Degrees of Freedom Region of a Class of Multisource Gaussian Relay Networks

We study a layered K-user M-hop Gaussian relay network consisting of Km nodes in the m^th layer, where M ≥ 2 and K=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 that di ≤ 1 for all i and Σ i=1K di ≤ K_Σ is achievable, where di is the DoF of the i^th source-destination pair and K_Σ is the maximum integer such that K_Σ ≤ minm{Km} and M/K_Σ is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if M/ 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.