  This paper proposes a novel framework of resource allocation in multi-cell
intelligent reflecting surface (IRS) aided non-orthogonal multiple access
(NOMA) networks, where an IRS is deployed to enhance the wireless service. The
problem of joint user association, subchannel assignment, power allocation,
phase shifts design, and decoding order determination is formulated for
maximizing the achievable sum rate. The challenging mixed-integer non-linear
problem is decomposed into an optimization subproblem (P1) with continuous
variables and a matching subproblem (P2) with integer variables. In an effort
to tackle the non-convex optimization problem (P1), iterative algorithms are
proposed for allocating transmission power, designing reflection matrix, and
determining decoding order by invoking relaxation methods such as convex upper
bound substitution, successive convex approximation, and semidefinite
relaxation. In terms of the combinational problem (P2), swap matching-based
algorithms are developed for achieving a two-sided exchange-stable state among
users, BSs and subchannels. Numerical results demonstrate that: 1) the sum rate
of multi-cell NOMA networks is capable of being increased by 35% with the aid
of the IRS; 2) the proposed algorithms for multi-cell IRS-aided NOMA networks
can enjoy 22% higher energy efficiency than conventional NOMA counterparts; 3)
the trade-off between spectrum efficiency and coverage area can be tuned by
judiciously selecting the location of the IRS.
