Closing the Gap in the Capacity of Wireless Networks Via Percolation Theory

Abstract

An achievable bit rate per source-destination pair in a wireless network of n randomly located nodes is determined adopting the scaling limit approach of statistical physics. It is shown that randomly scattered nodes can achieve, with high probability, the same 1= p n transmission rate of arbitrarily located nodes. This contrasts with previous results suggesting that a 1= p n log n reduced rate is the price to pay for the randomness due to the location of the nodes. The network operation strategy to achieve the result corresponds to the transition region between order and disorder of an underlying percolation model. If nodes are allowed to transmit over large distances, then paths of connected nodes that cross the entire network area can be easily found, but these generate excessive interference. If nodes transmit over short distances, then such crossing paths do not exist. Percolation theory ensures that crossing paths form in the transition region between these two extreme scenarios. Nodes along these paths are used as a backbone, relaying data for other nodes, and can transport the total amount of information generated by all the sources. A lower bound on the achievable bit rate is then obtained

Throughput and delay analysis of wireless random access networks

“…Under this assumption, the achievable network throughput scales as (1/ log ) n n Θ , where n is the total number of nodes in the network. A less pessimistic scaling law (1/ ) n Θ was observed in [6][7] using a similar network model. These results conclude that the network throughput will approach zero with an increasing n. This conclusion was further elaborated and verified in a series of follow-up papers [8][9][10][11].…”

“…This indicates that the network throughput should at least have an order of ~(1/ ) n λ Θ . Note that it has been proved in [7] that the network throughput λ also scales as ~(1/ ) n λ Θ even with the optimal scheduling. The fact that the network throughput has the same order performance in the worst (random access) and best (optimal scheduling) scenarios indicates that the local access protocols do not change the order results on the network throughput λ.…”

“…The above theorem provides the criteria to verify whether a scalable throughput is achievable for a given rate allocation pattern λ(l). For example, in [5][6][7][8][9][10][11] it is assumed that each node randomly picks a destination node with equal probability among all nodes in the network. This leads to the following rate allocation:…”

Capacity Scaling Laws for Underwater Networks

“…[1], [4]. These results cannot be directly applied to underwater acoustic networks in which the attenuation varies over the system bandwidth and α ≤ 2.…”

“…The original results obtained for nodes deployed in a disk of unit area motivated the study of capacity scaling laws in different scenarios, ranging from achievability results in random deployments using percolation theory [4] or cooperation between nodes [3], to the impact of node mobility over the capacity of the network, e.g. [2].…”