Estimation of the initial phase of a radio signal with an arbitrary shape and unknown appearance and disappearance moments

Quasi-likelihood and maximum likelihood algorithms for estimation the initial phase of a radio signal with an arbitrary shape of the envelope function and unknown amplitude, pulse leading edge and pulse trailing edge are synthesized. The structure of the initial phase meter is defined. The analysis of the synthesized algorithms is performed and expressions for the statistical properties of the initial phase estimation are found. Based on the obtained expressions, the accuracy of the estimates is compared depending on the choice of the block diagram of the meter and the difference between the measured parameters and the true ones. The statistical properties of the synthesized estimation algorithms are determined and the accuracy of the estimates of the initial phase is compared. The loss of the accuracy of the initial phase estimation due to a priori uncertainty of the time parameters of the signal is investigated.