Linear Wireless Networks with Variable Length and Density: Scaling Laws and Design Considerations

In this paper we consider linear wireless networks with variable number of nodes. We first derive a basic cut-set bound for transport capacity of this class of networks highlighting the functional dependence on both node density and network length. After, we investigate how transport throughput scales with respect to node density delta in a wireless network with multihop communication. While in linear multihop networks without fading transport throughput does not increase by increasing node density, i.e. it scales as delta⁰ with a gap with respect to capacity bounds, we show that a capacity increase up to log delta is achieved in the presence of fading by using, instead of a simple nearest- neighbor communication, suitable algorithms that adaptively schedule source-destination links in the networks. Finally, we compare multihop schemes with schemes based on distributed MIMO communication by discussing the relevant differences and showing that, despite the latter strategy is able to asymptotically achieve scaling law bound approaching delta, multihop schemes appear better in terms of capacity in a significant range of values of delta and when the network becomes extended.