Distinguishing between Two Ultra-Wideband Quasi-Radio Signals with Unknown Amplitudes and Initial Phases

Abstract

In this paper, we synthesize algorithms for distinguishing between two ultra-wideband quasi-radio signals of arbitrary shape with unknown initial phases and amplitudes, observed against a background of white Gaussian noise. 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 fulfilled. To synthesize the algorithm for distinguishing, the maximum likelihood method was used, according to which, based on the observed data, a logarithm of the likelihood ratio functional is formed, depending on the unknown signal parameters. Studying the statistical characteristics of random variables, expressions is obtained for the average error probability, which characterizes the effectiveness of the synthesized algorithm for distinguishing. The influence of the disorder of various signal parameters on the efficiency of the synthesized algorithm for distinguishing is investigated. Recommendations for the use of the synthesized algorithm are formulated.