# Dual-Hop Cooperative Relaying with Beamforming Under Adaptive Transmission in κ–μ Shadowed Fading Environments

Department of Electronics Engineering, Dong-A University, Busan 604-714, Korea

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Received: 28 March 2019 / Revised: 3 June 2019 / Accepted: 5 June 2019 / Published: 11 June 2019

(This article belongs to the Special Issue Cooperative Communications for Future Wireless Systems)

In this paper, we analyze the performance of a dual-hop cooperative decode-and-forward (DF) relaying system with beamforming under different adaptive transmission techniques over $\kappa \phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mu $ shadowed fading channels. We consider multiple antennas at the source and destination, and communication takes place via a single antenna relay. The published work in the literature emphasized the performance analysis of dual-hop DF relaying systems, in conjunction with different adaptive transmission techniques for classical fading channels. However, in a real scenario, shadowing of the line-of-sight (LoS) signal is caused by complete or partially blockage of the LoS by environmental factors such as trees, buildings, mountains, etc., therefore, transmission links may suffer from fading as well as shadowing, either concurrently or separately. Hence, the $\kappa \phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mu $ shadowed fading model was introduced to emulate such general channel conditions. The $\kappa \phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mu $ shadowed fading model is a general fading model that can perfectly model the fading and shadowing effects of the wireless channel in a LoS propagation environment, and it includes some classical fading models as special cases, such as $\kappa \phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}-\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\mu $ , Rician, Rician-shadowed, Nakagami- $\widehat{m}$ , One-sided Gaussian, and Rayleigh fading. In this work, we derive the outage probability and average capacity expressions in an analytical form for different adaptive transmission techniques: (1) optimal power and rate adaptation (OPRA); (2) optimal rate adaptation and constant transmit power (ORA); (3) channel inversion with a fixed rate (CIFR); and (4) truncated channel inversion with a fixed rate (TIFR). We evaluate the system performance for different arrangements of antennas and for different fading and shadowing parameters. The obtained analytical expressions are verified through extensive Monte Carlo simulations.