Linear Diversity Combining Techniques

Brennan, Donald G.

doi:10.1109/jrproc.1959.287136

Cited by 984 publications

(515 citation statements)

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“…Example 2 Sums of Rayleigh random variables occur extensively in the evaluation of equal gain combining systems when determining the BEP, see Brennan [34]. The BEP can be writ- ten as R = Pr(X 1 + X 2 + · · · + X L < X 1 + X 2 + · · · + X L ), where L is the number of fading channels and X 1 , X 2 , .…”

Section: Applicationmentioning

confidence: 99%

A Review of Results on Sums of Random Variables

Nadarajah

2008

Acta Appl Math

116

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Section: Applicationmentioning

confidence: 99%

A Review of Results on Sums of Random Variables

Nadarajah

2008

Acta Appl Math

116

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“…With b i = b j ∀ i = j, the cdf, pdf and LT of pdf of Z in (1) are respectively given by (6), (7), and (8), shown at the top of this page, where (6)- (8), and 2 F 1 (·, ·; ·; ·) is the hypergeometric function [2]. The proofs of (6)- (8) n i .…”

Section: Resultsmentioning

confidence: 99%

On a Ratio of Functions of Exponential Random Variables and Some Applications

Annavajjala

Chockalingam

Mohammed

2010

IEEE Trans. Commun.

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Consider L independent and identically distributed exponential random variables (r.vs) X1,X2,...,XL, and positive scalars b1,b2,...,bL. In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (X1 + X2 + ... + XL)2 /(b1*X1 + b2*X2 + ... + bL*XL). We show that the r.v Z appears in various communication systems such as 1) maximal ratio combining of signals received over multiple channels with mismatched noise variances, 2) M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and 3) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form. IEEE Transactions on CommunicationsThis 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-Consider L independent and identically distributed exponential random variables (r.vs) X1, X2, . . . , XL and positive scalars b1, b2, . . . , bL. In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.We show that the r.v Z appears in various communication systems such as i) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ii) M -ary phase-shift keying with spatial diversity and imperfect channel estimation, and iii) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.Index Terms-Exponential random variables, distribution of ratio of two random variables, bivariate Laplace transform, mismatched statistics, partial-band interference.

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“…The effects of short term fading are mitigated through microdiversity [20,21]. The widely used signal processing techniques in diversity systems are the maximal ratio combining (MRC), equal gain combining (EGC) and the selection combining (SC) algorithms [20][21][22][23].…”

Section: Diversity Combining Algorithmsmentioning

confidence: 99%

Performance Analysis of Diversity Combining Algorithms in Shadowed Fading Channels

Shankar

2006

Wireless Pers Commun

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A compound fading model incorporating short term fading and shadowing proposed recently is used to analyze the performance of wireless systems employing microscopic diversity to mitigate the effects of flat fading. This model can account for the presence of different levels of fading and shadowing and provide an analytical solution for the probability density function of the signal-to-noise ratio. Using that model, the performances of MRC and SC diversity combining algorithms were studied. The amount fading (AF) following diversity implementation was calculated and it is seen that the decline in the amount of fading is bound by the level of shadowing present, with the MRC providing a larger decrease in the amount of fading than the SC algorithm. The effect on the error rates was studied using the example of the coherent BPSK modem. Results show that the performances of wireless systems can be analyzed using the compound model for the shadowed fading channels.

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Linear Diversity Combining Techniques

Cited by 984 publications

References 25 publications

A Review of Results on Sums of Random Variables

A Review of Results on Sums of Random Variables

On a Ratio of Functions of Exponential Random Variables and Some Applications

Performance Analysis of Diversity Combining Algorithms in Shadowed Fading Channels

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