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In this study, two relay selection methods in the half-duplex decode-and-forward relaying for cooperative multipleinput multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) systems have been introduced. The relay selections are implemented using the symbol-based and subcarrier-based methods. By considering different number of antennas for source, each relay, and destination, the authors have derived closed-form outage expressions for these proposed methods. The MIMO channel model for each subcarrier, between source-relay and relay-destination is considered as a MIMO Rician fading channel with independent but not necessary identically distributed. Moreover, the outage expressions for MIMO independent and identically distributed Rician and Rayleigh fading channels are derived as special cases. Furthermore, the correlation among the OFDM subchannels is analysed. In addition, the implementation issues of both relay selection methods are also investigated. Monte Carlo simulations are performed to validate the outage analysis where the excellent agreement between the analytical and simulation results is observed.

In this paper, we propose a millimeter wave (mmWave) X-duplex (XD) amplify-and-forward (AF) multirelay system for 5G and beyond. Each XD AF relay is equipped with a shared antenna for both transmission and reception radio frequency (RF) chains. Also, the performance of mmWave XD AF multirelay system is analyzed, and a relay selection method in this scenario is suggested, where the best relay and the best operation mode are selected based on maximum end-to-end signal-to-interference-plus-noise ratio (SINR).XD relays can switch adaptively between half-duplex (HD) and full-duplex (FD) operation modes. As a practical channel model, Rician fading, path loss with line-of-sight (LOS) and non-line-of-sight (NLOS) propagation, and blockage effects are considered for mmWave channel model in both source-relay and relay-destination links. We derive closed-form expressions for end-to-end SINR and its distribution, outage probability, energy efficiency (EE), rate, and average symbol error rate (SER) based on the relay selection method. Monte Carlo simulations are performed to validate our analytical derivations, and also, the simulation results depict that XD relays outperform both HD and FD operation modes in terms of outage probability, EE, SER, and rate. Furthermore, the effects of self-interference (SI) cancellation, blockage, and number of XD AF relays over the performance and also the comparison of XD relay selection to different existing relay selection policies are presented. In addition, it is shown that the XD relay selection method in our proposed system eliminates the performance floor of the FD caused by the residual SI that it is considered as a significant advantage of our proposed system.

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