Connectivity Analysis of Wireless Ad Hoc Networks With Beamforming

Coll. of Eng. & Comput. Sci., Australian Nat. Univ., Canberra, ACT, Australia
IEEE Transactions on Vehicular Technology (Impact Factor: 1.98). 12/2009; 58(9):5247 - 5257. DOI: 10.1109/TVT.2009.2026049
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In this paper, we present an analytical model for evaluating the impact of shadowing and beamforming on the connectivity of wireless ad hoc networks accommodating nodes equipped with multiple antennas. We consider two simple beamforming schemes: random beamforming, where each node selects a main beam direction randomly with no coordination with other nodes, and center-directed beamforming, where each node points its main beam toward the geographical center of the network. Taking path loss, shadowing, and beamforming into account, we derive an expression for the effective coverage area of a node, which is used to analyze both the local network connectivity (probability of node isolation) and the overall network connectivity (1-connectivity and path probability). We verify the correctness of our analytical approach by comparing with simulations. Our results show that the presence of shadowing increases the probability of node isolation and reduces the 1-connectivity of the network, although moderate shadowing can improve the path probability between two nodes. Furthermore, we show that the impact of beamforming strongly depends on the level of the channel path loss. In particular, compared with omnidirectional antennas, beamforming improves both the local and the overall connectivity for a path loss exponent of alpha < 3. The analysis in this paper provides an efficient way for system designers to characterize and optimize the connectivity of wireless ad hoc networks with beamforming.

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    • "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. "
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    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; 4(4). DOI:10.1109/LWC.2015.2421903
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    • "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. "
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    • "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. "
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    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.
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