Abstract: The purpose of this paper is to provide the theoretical approach for determining a coherent quaternary phase-shift-keying performance by means of the system error probability at very low frequencies. An expression for the bit error probability is determined when the signal, thermal Gaussian noise, atmospheric noise, interference and imperfect carrier phase recovery are taken into consideration. Phase locked loop, as the constituent part of the receiver, is used in providing the synchronization reference signal extraction, which is assumed to be imperfect in this paper. The reference carrier is extracted by the non-linear first order PLL model with primary emphasis on the degradation in the system performance produced by imperfect carrier signal extraction.
Key words: QPSK, phase locked loop, atmospheric noise, interference.