Asymptotic Analysis of Amplify and Forward Relaying in a Parallel MIMO Relay Network

Abstract

This paper studies the setup of a parallel MIMO relay network in which K relays, each equipped with N antennas, assist in transmitting data between a source and a destination, each equipped with M antennas (M ≤ N), in the half-duplex mode. It is assumed that there is no direct source-destination link and the communication is performed in two hops. An amplify-and-forward relaying scheme called Incremental Cooperative Beamforming Scheme (ICBS) is introduced and shown to achieve the capacity of the network in the asymptotic case of K → ∞ with a gap scaling of at most [(log(K))/( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{4}</sup> √{K})]. This result is shown to hold as long as the power of each relay is significantly larger than [(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (K) log(log(K)))/(K)]. In addition, in the case that the source power is equal to the relays' power and both tend to infinity, the proposed scheme is shown to achieve the full multiplexing gain regardless of the number of relays. Simulation results confirm the validity of analytical arguments.