Optimal Energy-Efficient Source and Relay Precoder Design for Two-Way MIMO-AF Relay Systems

Abstract

Energy efficiency (EE) is a key figure of merit for designing the next generation of communication systems. Meanwhile, relay-based cooperative communication, through machine-to-machine and other related technologies, is also playing an important part in the development of these systems. This paper designs an energy efficient precoding method for optimizing the EE/energy consumption of two-way multi-input multi-output (MIMO)-amplify-and-forward (AF) relay systems by using pseudo-convexity analysis to design EE-optimal precoding matrices. More precisely, we derive an EE-optimal source precoding matrix in closed-form, design a numerical approach for obtaining an optimal relay precoding matrix, prove the optimality of these matrices, when treated separately, and provide lowcomplexity bespoke algorithms to generate them. These matrices are then jointly optimized through an alternating optimization process that is proved to be systematically convergent. Performance evaluation indicates that our method can be globally optimal in some scenarios and that it is significantly more energy efficient (i.e. up to 60% more energy efficient) than existing EEbased one-way or two-way MIMO-AF precoding methods. Index Terms-Energy efficiency, precoding/beamforming, MIMO, amplify-and-forward, two-way relay channel. I. INTRODUCTIONGreen and sustainable wireless communications have grown in importance over the last decade [1]-[3] to such an extent that energy efficiency (EE) is part of the design framework that has been set by the international telecommunication union (ITU) for 5G [4] . This framework targets a 100 fold improvement in EE going from 4G to 5G. Meanwhile, the research interest for relay-based cooperative communication has also significantly grown over the last two decades [5]- [7] given that relays have been proven useful for improving the spectral efficiency (SE) [7], extending the coverage of cellular networks [7], reducing the cost of network deployments [8], or more recently increasing the EE [9], [10]. Relay-based cooperative communication is already fully integrated in wireless communication standards [11] and will undoubtedly play a significant role in machine-to-machine communications (e.g. vehicle-to-vehicle (V2V), unmanned vehicle communications) in 5G systems [12]. abc abc abc

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