In this paper we calculate the exact cumulative distribution function (CDF) of the path distance (L1 norm) between a randomly selected intersection and the k-th nearest node of the Cox point process driven by the Manhattan Poisson line process. The CDF is expressed as a sum over the integer partition function$p\!\left(k\right)$, which allows us to numerically evaluate the CDF in a simple manner. The distance distributions can be used to study the k-coverage of broadcast signals in intelligent transportation systems (ITS) transmitted from a \ac{RSU} that is located at an intersection. They can also be insightful for network dimensioning in urban vehicle-to-everything (V2X) systems, because they can yield the exact distribution of network load within a cell, provided that the \ac{RSU} is located at an intersection. Finally, they can find useful applications in other branches of science like spatial databases, emergency response planning, and districting. We corroborate the applicability of the distance distribution model using the map of an urban area.

The Poisson point process (PPP) is not always a realistic model for the locations of vehicles along a road, because it does not account for the safety distance a driver maintains from the vehicle ahead. In this article, we model the inter-vehicle distance equal to the sum of a constant hardcore distance and a random distance following the exponential distribution. Unfortunately, the probability generating functional of this point process is unknown. To approximate the Laplace transform of interference at the origin, we devise simple approximations for the variance and skewness of interference, and we select suitable probability functions to model the interference distribution. When the coefficient-of-variation and the skewness of interference distribution are high, the PPP (of equal intensity) approximation of the outage probability becomes loose in the upper tail. Relevant scenarios are associated with urban microcells and highway macrocells with a low density of vehicles. The predictions of PPP deteriorate with a multi-antenna maximum ratio combining receiver and temporal indicators related to the performance of retransmission schemes. Our approximations generate good predictions in all considered cases.

In this paper we analyze synthetic mobility traces generated for three-lane unidirectional motorway traffic to find that the locations of vehicles along a lane are better modeled by a hardcore point process instead of the widely-accepted Poisson point process (PPP). In order to capture the repulsion between successive vehicles while maintaining a level of analytical tractability, we make a simple extension to PPP: We model the inter-vehicle distance along a lane equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We calculate the J-function and the Ripley's K-function for this hardcore point process. We fit its parameters to the available traces, and we illustrate that the higher the average speed along a lane, the more prominent the hardcore component becomes. In addition, we consider a transmitter-receiver link on the same lane, and we generate simple formulae for the moments of interference under reduced Palm measure for that lane, and without conditioning for other lanes. We illustrate that under Rayleigh fading a shifted-gamma approximation for the distribution of interference per lane provides a very good fit to the simulated outage probability using the synthetic traces, while the fit using the PPP is poor.

We present a flexible family of 3D mobility models suitable for unmanned aerial vehicles (UAV). Based on stochastic differential equations, the models offer a unique property of explicitly incorporating the mobility control mechanism and environmental perturbation, while enabling tractable steady state solutions for properties such as position and connectivity. Specifically, motivated by UAV flight data, for a symmetric mobility model with an arbitrary control mechanism, we derive the steady state distribution of the distance from the target position. We provide closed form expressions for the special cases of the Ornstein-Uhlenbeck (OU) process and on-off control (OC). We extend the model to incorporate imperfect positioning and asymmetric control. For a practically relevant scenario of partial symmetry (such as in the x-y plane), we present steady state position results for the OU control. Building on these results, we derive UAV connectivity probability results based on a SNR criterion in a Rayleigh fading environment.

The meta distribution of the signal-to-interference-ratio (SIR) is an important performance indicator for wireless networks because, for ergodic point processes, it describes the fraction of scheduled links that achieve certain reliability, conditionally on the point process. In this paper, we calculate the moments of the meta distribution in vehicular ad hoc networks (VANETs) along high-speed motorways. Due to the high speeds, the drivers maintain large safety distances, and the Poisson point process (PPP) becomes a poor deployment model. Because of that, we model the distribution of inter-vehicle distance equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We design a novel discretization model for the locations of vehicles which can be used to approximate well the meta distribution of the SIR due to the hardcore process. We validate the model against synthetic motorway traces. On the other hand, the PPP overestimates significantly the coefficient-of-variation of the meta distribution due to the hardcore process, and its predictions fail. In addition, we show that the calculation of the meta distribution becomes especially meaningful in the upper tail of the SIR distribution.

In this paper, we study the receiver performance with physical layer security in a Poisson field of interferers. We compare the performance in two deployment scenarios: 1) the receiver is located at the corner of a quadrant and 2) the receiver is located in the infinite plane. When the channel state information (CSI) of the eavesdropper is not available at the transmitter, we calculate the probability of secure connectivity using the Wyner coding scheme and show that hiding the receiver at the corner is beneficial at high rates of the transmitted code words and detrimental at low transmission rates. When the CSI is available, we show that the average secrecy capacity is higher when the receiver is located at the corner, even if the intensity of interferers in this case is four times higher than the intensity of interferers in the bulk. Therefore, boundaries can also be used as a secrecy enhancement technique for high-data-rate applications.

Adaptive transmission schemes are a crucial aspect of radio design for future wireless networks. This paper studies the performance of two classes of adaptive transmission schemes in cellular downlink. One class is based on physical layer rateless codes with constant transmit power and the other uses fixed-rate codes in conjunction with power adaptation. Using a simple stochastic geometry model for the cellular downlink, the focus is to compare the adaptivity of fixed-rate codes with power adaptation to that of physical layer rateless codes only. The performance of both the rateless and fixed-rate coded adaptive transmission schemes are compared by evaluating the typical user success probability and rate achievable with the two schemes. Based on both the theoretical analysis and simulation results, it is clearly shown that the fixed-rate codes require power control to maintain good performance, whereas the physical layer rateless codes with constant power can still provide robust performance.

Adaptive transmission schemes are a key part of the radio design for 5G wireless channels. The paper studies the performance of two types of adaptive transmission schemes in cellular downlink. One is based on rateless codes with constant power and the other is fixed-rate codes in conjunction with power adaptation. Using a simple stochastic geometry model for cellular downlink, the focus is to understand the key impact of power adaptation in rateless and fixed- rate coded adaptive transmission. The performance of both rateless and fixed-rate coded adaptive transmission schemes are compared by evaluating the typical user rate and success probability achievable with the two schemes. Based on both theoretical analysis and simulation results, the paper clearly shows that rateless coding simplifies the role of power control in an adaptive transmission scheme.

In practice, wireless networks are deployed over finite domains, the level of mobility is different at different locations, and user mobility is correlated overtime. All these features have an impact on the temporal properties of interference which is often neglected. In this paper, we show how to incorporate correlated user mobility into the interference and outage correlation models. We use the random waypoint mobility model over a bounded one-dimensional domain as an example model inducing correlation, and we calculate its displacement law at different locations. Based on that, we illustrate that the temporal correlations of interference and outage are location-dependent, being lower close to the center of the domain, where the level of mobility is higher than near the boundary. Close to the boundary, more time is also needed to see uncorrelated interference. Our findings suggest that an accurate description of the mobility pattern is important, because it leads to more accurate understanding/modeling of interference and receiver performance.

Interference statistics in vehicular networks have long been studied using the Poisson Point Process (PPP) for the locations of vehicles. In roads with a small number of lanes and restricted overtaking, this model becomes unrealistic because it assumes that the vehicles can come arbitrarily close to each other. In this paper, we model the headway distance (the distance between the head of a vehicle and the head of its follower) equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We study the mean, the variance, and the skewness of interference at the origin with this deployment model. Even though the pair correlation function becomes complicated, we devise a simple formulae to capture the impact of the hardcore distance on the variance of interference in comparison with a PPP model of equal intensity. In addition, we study the extreme scenario, where the interference originates from a lattice. We show how to relate the variance of interference due to a lattice to that of a PPP under Rayleigh fading.

One limiting factor to the performance of mobile ad hoc networks is the amount of interference that is experienced by each node. In this paper we will use the well established Random Waypoint Mobility Model (RWPM) to represent such a network of mobile devices, and show that the connectivity of a receiver at different parts of the network domain varies significantly. This is a result of a large portion of the nodes in the RWPM being located near the centre of the domain resulting in increased levels of interference between neighbouring devices. A non-trivial trade-off therefore exists between the spatial intensity of interfering signals and non-interfering (useful) ones. Using tools from stochastic geometry, we derive novel closed form expressions for the spatial distribution of nodes in a rectangle and the connection probability for an interference limited network indicating the impact an inhomogeneous distribution of nodes has on a network's performance. Results can therefore be used to analyse this trade-off and optimize network performance, for example through dynamic transmission schemes and adaptive routing protocols.

Random geometric networks are mathematical structures consisting of a set of nodes placed randomly within a bounded set V ⊆ ℝdmutually coupled with a probability dependent on their Euclidean separation, and are the classic model used within the expanding field of ad hoc wireless networks. In order to rank the importance of the network's communicating nodes, we consider the well established `betweenness' centrality measure (quantifying how often a node is on a shortest path of links between any pair of nodes), providing an analytic treatment of betweenness within a random graph model by deriving a closed form expression for the expected betweenness of a node placed within a dense random geometric network formed inside a disk of radius R. We confirm this with numerical simulations, and discuss the importance of the formula for mitigating the `boundary effect' connectivity phenomenon, for cluster head node election protocol design and for detecting the location of a network's `vulnerability backbone'.

We study wireless ad hoc networks in the absence of any channel contention or transmit power control and ask how antenna directivity affects network connectivity in the interference limited regime. We answer this question by deriving closed-form expressions for the outage probability, capacity and mean node degree of the network using tools from stochastic geometry. These novel results provide valuable insights for the design of future ad hoc networks. Significantly, our results suggest that the more directional the interfering transmitters are, the less detrimental are the effects of interference to individual links. We validate our analytical results through computer simulations.

Wireless networks are fundamentally limited by the intensity of the received signals and by their inherent interference. It is shown here that in finite ad hoc networks where node placement is modelled according to a Poisson point process and no carrier sensing is employed for medium access, the SINR received by nodes located at the border of the network deployment/operation region is on average greater than the rest. This is primarily due to the uneven interference landscape of such networks which is particularly kind to border nodes giving rise to all sorts of performance inhomogeneities and access unfairness. Using tools from stochastic geometry we quantify these spatial variations and provide closed form communication-theoretic results showing why the receiver's location is so important.

We study the effect of stochastic wireless channel models on the connectivity of ad hoc networks. Unlike in the deterministic geometric disk model where nodes connect if they are within a certain distance from each other, stochastic models attempt to capture small-scale fading effects due to shadowing and multipath received signals. Through analysis of local and global network observables, we present conclusive evidence suggesting that network behaviour is highly dependent upon whether a stochastic or deterministic connection model is employed. Specifically we show that the network mean degree is lower (higher) for stochastic wireless channels than for deterministic ones, if the path loss exponent is greater (lesser) than the spatial dimension. Similarly, the probability of forming isolated pairs of nodes in an otherwise dense random network is much less for stochastic wireless channels than for deterministic ones. The latter realisation explains why the upper bound of k-connectivity is tighter for stochastic wireless channels. We obtain closed form analytic results and compare to extensive numerical simulations.

We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice. To maximize practicality and applicability, we adopt a general point-to-point link model based on outage probability, and present example analytical and numerical results for a network employing 2 × 2 multiple-input multiple-output (MIMO) maximum ratio combining (MRC) link level transmission confined within particular bounding geometries. Furthermore, we provide suggestions for extending the approach detailed herein to more general convex geometries.

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 theoretical 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 inhomogeneous systems, and study the geometrical reasons why boundary effects cause directional radiating nodes to be 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.