For randomly distributed nodes sending packets to a central gateway using slotted Aloha with a constrained number of retransmissions over a wireless fading channel, we take an iterative approach to compute the total traffic density of packet transmissions and collision-induced retransmissions as a function of the node-gateway distance. From this, we compute the outage probability, throughput, and energy consumption. This method can be used to analyze and dimension Low-Power Wide-Area Networks (LPWANs). Applying it in LoRa illustrates design tradeoffs concerning outage probability, spreading factors, energy consumption, and cell size. It notably shows that permitting more retransmissions helps the nodes near the gateway but hurts distant ones.

The concept of pulse-coupled oscillators for self-organized synchronization has been applied to wireless systems. Putting theory into practice, however, faces certain obstacles, particularly in radio technologies that cannot implement pulses but use common messages for interactions between nodes. This raises the question of how to deal with interference between messages. We show that interference can disturb the synchronization process and propose low-complex, randomization-based techniques to address this issue. First, we demonstrate that randomly switching between two transmit power levels (without increasing the average power) can expedite synchronization. The high-power transmissions temporarily boost network connectivity with negligible impact on the average interference. Second, we reduce interference by blindly distributing the messages over the entire oscillator cycle. Instead of using a fixed oscillator phase at which the pulses are sent, each node chooses its own, randomly selected phase to send a synchronization message. This node-specific “fire phase” is contained in the message to permit others to compute the timing. Third, we suggest that such interference management can also be beneficial for other synchronization techniques and validate this claim using Glossy as an example. Our insights may contribute to feasible solutions for self-organized wireless synchronization. Further work is needed to gain a comprehensive understanding of the effects of randomization and to develop algorithms for the adaptability of local parameters.

We propose a scheme to reduce and balance the energy consumption of nodes in dense IoT use cases implemented with LoRa. We study a multiple gateways network with nodes uniformly distributed around each gateway, and restricted to use only short spreading factors. Relays using longer spreading factors, are added to the network infrastructure to forward the nodes transmissions that cannot reach a gateway directly. We find that the impact of the interference added by the relays on the probability of successful transmissions becomes marginal for high density networks. Furthermore, in such dense networks the consumption at the nodes is lowered one order of magnitude with marginal increase in the overall energy consumption of the network. Also, the consumption spread between nodes close and far from the gateway is effectively reduced.

We propose two application-layer coding schemes for delay-constrained point-to-point packet communications with restrictions on the transmitter's maximum duty-cycle. The schemes operate over GF(2) and utilize intermittently available receiver feedback for erasure correction. Applications that will benefit from the proposed schemes include wireless sensor networks in which energy constrained sensors must deliver readings to a gateway within a deadline. Simulation results for independent Bernoulli erasure channels, Gilbert-Elliott channels, and Long Range (LoRa) communications demonstrate orders-of-magnitude reductions in the delivery failure rate as compared to feedback-assisted repetition redundancy and a blind coding scheme that does not utilize feedback.

We derive the probability distribution of the link outage duration at a typical receiver in a wireless network with Poisson distributed interferers sending messages with slotted random access over a Rayleigh fading channel. This result is used to analyze the performance of random linear network coding, showing that there is an optimum code rate and that interference correlation affects the decoding probability and throughput.

This article takes an analytical approach to investigate the temporal dynamics of interference in wireless networks. We propose a framework to calculate the autocorrelation of interference in Poisson networks and derive closed-form expressions for the case of Nakagami fading. The framework takes three correlation sources into account: the location of interferers, the wireless channel, and the data traffic. We introduce the interference coherence time-in analogy to the well-established channel coherence time-and show how its basic qualitative behavior depends on the source of correlation. The insights gained can be useful in the design of medium access control and retransmission protocols.

A thorough understanding of the temporal dynamics of interference in wireless networks is crucial for the design of communication protocols, scheduling, and interference management. This article applies stochastic geometry to investigate the interference dynamics in a network of nodes that use carrier sense multiple access (CSMA). This type of network is approximated by a Matérn hard-core point process of type II with Nakagami fading. We derive and analyze expressions for the variance, covariance, and correlation of the interference power at an arbitrary location. Results show that even though the commonly used Poisson approximation to CSMA may have the same average interference as the Matérn model, the interference dynamics behaves significantly different. In this way, this study reveals a pitfall in the modeling of wireless systems and contributes to the theory of interference calculus.

We propose a communication scheme with relays to improve the reliability of a Long Range (LoRa) sensor network with duty-cycle limitations. The relays overhear the sensors' transmissions and forward them to a gateway. Simulations show that relaying is very beneficial, even though the nodes are not coordinated and duty cycling limits the number of sensor measurements that can be forwarded. In our setup, a single relay can halve the measurement loss rate and eight relays provide a gain of up to two orders of magnitude. Further improvements are achieved by including a few past measurements in each frame.

We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions characterizing the stochastic properties of the passenger queue length, waiting time, and cabin capacity are derived using queuing theory for a transport line with deterministic arrivals of cabins and Poisson arrivals of passengers. The expected cabin capacity and stability threshold for each station are derived for a general passenger arrival distribution. The results show that a significant reduction of the waiting time at a given station is only possible at the cost of making the stability of one of the preceding stations worse than that of the given station. Studies with real passenger arrivals are necessary to draw firm conclusions.

Our research investigates the concept of interference prediction as an unprecedented approach for interference management and medium access in wireless networks. This paper is a first step in this direction: it proposes and evaluates a simple interference prediction technique that is based on low-complexity learning. Nodes predict the interference situation they expect to experience in the near future and select the most favorable time slot to start the transmission of a multislot message. The performance gain is evaluated in a small-scale fading environment in terms of link outage and delay against random slot selection. Simulation results show that interference prediction is a promising building block for wireless systems. Additional studies are needed to explore advanced techniques and assess their feasibility.

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.

This work explores the benefits in terms of energy efficiency that can be provided by device-to- device (D2D) communications in cellular systems. Analyzing a large cellular network using stochastic geometry, considering Nakagami fading and realistic system parameters, we explore the reduction that can be achieved in network power consumption, and the impact this reduction has on the performance of cellular users. When the network is not fully loaded, switching some cellular users into D2D mode results in a significant reduction of the network power consumption while the overall network throughput is maintained. Furthermore, it is observed that the impact of the reduction in the inter-cell interference arising from switching cellular users to D2D mode surpasses that from the new non- orthogonal transmissions. This translates into a slight improvement in the users' rates. Both analytical and simulation results are provided.

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.

Device-to-device (D2D) communications is a promising candidate for increasing the throughput of cellular systems towards 5G. Its current consideration for inclusion in LTE-A is attracting a lot of research interest, including work on mode selection, bandwidth allocation, and power control. Some consider the uplink for D2D operation while others focus on operation over the downlink. It is still unclear, however, which link is preferable for D2D operation. This paper addresses this issue focusing on the outage performance of D2D receivers. We use stochastic geometry tools for our analysis, considering realistic system parameters and Nakagami fading. We find that the interference from the cellular system on the downlink, which is correlated over consecutive time slots, favors underlay D2D operation, resulting in a lower outage probability for the D2D transmissions.

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.

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.

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.

This paper studies probabilistic information dissemination in random networks. Consider the following scenario: A node intends to deliver a message to all other nodes in the network ("flooding"). It first transmits the message to all its neighboring nodes. Each node forwards a received message with some network-wide probability pf. A natural question arises: which forwarding probability pfshould each node use such that a flooded message is obtained by all nodes with high probability? In other words, what is the minimum pfto achieve a high global outreach probability? We first present a generic approach to estimate the probability for achieving global outreach. This approach is then employed in Erdos Renyi random graphs, where we derive an upper and a lower bound for the global outreach probability for given random network and flooding parameters. The analysis is complemented with simulation results showing the tightness of both bounds. As a final result, we take a system design perspective to show a number of parameter vectors leading to global outreach.

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.

The spatial distribution of nodes in wireless networks has important impact on network performance properties, such as capacity and connectivity. Although random sample models based on a uniform distribution are widely used in the research community, they are inappropriate for scenarios with clustered, inhomogeneous node distribution. This paper proposes a well-defined measure for the level of inhomogeneity of a node distribution. It is based on the local deviation of the actual value of the density of nodes from its expected value. Desired properties of the measure are defined and mathematically proven to be fulfilled. The inhomogeneity measure is also compared to human perception of inhomogeneity gained via an online survey. The results reveal that the measure well fits human perception, although there are notable deviations if linear operations are applied.

Most analysis and simulation of wireless systems assumes that the nodes are randomly located, sampled from a uniform distribution. Although in many real-world scenarios the nodes are non-uniformly distributed, the research community lacks a common approach to generate such inhomogeneities. This paper intends to go a step in this direction. We present an algorithm to create a random inhomogeneous node distribution based on a simple neighborhood-dependent thinning of a homogeneous Poisson process. We derive some useful stochastic properties of the resulting distribution (in particular the probability density of the nearest neighbor distance) and offer a reference implementation. Our goal is to enable fellow researchers to easily use inhomogeneous distributions with well-defined stochastic properties.