In a cognitive relay system, the secondary user is permitted to transmit data via a relay when licensed frequency bands are detected to be free. Previous studies mainly focus on reducing or limiting the interference of the secondary transmission on the primary users. On the other hand, however, the primary user traffic will also affect the data transmission performance of the secondary users. In this paper, we investigate the impact of the primary user traffic on the bit error rate (BER) of the secondary transmission, when the secondary user adopts adaptive transmission with a relay partially selected. From the numerical results, we can see that the primary user traffic seriously degrades average BER. The worse-link partial selection can perform almost as well as the global selection when the channel conditions of the source-relay links and the relay-destination links differ a lot. In addition, although the relay selection improves the spectral efficiency of the secondary transmission, numerical results show that it only has slight impact on the overall average BER, so that the robustness of the system will not be affected by the relay selection.