We analyze a multi-level MIMO relaying system where a multiple-antennatransmitter sends data to a multipleantenna receiver through several relaylevels, also equipped with multiple antennas. Assuming correlated fading ineach hop, each relay receives a faded version of the signal transmitted by theprevious level, performs precoding on the received signal and retransmits it tothe next level. Using free probability theory and assuming that the noise powerat the relay levels - but not at the receiver - is negligible, a closed-formexpression of the end-to-end asymptotic instantaneous mutual information isderived as the number of antennas in all levels grow large with the same rate.This asymptotic expression is shown to be independent from the channelrealizations, to only depend on the channel statistics and to also serve as theasymptotic value of the end-to-end average mutual information. We also providethe optimal singular vectors of the precoding matrices that maximize theasymptotic mutual information : the optimal transmit directions represented bythe singular vectors of the precoding matrices are aligned on the eigenvectorsof the channel correlation matrices, therefore they can be determined onlyusing the known statistics of the channel matrices and do not depend on aparticular channel realization.
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