Design of Optimal Finite Alphabet NOMA Scheme for Uplink Noncoherent Massive MIMO Channels

The main focus of this paper is on an uplink communication system with multiple single-antenna users utilizing the same frequency band and simultaneously transmitting their finite alphabet signals to one base station having a large number of antennas. It is assumed that small scale channel fading is Rayleigh fading and varies in every one time slot, and that the large scale fading coefficients are fixed and known at both the transmitter and the receiver. For such uplink non-orthogonal multiple access massive MIMO system, we aim at establishing a new criterion using a noncoherent maximum likelihood detector for collaboratively designing all such user constellations that once each received sum signal point has been recovered, all the user signal points can be uniquely determined, i.e., all the user constellations form a so called additively uniquely decomposable constellation group (AUDCG). To this end, we first derive a fast noncoherent ML detection algorithm for the received sum constellation and a corresponding closed form symbol error probability formula (SEP). Thus, two important concepts: full receiver diversity and geometrical coding gain, are introduced to quantitatively characterize how quickly SEP decays when the number of base station antennas goes to infinity. Then, the design of an optimal AUDCG is formally formulated into an optimization problem that maximizes both the receiver diversity and the geometrical coding gains subject to each user power constraint. Particularly for a two user system, with each user transmitting nonnegative binary constellation, an optimal closed form sum constellation is obtained. Computer simulations demonstrate that our proposed optimal constellation design substantially outperforms the currently available constellation designs for the same uplink massive MIMO system.