Bandwidth Efficient Digital Communication with Wavelet Approximations

  • Lo, Chet (Electrical and Computer Engineering Department, Utah State University) ;
  • Moon, Todd K. (Electrical and Computer Engineering Department Utah State University)
  • Published : 2002.06.01

Abstract

Based on their shift and scale orthogonality properties, scaling and wavelet functions may be used as signaling functions having good frequency localization as determined by the fractional-out-of-band power (FOOBP). In this paper, application of Daubechies' wavelet and scaling functions as baseband signaling functions is described, with a focus on finding discretely realizable pulse-shaping transfer function circuits whose outputs approximate scaling and wavelet functions when driven by more conventional digital signaling waveforms. It is also shown that the inter-symbol interference (ISI) introduced by the approximation has negligible effect on the performance in terms of signal-to-noise ratio (SNR). Moreover, the approximations are often more bandwidth efficient than the original wavelet functions. These waveforms thus illustrate an example solution of a tradeoff between residual ISI and bandwidth efficiency as a signal design problem.

Keywords

References

  1. T. K. Moon, 'Wavelets and orthogonal (lattice) spaces,' in Proc. Int. Symp. Inform, Theory, 1995, p. 250
  2. A. R. Lindsey, Generaliwd orthogonally multiplexed communication via wavelet packet bases, Ph.D. thesis, Ohio University, Athens, Ohio, June 1995
  3. M. Luise, M. Marselli, and R. Reggiannini, 'dock synchronization for wavelet-based multirate transmissions,' IEEE Trans. Commun., vol. 48, pp. 1047-1054, June 2000 https://doi.org/10.1109/26.848567
  4. E. Panayirci, T. Ozugur, and H. Caglar, 'Design of optimum Nyquist signals based on generalized sampling theory for data communications,' IEEE Trans. Signal Processing, vol. 47, pp. 1753-1759, June 1999 https://doi.org/10.1109/78.765161
  5. J. N. Livingston and C.-C. Tiing, 'Bandwidth efficient signaling using wavelets,' lEEETrans. Commun., vol. 44, pp. 1629-1631, Dec. 1996 https://doi.org/10.1109/26.545889
  6. C. Lo, 'Applicadon of wavelet function approximations for bandwidth-efficient digital communication,' Master's thesis, Utah State University, Logan, UT, Feb. 1998
  7. F. Daneshgaran and M. Mondin, 'Bandwidth efficient moduladon with wavelets,' Electron. Lett., vol. 30, pp. 1200-1202, July 1994 https://doi.org/10.1049/el:19940821
  8. R. E. Ziemer and W. H. Tranter, Principles a/communications. Boston: Houghton Mifflin Company, 3 ed., 1990
  9. I. Daubechies, Ten lectures on wavelets, Philadelphia, PA: Society for Industrial and Applied Mathematics, 1992
  10. A. Ralston and P. Rabinowitz, A first course in numerical analysis. New York: McGraw Hill, 2 ed., 1978
  11. W. H. Press et at., Numehcal recipes in C. New York: Cambridge Univer-sity Press, 2 ed., 1992