The NOMA system represents non-orthogonal multi-transmission techniques used under 5G mobile telecommunications. The NOMA system consists of two key methods that include the SIC method on the receiver side and superposition coding on the base station side. Within this paper, a simple simulation of the NOMA system in the MATLAB programming environment was developed. The introductory part of the paper describes the basic characteristics of the 5G system, defines important technologies that affect it's development and describes 5G technology within the possibilities of the Internet. The MIMO and NOMA systems are presented, with a detailed description of the mode of operation and the possibilities provided by their application. Within the practical part of the paper, a NOMA system with a SIC receiver in the MATLAB programming environment is simulated, and the results obtained by simulations are analysed. The NOMA system simulation was performed using MATLAB scripts. The generated graphical results show the dependence of the most important parameters of the NOMA system with the SIC receiver. The presented results were analysed in detail and their correctness was confirmed based on a comparison with theoretical predictions. The most important is the level of efficiency achieved by applying the NOMA system in comparison with OMA access methods. The NOMA transfer method is extremely suitable for application within future generations of mobile cellular systems. The SIC method plays an extremely important role in this because the success of the interference cancellation procedure depends on it. The development of future generations of mobile telecommunications requires the continuous advancement of the technology necessary for their proper functioning, with the method of multiple transmission being implied and improved.