Due to the exponential growth in the number of connected devices, the utilization of available resources becomes challenging. To meet this demand, novel techniques with significantly higher gain for efficient spectrum usage and reduced latency are required. Non-orthogonal multiple access (NOMA) is expected to be a promising solution for the scarcity of spectrum resources, which are shared in a non-orthogonal way such that multiple users can access the same frequency and time slots simultaneously. Although many studies concentrate on NOMA, a few of them give insight into how the channel estimation and channel quantization affect the performance of the system. Related to this issue, this study focuses on a downlink NOMA implementation. In the first part, we mainly concentrate on the analysis of the effect of channel estimation and channel quantization on the bit error rate (BER) performance with MATLAB simulations. For the second part, the BER performance of the system is analyzed through a practical two-user downlink NOMA system implemented with software-defined radios (SDRs).