Non-Orthogonal multiple access (NOMA) is a emerging potential multiple access technique for 5th generation (5G) wireless communication. To further enhance the performance of NOMA based system, a decode-and-forward (DF) cooperative NOMA scheme is analyzed in this paper. In particular, we present the performance analysis at near and far user of DF cooperative downlink NOMA in presence of successive interference cancellation (SIC) errors over Rayleigh fading channels. We derive the novel closed-form expressions of the symbol error rate (SER) for the considered system. Besides, we also present the achievable rate analysis and it is observed that the achievable rate for the NOMA based scheme is higher as compared to that of conventional orthogonal multiple access (OMA) schemes. Further, we also evaluate the optimized power allocation coefficient for the NOMA system. The analytical results are corroborated with Monte-Carlo simulations to demonstrate the accuracy.