Degrees of Freedom Region of a Class of Multisource Gaussian Relay Networks
Sang-Woon Jeon, Sae-Young Chung, Syed A. Jafar · IEEE Transactions on Information Theory · 2011
We study a layeredK-userM-hop Gaussian relay network consisting ofKmnodes in themthlayer, whereM≥ 2 andK=K1=KM+1. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the interuser interference. The proposed amplify-and-forward relaying scheme exploits such channel variations and works for a wide class of channel distributions including Rayleigh fading. We show a general achievable degrees of freedom (DoF) region for this class of Gaussian relay networks. Specifically, the set of all (d1,...,dK) such thatdi≤ 1 for alliand Σi=1K di≤KΣis achievable, wherediis the DoF of theithsource-destination pair andKΣis the maximum integer such thatKΣ≤ minm{Km} andM/KΣis an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound ifM/ minm{Km} is an integer; thus, interference-free communication is possible in terms of DoF. We further characterize an achievable DoF region assuming multi-antenna nodes and general message set, which again coincides with the cut-set outer bound for a certain class of networks.