  In this paper, we propose bi-directional cooperative non-orthogonal multiple
access (NOMA). Compared to conventional NOMA, the main contributions of
bi-directional cooperative NOMA can be explained in two directions: 1) The
proposed NOMA system is still efficient when the channel gains of scheduled
users are almost the same. 2) The proposed NOMA system operates well without
accurate channel state information (CSI) at the base station (BS). In a
two-user scenario, the closed-form ergodic capacity of bi-directional
cooperative NOMA is derived and it is proven to be better than those of other
techniques. Based on the ergodic capacity, the algorithms to find optimal power
allocations maximizing user fairness and sum-rate are presented. Outage
probability is also derived, and we show that bi-directional cooperative NOMA
achieves a power gain over uni-directional cooperative NOMA and a diversity
gain over non-cooperative NOMA and orthogonal multiple access (OMA). We finally
extend the bi-directional cooperative NOMA to a multi-user model. The analysis
of ergodic capacity and outage probability in two-user scenario is numerically
verified. Also, simulation results show that bi-directional cooperative NOMA
provdes better data rates than the existing NOMA schemes as well as OMA in
multi-user scenario.
