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Spectra and average out of band power characteristics of radio signals created on the basis of the generalized Nyquist algorithm


M.G. Didenko – Ph. D. (Eng.), Research Scientist, Relcom (Moscow). E-mail: G.V. Konovalov – Ph. D. (Eng.), Leading Research Scientist, Central SRI of Communications (Moscow). E-mail:

The problem of efficient use of the frequency resource is relevant for all radio communication applications. In particular, in satellite communications there are widely used methods, based on Nyquist algorithm, including methods, standardized by international organizations (ETSI, etc.) The article deals with the principles of signal shaping on the basis of the generalization Nyquist algorithm for a combination of transmitting and receiving filters, ensuring the absence of inter-symbol interference in the clock points. The proposed analytical approach allows to extend the class of signals with compact power spectrum. Paper contains analytical expressions for the calculation of the frequency response of the shaping filter and the impulse response on the basis of which average power spectral density and the out of band power emission can be calculated. Some options for approximation of the generalized impulse response of the shaping filter are offered and limitations on the approximating function are defined. According with mentioned analytical expressions calculations were made in order to illustrate the possibility of an appropriate choice of shaping filter parameters that can modify the spectral characteristics of the radio signals. Thus, depending on the selected optimization criterion, it is possible, for example, to minimize the width of the main lobe of the power spectrum by a predetermined level or decrease the duration of the symbol. Some investigations were performed to define how the power spectral density and average out of band power characteristics depends on the parameters of the shaping filter. These studies, in particular, show that for roll-off filter parameter α = 0,20…0,35 and for small deviations from ETSI patterns is possible noticeably decrease the occupied bandwidth or reduce the length of the symbol. It is also shown that for small values of α ≤ 0,05 impact of approximation of the shaping filter is almost eliminated. These features are confirmed by views of the power spectral density and the parameters characterizing out of the band emissions. Results presented in the article it is advisable to take into account in the design of modern radio frequency-effective systems, including those where there is an opportunity to achieve greater economy of the spectrum at acceptable deviations from standardized ETSI patterns.


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