Power allocation for SE maximization in uplink massive MIMO system under minimum rate constraint

In this paper, we optimize the spectrum efficiency (SE) of uplink massive multiple-input multiple-output (MIMO) system with imperfect channel state information (CSI) over Rayleigh fading channel. The SE optimization problem is formulated under the constraints of maximum power and minimum rate of each user. Then, we develop a near-optimal power allocation (PA) scheme by using the successive convex approximation (SCA) method, Lagrange multiplier method, and block coordinate descent (BCD) method, and it can obtain almost the same SE as the benchmark scheme with lower complexity. Since this scheme needs three-layer iteration, a suboptimal PA scheme is developed to further reduce the complexity, where the characteristic of massive MIMO (i.e., numerous receive antennas) is utilized for convex reformulation, and the rate constraint is converted to linear constraints. This suboptimal scheme only needs single-layer iteration, thus has lower complexity than the near-optimal scheme. Finally, we joint design the pilot power and data power to further improve the performance, and propose an two-stage algorithm to obtain joint PA. Simulation results verify the effectiveness of the proposed schemes, and superior SE performance is achieved.