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.