We address a fundamental question in wireless networks that, surprisingly, has not been studied before: what is the maximum density of concurrently active links that satisfy a certain outage constraint? We call this quantity the spatial outage capacity (SOC), give a rigorous definition, and analyze it for Poisson bipolar networks with ALOHA. Specifically, we provide exact analytical and approximate expressions for the density of links satisfying an outage constraint and give simple upper and lower bounds on the SOC. In the high-reliability regime where the target outage probability is close to zero, we obtain an exact closed-form expression of the SOC, which reveals the interesting and perhaps counter-intuitive result that all transmitters need to be always active to achieve the SOC, i.e., the transmit probability needs to be set to 1 to achieve the SOC.
A version of the TC based on the link success probability distribution is introduced in @cite_8 , but it does not consider a MAC scheme, , all nodes always transmit ( @math ). The choice of @math is important as it greatly affects the link success probability distribution as shown in Fig. . In this paper, we consider the general case with the transmit probability @math .
@cite_8
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The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward, but it only provides limited information on the success probabilities of the individual links. This paper focuses on the meta distribution of the SIR, which is the distribution of the conditional success probability @math given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as “What fraction of users in a Poisson cellular network achieve 90 link reliability if the required SIR is 5 dB?” Interestingly, in the bipolar model, if the transmit probability @math is reduced while increasing the network density @math such that the density of concurrent transmitters @math stays constant as @math , @math degenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability @math , the variance of @math approaches a non-zero constant when @math is reduced to 0 while keeping the mean success probability constant. This paper surveys and unifies a number of recent contributions that have collectively developed a metric for decentralized wireless network analysis known as transmission capacity. Although it is notoriously difficult to derive general end-to-end capacity results for multi-terminal or adhoc networks, the transmission capacity (TC) framework allows for quantification of achievable single-hop rates by focusing on a simplified physical MAC-layer model. By using stochastic geometry to quantify the multi-user interference in the network, the relationship between the optimal spatial density and success probability of transmissions in the network can be determined, and expressed-often fairly simply-in terms of the key network parameters. The basic model and analytical tools are first discussed and applied to a simple network with path loss only and we present tight upper and lower bounds on transmission capacity (via lower and upper bounds on outage probability). We then introduce random channels (fading shadowing) and give TC and outage approximations for an arbitrary channel distribution, as well as exact results for the special cases of Rayleigh and Nakagami fading. We then apply these results to show how TC can be used to better understand scheduling, power control, and the deployment of multiple antennas in a decentralized network. The paper closes by discussing shortcomings in the model as well as future research directions. In this paper, a mathematical model for the beacon-enabled mode of the IEEE 802.15.4 medium-access control (MAC) protocol is provided. A personal area network (PAN) composed of multiple nodes, which transmit data to a PAN coordinator through direct links or multiple hops, is considered. The application is query based: Upon reception of the beacon transmitted by the PAN coordinator, each node tries to transmit its packet using the superframe structure defined by the IEEE 802.15.4 protocol. Those nodes that do not succeed in accessing the channel discard the packet; at the next superframe, a new packet is generated. The aim of the paper is to develop a flexible mathematical tool able to study beacon-enabled 802.15.4 networks organized in different topologies. Both the contention access period (CAP) and the contention-free period defined by the standard are considered. The slotted carrier-sense multiple access with collision avoidance (CSMA CA) algorithm used in the CAP portion of the superframe is analytically modeled. The model describes the probability of packet successful reception and access delay statistics. Moreover, both star and tree-based topologies are dealt with; a suitable comparison between these topologies is provided. The model is a useful tool for the design of MAC parameters and to select the better topology. The mathematical model is validated through simulation results. The model differs from those previously published by other authors in the literature as it precisely follows the MAC procedure defined by the standard in the context of the application scenario described. In this paper we consider a network where the nodes locations are modeled by a realization of a Poisson point process and remains fixed or changes very slowly over time. Most of the literature focuses on the spatial average of the link outage probabilities. But each link in the network has an associated link-outage probability that depends on the fading, path loss, and the relative locations of the interfering nodes. Since the node locations are random, the outage probability of each link is a random variable and in this paper we obtain its distribution, instead of just the spatial average. This work supplements the existing results which focus mainly on the average outage probability averaged over space. We propose a new notion of transmission capacity (TC) based on the outage distribution, and provide asymptotically tight bounds for the TC.