Outage, local throughput, and capacity of random wireless networks

Abstract

Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness.The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interference-limited networks: the node distribution, the channel gains (fading), and the channel access (set of transmitting nodes). For the performance analysis, a new parameter, the so-called spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0.Outage is defined as the event that the signal-to-interference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived.Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unitdistance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates.

Stochastic analysis of Aloha in vehicular ad hoc networks

“…To the best of our knowledge, all these studies use simulations to evaluate the performances of these networks and/or assume simplified interference models. Aloha can be analyzed more easily than CSMA, even in a quite realistic SINR scenario, as was recently shown in [3][4][5]9]. However these studies assume planar (two-dimensional) networks.…”

“…[2,Section 16]) that the capture probability in the planar (two-dimensional) network model with slotted Aloha is equal to p s (λ) = exp(−κ s (β)λR 2 T 2/β ) where κ s (β) = 2π 2 /(β sin(2π/β)). In [9] the term spatial contention factor was proposed for this constant. We will use this term in what follows with respect to K s (β) as well as an analogous constant that will appear in the analysis of our linear model of non-slotted Aloha.…”

Vehicular Ad-hoc Networks using slotted Aloha: Point-to-point, emergency and broadcast communications

“…To the best of our knowledge, most of these studies use simulations to evaluate the performances of these networks and/or assume simplified interference models. Aloha can be analyzed more easily than CSMA, even in quite a realistic SINR scenario [5,6,9]. However these studies assume planar (two-dimensional) networks and a Poisson point process to model the location of the network nodes.…”

Asymptotic outage analysis of general motion-invariant Ad Hoc Networks

“…1, tight bounds on the success probability can be derived following the procedure in [6]: where m = η −1/2 is the distance between nearest transmitters, γ TDMA = 4ζ(α/2)β(α/2)θ with ζ the Riemann zeta and β the Dirichlet beta functions. If follows from (20) that…”

“…In this paper, we focus on Rayleigh fading and resort to the asymptotic regime, letting the density of interferers η go to zero. We will show the outage probability approaches is γη κ as η → 0, where γ is the network's spatial contention parameter [6], and κ is the interference scaling exponent. Interestingly, κ is confined to the range 1 ≤ κ ≤ α/2 for any reasonable 1 MAC scheme.…”