Influence of synchronization errors оn the noise immunity of coherent reception of M-PSK signals

Signals with multiple phase-shift keying (M-PSK) have long been successfully used for highspeed information transfer in many applications – a number of adopted protocols of IEEE 802.11 wireless networks, digital satellite television DVB-S, DVB-S2/S2X systems, cellular networks CDMA and others. The most important characteristic of such systems is their noise immunity, which depends not only on the propagation conditions of radio waves in the communication channel, but also on the quality of operation of the component nodes of the information transmission systems themselves. The paper investigates the influence of the inaccuracy of estimating the frequency and phase of the carrier and the inaccuracy of the clock synchronization system on the noise immunity of coherent reception of M-PSK signals. Analytical expressions were obtained by statistical radio engineering methods. The expressions allow calculating the dependence of the probability of a bit error on the signal-to-noise ratio for various errors of the receiver auxiliary systems. In this case, the magnitudes of the errors were assumed to be either constant (static error) or dynamically changing (dynamic error). The dynamic errors were modeled using the Monte Carlo method, and the dynamic errors themselves were assumed to be Gaussian random variables. It is shown that the inaccuracy of estimating these parameters strongly influences the noise immunity of the coherent reception of the M-PSK signal, and this effect increases with increasing signal positionality. Estimates of the maximum permissible errors of the analyzed systems are given. When M-PSK signals are received, a tolerable value of the frequency of the reference oscillations can be considered as a ∆ωTs value of about 0.05. The allowable inaccuracy of the carrier phase estimation depends on the positioning of the signal and varies from π/36–π/72 for 2PSK to π/180 for 32PSK. The allowable time offset of the clock moments can be considered the value of 3–5% of the clock interval duration.