Characterizing user access methods in heterogeneous cloud radio access networks (H-CRANs)is critical for performance optimization. Different from the user access in cloud radio access networks, the inter-tier interference from macro base station has a great impact on user access in H-CRANs. In this paper, after considering the inter-tier interference, the ergodic rates of downlink H- CRANs for two proposed user access methods, namely distance based and cluster based, are analyzed. The corresponding mathematical expressions of ergodic rates have been derived. In particular, the closed-form expression for the upper bound of ergodic rate is proposed. Simulation results corroborate the accuracy of the derived expressions for these two methods. Furthermore, the cluster based user access method outperforms the distance based user access method when the intensity of remote radio heads is sufficiently high.