Mathematical Model of Two-Fragment Signal with Non-Linear Frequency Modulation in Current Period of Time

Abstract

Advantages of using frequency-modulated signals for locating objects are the possibility of using long-term probing pulses. Such signals provide the required radiated power while maintaining the desired discriminating power from range. One such signal that has found wide application is a signal with linear frequency modulation. An undesirable effect of the matched filtering of such a radio pulse is a sufficiently large level of side lobes of the compressed signal at the output of the processing device, the maximum level of which is approximately minus 13 dB. Such an effect may lead to an increase in the probability of false detection or masking of less powerful signals by side lobes of signals with greater power. One method of reducing the level of side lobes is the use of signals with non-linear frequency modulation. An example of such signals is a known two-fragment signal consisting of linearly-frequency modulated fragments in time. However, the mathematical models used to describe such a signal do not fully reflect the effects that occur at the moment of transition from one fragment of the signal to the second. These effects are manifested in a sudden change in frequency and phase, which leads to distortion of the signal spectrum, an increase in the level of the side lobes of the autocorrelation function and sharp changes in their level. Such effects have not been studied in known works, as evidenced by the results of the analysis of studies and publications given in the first section of the article. In the second section of the work, the research task is formulated. The third section of the work is devoted to the development of a mechanism for compensating for the manifestation of detected effects and its mathematical description, which is verified by modeling. Taking into account the detected effects, a new mathematical model of a non-linear frequency modulated signal has been developed. In contrast to those known in the proposed model, instantaneous frequency and phase jumps are compensated for, which occur at the moments when the frequency modulation rate changes during the transition from one signal fragment to another. Further studies should be focused on the peculiarities of compensation for the manifestation of detected effects for signals with a large number of fragments, as well as combinations of fragments with different types of modulation, as indicated in the conclusions on the work.