On the Bivariate and Trivariate Rician Distributions

Dharmawansa, K.D.P.; Rajatheva, R.M.A.P.; Ahmed, K.M.

doi:10.1109/vtcf.2006.415

Cited by 10 publications

(9 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, attempting to calculate these angles via the scalar product of two vectors, as in (25), always leads to relative values in the range [0, π]. As such, although the cosines of the angles calculated with (25) have the correct sign (positive or negative); this is not true if we calculate sine ratios based on (25), since it would always produce positive values. To resolve this ambiguity, we propose the following simple solution.…”

Section: Appendix C Calculation Of Sin α and Sin β In (24)mentioning

confidence: 99%

“…Specifically, various forms of the bivariate and trivariate non-central χ 2 densities have been obtained in [18,19,23,24] and [25,26] respectively. It is clear, however, that these existing trivariate (and bivariate) results cannot be extended from the real domain to the more general complex domain.…”

Section: Introductionmentioning

confidence: 99%

“…To solve these integrals, we exploit a number of remarkable properties of classical ultraspherical polynomials, such as Dougall's identity, and utilize powerful surface-integration techniques from [19] wherever possible. We assume for the sake of analytical tractability (as in [25,26]) that the underlying covariance structure has a tri-diagonal inverse. We note that this structure embraces some of the most common covariance models employed in the literature for various applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

Dharmawansa

McKay

2009

Journal of Multivariate Analysis

View full text Add to dashboard Cite

a b s t r a c tThis paper derives the joint density of a particular trivariate non-central χ 2 distribution corresponding to the diagonal elements of a 3 × 3 complex non-central Wishart matrix.This distribution is important for a number of practical statistical signal processing applications, including synthetic aperture radar, extra-solar planet detection, and multiantenna wireless communications. The density expression is in the form of an infinite series representation which converges rapidly and is easy to compute. The joint density of the diagonal elements of a 2 × 2 complex non-central Wishart matrix is also derived by simple reduction of the trivariate result.

show abstract

Section: Appendix C Calculation Of Sin α and Sin β In (24)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

Dharmawansa

McKay

2009

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…The bivariate Rician pdf is given in [22], [23] and [24]. In [25] the authors propose an infinite series representation involving modified Bessel functions of the first kind for the trivariate Rician distribution when the underlying Gaussian components have a tridiagonal form of inverse covariance matrix. The non-central Wishart distribution derived in [26] can be thought of as a more generalized version of the non-central distribution.…”

Section: T He χmentioning

confidence: 99%

New series representation for the trivariate non-central chi-squared distribution

Dharmawansa

Rajatheva

Tellambura

2009

IEEE Trans. Commun.

View full text Add to dashboard Cite

Abstract-This paper derives a new infinite series representation for the trivariate Non-central chi-squared distribution when the underlying correlated Gaussian variables have a tridiagonal form of an inverse covariance matrix. The joint probability density function is derived using Miller's approach and Dougall's identity. Moreover, the trivariate cumulative distribution function (cdf) and characteristic function (chf) are also derived. Finally, the bivariate non-central chi-squared distribution and some known forms are shown to be special cases of the more general distribution. However, the derivation of non-central chi-squared distribution for an arbitrary covariance matrix seems intractable via Miller's approach. Two applications of the newly derived results are provided for performance analysis of multiple input multiple output (MIMO) systems with transmit antenna selection over a correlated Rician fading environment. Some numerical results are also presented to verify the accuracy of the analytical expressions.

show abstract

“…Relay assisted wireless communication has been widely studied [25][26][27][28][29][30][31][32][33][34][35][36][37][38]. [7][8][9] show the performance of relay using amplifying and forwarding.…”

Section: Introductionmentioning

confidence: 99%

Performance of decode and forward MIMO relaying for wireless uplink

Kamruzzaman

2012

2012 15th International Conference on Computer and Information Technology (ICCIT)

View full text Add to dashboard Cite

In this paper, performance of relay assisted wireless link is evaluated in the presence of rayleigh fading where mobile handset is equipped with single transmit antenna, relay is equipped with multiple transmit and receive antennas, and destination has multiple receive antennas. Data are modulated using QPSK or 16 QAM or 64 QAM modulator at handset and send to relay which combined and decode the incoming signal using Maximum Likelihood decoding and further encode the symbols using STBC, and the encoded data are split into n streams which are simultaneously transmitted using n transmit antennas of relay. It is observed that relay with 2 transmit antennas and 2,3,4,5 and 6 receive antennas provides 13 dB, 11 dB, 9 dB,6 dB and 5 dB gains respectively compared to direct link at 10 -5 . And there are around 1.5 dB to 6 dB gains for increasing number of receiving antennas of relay from 2 to 3 or 3 to 4 but there are very little gains for increasing number of receiving antennas of relay from 4 to 5 or 5 to 6.

show abstract

On the Bivariate and Trivariate Rician Distributions

Cited by 10 publications

References 31 publications

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

Diagonal distribution of a complex non-central Wishart matrix: A new trivariate non-central chi-squared density

New series representation for the trivariate non-central chi-squared distribution

Performance of decode and forward MIMO relaying for wireless uplink

Contact Info

Product

Resources

About