This article compares measures for quantifying the level of inhomogeneity of a given spatial point pattern. Comparisons are based on two main metrics: first, we evaluate the performance of the measures on both certain stochastic point processes and on very specific point patterns designed to expose potential weaknesses of the inhomogeneity measures. Second, we evaluate the computational complexity of the measures. Results show that choosing a measure is a tradeoff between accurate assessment of inhomogeneity and computational complexity. The only exception is the proposed extended wrap-around measure , which is performing well in terms of both metrics.

A time synchronization technique for networked devices with low-precision oscillators and low computational power is proposed and evaluated. We apply a dynamic stochastic model inserted into a Kalman filter formulation to track the clock evolution of oscillators and achieve synchrony to a central time reference. Indoor and outdoor experiments performed with commercially available wireless sensor platforms over several days serve as a proof of concept and show the synchronization accuracy under stable and varying temperature conditions.

The convergence and precision of synchronization algorithms based on the theory of pulse-coupled oscillators is evaluated on programmable radios. Measurements in different wireless topologies show that such algorithms reach precisions in the low microsecond range. Based on the observation that phase rate deviation among radios is a limiting factor for the achievable precision, we propose a distributed algorithm for automatic phase rate equalization and show by experiments that an improved precision below one microsecond is possible in the given setups. It is also experimentally demonstrated that the stochastic nature of coupling is a key ingredient for convergence to synchrony. The proposed scheme can be applied in wireless systems for distributed synchronization of transmission slots, or sleep cycles.

We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expected values of sum-products of functions. In proving the theorem, we present a variant of the Campbell-Mecke theorem from stochastic geometry. We proceed to apply our result in the calculation of expected values involving interference in wireless Poisson networks. Based on this, we derive outage probabilities for transmissions in a Poisson network with Nakagami fading. Our results extend the stochastic geometry toolbox used for the mathematical analysis of interference-limited wireless networks.

We investigate the statistics of the number of time slots T that it takes a packet to travel through a chain of wireless relays. Derivations are performed assuming an interference model for which interference possesses spatiotemporal dependency properties. When using this model, results are harder to arrive at analytically, but they are more realistic than the ones obtained in many related works that are based on independent interference models. First, we present a method for calculating the distribution of T. As the required computations are extensive, we also obtain simple expressions for the expected value E[T] and variance Var[T]. Finally, we calculate the asymptotic limit of the average speed of the packet. Our numerical results show that spatiotemporal dependence has a significant impact on the statistics of the travel time T. In particular, we show that, with respect to the independent interference case, E[T] and Var[T] increase, whereas the packet speed decreases.

Strict reliability and delay requirements of factory monitoring and control applications pose challenges for wireless communications in dynamic and cluttered industrial environments. To reduce outage in such fading-rich areas, cooperative relays can be used to overhear source-destination transmissions and forward data packets that a source fails to deliver. This paper presents the results of an experimental study of selective cooperative relaying protocols that are implemented in off-the-shelf IEEE 802.15.4-compatible devices and evaluated in an industrial production plant. Three practical relay update schemes, which define when a new relay selection is triggered, are investigated: 1) periodic; 2) adaptive; and 3) reactive relay selections. The results show that all relaying protocols outperform conventional time diversity retransmissions in delivery ratio and number of retransmissions for packet delivery. Reactive selection provides the best overall delivery ratio of nearly 99% over the tested network. There is a tradeoff, however, between achievable delivery ratio and required selection overhead. This tradeoff depends on protocol and network parameters, and is studied via protocol emulation using empirical channel values.

We show by means of stochastic geometry that interference dynamics has a strong impact on the performance of cooperative relaying. For both conventional and multi-hop-aware cooperative relaying we show that the packet delivery probability significantly changes with the dependence of interference among the links. Depending on the scenario under consideration, this change could be either an increase or decrease of the packet delivery probability. Especially for multi-hop-aware cooperative relaying, the performance gain is heavily reduced when interference possesses high temporal and spatial dependence.

Cooperative relaying is a communication technique that has been shown to improve link reliability between communicating entities. Most results in this area are obtained either analytically or via simulations. Rather few real-world experiments are conducted to backup theoretical results. This paper intends to go a step in this direction of applied research. We study the performance of cooperative relaying for industrial applications based on real-world measurements. These link-level measurements are conducted employing low-cost, off-the-shelf IEEE 802.15.4 devices in a factory characterized by a harsh and cluttered environment. Using the measured data, we emulate a simple cooperative relaying protocol to investigate the performance in terms of outage and packet delivery ratio and study parameters suitable for relay selection.

The temporal correlation of interference is a key performance factor of several technologies and protocols for wireless communications. A comprehensive understanding of interference correlation is especially important in the design of diversity schemes, whose performance can severely degrade in case of highly correlated interference. Taking into account three sources of correlation—node locations, channel, and traffic—and using common modeling assumptions—random homogeneous node positions, Rayleigh block fading, and slotted ALOHA traffic—we derive closed-form expressions and calculation rules for the correlation coefficient of the overall interference power received at a certain point in space. Plots give an intuitive understanding as to how model parameters influence the interference correlation.

We investigate the impact of time diversity and space-time diversity schemes on the traffic capacity of large-scale wireless networks with low-cost radios. Especially, we analyze the tradeoff between relaying gain and increased interference due to additional traffic. The results of a simulation-based study imply that cooperative relaying with selection combining shows benefits for low interference scenarios. For high traffic, however, higher-order modulation schemes outperform the investigated cooperative relaying scenario due to lower interference.

Consider n nodes competing for access on a channel using slotted ALOHA. Our aim is to maximize the probability Phi that the first message within s slots does not collide. We derive an expression for the transmit probabilities in each slot, maximizing Phi. As opposed to previous work, the expression is non-recursive, thus easier to calculate and more convenient for practical implementations. Furthermore, we address the problem that, in practical applications, the number of competing nodes n is likely to be unknown and has to be estimated by each node. We study the sensitivity of channel access scheme with respect to deviations from the actual n via simulations. It is shown that overestimation of n is a better strategy than underestimation.

Simulation results of wireless networks heavily depend on the spatial distribution of its nodes. Even though the initial distribution may match the expectations of the researcher, its properties may get lost due to the applied mobility model after a few seconds. This paper analyzes the effects of three well-known mobility models on the inhomogeneity of the spatial distribution. Furthermore, the effects of penetrable borders of the simulation area on the node distribution are analyzed. Due to the encountered deviations, we propose and analyze the inhomogeneous random waypoint (IRWP) model. It maintains a desired inhomogeneity level in the long run and generates random clusters with respect to shape, size, position, and member nodes.

Considering n nodes performing random access using ALOHA with s slots, we study the probability that there occurs a non-colliding message in the first non-empty slot. If each node transmits with probability p in each slot and the number of slots is sufficiently large, a non-colliding first message occurs with probability Phi = 1-np/2 for large n and small np. If the number of slots is limited, the probability Phi is lower but can be maximized choosing an optimal p. To maximize Phi further, nodes can apply a slot-dependent transmit probability pi with i = 1, ..., s. It is shown that a ldquoslow start strategy,rdquo in which piis low for low i and increases with increasing i, is beneficial. Our main contribution is an equation for the pivalues that maximize Phi. We analyze how a higher probability of a non-colliding first message comes at the price of an increased delay of such a message. Besides being of interest for the theory of random access, the results are practically applicable to node selection protocols, such as relay selection in cooperative wireless networks.