The process of estimating the carrier frequency of the signal received by the satellite communication system in the packet mode according to the rule of maximum similarity (MP-estimation) is considered. Goal. Development of functional dependencies and, based on them, development of the procedure for estimating the carrier frequency of the signal received by the satellite communication system in a continuous mode according to the rule of maximum likelihood. Method. The proposed procedure and the algorithm developed on its basis allows to perform MP-estimation of the carrier frequency taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in packet mode at short observation intervals. Results. Functional dependences are determined, based on them a rule is formed and an algorithm for estimating the carrier frequency of a signal received by a satellite communication system in a packet mode according to the rule of maximum likelihood using a sliding FFT that provides short observation intervals is proposed. This algorithm makes it possible to estimate the frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in packet mode at short intervals of observation. Conclusions. A comparative analysis of the results of the evaluation of a complex sinusoidal signal in a noise environment, carried out on the basis of an algorithm using a sliding FFT, which is provided by the dichotomous search procedure and depends on the offset value, showed that this estimate is asymptotically unbiased with its root mean square Cramer-Rao. This confirmed the feasibility and relevance of the approach specified in this paper to estimate the carrier frequency of the signal received by the satellite communication system in packet mode.
The problems of signal transmission in modern satellite systems are determined by certain features, both the construction of the system itself, and the problems of signal processing and signal processing. A characteristic feature of the satellite communication channel is the significant uncertainty of the signal received on the frequency (frequency uncertainty of the signal.) Therefore, for the demodulators of satellite modems, the problem of synchronization on the frequency of the carrier oscillation is the most significant. Based on this, when developing algorithms for coherent signal demodulation, the solution to the synchronization problem is crucial. The process of estimating the carrier frequency of a signal received in satellite systems is considered. Quantitative characterization of the minimum boundary variance of satellite carrier frequency estimation is substantiated. Functional dependencies are proposed to determine the Cramer-Rao lower bound, which is proposed as a quantitative characteristic of the minimum boundary variance of the carrier frequency estimation of a radio communication channel. It is established that the Cramer-Rao lower bound, adopted for determining the estimate of the minimum limiting variance of the carrier frequency estimation, is functionally dependent on the energy of the single signal pulse, the interval of information pulses of the complex envelope received, and the interval at which the estimate is made. The dependencies obtained make it possible to set the Cramer-Rao lower bound and the minimum variance of the carrier frequency estimation by its value, provided that other signal parameters are known. Under real conditions, the minimum variance of carrying out an MP estimation of the carrier frequency with the uncertainty of all satellite signal parameters may differ significantly from the minimum variance obtained based on the application of the proposed Cramer-Rao lower bound, which determines the further direction of prospective studies. Prospective research, development and creation of algorithms and techniques aimed at the rules of maximum likelihood of a carrier frequency with a minimum limiting dispersion under the conditions of uncertainty of all signal parameters should be aimed at maximally approximating the indicated dispersion of the estimate of the carrier frequency of the real signal to the lower Cramer-Rao boundary determined for carrier frequency under conditions of certainty of other signal parameters.
The use in radio communication systems of phase modulation of a signal intended for the transmission of useful information in a continuous mode creates the problem of frequency uncertainty of the received signal by frequency.In practice, it is not possible to implement frequency estimation in the conditions of chat uncertainty of the signal in the channel with low energy of the signal received in the continuous mode. Therefore, the estimation of the carrier frequency offset of the signal received relative to the nominal value is carried out before other synchronization procedures are included, namely: phase synchronization and clock synchronization. The paper generalizes the procedure and forms a two-step procedure for calculating the carrier frequency of the phase-modulated signal of a radio communication system for data transmission in a continuous mode, taking into account the condition of uncertainty of all signal parameters. Achieving the minimum observation interval in the given order of calculation of the carrier frequency is ensured by the use of the fast Fourier transform function. In order to analyze the effectiveness of this procedure, the process of estimating the carrier frequency of the phase-modulated signal of the radio communication system during data transmission in continuous mode and functional dependences of the maximum frequency in the signal spectrum and the minimum variance of carrier frequency estimation. This procedure allows a two-stage assessment of the carrier frequency according to the rule of maximum likelihood, taking into account the condition of uncertainty of all parameters of the signal received by the satellite communication system in a continuous mode with a minimum observation interval. Achieving the minimum observation interval in the given order of carrier frequency estimation is ensured by using the fast Fourier transform function and two estimation steps. The analysis of the efficiency of the estimation of the specified order was carried out on the basis of comparison of a ratio of the received minimum variance of an estimation of a carrier frequency and theoretically possible border of the minimum variance.
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