Wireless small-world networks with beamforming

To maximize the gain of multi-hop transmissions, we have to let the number of hops as small as possible, decreasing multi-hop transmission delay. In this paper, we propose how the average number of hop counts can be reduced in wireless multi-hop networks by constructing a few long-range edges that can act as if they were highways in the networks. For this purpose, we adopt the concept of small-world phenomenon and suggest two methods for giving randomness in connectivity, power control and beamforming. Based on these methods, we investigate how the network capacity can be improved by utilizing the small-world characteristics. From our numerical examples, we have found that power control with single antenna decreases not the average hop counts, but also the end-to-end throughput of the network. Power control with beamforming, however, can somewhat overcome this throughput degradation only with two antennas, where the average number of hop counts is reduced like in small-world networks.