On the capacity improvement of ad hoc wireless networks using directional antennas
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
Hop distances and flooding in wireless multihop networks with randomized beamforming
MSWiM '05 Proceedings of the 8th ACM international symposium on Modeling, analysis and simulation of wireless and mobile systems
The capacity of wireless networks
IEEE Transactions on Information Theory
On connectivity limits in ad hoc networks with beamforming antennas
EURASIP Journal on Wireless Communications and Networking - Special issue on optimization techniques in wireless communications
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In previous work, the effects of randomized beamforming, i.e., the strategy of every node in a wireless multihop network directing its antenna in a randomly chosen direction, on connectivity are studied by simulation. In this paper, we study some such effects analytically under similar but slightly simplified modeling assumptions. We begin by generalizing the notion of the threshold range for k-connectivity from the traditional Boolean network model to networks with arbitrary link attenuations. Then, for a network of uniformly distributed nodes with randomized beamforming, we derive analytically and evaluate numerically the degree distribution of a random node. Based on this, we apply a commonly used approximation to the probability that such a network is k-connected.We find that because the randomness caused by this strategy in the link attenuations shifts the network topology from being strictly a geometric random graph towards being a pure random graph, the k-connectivity probability of a network applying randomized beamforming can be approximated more accurately than that of a network with omnidirectional antennas. This added randomness also manifests itself as the increased variance of the node degree and the threshold attenuation range for k-connectivity. The main conclusion from our findings is that randomized beamforming cannot be said to strictly improve -- nor to degrade -- the connectivity of random wireless multihop networks.