#### Demystifying the Scaling Laws of Dense Wireless Networks: No Linear Scaling in Practice

##### Song-Nam Hong, Giuseppe Caire

We optimize the hierarchical cooperation protocol of Ozgur, Leveque and Tse, which is supposed to yield almost linear scaling of the capacity of a dense wireless network with the number of users $n$. Exploiting recent results on the optimality of "treating interference as noise" in Gaussian interference channels, we are able to optimize the achievable average per-link rate and not just its scaling law. Our optimized hierarchical cooperation protocol significantly outperforms the originally proposed scheme. On the negative side, we show that even for very large $n$, the rate scaling is far from linear, and the optimal number of stages $t$ is less than 4, instead of $t \rightarrow \infty$ as required for almost linear scaling. Combining our results and the fact that, beyond a certain user density, the network capacity is fundamentally limited by Maxwell laws, as shown by Francheschetti, Migliore and Minero, we argue that there is indeed no intermediate regime of linear scaling for dense networks in practice.

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