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Conditional bias of QL estimate of initial phase as a function of SNR

Estimation of the initial phase of narrowband radio signal with unknown amplitude and duration

Andrey P. Trifonov, Yu. E. Korchagin, M. V. Trifonov, K. S. Kalashnikov


The quasi-likelihood and maximum likelihood algorithms for estimating the initial phase of radio signal with arbitrary shaped envelope and unknown duration and amplitude have been synthesized. Schematic block diagrams of initial phase meters are proposed. Characteristics of the synthesized algorithms were determined, and errors of the initial phase estimates were compared. The structure of quasi-likelihood estimate of the initial phase is shown to be invariant with respect to the lack of knowledge of radio signal amplitude. However, a mismatch between the expected value of signal duration and its true value can lead to a marked increase of dispersion of the initial phase quasi-likelihood estimate. The loss in accuracy of the initial phase estimate due to a priori lack of knowledge of signal duration has been determined. Analytical expressions for statistical characteristics of maximum likelihood estimate of initial phase at large signal-to-noise ratios are shown to coincide asymptotically with the characteristics of maximum likelihood estimate of the initial phase of radio signal with a priori known amplitude and duration. Therefore, a priori unknown signal duration (asymptotically with an increase of signal-to-noise ratio) does not affect the accuracy of the maximum likelihood estimate of initial phase. The computer methods of statistical simulation were used to determine the applicability limits of asymptotic expressions for characteristics of the maximum likelihood estimate in respect of signals with linear and exponential envelopes.


maximum likelihood estimate; quasi-likelihood estimate; initial phase; duration; amplitude; bias; dispersion

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