Many-parameter m-complementary Golay sequences and transforms
Labunets V.G., Chasovskikh V. P., Smetanin Ju.G., Ostheimer E.

 

Ural State Forest Engineering University, Sibirskiy trakt, 37, Ekaterinburg, Russia, 620100,
Federal Research Center “Information and Control” of the RAS, Vavilov street 44 /(2), Moscow, Russia, 119333,

Capricat LLC, Pompano Beach, Florida, USA

 PDF

Abstract:
In this paper, we develop the family of Golay–Rudin–Shapiro (GRS) m-complementary many-parameter sequences and many-parameter Golay transforms. The approach is based on a new generalized iteration generating construction, associated with n unitary many-parameter transforms and n arbitrary groups of given fixed order. We are going to use multi-parameter Golay transform in Intelligent-OFDM-TCS instead of discrete Fourier transform in order to find out optimal values of parameters optimized PARP, BER, SER, anti-eavesdropping and anti-jamming effects.

Keywords:
complementary sequences, many-parameter orthogonal transforms, fast algorithms, OFDM systems.

Citation:
Labunets VG, Chasovskikh VP, Smetanin JuG, Ostheimer E. Many-parameter m-complementary Golay sequences and transforms. Computer Optics 2018; 42(6): 1074-1082. DOI: 10.18287/2412-6179-2018-42-6-1074-1082.

References:

  1. Golay MJE. Multi-slit spectrometry. J Opt Soc Am 1949; 39(6): 437-444. DOI: 10.1364/JOSA.39.000437.
  2. Golay MJE. Complementary series. IRE Transaction on Information Theory 1961; 7(2): 82-87. DOI: 10.1109/TIT.1961.1057620.
  3. Golay MJE. Sieves for low autocorrelation binary sequences. IEEE Transactions on Information Theory 1977; 23(1): 43-51. DOI: 10.1109/TIT.1977.1055653.
  4. Shapiro HS. Extremal problems for polynomials and power series. ScM.Thesis. Massachusetts Institute of Technology; 1951.
  5. Shapiro HS. A power series with small partial sums. Notices of the AMS 1958; (6)3: 366-378.
  6. Rudin W. Some theorems on Fourier coefficients. Proceedings of the American Mathematical Society 1959; 10(6): 855-859. DOI: 10.2307/2033608.
  7. Labunets VG, Chasovskikh VP, Ostheimer E. Multiparameter Golay 2-complementary sequences and transforms. In Book: Information Technologies and Nanotechnologies. Samara: “Novaya Tehnika” Publisher; 2018: 1013-1022.
  8. Labunets VG, Chasovskikh VP, Ostheimer E. Multiparameter Golay m-complementary sequences and transforms.  In Book: Information Technologies and Nanotechnologies. Samara: “Novaya Tehnika” Publisher; 2018: 1005-1012.
  9. Jacobi CGJ. Uber ein leichtes verfahren die in der theorie der sacularstorungen vorkommendern gleichungen numerische aufzulosen. Jurnal fur die Reine und Angewandte Mathematik 1846; 30: 51-94.
  10. Brent RP, Luk FT. The solution of singular-value and symmetric eigenvalue problems on multiprocessor Arrays. SIAM J Sci and Stat Comput 1985; 6(1): 69-83. DOI: 10.1137/0906007.
  11. Lei ZX. Some properties of generalized Rudin-Shapiro polynomials. Chinese Ann Math: Ser A 1991; 12(2): 145-153.Golay MJE.  Multi-slit spectrometry. Journal of the Optical Society of America 1949; 39: 437-444.
© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: journal@computeroptics.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20