Joint Cooperation and Multi-Hopping Increase the Capacity of Wireless   Networks
  The problem of communication among nodes in an \emph{extended network} is considered, where radio power decay and interference are limiting factors. It has been shown previously that, with simple multi-hopping, the achievable total communication rate in such a network is at most $\Theta(\sqrt{N})$. In this work, we study the benefit of node cooperation in conjunction with multi-hopping on the network capacity. We propose a multi-phase communication scheme, combining distributed MIMO transmission with multi-hop forwarding among clusters of nodes. We derive the network throughput of this communication scheme and determine the optimal cluster size. This provides a constructive lower bound on the network capacity. We first show that in \textit{regular networks} a rate of $\omega(N^{{2/3}})$ can be achieved with transmission power scaling of $\Theta(N^{\frac{\alpha}{6}-{1/3}})$, where $\alpha>2$ is the signal path-loss exponent. We further extend this result to \textit{random networks}, where we show a rate of $\omega (N^{2/3}(\log{N})^{(2-\alpha)/6})$ can be achieved with transmission power scaling of $\Theta(N^{\alpha/6-1/3}(\log{N})^{-(\alpha-2)^2/6})$ in a random network with unit node density. In particular, as $\alpha$ approaches 2, only constant transmission power is required. Finally, we study a random network with density $\lambda=\Omega(\log{N})$ and show that a rate of $\omega((\lambda N)^{2/3})$ is achieved and the required power scales as $\Theta(N^{\alpha/6-1/3}/\lambda^{\alpha/3-2/3})$. 
Sam Vakil and Ben Liang