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

Abstract

Abstract-The present paper studies the asymptotic performance of multi-hop amplify-and-forward relay multiple-antenna communication channels. Each multi-antenna relay terminal in the considered network amplifies the received signal, sent by a source, and retransmits it upstream towards a destination. Achievable ergodic rates of the relay channel with both jointly optimal detection and decoding and practical separate-decoding receiver architectures for arbitrary signaling schemes, along with average bit error rates for various types of detectors 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.

A Survey on MIMO Transmission with Discrete Input Signals: Technical Challenges, Advances, and Future Trends

“…Rayleigh fading for K-hop AF relay MIMO channels [121]. For other performance criterions, R. R. Müller et al obtain an asymptotic expression for the average minimum transmit power for i.i.d.…”

Capacity and Power Scaling Laws for Finite Antenna MIMO Amplify-and-Forward Relay Networks

“…The singular vectors of the optimal precoding matrices for such a network when noise was negligible at the relays was also established in [6]. When noise was present at the relays, ergodic capacity and average bit error rate results were established in [7] for multihop AF MIMO networks when arbitrary signaling occurs at the source node and, again, d grows without bound. Meanwhile, in [14], c n was assessed for general n-hop AF networks in terms of the limiting (in d) eigenvalue distribution of products of random matrices when noise was not negligible at the relay nodes.…”

“…1). The end-to-end capacity, c n , of such links has been studied in many works: see, e.g., [4]- [7] for amplify-andforward (AF) studies, and [8]- [11] for decode-and-forward (DF) studies. It is known, [12], that the capacity of such networks is achieved by employing DF relaying.…”