Terminological features of the concept of signal-to-noise ratio when processing ultra-wideband signals

Currently, when processing various signals and studying various types of receivers, there are many definitions for one of the basic characteristics of radio systems – signal-to-noise ratio (SNR). At the same time, the terminological feature of the SNR concept is that any definition within the framework of a locally solvable signal processing problem is correct. However, difficulties arise when comparing the effectiveness of one algorithm with another, when studying different signal models, or when measuring the SNR in different parts of the receiving system. Some researchers ignore this fact due to the apparent absolute clarity of this issue, which leads to incorrect comparison of various processing algorithms or the formation of obviously unrealizable requirements for the designed equipment. In each locally solved problem, the determination of SNR will be individual, and comparison of efficiency at a fixed SNR must be carried out with mandatory scaling of signal energies depending on the formulation of the problem. This paper systematizes the terminological features of the SNR concept in order to ensure uniformity of its application by researchers and engineers. The purpose of the work is to systematize the definition of SNR for various signal models and conditions for measuring this characteristic, to specify the results in terms of terminological features of UWB signal processing and to propose a model for recalculating the SNR depending on the stage of the signal transmission and reception process. The paper examines the determination of SNR at the input and output of optimal and matched filters, at the output of optimal receivers operating under conditions of various a priori uncertainties, as well as when processing various classes of signals. By determining the SNR at the output of the matched filter and the SNR at the output of the maximum likelihood receiver for a rectangular video pulse, the discrepancy between the signal energies, all other things being equal, is clearly demonstrated. A connection has been established between the SNR when processing ultra-wideband signals at the output of the optimal receiver with similar devices for processing other types of signals, as well as with the SNR at the input of the receiving system. Systematization of the terminological features of the SNR concept will allow theoretical researchers to choose SNR definitions that are as close as possible to practical applications when analyzing the effectiveness of synthesized algorithms, and will allow practicing engineers to correctly interpret the results of theoretical calculations when developing or testing radio engineering systems.