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 = K 1 = 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 ( d 1 ,..., dK ) such that di ≤ 1 for all i and Σ i =1 K 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 ≤ min m { 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 / min m { 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.