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Single-threshold sequential algorithm for receiving a signal with unknown duration

“…Assume that the observation interval [0, T m ] satisfies the condition 0 < T 1 ≤ T 2 ≤ T m , so that signal (1) totally lies in this interval. In this case, the logarithm of the likelihood-ratio functional depends on two parameters γ and τ and, according to [2,4,6], is written in the form…”

“…In accordance with [6], the ML algorithm of detection consists in comparison of the absolute (largest) maximum L = sup L(τ ) of the decision statistic…”

“…In the opposite case, the decision on the signal absence in the received realization is made. If the threshold h is not equal to zero, then such an observation algorithm is called the generalized ML algorithm [1,6].…”

“…To find function (6), we use the method of [5,6]. Since logarithm (2) of the likelihood-ratio functional is a linear transformation of the Gaussian random process x(t), it is also a Gaussian process.…”

“…The problem of optimal reception of a signal with unknown duration against the background of Gaussian white noise has been considered in a number of papers [1][2][3][4][5][6][7]. It was shown that the signal is discontinuous with respect to an unknown parameter and the maximum-likelihood (ML) and Bayesian reception algorithms were synthesized.…”