Multipair Relaying With Space-Constrained Large-Scale MIMO Arrays: Spectral and Energy Efficiency Analysis With Incomplete CSI

In this paper, we study a multi-pair two-way large-scale multiple-input multiple-output (MIMO) decode-and-forward relay system. Multiple single-antenna user pairs exchange information via a shared relay working at half-duplex. The proposed scenario considers a practical case where an increasing number of antennas is deployed in a fixed physical space, giving rise to a trade-off between antenna gain and spatial correlation. The channel is assumed imperfectly known, and the relay employs linear processing methods. We study the large-scale approximations of the sum spectral efficiency (SE) and investigate the energy efficiency (EE) with a practical power consumption model when the number of relay antennas becomes large. We demonstrate the impact of the relay antenna number and spatial correlation with reducing inter-antenna distance on the EE performance. We exploit the increasing spatial correlation to allow an incomplete channel state information (CSI) acquisition where explicit CSI is acquired only for a subset of antennas. Our analytical derivations and numerical results show that applying the incomplete CSI strategy in the proposed system can improve the EE against complete CSI systems while maintaining the average SE performance.