A simplified expression for the probability of error for binary multichannel communications

O’Driscoll, Cillian; Murphy, Colin C.

doi:10.1109/tcomm.2009.0901.060131

Cited by 16 publications

(21 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where a > 0 and b ≥ 0 are real parameters and I m (·) is the mth order modified Bessel function of the first kind. The order index m is an integer and typically m ≥ 0, yet (1) holds for negative orders too and a useful relationship between Marcum-Q functions with positive and negative orders has been reported March 25, 2013 DRAFT in [27], namely…”

Section: Definitionmentioning

confidence: 99%

Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Morales-Jiménez

López‐Martínez

Martos-Naya

et al. 2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, Φ 3 . This result is then applied to the closed-form characterization of the bivariate Nakagami-m distribution and of the distribution of the minimum eigenvalue of correlated non-central Wishart matrices, both important in communication theory. New expressions for the corresponding cumulative distributions are obtained and a number of communication-theoretic problems involving them are pointed out. Index TermsMarcum-Q function, confluent hypergeometric functions, bivariate Nakagami-m, non-central Wishart matrix, minimum eigenvalue distribution.

show abstract

Section: Definitionmentioning

confidence: 99%

Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Morales-Jiménez

López‐Martínez

Martos-Naya

et al. 2014

IEEE Trans. Inform. Theory

View full text Add to dashboard Cite

show abstract

“…and Nakagami-m cases included as references. Exact results obtained using [16], asymptotic results given by (9) and (20). V. CONCLUSION We provided new insights for the κ-µ-E fading distribution.…”

Section: Introductionmentioning

confidence: 79%

Novel Results for the $\kappa$– $\mu$ Extreme Fading Distribution: Generation of White Samples and Capacity Analysis

2015

View full text Add to dashboard Cite

We provide new analytical results for the κ-µ extreme (κ-µ-E) fading distribution, which is useful to model propagation conditions more severe than Rayleigh fading. First, we calculate a closed-form expression for the cumulative distribution function in terms of the first-order Marcum Q-function, which allows us to accurately generate κ-µ-E distributed random variables using the inversion method. Then, we investigate the ergodic capacity in this scenario. Strikingly, we observe that the capacity in the high-SNR regime scales differently than in all conventional fading models.

show abstract

“…(17)- (18). These facts resulted in establishing a connection between the hypergeometric function Ψ 2 and modified Marcum Q function, see (20), as well as between Ψ 2 and Bessel I functions, see (21).…”

Section: Discussionmentioning

confidence: 99%

Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Ermolova

Tirkkonen

2014

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

The evaluation of integral transforms of special functions is required in different research and practical areas. Analyzing the κ-µ fading distribution also khown as the generalized Rician distribution, we find out that the assessment of a few different performance metrics, such as the probability of energy detection of unknown signals and outage probability under co-channel interference, involves the evaluation of an infinite-range integral, which has the form of Laplace transform of product of Marcum Q, Bessel I, and power functions. We evaluate this integral in a closed-form and present numerical estimates. Index TermsBessel I function, co-channel interference, confluent hypergeometric functions of two variables, detection probability, generalized fading distributions, Laplace transform, Marcum Q function, outage probability.

show abstract

A simplified expression for the probability of error for binary multichannel communications

Cited by 16 publications

References 9 publications

Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Connections Between the Generalized Marcum $Q$-Function and a Class of Hypergeometric Functions

Novel Results for the $\kappa$– $\mu$ Extreme Fading Distribution: Generation of White Samples and Capacity Analysis

Laplace Transform of Product of Generalized Marcum Q, Bessel I, and Power Functions With Applications

Contact Info

Product

Resources

About