Degrees of Freedom Region of a Class of Multi-source Gaussian Relay Networks

Abstract

We study a layered $K$-user $M$-hop Gaussian relay network consisting of $K_m$ nodes in the $m^{\mathrm{th}}$ layer, where $M\ge 2$ and $K=K_1=K_{M+1}$. We observe that the time-varying nature of wireless channels or fading can be exploited to mitigate the inter-user 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 $d_i\le 1$ for all $i$ and ${\sum }_{i=1}^K{d}_i\le K_{\Sigma }$ is achievable, where $d_i$ is the DoF of the $i^{\mathrm{th}}$ source--destination pair and $K_{\Sigma }$ is the maximum integer such that $K_{\Sigma }\le {\min }_m\{K_m\}$ 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.

19 pages, 5 figures, published in IEEE Transactions on Information Theory

References in corpus (4)

• The Approximate Capacity of the Many-to-One and One-to-Many Gaussian Interference Channels
• Approximate Capacity of Gaussian Relay Networks
• Ergodic Interference Alignment
• Degrees of Freedom of Multi-Source Relay Networks