LAUSR

In this article, we study the energy-efficient power allocation (PA) for multiuser distributed multiple-input-single-output (D-MISO) system with beamforming (BF) and imperfect channel state information (CSI). Given a target bit error rate, the system energy efficiency (EE) with imperfect CSI is deduced. Subject to the power budget constraints, a constrained optimization problem is first formulated to maximize EE of single-user D-MISO. The optimal BF is shown to be aligned with the channel direction that renders the joint optimization problem to be a PA problem. A near-optimal PA scheme is proposed to tackle this problem by using the concave–convex procedure method and fractional programming (FP) and block coordinate descent (BCD) method, and it can provide nearly optimal performance close to that of optimal exhaustive search scheme with less complexity. On this basis, a suboptimal PA scheme based on the FP and BCD method is developed to further decrease the complexity and maintain similar performance to near-optimal scheme, and it is suitable for the system with more distributed antennas. With these results, two PA schemes are, respectively, proposed for multiuser D-MISO with imperfect CSI to maximize EE. The first scheme can obtain better performance with relatively higher complexity, and the second scheme can gain the performance close to the first scheme with lower complexity, and only smaller performance loss is found. Interestingly, these two schemes have the same optimal performance for perfect CSI, and include the existing ones under perfect CSI as special cases. Simulation results verify the effectiveness of the developed schemes.