Due to the rapid development of communication systems with time division multiple access (TDMA) there is a need to estimate the carrier frequency of signal bursts with phase shift keying. This paper presents the carrier frequency estimation of signal bursts with phase shift keying based on previously developed methods of optimal weighting of the difference-phase statistics without significant computational costs. Algorithms of computationally efficient methods for estimating the carrier frequency of packet signals with Binary Phase Shift Keying (BPSK) and Quadrature Phase Shift Keying (QPSK), as well as with quadrature amplitude digital modulation, using optimal weighting of the difference-phase statistics are presented. A comparative analysis of computationally efficient methods for estimating the carrier frequency of signal bursts with QPSK is performed for various methods using optimal weighting of the difference-phase statistics, based on the results of experimental observations of packet communication signals of an aircraft under various reception conditions. Statistical simulation of estimation algorithms is performed. Estimation results for different signal-to-noise ratios are illustrated. The proposed algorithms for computationally efficient estimation of the carrier frequency of signal bursts with digital modulation using optimal weighting of phase-difference statistics allow to increase the accuracy of measuring the carrier frequency of these signals for different dynamics of the observed aircraft motion, which is of great importance when receiving signals from low earth orbit (LEO) spacecraft. The proposed algorithms for estimating the carrier frequency of signal bursts with phase shift keying are characterized by high computational efficiency and allow to increase the accuracy of estimating the carrier frequency of signal bursts with phase shift keying under different reception conditions at moderate signal-to-noise ratios, which makes it advisable to use the presented algorithms in the equipment of multi-satellite communication systems based on LEO such as Starlink and OneWeb.
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