Amplitude estimation of rectangular narrow-band radio pulse with unknown duration and initial phase

Abstract

This study investigates algorithms for the estimation of amplitude of the radio signal with rectangular envelope and unknown duration and initial phase. The synthesis and analysis of quasi-likelihood and quasi-coherent estimation algorithm have been performed. This algorithm implies that the unknown duration and initial phase are replaced with certain expected values of these parameters. The loss in accuracy of amplitude estimation owing to the a priori lack of knowledge of the duration and the initial phase is analyzed. The quasi-likelihood noncoherent algorithm for amplitude estimation with the initial phase adaptation is synthesized and its statistical characteristics such as the estimate bias and variance are determined. The relationships of the loss in estimation accuracy owing to the a priori lack of knowledge of signal duration are derived. The maximum likelihood algorithm for amplitude estimation was synthesized and analyzed. This algorithm implies that the unknown duration and the initial phase are replaced with their maximum likelihood estimates. The gain in accuracy of the maximum likelihood estimate as compared to the quasi-likelihood ones was investigated. It is shown that a priori lack of knowledge of the signal duration does not affect asymptotically the accuracy of maximum likelihood estimate of amplitude at large values of signal-to-noise ratio.