Performance Analysis of an Optimal Circular 16-QAM for Wavelet Based OFDM Systems
- 1
- 2
- 3
Abstract
The BER performance for an optimal circular 16-QAM constellation is theoretically derived and applied in wavelet based OFDM system in additive white Gaussian noise channel. Signal point constellations have been discussed in much literature. An optimal circular 16-QAM is developed. The calculation of the BER is based on the four types of the decision boundaries. Each decision boundary is determined based on the space distance d following the pdf Gaussian distribution with respect to the in-phase and quadrature components nI and nQ with the assumption that they are statistically independent to each other. The BER analysis for other circular M-ary QAM is also analyzed. The system is then applied to wavelet based OFDM. The wavelet transform is considered because it offers a better spectral containment feature compared to conventional OFDM using Fourier transform. The circular schemes are slightly better than the square schemes in most SNR values. All simulation results have met the theoretical calculations. When applying to wavelet based OFDM, the circular modulation scheme has also performed slightly less errors as compared to the square modulation scheme.
- J. G. Proakis, “Digital communications,” Fourth edition, New York: McGraw-Hill, 2001.
- R. V. Nee and R. Prasad, “OFDM for wireless multimedia communications,” Boston: Artech House, 2000.
- M. P. Fitz and J. P. Seymour, “On the bit error probability of QAM modulation,” International Journal of Wireless Information Networks, Vol. 1, No. 2, pp. 131–139, 1994.
- K. Cho and D. Yoon, “On the general BER expression of one and two dimensional amplitude modulations,” IEEE Transactions on Communications, Vol. 50, No. 7, pp. 1074–1080, July 2002.
- I. Daubechies, “Ten lectures on wavelets,” Philapdelphia: Society for Industrial and Applied Mathematics, 1992.
- M. Weeks, “Digital signal processing using matlab and wavelets,” Infinity Science Press LLC, 2007.
- C. S. Burrus, R. A. Gopinath, and H. Guo, “Introduction to wavelets and wavelet transforms,” Upper Sadle River, NJ: Prentice-Hall, 1998.
- R. Mirghani and M. Ghavami, “Comparison between wa- velet-based and Fourier-based multicarrier UWB systems,” IET Communications, Vol. 2, No. 2, pp. 353–358, 2008.
- S. D. Sandberg and M. A. Tzannes, “Overlapped discrete multitone modulation for high speed copper wire communications,” IEEE Journal on Selected Areas in Communications, Vol. 13, No. 9, pp. 1571–1585, 1995.
- F. Xiong, “Digital modulation techniques,” Second edition, Boston: Artech House, 2006.
- I. Daubechies, “Orthonormal bases of compactly supported wavelets,” Communications in Pure and Applied Math., Vol. 41, pp. 909–996, 1988.
- A. N. Akansu, “Wavelets and filter banks: A signal processing perspective,” Tutorial in Circuit and Devices, November 1994.
- L. Cui, B. Zhai, and T. Zhang, “Existence and design of biorthogonal matrix-valued wavelets,” Nonlinear Analysis: Real World Applications, Vol. 10, pp. 2679–2687, 2009.
- R. M. Rao and A. S. Bopardikar, “Wavelet transforms: Introduction to theory and applications,” MA: Addison- Wesley, 1998.
- R. K. Young, “Wavelet theory and its applictions,” Massachusetts: Kluwer Academic, 1993.
- B. G. Negash and H. Nikookar, “Wavelet based OFDM for wireless channels,” Vehicular Technology Conference, 2001.
- N. Ahmed, ”Joint detection strategies for orthogonal frequency division multiplexing,” Dissertation for Master of Science, Rice University, Houston, Texas, pp. 1–51, April 2000.