Detection of Incoherent Sequence of Rectangular Ultra-Wideband Quasi-Radio Signals

The maximum likelihood algorithm for detection of incoherent sequence of rectangular ultra-wideband signals with unknown amplitude and initial phase viewed against background Gaussian white noise was reviewed. Among the variety of ultra-wideband signals, the specific class is distinguished: ultra-wideband quasi-radio signals, the structure of which is same as narrowband radio signals, but the condition of relative bandlimitedness is not met for them. To synthesize the signal detection algorithm, the maximum likelihood method was used, according to which, based on the observed data, a logarithm of the likelihood ratio functional was formed, depending on the state parameter and unknown signal parameters. Using the theory of matrix operations, a detector structure was determined. Studying the statistical characteristics of random variables, expressions are obtained for the probability of false alarm and the probability of missing a signal, which characterize the effectiveness of the synthesized detector. Conclusions are drawn about the effectiveness of receiving a sequence of pulses in comparison with a single signal.