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Abstract
The work synthesizes a quasi-likelihood algorithm for estimating the frequency of a coherent sequence of ultra-wideband quasi-radio signals with unknown duration against a background of white Gaussian noise. When synthesizing the frequency estimation algorithm, instead of an unknown duration, some of its expected value is used. Analytical expressions are obtained for the statistical characteristics of the frequency estimate of a sequence of ultra-wideband quasi-radio signals depending on the pulse duration detuning parameter. In particular, the dependence of the variance of the frequency estimate of a sequence of ultra-wideband quasi-radio signals on the signal-to-noise ratio is obtained for different values of the duration detuning and the number of sequence pulses. It has been established that the frequency estimate bias does not depend on the number of pulses in the sequence, and for large values of the narrowband parameter there is no frequency estimate bias. It is shown that the duration detuning has a significant impact on the characteristics of the frequency estimate of a sequence of ultra-wideband quasi-radio signals, while at large values of the narrowband parameter the obtained expressions coincide with the known expressions for the variance and bias of the frequency estimates of a sequence of narrow-band radio signals.
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