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., $kle mle n$), respectively and when nodes are endowed with multi-packet transmission (MPT) or multi-packet reception (MPR) capabilities. We show that $Thetaleft(T(n)sqrt{m}/kright)$, $Thetaleft(1/kright)$, and $Thetaleft(T^{2}(n)right)$ bits per second constitute a tight bound for the throughput capacity of random wireless ad hoc networks under the protocol model when $ m=Oleft(T^{-2}(n)right)$, $Omega(k)= T^{-2}(n)= O(m)$, and $k=Omegaleft(T^{-2}(n)right) $, 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 $Thetaleft(sqrt{log n/n}right)$ 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).