Estimation of ultrawideband quasi-radio signal duration

Abstract

Quasi-likelihood and maximum likelihood algorithms of duration estimation for ultra-wideband quasi-radio signal of arbitrary shape with unknown amplitude and initial phase, influenced by additive Gaussian white noise, are synthesized. It was considered that conditions of relatively narrow band of received signal are not satisfied and its duration can constitute only several periods or a fraction of period of harmonic oscillation. It is shown that the structure of the algorithm for duration estimation of ultra-wideband quasi-radio signal is significantly different from the structure of duration estimation algorithm for narrowband radio signal. Relative bias and variance are determined as the statistical characteristics of synthesized duration estimates. The influence of unknown amplitude and initial phase on the accuracy of duration estimation is investigated. Quantitative limits for relation of signal bandwidth to its center frequency are formulated, such that the classical solution of the problem of duration estimation for narrowband radio signal possesses the required accuracy.