Optimal Power Allocation and User Pairing for Layer-1 and Layer-2 Sum-Rate Maximization in NOMA Uplink Networks

We investigate the optimal power allocation and user-pairing in non-orthogonal multiple access (NOMA) uplink networks, in the asymptotic (infinite blocklength) and in the finite

blocklength regimes. Firstly, in the asymptotic blocklength, we identify the optimal power allocation that maximizes the Layer-1(L1) sum-rate in a two-user network, while ensuring that the individual NOMA rates are lower-bounded by the corresponding orthogonal multiple access (OMA) rates, and, further provide an analytic expression for the Layer-2 (L2) optimal power allocation in high SNRs. Secondly, in the finite blocklength, we provide analytic expressions for the L1 optimal power coefficients in high SNRs; at L2, we first derive novel analytic expressions for the individual effective rates (ERs) validated through Monte-Carlo simulations. These expressions are used to obtain the L2 optimal power coefficients in high SNRs. What emerges from this analysis

is that reducing the delay beyond a certain threshold results in a performance degradation of NOMA compared to OMA. Finally, with respect to user-pairing, our results show that the optimal pairing reduces to near-far pairing, i.e., pairing the user of index k with the user of index 2K-k+1; interestingly, this conclusion is drawn for both L1 and L2, in both the asymptotic and the finite blocklengths.