Exact Capacity Scaling of Extended Wireless Networks

n source and destination pairs randomly located in an area extending linearly with n want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power attenuation of r^{-alpha} and random phase changes. Classical multihop architectures that decode and forward packets can deliver a sqrt{n}-scaling of the aggregate throughput, while recently proposed hierarchical cooperation achieves n^{2-alpha/2}-scaling, which is superior to multi-hop for alpha4, while the moderate-attenuation regime (2 < alpha < 4) remains uncharacterized. We close this gap by deriving a tight upper bound on the scaling of the aggregate throughput, valid for all alpha >2. Our result shows that the mentioned schemes are scaling-optimal, namely that no other scheme can beat hierarchical cooperation when alpha 3. The key ingredient is a careful evaluation of the scaling of the cut-set bound.