Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Connectivity of confined 3D Networks with Anisotropically Radiating Nodes

Nodes in ad hoc networks with randomly oriented directional antenna patterns typically have fewer short links and more long links which can bridge together otherwise isolated subnetworks. This network feature is known to improve overall connectivity in 2D random networks operating at low channel path loss. To this end, we advance recently established results to obtain analytic expressions for the mean degree of 3D networks for simple but practical anisotropic gain profiles, including those of patch, dipole and end-fire array antennas. Our analysis reveals that for homogeneous systems (i.e. neglecting boundary effects) directional radiation patterns are superior to the isotropic case only when the path loss exponent is less than the spatial dimension. Moreover, we establish that ad hoc networks utilizing directional transmit and isotropic receive antennas (or vice versa) are always sub-optimally connected regardless of the environment path loss. We extend our analysis to investigate boundary effects in inhomogeneous systems, and study the geometrical reasons why directional radiating nodes are at a disadvantage to isotropic ones. Finally, we discuss multi-directional gain patterns consisting of many equally spaced lobes which could be used to mitigate boundary effects and improve overall network connectivity.Comment: 12 pages, 10 figure

Scaling Laws for Infrastructure Single and Multihop Wireless Networks in Wideband Regimes

With millimeter wave bands emerging as a strong candidate for 5G cellular networks, next-generation systems may be in a unique position where spectrum is plentiful. To assess the potential value of this spectrum, this paper derives scaling laws on the per mobile downlink feasible rate with large bandwidth and number of nodes, for both Infrastructure Single Hop (ISH) and Infrastructure Multi-Hop (IMH) architectures. It is shown that, for both cases, there exist \emph{critical bandwidth scalings} above which increasing the bandwidth no longer increases the feasible rate per node. These critical thresholds coincide exactly with the bandwidths where, for each architecture, the network transitions from being degrees-of-freedom-limited to power-limited. For ISH, this critical bandwidth threshold is lower than IMH when the number of users per base station grows with network size. This result suggests that multi-hop transmissions may be necessary to fully exploit large bandwidth degrees of freedom in deployments with growing number of users per cell.Comment: 5 pages, 3 figure