In a heterogeneous cellular network (HetNet), consider that a base station in the HetNet is able to simultaneously schedule and serve K users in the downlink by performing the power-domain non-orthogonal multiple access (NOMA) scheme. This paper aims at the preliminary study on the downlink coverage and throughput performances of the HetNet with the non-coordinated NOMA and the proposed coordinated joint transmission NOMA (JT-NOMA) schemes. First, the coverage probability and link throughput of K users in each cell are studied and their accurate expressions are derived for the noncoordinated NOMA scheme in which no BSs are coordinated to jointly transmit the NOMA signals for a particular user. We show that the coverage and link throughput can be largely reduced if transmit power allocations among the K users do not satisfy the constraint derived. Next, we analyze the coverage and link throughput of K users for the coordinated JT-NOMA scheme in which the void BSs without users are coordinated to enhance the farthest NOMA user in a cell. The derived accurate results show that coordinated JT-NOMA can significantly improve the coverage and link throughput of all users. Finally, we show that there exist optimal power allocation schemes that maximize the average cell coverage and throughput under some derived power allocation constraints and numerical results validate our analytical findings.