Largest Eigenvalue Distribution of Noncircularly Symmetric Wishart-Type Matrices With Application to Hoyt-Faded MIMO Communications

Moreno-Pozas, Laureano; Morales-Jiménez, David; McKay, Matthew R.; Martos-Naya, Eduardo

doi:10.1109/tvt.2017.2737718

Cited by 5 publications

(13 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the asymptotic outage expression remains valid even when T is rank deficient. Since we are interested in outage probability, we may use (16) to approximately characterize it, for sufficiently large K values, as…”

Section: B the Effect Of Kmentioning

confidence: 99%

“…In [15], the statistical properties of the Gram matrix W = HH † , where H is a 2 × 2 complex central Gaussian matrix whose elements have arbitrary variances, have been investigated, resulting in exact distributions of W and its eigenvalues. In [16], the exact and asymptotic largest eigenvalue distributions of W are derived when H is a complex Gaussian matrix with unequal variances in the real and imaginary parts of its entries, or equivalently H belongs to the non-circularly-symmetric Gaussian subclass. These results have been then leveraged to analyze the outage performance of multi-antenna systems with MRC over Nakagami-q (Hoyt) fading.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Exact Outage Probability of 2×2 MIMO-MRC in Correlated Rician Fading

Dharmawansa

Kahatapitiya

Atapattu

et al. 2020

2020 IEEE Wireless Communications and Networking Conference (WCNC)

View full text Add to dashboard Cite

This paper addresses a classical problem in random matrix theory-finding the distribution of the maximum eigenvalue of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative distribution function (c.d.f.) of the maximum eigenvalue of a 2 × 2 correlated non-central Wishart matrix with rank-1 mean. By using this new result, we derive the exact outage probability of 2 × 2 multipleinput multiple-output maximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlation and a strong line-ofsight (LoS) component (rank-1 channel mean). We also show that the outage performance is affected by the relative alignment of the eigen-spaces of the mean and correlation matrices. In general, when the LoS path aligns with the least eigenvector of the correlation matrix, in the high transmit signal-to-noise ratio (SNR) regime, the outage gradually improves with the increasing correlation. Moreover, we show that as K (Rician factor) grows large, the outage event can be approximately characterized by the c.d.f. of a certain Gaussian random variable.

show abstract

Section: B the Effect Of Kmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Exact Outage Probability of 2×2 MIMO-MRC in Correlated Rician Fading

Dharmawansa

Kahatapitiya

Atapattu

et al. 2020

2020 IEEE Wireless Communications and Networking Conference (WCNC)

View full text Add to dashboard Cite

show abstract

“…The typical scenarios are MIMO maximal ratio combining (MRC) [1], [2], MIMO beamforming [3], [25], and singular value decomposition (SVD) MIMO systems [4] in which the maximum output signal-to-noise ratio (SNR) of the receiver hinges on the largest eigenvalue of the random matrix H H H. Motivated by this, the largest eigenvalue distribution of the random Gram matrix has been extensively studied in the context of MIMO communications. Many pioneering works have obtained several exact and asymptotic expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the largest eigenvalue of Wishart matrices [1]- [3], pseudo-Wishart matrices [1], and noncircularly symmetric Wishart-type matrices [6]. Each expression is then applied to analyze the outage performance and/or symbol error rate (SER) of MIMO MRC, MIMO beamforming, or SVD MIMO systems subject to a Rayleigh [1], [4], Rice [2]- [4], or Hoyt [6] fading channel.…”

Section: Introductionmentioning

confidence: 99%

“…Many pioneering works have obtained several exact and asymptotic expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the largest eigenvalue of Wishart matrices [1]- [3], pseudo-Wishart matrices [1], and noncircularly symmetric Wishart-type matrices [6]. Each expression is then applied to analyze the outage performance and/or symbol error rate (SER) of MIMO MRC, MIMO beamforming, or SVD MIMO systems subject to a Rayleigh [1], [4], Rice [2]- [4], or Hoyt [6] fading channel.…”

Section: Introductionmentioning

confidence: 99%

Coulomb Gas Analogy: A Statistical Physics Approach to Performance Analysis of MIMO Systems

Qian

2019

IEEE Trans. Veh. Technol.

View full text Add to dashboard Cite

In this correspondence, by adopting the Coulomb gas analogy that is an analytical approach from statistical physics, we derive a closedform approximation of the cumulative distribution function (CDF) of the largest eigenvalue of a random Gram matrix H H H, where H denotes the channel matrix of a multiple-input multiple-output (MIMO) system. The expression of approximation has a simple structure in terms of several elementary functions, which is derived by assuming that the entries of H have Nakagami-m distributed amplitude with an independent phase. This assumption is made because it applies in two common cases of the Nakagami-m distributions, i.e., with a uniformly distributed phase and a complex signal model. Simulation results indicate that the theoretical expression also provides a good approximation to the CDF for Rice and Hoyt distributions when the CDF is within a near-one range. This range takes the form of (P no , 1), where we assume P no = 10 −3 by default in this study. The derived approximation can find many uses for the performance analysis of MIMO beamforming and singular value decomposition MIMO systems, e.g., evaluating the outage probability for these systems.

show abstract

“…In [12], the statistical properties of the Gram matrix W = HH † , where H is a 2 × 2 complex central Gaussian matrix whose elements have arbitrary variances, have been investigated, resulting in exact distributions of W and its eigenvalues. In [13], the exact and asymptotic largest eigenvalue distributions of W are derived when H is a complex Gaussian matrix with unequal variances in the real and imaginary parts of its entries, or equivalently H belongs to the non-circularly-symmetric Gaussian subclass. These results have been then leveraged to analyze the outage performance of multi-antenna systems with MRC over Nakagami-q (Hoyt) fading.…”

Section: Introductionmentioning

confidence: 99%

Outage Analysis of $2\times2 $ MIMO-MRC in Correlated Rician Fading

Dharmawansa,

Kahatapitiya,

Atapattu

et al. 2018

Preprint

View full text Add to dashboard Cite

This paper addresses one of the classical problems in random matrix theory-finding the distribution of the maximum eigenvalue of the correlated Wishart unitary ensemble. In particular, we derive a new exact expression for the cumulative distribution function (c.d.f.) of the maximum eigenvalue of a 2 × 2 correlated non-central Wishart matrix with rank-1 mean. By using this new result, we derive an exact analytical expression for the outage probability of 2 × 2 multiple-input multiple-output maximum-ratio-combining (MIMO-MRC) in Rician fading with transmit correlation and a strong line-of-sight (LoS) component (rank-1 channel mean). We also show that the outage performance is affected by the relative alignment of the eigen-spaces of the mean and correlation matrices. In general, when the LoS path aligns with the least eigenvector of the correlation matrix, in the high transmit signal-to-noise ratio (SNR) regime, the outage gradually improves with the increasing correlation. Moreover, we show that as K (Rician factor) grows large, the outage event can be approximately characterized by the c.d.f. of a certain Gaussian random variable.

show abstract

Largest Eigenvalue Distribution of Noncircularly Symmetric Wishart-Type Matrices With Application to Hoyt-Faded MIMO Communications

Cited by 5 publications

References 18 publications

On the Exact Outage Probability of 2×2 MIMO-MRC in Correlated Rician Fading

On the Exact Outage Probability of 2×2 MIMO-MRC in Correlated Rician Fading

Coulomb Gas Analogy: A Statistical Physics Approach to Performance Analysis of MIMO Systems

Outage Analysis of $2\times2 $ MIMO-MRC in Correlated Rician Fading

Contact Info

Product

Resources

About