Non-orthogonal multiple access (NOMA) is one of the potential technologies for fifth generation (5G) cellular networks. This technique can combine with other techniques such as Orthogonal Frequency Division Multiplexing (OFDM) and Multiple Input Multiple Output (MIMO). In NOMA downlink, signals from multiple users are superposed in time-frequency domain. Hence, NOMA systems have a larger throughput than orthogonal multiple access systems. There are several schemes for NOMA detection. The successive interference cancellation (SIC) is commonly used to decode desired signals at the receivers. Some NOMA schemes with SIC are ideal SIC, symbol-level SIC and codeword-level SIC. The previous studies showed that the log-likelihood ratio (LLR) has a performance as ideal SIC. In this paper, we derive the bit error rate for a NOMA downlink system with 2 users (UE) using LLR receiver. This study considers the system over a Rayleigh fading channel and the presence of Additive White Gaussian Noise. The closed-form equations have been proposed for each user with QPSK mapping. The simulation results show that the performance of the system is consistent with the proposed formula