A Framework of Hybrid Transceiver Optimizations With Eigenvalue Constraints for Multi-Hop Networks

In this paper, we propose a general framework on the hybrid analog-digital transceiver design for multi-hop communications. For the inclusive purpose, a transceiver model unifying both linear and nonlinear transceivers has been taken into account. Various performance metrics, including the most representative capacity and weighted mean-squared error (MSE), have been investigated in a unified manner. In particular, to meet practical needs for the quality of services (QoS), a general eigenvalue power constraint model is introduced, which contains a sum power constraint and box eigenvalue constraints as special cases. Specifically, by carefully designing the auxiliary analog and digital beamformers, the multi-hop transceiver optimization is decomposed into a series of independent sub-problems, where the analog beamformers for different hops are completely decoupled. Based on that, this framework establishes a majorization-minimization (MM) based analog beamformer design algorithm, which is able to handle the complicated weighted unit-modulus matrix optimizations by finding their semi-closed-form solutions. Furthermore, an efficient waterfilling algorithm is proposed for the digital beamformer designs to deal with the difficulties of optimizations subject to the multiple eigenvalue power constraints. The numerical results are provided to demonstrate the performance advantages of the proposed framework.