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In wireless networks assisted by intelligent reflecting surfaces (IRSs), jointly modeling the signal received over the direct and indirect (reflected) paths is a difficult problem. In this work, we show that the network geometry (locations of serving base station, IRS, and user) can be captured using the so-called triangle parameter $\Delta$. We introduce a decomposition of the effect of the combined link into a signal amplification factor and an effective channel power coefficient $G$. The amplification factor is monotonically increasing with both the number of IRS elements $N$ and $\Delta$. For $G$, since an exact characterization of the distribution seems unfeasible, we propose three approximations depending on the value of the product $N\Delta$ for Nakagami fading and the special case of Rayleigh fading. For two relevant models of IRS placement, we prove that their performance is identical if $\Delta$ is the same given an $N$. We also show that no gains are achieved from IRS deployment if $N$ and $\Delta$ are both small. We further compute bounds on the diversity gain to quantify the channel hardening effect of IRSs. Hence only with a judicious selection of IRS placement and other network parameters, non-trivial gains can be obtained.

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.

A comprehensive vehicular network analysis requires modeling the street system and vehicle locations. Even when Poisson point processes (PPPs) are used to model the vehicle locations on each street, the analysis is barely tractable. That holds for even a simple average-based performance metric -- the success probability, which is a special case of the fine-grained metric, the meta distribution (MD) of the signal-to-interference ratio (SIR). To address this issue, we propose the transdimensional approach as an alternative. Here, the union of 1D PPPs on the streets is simplified to the transdimensional PPP (TPPP), a superposition of 1D and 2D PPPs. The TPPP includes the 1D PPPs on the streets passing through the receiving vehicle and models the remaining vehicles as a 2D PPP ignoring their street geometry. Through the SIR MD analysis, we show that the TPPP provides good approximations to the more cumbrous models with streets characterized by Poisson line/stick processes; and we prove that the accuracy of the TPPP further improves under shadowing. Lastly, we use the MD results to control network congestion by adjusting the transmit rate while maintaining a target fraction of reliable links. A key insight is that the success probability is an inadequate measure of congestion as it does not capture the reliabilities of the individual links., Comment: 32 pages, 29 figures, in IEEE Transactions on Wireless Communications