Network coding is a promising technique for improving system performance in wireless multihop networks. In this paper, the throughput and fairness in single-relay multi-user wireless networks are evaluated. The carrier sense multiple access with collision avoidance (CSMA/CA) protocol and network coding are used in the medium access control (MAC) sublayer in such networks. The fairness of wireless medium access among stations (STAs), the access point (AP), and the relay station (RS) results in asymmetric bidirectional flows via the RS; as a result the wireless throughput decreases substantially. To overcome this problem, an autonomous optimization of minimum contention window size is developed for CSMA/CA and network coding to assign appropriate transmission opportunities to both the AP and RS. By optimizing the minimum contention window size according to the number of STAs, the wireless throughput in single-relay multi-user networks can be improved and the fairness between bidirectional flows via the RS can be achieved. Numerical analysis and computer simulations enable us to evaluate the performances of CSMA/CA and network coding in single-relay multi-user wireless networks.