tric provides the maximum information rate that can be reliably transmitted for a given channel state information. In a single-user case, the average mutual information is calculated for the signal after constellation mapping and before the soft demapping. This analysis can be extended to the multiuser case for evaluating the achievable sum-rate of the NOMA schemes. Let X = XJ] denote the multi-user modulation symbol vector before the NOMA signature pattern, and y=[y1 y2 denote channel output bol vector at the receiver, in which J, K, M, andNrx represent the number of users, the NOMA signature length, the order of modulation, and the number of receive antennas, respectively. Assuming equi-probable input constellation points and the high-dimensional The average mutual information is defined as the weighted sum of the mutual information between each pair of the input and output events Xi and yj. The average mutual information is a measure of independence between the two random variables X and Y. In mathematical terms I(X; = E[I(x;yi)] = and I(x{;yi) = 368 Chapter 3 constellation set given by S = {W1,W2, 1}, the average mutual information in the multi-user case can be written A Monte Carlo simulation can be used to calculate the expectation function in the above equation. Assuming a six-user uplink multiple access channel, a tapped delay line TDL-A- 30 ns channel H and ideal channel estimation, multi-user average mutual information of the NOMA schemes under consideration in 3GPP for Rel-16 and OFDMA have been calculated and compared in Fig. 3.37. In this analysis, the overloading factor is 150%, spectral effi- ciency per user is 0.25 bps/Hz, and the sum-rate is 1.5 bps/Hz. The SNR is defined as the ratio of average total received multi-users' power to the noise power at each receive antenna for given bandwidth. Multiple UEs are assumed to share the same six physical resource blocks. The number of users, SE per user, and transmission bandwidth are identical for both NOMA and OFDMA schemes to ensure fairness. Fig. 3.3