Optimal nonlinear filtering of MPSK signals in the presence of a Doppler frequency shift

Abstract

Objectives. Phase-shift keyed (PSK) signals are widely used in many telecommunication, communication, and cellular information transmission systems. Phase-shift keying provides a higher noise immunity than amplitude and frequency modulations do. An increase in the modulation order of such a signal leads not only to an increase in its spectral efficiency, but also to a certain decrease in the noise immunity of reception. To ensure a high noise immunity of reception of multiple phase-shift keyed (MPSK) signals, a demodulator should provide the coherence of the reference oscillation with the carrier. Ignorance of the frequency and phase of the received signal leads to significant energy losses. The purpose of this work was to synthesize and analyze algorithms for receiving MPSK signals with phase fluctuations caused by changes in the carrier frequency due to the Doppler effect against the background of white Gaussian noise.Methods. The problem was solved using the apparatus of optimal nonlinear filtering and methods of statistical radio engineering.Results. A demodulator was synthesized, which includes two interconnected units. One of them is a discrete symbol estimation unit, at the output of which a decision on the received symbol is issued, and the other is a phase-lock circuit. Analytical expressions were derived to estimate the characteristics of the receiver noise immunity as functions of the signalto-noise ratio and fluctuation parameters. It was shown that the synthesized quasi-coherent algorithm compensates well for the MPSK signal phase fluctuations caused by the instability of the master oscillator and the Doppler effect.Conclusions. Comparison of the results of this work with results obtained in the case of the absence of fluctuations in the initial phase showed that, at a high relative speed of the transmitter and the receiver (satellite radio channel), the energy loss is no more than 1 dB, and at lower speeds of the objects, it is about 0.2 dB and less.

Keywords

• multiple phase-shift keying
• doppler effect
• optimal nonlinear filtering
• noise immunity
• bit error probability