Mathematical Model of the MIMO-NOMA System

Relevance of the Study. Modern next-generation mobile networks impose extremely high requirements on spectral efficiency, reliability, and robustness in urban environments with high user density. The MIMO-NOMA technology, despite its proven potential, requires a revision of existing models due to the need to account for users' spatial dynamics, polarization distortions, hardware nonlinearity, and channel state information (CSI) estimation errors. The lack of comprehensive models capable of simultaneously addressing these factors significantly limits the ability to effectively optimize systems in practical scenarios. Research Objective. The study aims to develop a comprehensive mathematical model of the MIMO-NOMA segment between the precoder and the summation scheme in the complex baseband domain, accounting for terminal mobility and orientation, antenna polarization, amplifier nonlinearities, and CSI errors, to analyze and optimize precoding and successive interference cancellation (SIC) algorithms. Research Methods. The modeling incorporates: stochastic processes (including the Ornstein–Uhlenbeck model and social force models) to describe user mobility; analytical geometry to represent the spatial orientation of antennas; electromagnetic propagation theory methods to model cross-polarization effects; and Saleh and Volterra models to describe power amplifier nonlinearities in the FR1 and FR2 frequency ranges. Research Results. A vector signal model was derived, incorporating the effects of terminal orientation, interference, polarization and nonlinear distortions, and CSI errors. Analytical expressions were obtained for evaluating SINR, SER, throughput, and energy efficiency, considering all distortions. A comparative analysis of the proposed model against existing standards (3GPP, ITU-R) and academic approaches (DL-based, IRS-assisted) demonstrated its superiority in terms of realism and analytical completeness. Scientific Novelty. For the first time, a mathematical model of the MIMO-NOMA system is proposed that simultaneously accounts for terminal dynamics, dual polarization, nonlinearities with memory effects, and multipath scenarios, providing an analytical description within a unified parameter space. Theoretical and Practical Significance. The model refines the description of the MIMO-NOMA channel and supports the optimization of precoders, summation schemes in the complex baseband domain, and SIC algorithms in next-generation mobile networks, particularly in conditions of high mobility and dense urban environments.