Achievable Rate Analysis for NOMA-Aided Massive MIMO Uplink

The performance of non-orthogonal multiple-access (NOMA)-aided massive multiple-input multiple-output (MIMO) uplink is investigated. Spatially-distributed user nodes are grouped into multiple clusters based on spatial-directional information, and a set of orthogonal pilots are assigned to these clusters. To strike a balance between the pilot training overhead and the number of users that can be served simultaneously in the same time-frequency resource block, the NOMA-enabled users within a given cluster share the same pilot sequence. The uplink channels are estimated at the massive MIMO base-station (BS) by using the pilots transmitted by the user nodes in all clusters. A computationally-efficient maximal ratio combiner is constructed at the BS via the estimated uplink channels. The achievable rates of this system set-up are derived for both finite and infinite BS antenna regimes. Thereby, the effects of imperfectly estimated channel state information, intra-cluster pilot contamination, and imperfect successive interference cancellation are analytically quantified. In order to guarantee user-fairness and thereby to mitigate near-far effects in uplink NOMA transmissions, a max-min transmit power control is invoked. Thereby, max-min fairness optimal transmit power control coefficients are derived. These power control coefficients depends only on statistical knowledge of downlink channels. Thus, the proposed transmit power control can readily be implemented at NOMA user nodes, which primarily rely on channel hardening with no downlink pilots are being transmitted by the BS in an attempt to minimize the training overhead. Our analysis and numerical results reveal that the proposed system can be exploited to enable massive access by optimizing the fundamental tradeoff among the number of simultaneously served NOMA users, uplink achievable rates and implementation complexity.