We propose a coherent automatic gain control (AGC) scheme with low complexity for high-speed satellite communications. A mathematical model for the gain detector and a stochastic difference equation are established to investigate the characteristics of the scheme. Based on the random process theory with the equation, we analyze the acquisition and tracking performance of the AGC loop. It has been verified that the results by the analytical method agree with the simulation results obtained in the presence of small amount of phase offsets in the carrier recovery circuits for the QPSK system. Though the analytical results deviate from the simulation results slightly in the presence of maximum phase offset, they give us the insight in analyzing the characteristics of the proposed scheme.

We propose a phase lock detector for 16-QAM systems for high-speed wireless communications. The detector gathers the phase estimates statistically according to the predetermined symbols, filters them through an average filter, and indicates the phase lock state by comparing the filtered resultants to a threshold value. The statistical property of the proposed detector is analyzed using the stochastic process theory. First, we obtain the characteristic function of a random variable describing the filter output. Second, through inverse Laplace transform, we get the probability density function of the random variable. Third, we can obtain the phase lock detection probability using the probability density function. Finally, to investigate its accuracy, we obtain the probability density function of a random variable for the detector output, and compare it to the simulation result.