Asymptotic Capacity and Optimal Precoding Strategy of Multi-Level Precode & Forward in Correlated Channels

TL;DR

This paper derives a closed-form expression for the asymptotic mutual information in multi-level MIMO relaying systems with correlated channels, revealing optimal precoding strategies based solely on channel statistics.

Contribution

It provides the first analytical characterization of the asymptotic capacity and optimal precoding directions in multi-level correlated MIMO relay channels.

Findings

Asymptotic mutual information depends only on channel statistics.

Optimal precoding aligns with eigenvectors of channel correlation matrices.

Closed-form expression valid as number of antennas grows large.

Abstract

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