A Framework for Energy-Efficient Hybrid Transceiver Design in Multi-Hop Communications

In this paper, we propose a general energy efficiency (EE) optimization framework for the hybrid analog-digital transceivers design in multi-hop communication systems. The analog and digital beamforming matrices are jointly optimized considering two kinds of practical power constraint models, i.e., sum power with box eigenvalue constraints (SPBECs) and multiple weighted power constraints (MWPCs), and unit-modulus constraints on analog beamforming matrices. For both the SPBECs and MWPCs cases, to tackle the challenging problem involving highly-coupled variables, an effective decoupling approach is first proposed. Specifically, a set of auxiliary variables are introduced to equivalently transform the original problem into a decoupled form with respect to the variables of each node. Then, for each node, we propose an efficient two-stage analog and digital beamforming optimization algorithm. To be specific, we optimize the analog beamforming matrices in the first stage by jointly exploiting the matrix-monotonic optimization framework and channel-alignment strategy. Then, we optimize the digital beamforming matrices in the second stage based on the multi-node water-filling methodology. Furthermore, in order to compute the parameters involved in the multi-node water-filling solutions for the SPBECs case, we propose two novel strategies, i.e., the Dinkelbach based strategy and the per-node penalty based strategy, which derive the parameters in closed-forms and offer clear physical interpretations. Moreover, the per-node penalty based strategy is effectively extended to the MWPCs case by additionally employing the Lagrangian duality theory. Simulation results demonstrate the superior performance and high efficiency of our proposed algorithms.