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...e independence assumption is generally considered appropriate for far-field transmission and has been widely used in the literature under many channel models including lognormal shadowing model [35], =-=[36]-=-, [30], [37]. Note that the unit disk model is a special channel model which fulfills the independence assumption by nature [38, pg. 12]. This is because for the unit disk model, two vehicles are dire...

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... such as radiation patterns, fading and shadowing. As a deterministic study requires the knowledge of a specific environment, these phenomena are generally considered from a statistical point of view =-=[2, 11, 16, 17]-=-. Taking into account interference is a second way to improve the realism of multi-hop networks modeling. Several works have introduced interference [11, 20] by modeling the overall interference power...

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...], [27] considered a probabilistic connection model whereby log-normal shadowing was incorporated into the path loss model. Both 1-connectivity and k-connectivity2 were considered in those papers. In =-=[29]-=-, the authors considered the effects of fast fading (in particular, Rayleigh and Rician fading) on full connectivity in dense networks, and derived expressions for the node isolation probability for s...

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... (or asymptotically infinite) network on a finite (or asymptotically infinite) area in ℜ2 [10]. In addition to the above work based on the unit disk connection model, there is also limited work [11], =-=[12]-=- dealing with the necessary condition for a random network to be connected under the log-normal shadowing connection model. Under the log-normal shadowing connection model, two nodes are directly conn...

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... environment, the path loss model, and the geometry in which the network resides. While the first two properties have been thoroughly studied within the construct of network analysis (see, e.g., [11]–=-=[13]-=-), the effect that the confining geometry has on connectivity is altogether more complicated to observe analytically. Until recently, geometric considerations were limited to simplistic scenarios, inc...

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...er, neither of these approaches is reasonable for realistic networks, where we must consider the effects of fading and interference. The impact of fading on network connectivity has been addressed in =-=[13]-=-–[16]. Of particular interest to this paper is [13], which showed that multiple antennas can significantly reduce the node isolation probability in an interference-free network, and [16], whose simula...

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...ness caused by shadowing can improve network connectivity by reducing the number of isolated nodes. In [11], a probability density function (pdf) of the distance between two nodes in a rectangular or hexagonal region was analytically derived using a space decomposition method and was used to calculate the average number of neighbors of a node (i.e., node degree) with a simple path loss model. The results were extended for the case of multihop networks in a shadowing environment in [12]. An alternative analytical method, which is based on the concept of effective coverage area, was proposed in [13] to analyze the effect of path loss and shadowing on the connectivity of wireless ad hoc networks. It must be noted that the shadowing channel model used in [10], [12], and [13] increases the average channel gain, whereas in a practical wireless channel, shadowing affects only the randomness and not the average value of the channel gain. More recently, the connectivity of wireless ad hoc networks with different beamforming schemes has been studied in [16]– [22]. Although the size, cost, and power consumption issues limit the applicability of large antenna arrays for wireless mobile devices, th...