire and Subharmonic Functions. Vol. 11 of the series Advances in Soviet Mathematics. Berlin: Springer-Verlag, 1989