Spectrum Efficiency Optimization for Uplink Massive MIMO System with Imperfect Channel State Information

Based on imperfect channel state information (CSI) available, the power allocation (PA) schemes for spectrum efficiency (SE) optimization in uplink massive MIMO systems with continuous-rate adaptive modulation (CAM) are studied. Conditioned on target BER, the SE of massive MIMO with CAM in the presence of imperfect CSI is derived. As a result, closed-form expression is attained. Using this result, subject to the maximum transmit power per user, a constrained non-concave optimization problem of PA to maximize the SE is formulated. A near-optimal PA scheme with the concave-convex procedure (CCCP) method is then developed, which offers nearly optimal performance as the exhaustive search scheme. This PA scheme has relatively high complexity since more iterations from CCCP method are required. For this reason, we introduce an optimized parameter to simplify the original optimization problem. With this parameter, the original non-concave problem is transformed into two concave subproblems. By solving these subproblems, a low-complexity suboptimal PA scheme is presented, and it can provide closed-form PA. Simulation results reveal that the developed two schemes are valid, the near-optimal PA scheme has almost the same SE as the optimal one with the exhaustive search method, but the complexity is lower than the latter. The iteration free suboptimal PA scheme has the SE close to that of near-optimal PA scheme but offers lower complexity. Meanwhile, the PA from suboptimal scheme can be used as an initial value of the near-optimal scheme to speed up the CCCP method.