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**1 - 1**of**1**### Relay Selection for MIMO and Massive MIMO Two-Way Relay Networks

"... Relay selection strategies help to improve spectral and energy efficiencies, to en-hance transmission robustness, or to reduce latency in multi-relay cooperative wire-less networks. Two novel relay selection strategies are proposed and analysed here for 1. Multiple-input multiple-output (MIMO) 2. Ma ..."

Abstract
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Relay selection strategies help to improve spectral and energy efficiencies, to en-hance transmission robustness, or to reduce latency in multi-relay cooperative wire-less networks. Two novel relay selection strategies are proposed and analysed here for 1. Multiple-input multiple-output (MIMO) 2. Massive MIMO, amplify-and-forward (AF) two-way relay networks (TWRNs). Specifically, they are designed to minimize the overall outage probability or maximize the achievable sum rate. Interestingly, the first strategy amounts to maximizing the minimum of the eigen-values of the Wishart matrices of the channels from the selected relay to the two user nodes. Counter-intuitively, the latter strategy amounts to maximizing the min-imum of the determinant of the same Wishart matrices. The performance of these two strategies is investigated by deriving lower/upper bounds of the overall outage probability and the average sum rate approximations in closed-form. Further, the asymptotic high SNR approximations of the outage probability are derived, and thereby, the achievable diversity-multiplexing trade-off is quantified. Our analysis shows that the transmit power at user nodes can be scaled down proportional to their number of antennas and thus the use of a large scale antennas systems results in significant power savings. Further use of large number of anten-nas makes relay selection process simple and deterministic. Our results reveal that relay selection indeed significantly increases the sum rate and decreases the outage probability of wireless systems and will be useful for the wireless systems. ii