Mathematical model of the functioning of a mobile radio communication system built on software-defined means

The purpose of the study was to develop a generalised mathematical model of the functioning of multi-antenna radio communication systems under the influence of random and intentional interference and to analytically describe the influence of interference-noise and non-stationary factors on the security and reliability of information transmission. The work used a matrix channel model, space-time block coding, orthonormal representation of signals in a common signal space and statistical modelling of noise and interference in the coordinates of the basis. The results of the study showed that under quasi-stationarity of the channel on the interval of block transmission and orthogonality of the space-time structure, an inverse channel operator was formed. Under such conditions, linear recovery of the transmitted symbol vector and coherent summation of the useful component were ensured with statistical independence of noise components at the decoder output. The desired signal, fluctuating noise, and intentional interference had a consistent coordinate structure in the same orthonormal signal space. As a result, the quality of each antenna channel was determined by the energy balance between the desired energy and the spectral parameters of noise and interference, which determined the distance of signal points from the regions of false decision. The constellation degradation was described by the composition of geometric transformations (rotation, scaling, quadrature deformation) and stochastic perturbations (phase jitter, interference, additive noise), and the parameters of these distortions were identified by the mathematical expectation, dispersion, and covariance of the coordinates of the received symbols. The temporal nonstationarity of the channel was determined by the Doppler shift and the correlation structure of the transmission coefficient, and the elliptical geometric scattering model related the delays of multipath components to the spatial configuration of the scatterers. The practical significance of the results lay in the possibility of using the proposed model for analysis and optimisation of multi-antenna radio systems on software-defined devices in conditions of noise, interference and non-stationary channel. Its application contributed to the justification of modulation and coding parameters, as well as to increasing the reliability and interference immunity of radio communications