The redundancy of a multichannel data transmission system increases its reliability. During the operation of the system, it is necessary to diagnose and switch failed channels. To solve this problem, the set of input signals of the system is considered as a vector signal, whose scalar components are the coordinates of the vector in a given dimensional space. The diagnosis is performed using a scalar criterion, whose relative simplicity is ensured by the linearity of the signal transformations applied. To minimize the total probability of diagnostic error, the task of optimizing the tolerance on the diagnostic parameter is solved. The possibility of technical implementation of the proposed method is shown based on matrix transformations of the system's input and output signals. The system efficiency was assessed according to the "reliability-cost" criterion. Scientific novelty of the work consists in the fact that analytical expressions for matrix transformations of input and output vector signals of a multichannel data transmission system have been developed. Realization of these transformations provides diagnostics of the system according to the developed scalar criterion both in the test mode and in the mode of functioning as intended. 

This paper proposes a new approach to estimating the contour of the coverage zone for a cellular communications base station that takes into account meaningful reflecting objects located out of the considering zone. Based on this approach, the procedure for modeling and designing the cellular system coverage area. Unlike known methods, the developed procedure considers the influence of electromagnetic wave reflection from external details of the relief, in particular essential reflecting objects located outside the considered cell. The effect of the external objects on the formation of the coverage area resulting contour is considered analytically, numerically and experimentally. The proposed solution leads to more accurate designing of the coverage area for each cell. This creates the opportunity for further development of designing techniques to more effective engineering solutions at developing and applying cellular communication systems in real situations and at various scenarios.