In order to improve the uplink performance of heterogeneous networks and coverage probability, this paper proposes a non-orthogonal multiple access (NOMA) heterogeneous network model by integrating decoupled uplink/downlink association (DUDA) and dual-connectivity schemes, and an analysis framework of conditional decoupled uplink and downlink association is designed. Meanwhile, three possible uplink association scenarios are considered, the design and analysis of the decoupled uplink associations are performed under the given conditional downlink association, and the probability expressions of the coupled uplink associations are derived. We get the statistical description of the primary and secondary access distances. Firstly, the numerical and simulation analysis shows the effect of system parameters on the association probability. Secondly, we study the conditional coverage probability and spectrum efficiency of the NOMA heterogeneous network under coupled uplink and downlink association and coupled uplink and downlink association schemes, respectively. The experimental results show that, the coverage probability performance of the proposed DUDA scheme is better than the traditional coupled uplink and downlink association (CUDA) scheme. In addition, the spectrum efficiency performance of the two schemes is related to system parameters.