  This paper investigates the coexistence of non-orthogonal multiple access
(NOMA) and full-duplex (FD) to improve both spectral efficiency (SE) and user
fairness. In such a scenario, NOMA based on the successive interference
cancellation technique is simultaneously applied to both uplink (UL) and
downlink (DL) transmissions in an FD system. We consider the problem of jointly
optimizing user association (UA) and power control to maximize the overall SE,
subject to user-specific quality-of-service and total transmit power
constraints. To be spectrally-efficient, we introduce the tensor model to
optimize UL users' decoding order and DL users' clustering, which results in a
mixed-integer non-convex problem. For practically appealing applications, we
first relax the binary variables and then propose two low-complexity designs.
In the first design, the continuous relaxation problem is solved using the
inner convex approximation framework. Next, we additionally introduce the
penalty method to further accelerate the performance of the former design. For
a benchmark, we develop an optimal solution based on brute-force search (BFS)
over all possible cases of UAs. It is demonstrated in numerical results that
the proposed algorithms outperform the conventional FD-based schemes and its
half-duplex counterpart, as well as yield data rates close to those obtained by
BFS-based algorithm.
