Capacity scaling laws of information dissemination modalities in wireless ad hoc networks

Abstract

We present capacity scaling laws for random wireless ad hoc networks under (n, m, k)-cast formulation, where n, m, and k denote the number of nodes in the network, the number of destinations for each communication group, and the actual number of communication group members that receive information (i. e., k les m les n), respectively and when nodes are endowed with multi-packet transmission (MPT) or multi-packet reception (MPR) capabilities. We show that Theta(T(n)radicm/k), Theta(1/k), and ThetaT <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (n) bits per second constitute a tight bound for the throughput capacity of random wireless ad hoc networks under the protocol model when m = O (T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> (n)), Omega(k) = T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> (n) = O(m), and k = Omega(T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> (n)), respectively. This result applies to both MPR and MPT, where T(n) denotes the transceiver range, which depends on the complexity of the nodes. For the minimum transceiver range of Theta (radic(log n/n)) to guarantee network connectivity, a gain of Theta(log n) for (n, m, k)-casting is attained with either MPT or MPR compared to the capacity attained when transmitters and receivers can encode and decode at most one transmission at a time (i.e., point-to-point communication).