Non-orthogonal multiple access (NOMA), is one of the fundamental radio access techniques recommended for 5G communication networks that increases the spectral efficiency by multiplexing the users in the power domain to compensate for the increasing bandwidth requirements. Although there are plenty of theoretical studies, there is only a couple of experimental studies about NOMA. In this study, a practical downlink NOMA system based on software-defined radio (SDR) platform is implemented with the number of users increased to four. Our NOMA system, which makes use of power domain NOMA mainly focuses on four user superposition coding at the transmitter and successive interference cancelation (SIC) at each receiver. The designed NOMA system has been tested over real-time experiments and constellation differences are compared with SIC output. In addition to these, bit error rate (BER) results have been proposed.