Asymptotic Performance Analysis of a K-Hop Amplify-and-Forward Relay MIMO Channel

The present paper studies the asymptotic performance of multi-hop amplify-and-forward relay multiple-antenna communication channels. Each multi-antenna terminal in the network amplifies the received signal, sent by a source, and retransmits it upstream towards a destination. Achievable ergodic rates under both jointly optimal detection and decoding and practical separate decoding schemes for arbitrary signaling schemes, along with the average bit error rate for various receiver structures are derived in the regime where the number of antennas at each terminal grows large without a bound. To overcome the difficulty of averaging over channel realizations we apply large-system analysis based on the replica method from statistical physics. The validity of the large-system analysis is further verified through Monte Carlo simulations of realistic finite-sized systems.