# Connectivity Analysis of Wireless Ad Hoc Networks With Beamforming

### Full-text

Salman Durrani, Jul 30, 2015 Available from:-
- "Recently, a recursive formula for calculating the probability that a pair of nodes (i, j) separated by a distance r ij is connected in at least k-hops was given in [4]. The effects of randomly oriented directional (or anisotropic) antennas or random beamforming schemes (where nodes beamform in a random direction) were numerically studied in [5], [6] suggesting that such simple schemes can lead to network performance gains in routing, end-to-end delay, reachability, interference Fig. 1. Left: Example network realization with N = 100 random directional nodes in a disk domain, using ρ = β = = 1 and η = 4. "

[Show abstract] [Hide abstract]

**ABSTRACT:**Directional antennas and beamforming can significantly improve point-to-point wireless links when perfectly aligned. In this letter we investigate the extreme opposite where antenna orientations and positions are chosen at random in the presence of Rayleigh fading. We show that while the 1-hop network connectivity is deteriorated, the multihop routes improve, especially in the dense regime. We derive closed form expressions for the expectation of the $1$-hop and $2$-hop degree which are verified through computer simulations. We conclude that node density does not greatly affect the number of hops required between stations whilst simple random beamforming schemes do, thus returning substantial network performance benefits due to the existence of shorter multi-hop paths.IEEE Wireless Communication Letters 04/2015; DOI:10.1109/LWC.2015.2421903 -
- "where j is the imaginary unit for which j 2 = −1, k = 2π/λ, λ is the wavelength of the propagating signal, φ m = 2πm/M is the angular position of mth element on xy-plane, I m is the amplitude excitation of the mth element, which is set to be 1, similar to [11]. We let θ 0 = π/2 (i.e., the xy plane) and φ 0 ∈ [0, 2π] is the azimuth angle of the desired main beam. "

##### Conference Paper: An Analytical Model on Eavesdropping Attacks in Wireless Networks

[Show abstract] [Hide abstract]

**ABSTRACT:**This paper concerns the eavesdropping problem from the eavesdroppers' perspective, which is new since most of previous studies only concentrate on the good nodes. We propose an analytical framework to investigate the eavesdropping attacks, taking account into various channel conditions and antenna models. Our extensive numerical results show that the probability of eavesdropping attacks heavily depends on the shadow fading effect, the path loss effect and the antenna models; particularly, they imply that using directional antennas at eavesdroppers can increase the probability of eavesdropping attacks when the path loss effect is less notable. This study is helpful for us to prevent the eavesdropping attacks effectively and economically.IEEE International Conference on Communication Systems; 11/2014 -
- "How this improvement is achieved was first addressed in [17], and later in [18] where it was argued that randomized beamforming cannot be said to strictly improve/degrade connectivity. To this end, it was numerically estimated in [19] (and similar papers by the same authors) that the critical path loss exponent below which improvements are observed is 3. This was analytically pushed down to 2 in [20] where it was also shown that this number is independent of the small-scale fading model used. "

[Show abstract] [Hide abstract]

**ABSTRACT:**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.IEEE Transactions on Wireless Communications 10/2013; 13(8). DOI:10.1109/TWC.2014.2314109 · 2.76 Impact Factor