Optimal algorithm for detection of signal with unknown amplitude in uncorrelated noise

Abstract

The main sources of noise and interference, features of detecting signals in noise, methods of combating them during transmission over various distances are considered. In a number of tasks of receiving signals in the presence of noise, one cannot limit oneself to such a general criterion as the signal/noise ratio. There is a need to use finer statistical properties of processes that make it possible to quantitatively assess the reliability of data. Noises represent an important problem in science and technology, as they determine the lower limits both in relation to the accuracy of any measurements and in relation to the magnitude of signals that can be processed by electronic means. The situation in the operation of any information system is that its input receives a signal distorted by random interference, in which some information, parameter values, process implementations are encoded. These information and parameters, in turn, are random. The information system contains a receiver of signals - information carriers, in which the transformations necessary for extracting information are carried out. They are followed by the processing of information intended to ensure the system's performance of its functions. Adaptive detection of signals in noise is determined, while using the optimal detection algorithm for analysis procedures. An algorithm for detecting a signal with an unknown amplitude in uncorrelated noise is proposed. Probabilistic characteristics of signal detection with unknown amplitude in noise are constructed. Appropriate detection algorithms were found both during discrete observation and when switching to continuous observation of signals. Probabilistic detection characteristics are also constructed, comparing them with cases of known parameters of signals and noises, when the optimal algorithms are not adaptive.