Network Simplification: The Gaussian diamond network with multiple antennas

Abstract

We consider the N-relay Gaussian diamond network when the source and the destination have n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ≥ 2 and n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> ≥ 2 antennas respectively. We show that when n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> = 2 and when the individual MISO channels from the source to each relay and the SIMO channels from each relay to the destination have the same capacity, there exists a two relay sub-network that achieves approximately all the capacity of the network. To prove this result, we establish a simple relation between the joint entropies of three Gaussian random variables, which is not implied by standard Shannon-type entropy inequalities.