Digital modulation scheme in four dimensions based on wavelets

  • Jesús Mauricio Ramírez Viáfara Universidad del Cauca
  • Harold Armando Romo Romero Universidad del Cauca
Keywords: Constellation, spectral efficiency, orthonormal wavelet basis, wavelet.


Information transmission over noisy channels in an efficient and reliable way is a primary objective of digital communication. In this article we propose a digital modulation scheme with a signal space of four dimensions to increase reliability. The signal space of this scheme is constructed on an orthonormal wavelet basis and its constellation is shaped by the eight farthest vertices of a hypercube centered on origin. For decisions based on minimum Euclidean distance, the proposed modulation scheme overcomes the performance against noise of that of quaternary quadrature amplitude modulation (4-QAM). This result allows us to say that a suitable design of constellation over a signal space with more than two dimensions can achieve a reduction in the bit error rate without a significant reduction of spectral efficiency.


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Author Biographies

Jesús Mauricio Ramírez Viáfara, Universidad del Cauca

Engineer in Electronics and Telecommunications and Master (c) in Electronics and Telecommunications (Universidad del Cauca). Professor and researcher of the Electronics and Telecommunications Faculty at the Universidad del Cauca. IEEE member.


Harold Armando Romo Romero, Universidad del Cauca

Bachelor degree in Mathematics (Universidad de Nariño, Pasto-Colombia); Engineer in Electronics, Specialist in Networks and Telematic Services, and Master in Electronics and Telecommunications (Universidad del Cauca, Popayán-Colombia). Professor and researcher of the Electronics and Telecommunications Faculty at the Universidad del Cauca. His main interest areas are signal processing and wireless communications. IEEE member.


Benvenutto, N. & Cherubini, G. (2002). Algorithms for communication systems and their applications. New York, NY: Wiley.

Cover, M. & Thomas, J.A. (2006). Elements of information theory (2nd ed.). New York, NY: Wiley.

Daubechies, I. (1988). Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics, 4, 909-996.

Daubechies, I. (1992). Ten Lectures on Wavelets. Philadelphia, PA: SIAM.

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

Forney, G.D. (2005). Principles of digital communications II. Boston, MA: MIT.

Forney, G.D. & Ungerboeck, G. (1998). Modulation and coding for linear Gaussian channels. IEEE Transactions on Information Theory, 44(6), 2384-2415.

Gallager, R.G. (1968). Information theory and reliable communication. New York, NY: Wiley.

Gallager, R.G. (2006). Principles of digital communications I. Boston, MA: MIT.

Hartley, V.L. (1928). Transmission of information. Bell System Technical Journal, 7, 535-563.

Haykin, S. (2002). Communication systems. New York, NY: Wiley.

Lindsey, A.R. (1997). Wavelet packet modulation for orthogonally multiplexed communications. IEEE Transactions on Signal Processing, 45(5), 1336-1339.

Lindsey, A.R. & Medley, M.J. (1996). Wavelet transform and filter banks in digital communications. SPIE Proceedings [Wavelet Applications III], 2762(48). doi:10.1117/12.236018

Livingston, J.N. & Tung, C. (1996). Bandwidth efficient PAM signaling using wavelets. IEEE Transactions in Communications, 44(12), 1629-1631.

Mallat, S. (1998). A wavelet tour of signal processing. London, UK: Academic Press.

Noguchi, T., Daido, Y., & Nossek, J. (1986). Modulation techniques for microwave digital radio. IEEE Communications Magazine, 24(10), 21-30.

Nyquist, H. (1928). Certain topics in telegraph transmission theory. Transactions AIEE, 47, 627-644.

Proakis, G. (2000). Digital communications (4th ed.). New York, NY: McGraw-Hill.

Pursley, M. (2005). Introduction to digital communications. Englewood Cliffs, NJ: Prentice-Hall.

Shannon, C.E. (1948). A mathematical theory of communications. Bell System Technical Journal, 27, 379-423, 623-656.

Wornell, G.W. & Oppenheim, A.V. (1992). Wavelet-based representations for a class of self-similar signals with application to fractal modulation. IEEE Transactions in Information Theory, 38(2), 785-800.
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