Closing the gap in the capacity of random wireless networks

We consider the problem of how throughput in a wireless network with randomly located nodes scales as the number of users grows. Following the physical model of Gupta and Kumar, we show that randomly scattered nodes can achieve the optimal 1/(n)¹2/ per-node transmission rate of arbitrarily located nodes. This contrasts with previous achievable results suggesting that a 1/(n log n)¹2/ reduced rate is the price to pay for the additional randomness introduced into the system. Our results rely on percolation theory arguments. In the high density regime the network is fully connected but generates excessive interference. In the low density regime the network loses connectivity. Percolation theory ensures that a wireless backbone forms in the transition region between this two extreme scalings. This backbone does not cover all the nodes, nevertheless it is sufficiently rich in crossing paths so that it can transport all the traffic in the network. By operating the network in this transition region between order and disorder, we are able to prove our tight bound.