Optimum reception of a signal with unknown duration against the background of white noise

Algorithms for the Detection of a Signal with Unknown Amplitude and Duration against White

“…The simplest algorithm in terms of the hardware implementation is QL algorithm (4). Really, it is only required to form a random variable for the decision making here, and this variable linearly depends on the realization of the observable data.…”

“…In Eq. (1) , are the designations of the signal amplitude and duration accordingly, and is the function describing the form of a signal.…”

“…With observable realization and prior information, it is necessary to made the decision on presence or absence of a useful signal (1).…”

“…So, in works [1,2] the reception of a rectangular pulse with unknown duration against white noise was considered. In [3] algorithms of reception of a free-form pulse with unknown duration were studied.…”

“…However, in a number of practical applications the received signal amplitude is also unknown. In work [4] algorithms of reception of a rectangular pulse with unknown duration and amplitude were synthesized. The asymptotic expressions for detection error probabilities, and for distribution functions and variances of joint maximum likelihood estimates of a signal amplitude and duration were found.…”