Decentralized Beamforming for Weighted Sum Energy Efficiency Maximization in MIMO Systems

This paper considers a joint transceiver design for the weighed sum energy efficiency maximization problem for downlink transmissions in a multi-cell multi-user multiple-input multiple-output (MIMO) system. To make the formulated problem be more valuable in practice, a more practical power consumption model is adopted in which part of the processing power is dependent on data rate. With per-user rate requirements and per-base station (BS) power constraints, the resulting optimization problem is non-convex. A centralized solution is firstly proposed, which alternatively performs transmit beamforming optimization and receive beamforming optimization with the help of successive convex approximation (SCA) based iteration. Based on the centralized design that requires global channel state information (CSI), a more meaningful decentralized algorithm is further designed, which solves the problem with the requirement of only exchanging quite a small amount of information among BSs. Specifically, the key methodology used in the decentralized algorithm is to reformulate transmit beamforming optimization as an equivalent global consensus problem when receive beamforming is fixed as minimum mean square error (MMSE) receiver, which is solved effectively by exploiting the alternative direction method of multipliers (ADMM) technique. Numerical results demonstrate the effectiveness and superiority of our proposed algorithms, and also illustrate the impact of the rate-dependent power consumption on the energy efficiency.