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Exceeding the «nyquist barrier» by single-carrier nonorthogonal multicomponent signals

Keywords:

A.L. Gelgor – Ph. D. (Eng.), Associate Professor, Department «Radioelectronic Facilities of Information Securi-ty», St. Petersburg State Polytechnical University E-mail: A_Gelgor@mail.ru A.I. Gorlov – Assistant, Department «Radioelectronic Facilities of Information Security», St. Petersburg State Polytechnical University E-mail: anton.gorlov@yandex.ru E.A. Popov – Ph. D. (Eng.), Associate Professor, Department «Radioelectronic Facilities of Information Securi-ty», St. Petersburg State Polytechnical University E-mail: popov@spbstu.ru


Work is devoted to research possibilities of increasing the effectiveness of single-carrier signals by introduction the inter-symbol interference (ISI). For convenient description of single-carrier and multi-carrier signals with ISI the concept of multi-component signals was introduced. Components are single-carrier signals with amplitude-phase-shift keying and without inter-symbol interference. Regulation of the level of ISI between components is provided by four ways: by choosing pulse waveform of components, by frequency shifting of components relatively to each other, by time shifting of components relatively to each other, by introduction of dependence between signal constellations of nearby components (e.g., rotation of constellations). Widely used single-carrier signals with Nyquist pulse and multi-carrier OFDM-signals are a subclass of the proposed signal with zero ISI. In this paper multicomponent single-carrier signals without rotation of constellations and with time shifting of components equal to symbol duration are under analysis. The expressions for the energy spectrum and the peak to average ratio of single-carrier multicomponent signals were derived; correlation characteristics – partial and group correlation are intro-duced. The value of ISI is equated with the maximal value of the group correlation, which is numerically equal to the coeffi-cient of correlation of single symbol duration signal of one of the components with all other components. The problem of finding optimal pulse waveform of multicomponent signals on the criterion of minimizing the bandwidth containing 99% of the signal’s energy was solved. Additional variable restrictions are level of inter-symbol interference and peak to average ratio. By decomposing the sought pulse in a truncated Fourier series variational isoperimetric problem is transformed to the search of a maximum of multivariable function, which can be solved by numerical methods. Using the simulation noise immunity curves of reception with Viterbi algorithm of multicomponent signals with optimal pulses were calculated. To assess the results comparing the efficiencies of the optimal multicomponent signals and signals with Nyquist pulse was produced. The energy efficiency parameter which takes into account the value of the peak to average ratio was proposed. It is shown that the using of multicomponent signals with the ISI provides a gain in relation to signals with Nyquist pulse. Compared with Nyquist pulse signals with PM4 signal constellation and a roll-off factor α = 0,2 multicomponent signals provides gain in the energy efficiency of 2.9 dB with the same value of spectral efficiency, or gain 28% in the spectral effi-ciency with the same value of energy efficiency.
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