Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks

Abstract

n source and destination pairs randomly located in an area want to communicate with each other.Signals transmitted from one user to another at distance r apart are subject to a power loss of r −α as well as a random phase. We identify the scaling laws of the information theoretic capacity of the network. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n 2/3 of [1]. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n 2−α/2 for 2 ≤ α < 3 and √ n for α ≥ 3. The best known earlier result [2] identified the scaling law for α > 4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation. I. INTRODUCTIONThe seminal paper by Gupta and Kumar [3] initiated the study of scaling laws in large adhoc wireless networks. Their by-now-familiar model considers n nodes randomly located in the unit disk, each of which wants to communicate to a random destination node at a rate R(n) bits/second. They ask what is the maximally achievable scaling of the total throughput T (n) = n R(n) with the system size n. They showed that classical multihop architectures with conventional single-user decoding and forwarding of packets cannot achieve a scaling better

Throughput and delay analysis of wireless random access networks

“…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]. More sophisticated models were also developed to incorporate node mobility or fading [12][13][14][15][16][17] --they were obviously inspired by this rather pessimistic result and aimed at improving the network throughput. As mentioned earlier, the input rate λ and the SD distance L are intrinsic elements affecting the network throughput.…”

Network dimensioning with carrier aggregation

“…Scaling laws in wireless and wired networks have been studied in various contexts [18][19][20][21]. The work of Bolcskei et al, for example, focuses on the gains realized by increasing the number of antennas in a MIMO relay network.…”

Capacity Scaling Laws for Underwater Networks

“…For example, we could allow cooperation between nodesà la Ozgur et al [3] taking advantage of the distance-band separation. That is, instead of performing time division between long and short transmissions, we could simply transmit in different bands that do not interfere with one another.…”

“…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].…”