Method for Estimation the Number of Frequency Elements per Symbol for Signal with Fast Frequency Hopping and Frequency Manipulation

Introduction. Frequency hopping spread spectrum (FHSS) is widely used in modern digital communication systems to increase their noise immunity and intelligence protection. Radio systems using fast FHSS are characterized by a wide range of operating frequency, which leads a large number of interference at the input of the radio monitoring station, short duration of frequency elements, and division of information symbols into subsymbols transmitted at different frequencies. Review of related works. The main trends in solving problem of estimating the parameters of FHSS in most publications are related to the use of time-frequency and wavelet analysis. But this methods and algorithms do not provide estimates of frequency elements number per information symbol for fast FHSS in case of interference. Purpose and objectives of research. The purpose of this research is to develop an automated method for estimating the number of frequency elements of signals with fast FHSS per one information symbol with frequency shift keying. Methodology of research. The proposed method consists of three stages: search for interference emissions and forming of notch filters; estimating of frequency elements; estimating the number of frequency elements per information symbol. Detection of interference emissions is realized by the time criterion. On the basis of the calculated frequency parameters of such radiations notch filters are formed. Window Fourier transform and discrete spectral interpolation were used to increase the accuracy of frequency element calculations. It is shown that to ensure the required accuracy of frequency calculation in a wide range of signal to noise ratio (SNR) values, it is advisable to use Gaussian spectral interpolation and Gaussian smoothing window with the parameter 0,3. Mathematical expressions are obtained for the probability of occurrence of a set of several frequency elements in a sequence, the difference between which is close to the step of the frequency grid. A criterion and algorithm for deciding on the number of frequency elements per one information symbol, based on statistical characteristics of the differences in the denominations of adjacent frequency elements was developed. Simulation results. The efficiency and effectiveness of the developed method were tested by modeling with MATLAB software. The average probability of correctly estimating the number of frequency elements per symbol is not less than 0,9 at SNR above -10 dB. Conclusions. Obtained probabilistic characteristics can be used in the development of methods for estimating other parameters of fast FHSS signals with frequency shift keying.