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

Abstract

We study a layered K-user M-hop Gaussian relay network consisting of K(m) nodes in the m(th) layer, where M >= 2 and K = K(1) = K(M11). 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), ... , d(K)) such that d(i) <= 1 for all i and Sigma(K)(i=1) d(i) <= K(Sigma) is achievable, where d(i) is the DoF of the i(th) source-destination pair and K(Sigma) is the maximum integer such that K(Sigma) <= min(m) {K(m)} and M/K(Sigma) is an integer. We show that surprisingly the achievable DoF region coincides with the cut-set outer bound if M/min(m) {K(m)} 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.