Propagation Channel Characterization for Amplify-and-Forward MIMO-Relaying Systems

In this contribution, we derive the spread function and power spectrum of the so-called "relay channel\´\´ along which electromagnetic waves propagate from a source station to a destination station via multiple amplify-and-forward (AF) relay stations. These results show analytically that the propagation over such a relay channel can be influenced by the propagation in individual "hops\´\´ and the responses of the relay stations. Furthermore, we find that the uncorrelated-scattering assumption is inapplicable for the AF-relay channels in the case where the relay stations receive and retransmit signals using mulitple antennas. We propose to simulate the relay channels by three steps: i) selecting channel models for individual "hops\´\´; ii) defining the correlations of model parameters among the hops; and iii) constructing realizations of relay channels by taking into account the responses of relay stations, which are specified by considering the response of antennas and the relay mode according to system configurations. We also show in this contribution that the spreads of a multi-relay channel in delay, Doppler frequency and directions are lower-bounded by the weighted summation of the spreads of individual source-relay-destination channels.