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Possibilities of “Nyquist Barrier” Breaking by Optimal Signal Selection

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Internet of Things, Smart Spaces, and Next Generation Networks and Systems (ruSMART 2016, NEW2AN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 9870))

Abstract

A possibility of overcoming the “Nyquist barrier” by finding the optimal waveform for a binary signal is investigated. The same BER performance as of BPSK signals is required. This problem can be viewed as an optimization problem. Parameters to be optimized are the rate of decay with frequency of out-of-band emissions, duration of signals and BER performance. BER performance is determined by a cross-correlation coefficient. Solutions to the optimization problem are obtained numerically. These solutions have the form of the coefficients of the truncated Fourier series of the waveforms obtained under different restrictions. Corresponding power spectra are analyzed. It is shown that the doubling of data rate leads to 30 % increase in bandwidth. Spectral efficiency can be increased by the use of longer signals. But the increase in signals duration leads to the increase of peak-to-average ratio of random sequence of signals. At the same time BER performance degrade insignificantly. Additional energy losses are no more than 0.5 dB.

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Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia

    Sergey V. Zavjalov, Sergey B. Makarov & Sergey V. Volvenko

  2. Jiangsu Normal University, Suychzhou, China

    Shen De Yuan

Authors
  1. Sergey V. Zavjalov
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  2. Sergey B. Makarov
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  3. Sergey V. Volvenko
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  4. Shen De Yuan
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Corresponding author

Correspondence to Sergey V. Volvenko .

Editor information

Editors and Affiliations

  1. Tampere University of Technology , Tampere, Finland

    Olga Galinina

  2. FRUCT Oy , Helsinki, Finland

    Sergey Balandin

  3. Tampere University of Technology , Tampere, Finland

    Yevgeni Koucheryavy

Appendix A

Appendix A

The Fourier Series Coefficients of the Waveform a(t).

It should be noted that the accuracy of the representation of the function a(t) depends on the number of terms of the truncated Fourier series. The number of terms in the truncated Fourier series can be determined using the standard deviation between the values of the functions a m(t) and a m–1(t), which are calculated using m and (m – 1) terms of the truncated Fourier series:

$$ \varepsilon (m) = \sqrt {\int\limits_{ - T/2}^{T/2} {\left( {a_{m} \left( t \right) - a_{m - 1} \left( t \right)} \right)^{2} dt} } . $$

If we restrict the number of terms in the truncated Fourier series to m = 7 then the standard deviation ε is less than 10−2. Solutions to the problem of finding an optimal waveform a(t), in the form of the coefficients of the truncated Fourier series, are listed in Table A.1.

Table A.1. The Fourier series coefficients of the waveform a(t) for α = 0.7, K 0 = 10−2, n = 2 and different values of T c.
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Zavjalov, S.V., Makarov, S.B., Volvenko, S.V., De Yuan, S. (2016). Possibilities of “Nyquist Barrier” Breaking by Optimal Signal Selection. In: Galinina, O., Balandin, S., Koucheryavy, Y. (eds) Internet of Things, Smart Spaces, and Next Generation Networks and Systems. ruSMART NEW2AN 2016 2016. Lecture Notes in Computer Science(), vol 9870. Springer, Cham. https://doi.org/10.1007/978-3-319-46301-8_52

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  • DOI: https://doi.org/10.1007/978-3-319-46301-8_52

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46300-1

  • Online ISBN: 978-3-319-46301-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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