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We investigate the performance of a random access network consisting of source-destination dipoles. The source nodes transmit information packets to their destinations over a shared spectrum. All the transmitters in this network adhere to an age threshold slotted ALOHA (TSA) protocol: every source node remains silent until the age of information (AoI) reaches a threshold, after which the source accesses the radio channel with a certain probability. We derive a tight approximation for the signal-to-interference-plus-noise ratio (SINR) meta distribution and verify its accuracy through simulations. We also obtain analytical expressions for the average AoI. Our analysis reveals that when the network is densely deployed, employing TSA significantly decreases the average AoI. The update rate and age threshold must be jointly optimized to fully exploit the potential of the TSA protocol.

The current analysis of wireless networks whose transceivers are confined to streets is largely based on Poissonian models, such as Poisson line processes and Poisson line Cox processes. We demonstrate important scenarios where a model with a finite and deterministic number of streets, termed binomial line process, is more accurate. We characterize the statistical properties of the BLP and the corresponding binomial line Cox process and apply them to analyze the performance of a network whose access points are deployed along the streets of a city. Such a deployment scenario will be typical for 5G and future wireless networks. In order to obtain a fine-grained insight into the network performance, we derive the meta distribution of the signal-to-interference and noise ratio. Accordingly, we investigate the mean local delay in transmission and the density of successful transmission. These metrics, respectively, characterize the latency and coverage performance of the network and are key performance indicators of next-generation wireless systems., Comment: Submitted to IEEE Transactions on Wireless Communications

Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment sequences are discussed and applied. Also, some of the approximations have been rewritten as linear transforms, and detailed accuracy requirements are analyzed. Our finding shows that the performance of the approximations differs significantly in their convergence properties, accuracy, and numerical complexity and that the decay type of the moment sequence strongly affects the accuracy requirement.

In the performance analyses of wireless networks, asymptotic quantities and properties often pro- vide useful results and insights. The asymptotic analyses become especially important when complete analytical expressions of the performance metrics of interest are not available, which is often the case if one departs from very specific modeling assumptions. In this paper, we consider the asymptotics of the SIR distribution in general wireless network models, including ad hoc and cellular networks, simple and non-simple point processes, and singular and bounded path loss models, for which, in most cases, finding analytical expressions of the complete SIR distribution seems hopeless. We show that the lower tails of the SIR distributions decay polynomially with the order solely determined by the path loss exponent or the fading parameter, while the upper tails decay exponentially, with the exception of cellular networks with singular path loss. In addition, we analyze the impact of the nearest interferer on the asymptotic properties of the SIR distributions, and we formulate three crisp conjectures that -if true- determine the asymptotic behavior in many cases based on the large-scale path loss properties of the desired signal and/or nearest interferer only.

Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical queueing theory, the delay of multi-point to multi-point communications, such as in ultradense networks, has not been explored in depth. The main technical difficulty lies in the interacting queues problem, in which the service rate is coupled with the statuses of other queues. In this article, we elaborate on the main challenges in the delay analysis in ultradense networks. Several promising approaches, such as introducing the dominant system and the simplified system, to bypass these difficulties are proposed and summarized to provide useful guidance., Comment: 17 pages, 4 figures, 1 table, accepted in IEEE Communications Magazine

It was recently conjectured that the permanent of a ${P}$-lifting $\theta^{\uparrow{P}}$ of a matrix $\theta$ of degree $M$ is less than or equal to the $M$th power of the permanent perm$(\theta)$, i.e., perm$(\theta^{\uparrow{P}})\leq(\text{perm}(\theta))^M$ and, consequently, that the degree-$M$ Bethe permanent $\text{perm}_{M,\mathrm{B}} (\theta)$ of a matrix $\theta$ is less than or equal to the permanent perm$(\theta)$ of $\theta$, i.e., perm$_{M, \mathrm{B}} (\theta)\leq \text{perm}(\theta)$. In this paper, we prove these related conjectures and show in addition a few properties of the permanent of block matrices that are lifts of a matrix. As a corollary, we obtain an alternative proof of the inequality perm$_{\mathrm{B}} (\theta)\leq \text{perm}(\theta)$ on the Bethe permanent of the base matrix $\theta$ that uses only the combinatorial definition of the Bethe permanent.

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 propose a new model for heterogeneous cellular networks that incorporates dependencies between the layers. In particular, it places lower-tier base stations at locations that are poorly covered by the macrocells, and it includes a small-cell model for the case where the goal is to enhance network capacity.

Channel coding alone is not sufficient to reliably transmit a message of finite length $K$ from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure correcting schemes on a higher layer, such as a time-division multiple access (TDMA) system paired with automatic repeat request (ARQ) or random linear network coding (RLNC). We consider binary channel coding on a binary symmetric channel (BSC) and q-ary RLNC for erasure correction in a star network, where Y sources send messages to each other with the help of a central relay. In this scenario RLNC has been shown to have a throughput advantage over TDMA schemes as K and q tend to infinity. In this paper we focus on finite block lengths and compare the expected throughputs of RLNC and TDMA. For a total message length of K bits, which can be subdivided into blocks of smaller size prior to channel coding, we obtain the channel coding rate and the number of blocks that maximize the expected throughput of both RLNC and TDMA, and we find that TDMA is more throughput-efficient for small message lengths K and small q., Comment: Submitted to IEEE Transactions on Communications, Dec. 2012

Lattices are important as models for the node locations in wireless networks for two main reasons: (1) When network designers have control over the placement of the nodes, they often prefer a regular arrangement in a lattice for coverage and interference reasons. (2) If nodes are randomly distributed or mobile, good channel access schemes ensure that concurrent transmitters are regularly spaced, hence the locations of the transmitting nodes are well approximated by a lattice. In this paper, we introduce general interference bounding techniques that permit the derivation of tight closed-form upper and lower bounds for all lattice networks, and we present and analyze optimum or near-optimum channel access schemes for one-dimensional, square, and triangular lattices., 17 pages, 10 figures. Submitted to IEEE Trans. Comm.

In a wireless network the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Previously, connectivity in wireless networks was analyzed using static geometric graphs, and as we show leads to an overly constrained design criterion. The dynamic nature of the transmitting set introduces additional randomness in a wireless system that improves the connectivity, and this additional randomness is not captured by a static connectivity graph. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the MAC contention and introduce a random dynamic multi-digraph to model its connectivity. We first provide analytical results about the degree distribution of the graph. Next, defining the path formation time as the minimum time required for a causal path to form between the source and destination on the dynamic graph, we derive the distributional properties of the connection delay using techniques from first-passage percolation and epidemic processes. We consider the giant component of the network formed when communication is noise-limited (by neglecting interference). Then, in the presence of interference, we prove that the delay scales linearly with the source-destination distance on this giant component. We also provide simulation results to support the theoretical results., Comment: Submitted to IEEE Transactions on Information Theory.

In wireless channels, the path loss exponent (PLE) has a strong impact on the quality of links, and hence, it needs to be accurately estimated for the efficient design and operation of wireless networks. In this paper, we address the problem of PLE estimation in large wireless networks, which is relevant to several important issues in networked communications such as localization, energy-efficient routing, and channel access. We consider a large ad hoc network where nodes are distributed as a homogeneous Poisson point process on the plane and the channels are subject to Nakagami-m fading. We propose and discuss three distributed algorithms for estimating the PLE under these settings which explicitly take into account the interference in the network. In addition, we provide simulation results to demonstrate the performance of the algorithms and quantify the estimation errors. We also describe how to estimate the PLE accurately even in networks with spatially varying PLEs and more general node distributions., Comment: Work underway