A New Construction of 16-QAM Codewords with Low Peak Power

Authors: Jiaxiang Zhao

Abstract:

We present a novel construction of 16-QAM codewords of length n = 2k . The number of constructed codewords is 162×[4k-1×k-k+1] . When these constructed codewords are utilized as a code in OFDM systems, their peak-to-mean envelope power ratios (PMEPR) are bounded above by 3.6 . The principle of our scheme is illustrated with a four subcarrier example.

Keywords: Extended Rudin-Shapiro construction, orthogonal frequency division multiplexing (OFDM), peak-to-mean envelope power ratio (PMEPR)

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078757

References:

[1] C. R┬¿oβing and V. Tarokh, "A construction of OFDM 16-QAM codewords having low peak powers", IEEE Trans. Inform. Theory, Vol. 47, No. 5, pp. 2091-2094, Nov. 2001.
[2] A.E. Jones, T.A. Wilkinson and S.K. Barton, "Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes", Electron. Lett., Vol. 30, No. 25, pp. 2098-2099, Dec. 1994.
[3] C.V. Chong, R. Venkataramani and V. Tarokh, "A new construction of 16-QAM Golay complementary sequences", IEEE Trans. Inform. Theory, Vol. 49, No. 11, pp. 2953-2959, Nov. 2003.
[4] S. Boyd, "Multitone signals with low crest factor", IEEE Trans. Circuits Syst., Vol. CAS-33, No. 10, pp. 1018-1022, 1986.
[5] J. A. Davis and J. Jedwab, "Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes", IEEE Trans. Inform. Theory, Vol. 45, No. 7, pp. 2397-2417, Nov. 1997.
[6] J. A. C. Bingham, "Multicarrier modulation for data transmission: An idea whose time has come", IEEE Commun. Mag., Vol. 28, No. 1, pp. 5-14, May 1990.
[7] X. Li and L. J. Cimini Jr., "Effects of clipping on the performance of OFDM with transmitter diversity", Proc. IEEE VTC97, pp. 1634-1638, May 1997.
[8] M. G. Parker and C. Tellambura, "Generalised Rudin-Shapiro constructions", Electronic Notes in Discrete Mathematics, WCC2001 International Workshop on Coding and Cryptography, Vol. 6, Paris, April 2001.
[9] M. An, J. Byrnes, W. Moran, B. Saffari, H. S. Shapiro and R. Tolimieri, "PONS, Reed-Muller codes, and group algebras", NATO Advanced Study Institute: Computational Noncommutative Algebra and Applications, Tuscany, Italy, July 2003.
[10] J. Zhao, "Efficient identification of the codewords with low peak-tomean envelope power ratio of multicarrier transmission", Proc. IEEE VTC04, pp. 373-377, Sept. 2004.
[11] J. Zhao, "A peak-to-mean power control scheme-the extended Rudin- Shapiro construction", Proc. IEEE VTC04, pp. 621-625, Sept. 2004.
[12] D. Wulich, "Reduction of peak-to-mean ratio of multicarrier modulation using cyclic coding", Electron. Lett., Vol. 32, No. 5, pp. 432-433, Feb. 1996.
[13] R. B¨auml, R. Fischer and J. Huber, "Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping", Elect. Letts., Vol. 32, No. 22, pp. 2056-2057, Oct. 1996.