Device-to-device (D2D) aided cooperative nonorthogonal multiple access (DC-NOMA) can enhance the spectral efficiency by integrating D2D communication into cooperative NOMA systems. In this paper, we analyze the performance of DC-NOMA with imperfect channel state information (CSI). We first derive the ergodic rates of both cellular users and D2D users. Then, we formulate a joint relay selection and power allocation problem aiming at maximizing the system sum rate. Finally, we solve the joint problem by modeling it as a two-sided matching problem with one-sided preference. Simulation results are provided to verify our analysis and show that the proposed scheme outperforms conventional cooperative orthogonal multiple access (C-OMA) schemes.