S.B. Makarov - Dr. Sc. (Eng.), Professor, Director of Institute of Physics, Nanotechnology and Telecommunications of Peter The Great St.Petersburg Polytechnic University E-mail: makarov@cee.spbstu.ru S.V. Zavjalov - Ph. D. (Eng.), Associate Professor, Department «Radio Engineering and Telecommunication Systems», Institute of Physics, Nanotechnology and Telecommunications of Peter The Great St.Petersburg Polytechnic University E-mail: zavyalov_sv@spbstu.ru

A method of optimization of spectrally efficient non-orthogonal single-frequency and multi-frequency signals is proposed in this paper. Proposed optimal signals have predetermined decreasing rate of the level of the energy spectrum in the presence of various restrictions. Restrictions, which can be used: restriction on the signal energy, restriction on BER performance, restriction of peak-to-average power ratio of emissions. Optimization problems for a wide range of spectrally-efficient signal can be solved via proposed technique. The analytical solution of the optimization problem for small values of decreasing rate of the level of the energy spectrum without inter-symbol interference is shown. We must use the technique of numerical solution of the optimization problem for various values of decreasing rate of the level with restrictions on BER performance and peak-to-average power ratio. The decomposition of the function in a limited number of Fourier series is used for numerical solution of optimization problem. The method of selecting the number of expan-sion coefficients in the Fourier series limited is presented. Various forms of the optimal single-frequency spectrally efficient signal wit intersymbol interference are shown. The effects of restric-tions on the solution of the optimization problem are demonstrated. In particular, it is shown that the occupied bandwidth increase with increasing of the number of restrictions of optimization problem. However, this increasing is not significant. Restrictions on the solution of the optimization problem for the multi-frequency signals are proposed. It is also proposed a method for constructing optimal multi-frequency signals (selection of frequency spacing between the subcarrier frequencies). The envelopes of signals on each subcarrier frequency are found for these restrictions. These signals have a minimum value of the occupied bandwidth and a predetermined decreasing rate of the level of the energy spectrum. Energu losses in BER performance for these signals is less than 0.5 dB.

 

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