Ergodic Sum Rate Expressions for Uplink MIMO-NOMA Under Spatial Correlation and Imperfect Channel Estimation

This article conducts an analytical study for the ergodic sum rate (ESR) of uplink multiple-input multiple-output nonorthogonal multiple access (MIMO-NOMA) networks under spatially correlated channels and imperfect channel state information (CSI) at the base station. We provide closed-form lower bounds for the ESR when MIMO channels have no correlation or exhibit correlation at the receive side, transmit side, and both sides. These bounds are attained by representing the determinant function by simple polynomial expansions. They are appropriate for a general setup of the MIMO-NOMA network and do not constrain the number of antennas or uplink users to be unbounded. Moreover, we give simplified ESR formulas for the investigated correlation scenarios in the high signal-to-noise ratio (SNR) regime. Numerical results corroborate accuracy of the derived expressions over different antenna configurations, number of users, channel conditions, and SNRs. The new ESR equations extend the state-of-the-art and enable an elegant and efficient performance evaluation of MIMO-NOMA for next-generation systems.