Non-orthogonal multiple access (NOMA) is widely recognized as a potential multiple access (MA) technology for efficient spectrum utilization in the fifth-generation (5G) wireless standard. In this paper, we present the achievable sum rate analysis of a cooperative relaying system (CRS) using NOMA with two different receive diversity schemes - selection combining (SC), where the antenna with highest instantaneous signal-to-noise ratio (SNR) is selected, and maximal-ratio combining (MRC). We also present the outage probability and diversity analysis for the CRS-NOMA system. Analytical results confirm that the CRS-NOMA system outperforms the CRS with conventional orthogonal multiple access (OMA) by achieving higher spectral efficiency at high transmit SNR and achieves a full diversity order.