  In a heterogeneous cellular network (HetNet) consisting of $M$ tiers of
densely-deployed base stations (BSs), consider that each of the BSs in the
HetNet that are associated with multiple users is able to simultaneously
schedule and serve two users in a downlink time slot by performing the
(power-domain) non-orthogonal multiple access (NOMA) scheme. This paper aims at
the preliminary study on the downlink coverage performance of the HetNet with
the \textit{non-cooperative} and the proposed \textit{cooperative} NOMA
schemes. First, we study the coverage probability of the NOMA users for the
non-cooperative NOMA scheme in which no BSs are coordinated to jointly transmit
the NOMA signals for a particular cell and the coverage probabilities of the
two NOMA users of the BSs in each tier are derived. We show that the coverage
probabilities can be largely reduced if allocated transmit powers for the NOMA
users are not satisfied with some constraints. Next, we study and derive the
coverage probabilities for the proposed cooperative NOMA scheme in which the
void BSs that are not tagged by any users are coordinated to enhance the far
NOMA user in a particular cell. Our analyses show that cooperative NOMA can
significantly improve the coverage of all NOMA users as long as the transmit
powers for the NOMA users are properly allocated.
