Application of the decision trees to recognize the types of digital modulation of radio signals in cognitive systems of HF communication

Organization of high-speed long-distance radio communication for many years stay actual task. High efficiency in the organization of long-distance radio communication by the criterion “signal power - range of action” is demonstrate by ionospheric communication systems. However, such systems have a number of disadvantages, first of all-low speed and insufficient noise immunity of information transmission. One of the promising ways to remove these disadvantages is the introduction of cognitive technologies, including automatic adaptation to changing conditions of dissemination and noises in the system of long-distance HF communication. One of the parameters affecting the bit rate and noise immunity is the type of the radio signal modulation. Most of the existing and perspective systems of ionospheric HF communication are digital, for this reason this article considers only signals with digital modulation (manipulation): FSK (Frequency-Shift Keying), PSK (Phase-Shift Keying) and QAM (Quadrature Amplitude Modulation). In present cognitive systems, as a rule, information about the used signal modulation type is transmitted as a part of the service message. In the conditions of high dynamics of change of a background situation, frequency of transmission of service messages is rather big that leads to decrease channel capacity of the communication, which in a range HF and so is not very big. As a result, in the last two decades, appeared a rather large number of works designed at solution the problem of recognizing the type of modulation of a radio signal in conditions it's a priori uncertainty. As features of recognition, is proposed to use various statistical features of radio signals having different efficiency for recognizing one or another type of modulation. To select informative features for recognition of the type of modulation of radio signals of distant HF communication, the article analyzes the following set of features: the maximum value of the power spectral density of the normalized-centered instantaneous amplitude of the received signal ($(\gamma _{max})$, standard deviation of the absolute value of the centered nonlinear component of the instantaneous phase ($(\sigma _{ap})$, standard deviation of the nonlinear component of the direct (not absolute) instantaneous phase $(\sigma _{dp})$, standard deviation of the absolute value of the normalized- centered instantaneous amplitude of the signal ($\sigma _{aa})$, standard deviation of the absolute value of the normalized-centered instantaneous frequency ($\sigma _{fa})$, signal amplitude scatter (Ra), signal phase scatter (Rp), and signal frequency scatter (Rf), cumulants of different order (C11, C21, C31, C41, C51, C22, C32, C42, C33). To select informative features for object recognition, the mathematical apparatus of decision trees was used. As a result of the model experiment, as the final set of features for recognizing the types of digital modulation, radio signals of the HF communication are selected: $\sigma _{fp}$ and $\sigma _{ap}$, C42. This set of features allows solving the problem of recognition of frequency, phase and quadrature amplitude manipulation of radio signals with accuracy not worse than 92% with SNR =5 dB. The discrepancy between the results obtained and the known ones is explained by the fact that the latter does not take into account the specifics of the construction of real radio communication systems (various symbolic speeds signal and the use of Nyquist shaping filters).