Application of Random Matrix Theory to Multivariate Statistics

Dieng, Momar; Tracy, Craig A.

doi:10.1007/978-1-4419-9514-8_7

Cited by 16 publications

(31 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result agrees with [8] in the GSE case, if f is a constant multiple J , where J is the characteristic function of the interval J. Now we use the commutator OED, f :D Df fD to obtain a result better suited for our purpose.…”

Section: Remarksupporting

confidence: 74%

“…We follow closely the computations of Dieng [8] and Tracy and Widom [9]. From Theorems 2.4 and 2.5 and some linear algebra, we obtain…”

Section: General Casementioning

confidence: 96%

“…In the case, w.x/ D e x 2 , x 2 R. We again follow the discussions [8,9] and choose a special j to simplify M .4/ as much as possible. To proceed, let…”

Section: Gaussian Symplectic Ensemblementioning

confidence: 99%

“…We follow the treatment of [8,9]; firstly using Theorem 2.5 and followed by some computations, we find…”

Section: General Casementioning

confidence: 99%

See 3 more Smart Citations

Linear statistics of matrix ensembles in classical background

Min

Chen

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

Given a joint probability density function of N real random variables, fx j g N jD1, obtained from the eigenvector-eigenvalue decomposition of N N random matrices, one constructs a random variable, the linear statistics, defined by the sum of smooth functions evaluated at the eigenvalues or singular values of the random matrix, namely, P N jD1 F.x j /. For the joint PDFs obtained from the Gaussian and Laguerre ensembles, we compute, in this paper, the moment-generating function Eˇ.exp. P j F.x j ///, where Eˇdenotes expectation value over the orthogonal (ˇD 1) and symplectic (ˇD 4) ensembles, in the form one plus a Schwartz function, none vanishing over R for the Gaussian ensembles and R C for the Laguerre ensembles. These are ultimately expressed in the form of the determinants of identity plus a scalar operator, from which we obtained the large N asymptotic of the linear statistics from suitably scaled F. /.

show abstract

Section: Remarksupporting

confidence: 74%

“…We follow closely the computations of Dieng [8] and Tracy and Widom [9]. From Theorems 2.4 and 2.5 and some linear algebra, we obtain…”

Section: General Casementioning

confidence: 96%

See 2 more Smart Citations

Linear statistics of matrix ensembles in classical background

Min

Chen

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…We know that calculation of the exact ergodic capacity is extremely difficult and complicated, since the expectation of the instantaneous capacity should be integrated over the channel distribution. We apply the Tracy-Widom law (Dieng, et al, 2011) that exploits the eigenvalue distribution of complex Wishart matrices. Then, we derive asymptotic closed-form expressions on the ergodic capacity of the FD MIMO AF relay channel for several antenna configurations.…”

mentioning

confidence: 99%

Ergodic Capacity Analysis of Full-duplex Mimo Relay Channel using Tracy-Widom Distribution with Processing Delay

Arifin¹,

Ohtsuki²

2015

IJTech

View full text Add to dashboard Cite

We explore a full-duplex technique in wireless communication particularly for relay networks. We consider the relay to operate in full-duplex, which occurs when transmission and reception are conducted in the same channel. We investigate potential benefits of full-duplex technique in relay networks, which uses multiple antennas for transmission and reception combined with the Amplify-Forward (AF) scenario. We study the effects of multiple antennas in terms of relay capacity. We derive an ergodic capacity expression using the Tracy-Widom distribution. Using Singular Value Decomposition (SVD) and perfect Channel State Information (CSI), we investigate these three scenarios: First, we consider the relay to have an antenna larger than that of both source and destination. Second, we consider both relay and destination to have an antenna larger than that of the source. Third, we consider both relay and source to have antenna larger than that of the destination. We show the results that the capacity of the relay with a fullduplex technique is almost twice the capacity of an half-duplex. We show that increasing the number of destination antennas is not help much when one of the source antennas is small. Moreover, the capacity decreases due to a channel hardening effect, when the number of destination antennas is larger than that of the source.

show abstract