Application of optimal amplitude-phase modulation signals in channels with Doppler frequency shift

The paper addresses the problem of improving the spectral efficiency of radio communication systems operating in channels with Doppler frequency shift by employing optimal signals with amplitude-phase modulation. The relevance of the study is driven by the need for high data rate transmission in low-Earth orbit satellite communication systems, where conventional signals based on RRC pulses exhibit significant energy losses when the symbol rate is increased. A synthesis technique for optimal shaping pulses is proposed, based on the criterion of out-of-band emission suppression under given constraints on the cross-correlation coefficient that determines the BER performance. A computer simulation model of the transmission channel is developed, taking into account carrier frequency instability, timing synchronization offset, and Doppler shift modeled with time-scale transformation. Numerical simulations for 64APSK constellation and coding rate 4/5 demonstrate that the use of optimal signals with doubled symbol rate provides a spectral efficiency gain of up to 12.7% compared to RRC-based signals when the occupied bandwidth is estimated by the 99% energy concentration criterion. The associated energy penalties range from 3 to 4 dB depending on the satellite elevation angle, which is attributed to the need for wider receiver front-end bandwidth under Doppler-induced spectral distortions. It is shown that the choice of the cross-correlation coefficient enables a trade-off between BER performance and spectral efficiency. The obtained results confirm the feasibility of optimal signals in satellite communication systems with high spectral efficiency requirements and limited link power budgets.