  Reconfigurable intelligent surface (RIS) has been regarded as a promising
tool to strengthen the quality of signal transmissions in non-orthogonal
multiple access (NOMA) networks. This article introduces a heterogeneous
network (HetNet) structure into RIS-aided NOMA multi-cell networks. A practical
user equipment (UE) association scheme for maximizing the average received
power is adopted. To evaluate system performance, we provide a stochastic
geometry based analytical framework, where the locations of RISs, base stations
(BSs), and UEs are modeled as homogeneous Poisson point processes (PPPs). Based
on this framework, we first derive the closed-form probability density function
(PDF) to characterize the distribution of the reflective links created by RISs.
Then, both the exact expressions and upper/lower bounds of UE association
probability are calculated. Lastly, the analytical expressions of the
signal-to-interference-plus-noise-ratio (SINR) and rate coverage probability
are deduced. Additionally, to investigate the impact of RISs on system
coverage, the asymptotic expressions of two coverage probabilities are derived.
The theoretical results show that RIS length is not the decisive factor for
coverage improvement. Numerical results demonstrate that the proposed RIS
HetNet structure brings significant enhancement in rate coverage. Moreover,
there exists an optimal combination of RISs and BSs deployment densities to
maximize coverage probability.
