Asymptotic Gain Analysis of Cooperative Broadcast in Linear Wireless Networks

Abstract

We analyze the maximum gain that can be achieved through cooperative broadcast with energy accumulation and memory. We consider a linear network, where a known number of nodes are placed on a line, and derive an upper bound on $G_{tot}$ , the gain of cooperative broadcast over noncooperative broadcast with respect to total power consumption. Specifically, we prove that, in linear networks with path loss exponent $\alpha=2$ , $G_{tot} \leq \frac{\pi^2}{12-\pi^2}\approx 4.64$ , irrespective of the number of devices, the size of the network, the node placement strategy, and the cooperative broadcast strategy. We extend this result to any path loss exponent $\alpha\geq 2$ . We also show that the cooperation gain in short-range transmissions, wherein the circuit energy consumption is nonnegligible, is smaller than that in long-range transmissions. We further study the cooperative broadcast gain when the objective is to reduce the maximum transmission power used by any node in the network. In this case, we show that, when nodes are distributed uniformly at random, the maximum cooperation gain will be $O$ (log $n$ ), with high probability, where $n$ is the number of nodes in the network. These are important observations that should be considered in designing power-efficient broadcast algorithms in future network-wide cooperative broadcast.