Exact analysis of the outage probability in multiple-user mobile radio

Linnartz, Jean-Paul M. G.

doi:10.1109/26.126703

Cited by 107 publications

(47 citation statements)

References 13 publications

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“…The following argument was made precise by Baccelli et al [24], but can be traced to [60], [61]. Define the aggregate interference seen at the origin as Z = i∈Π(λ) H i0 |X i | −α , and denote the Laplace transform of Z by L Z (s) = E e −sZ .…”

Section: B Rayleigh Fadingmentioning

confidence: 99%

An Overview of the Transmission Capacity of Wireless Networks

Weber

Andrews

Jindal

2010

IEEE Trans. Commun.

384

351

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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 ad hoc networks, the transmission capacity (TC) framework allows for quantification of achievable single-hop rates by focusing on a simplified physical/MAClayer 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.

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Section: B Rayleigh Fadingmentioning

confidence: 99%

An Overview of the Transmission Capacity of Wireless Networks

Weber

Andrews

Jindal

2010

IEEE Trans. Commun.

384

351

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“…In [4], outage probabilities for cellular networks are calculated for channels with Rayleigh fading and shadowing while [3] determines outage probabilities to determine the optimum transmission range in a Poisson network. [12] combined the two approaches to determine the optimum transmission range under Rayleigh fading and shadowing.…”

Section: Related Workmentioning

confidence: 99%

“…As was noted in [4], [6], [12], the success probability p s can be expressed as the product of the Laplace transforms of the interference and noise:…”

Section: Related Workmentioning

confidence: 99%

Outage, local throughput, and capacity of random wireless networks

Haenggi

2009

IEEE Trans. Wireless Commun.

113

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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.

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“…The sum of Suzuki RVs has instead been approximated by another Suzuki RV in [22]. Exact formulae are available in the literature that express the outage probability of a sum of lognormal-Rice RVs in the form of a single integral, which is evaluated numerically [23], [24]. However, these do not address the problem of approximating by a single lognormal RV.…”

Section: Sum Of Independent Suzuki or Lognormal-rice Random Varimentioning

confidence: 99%

Approximating the Sum of Correlated Lognormal or, Lognormal-Rice Random Variables

Mehta

Molisch

et al. 2006

2006 IEEE International Conference on Communications

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A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormal-Rice or Suzuki random variables by the lognormal distribution. The method is based on matching a low-order Gauss-Hermite approximation of the moment-generating function of the sum of random variables with that of a lognormal distribution at a small number of points. Compared with methods available in the literature such as the Fenton-Wilkinson method, Schwartz-Yeh method, and their extensions, the proposed method provides the parametric flexibility to address the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function. ICC 2006This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-A simple and novel method is presented to approximate by the lognormal distribution the probability density function of the sum of correlated lognormal random variables. The method is also shown to work well for approximating the distribution of the sum of lognormal-Rice or Suzuki random variables by the lognormal distribution. The method is based on matching a low-order Gauss-Hermite approximation of the moment-generating function of the sum of random variables with that of a lognormal distribution at a small number of points. Compared with methods available in the literature such as the Fenton-Wilkinson method, Schwartz-Yeh method, and their extensions, the proposed method provides the parametric flexibility to address the inevitable trade-off that needs to be made in approximating different regions of the probability distribution function.

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Exact analysis of the outage probability in multiple-user mobile radio

Cited by 107 publications

References 13 publications

An Overview of the Transmission Capacity of Wireless Networks

An Overview of the Transmission Capacity of Wireless Networks

Outage, local throughput, and capacity of random wireless networks

Approximating the Sum of Correlated Lognormal or, Lognormal-Rice Random Variables

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