Energy-Efficient Power Allocation Maximization for Multi-User MIMO Broadcast Channel

This paper proposes an iterative water-filling algorithm (IWF) for the energy-efficiency (EE) maximization problem of the multi-user multiple-input and multiple-output (MIMO) broadcast channel (BC). This algorithm is termed as IWF-EE-BC and has two levels of operations. The inner level computes solutions, by an algorithm, is named as water-filling for the EE of the BC, which is implemented within a single iteration, with the short name: WF-EE-BC1. The solutions by WF-EE-BC1 are the optimal solutions of the auxiliary energy-efficiency maximization problems. Each term of the added throughput part in these auxiliary problems is decoupled in power variables for all users. Then the outer level determines when to output a good solution to the considered problem, based on the results obtained by the inner level. The considered problem has complex-valued matrix optimization variables, beyond the range of the optimization problems whose optimization variables are often real-valued variables. Particularly, it is a semi-definite optimization problem (SDO) with a more complicated form of the objective function, over the field of complex numbers. Since existing results on optimization algorithms, including SDO ones, cannot guarantee convergence of IWF-EE-BC, the novel fixed point method is designed and used. Overcoming these difficulties, this paper obtains convergence of IWF-EE-BC, with efficiency.