We propose a unique word detection scheme having the correction of the phase ambiguity that remains in the output of a carrier recovery circuit for QPSK systems. The performance of the proposed scheme is analyzed by obtaining the probability generating function (PGF) for the output of the detector. The PGF is obtained from the z-transform of the probability density function (PDF) for each matched symbol with the reference symbol and by using the characteristics at this time that the random variables for matched symbols are independent and identically distributed. Then the total PGF for a unique word is obtained from powering the PGF for the individual symbol. From the total PGF, the length of a UW and the threshold value for detection can be obtained with a detection probability defined in a required system specification.

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.

A decision-directed carrier phase recovery scheme for high-speed satellite communications is proposed. Since the estimation is performed in complex domain from the baseband signal, the scheme has fast acquisition performance, unlike the conventional PLL. This merit makes it applicable for various wireless systems such as wireless local area networks (LANs), wireless asynchronous transfer modes (ATMs) and local multipoint distribution systems (LMDSs) that need high-speed burst signal communications. Also, this scheme can be implemented easily because low pass filters (LPFs) are utilized in filtering the estimates in order to suppress the noise within the carrier recovery loop. Moreover it does not require any divider or voltage-controlled oscillator (VCO). The performance is analyzed through analytical methods and simulation.

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.