Broadcast capacity for wireless ad hoc networks

Abstract

The capacity of a wireless network has been widely studied in the literature, including the capacity for unicast and the capacity for broadcast. In this paper, we studied the capacity of a wireless network for broadcast. Previous studies on broadcast capacity either assume that all links in the wireless network has the same channel capacity, or assume that the transmission ranges of a wireless node can be arbitrarily large. In this paper we derive analytical upper bounds and lower bounds on broadcast capacity of a wireless network when all nodes in the network has the same bounded transmission power P and all nodes are placed in a square of side-length a. When the fixed data rate channel is used (each node can send W bits/second to nodes within its transmission range if no interference happened), we prove that the broadcast capacity is Θ(W) under the physical interference model. When the Gaussian channel capacity is used, we show that the total broadcast capacity is only Θ((α√log n/n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−β</sup> when α√log n/n → ∞. When a α√log n/n → O(1), we show that the broadcast capacity is Θ(1). We also generalize our results to multicast capacity for physical interference model.