Multi-hopping loss in MIMO decode-and-forward cooperative relaying

It is well-known that relaying can extend the communication range. However, the performance of the relaying network is inferior compared to a single-hop system where the destination is placed hypothetically at the relay. The gap between the single-hop and relay network, dubbed the multi-hopping or relaying loss, is studied in this paper. In particular, we investigate the increase in outage probability and the degradation in ergodic capacity incurred due to the multi-hopping loss in a dualhop multiple-input multiple-output decode-and-forward relaying network operating in the single-source single-relay single-user topology. Moreover, we show that a cooperative relaying scheme, called the best relay scheme, in the single-source K-relays single-user topology can recover a significant portion of the multi-hopping loss. In both topologies, we derive closed-form approximations for the outage probability and ergodic capacity using the well-known Gaussian approximation.