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.