Probabilistic analysis of generalised statistic model for multipath channel of SIMO sistems with fading and correlated shadowing

The paper considers the problem of analysis of the information transmission process by multi-element communication systems in presence of a multipath signal propagation channel. To generalize the propagation effects, the model of the $\kappa$–$\mu$ fading channel with correlated shadowing was assumed, and the technology used for organizing a multi-element system was the SIMO system, equipped with the maximum-ration combiner of the signal on the receiving side. To describe the characteristics of the information transfer process, an approach based on the higher-order statistics of the ergodic capacity was used. Closed-form analytical expressions for arbitrary-order capacity higher-order statistics were obtained for the channel model under consideration. The behavior of the first four statistics (ergodic capacity, its reliability, skewness and kurtosis coefficients) is analyzed depending on the channel parameters (the number of multipath propagation clusters, the ratio of power of the dominant components to the total power of multipath waves, the degree of shadowing of the dominant components, and the shadowing correlation coefficient). Within the framework of the study, 4 distinct situations of the assumed channel model behavior were considered, which significantly differ in their properties. It is noted that, in contrast to the capacity, its higher-order statistics are significantly more sensitive to the channel parameters and, as a result, are more significant indicators of fluctuations in the information transfer rate within the communication channel. The existence of a pronounced extremum (minimum) of the reliability ergodic capacity dependence from the signal-to-noise ratio was established. It should be accounted for in practical applications, when the requirements of the signal-to-noise ratio that guarantees the desired communication link quality are set.