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Keywords
(17)
Channel Capacity
Communication System
Eigenvalues
hypergeometric function
Information Theory
mimo channel
mimo system
Multiple Antennas
Multiple Input Multiple Output
Mutual Information
Probability Density Function
Quadratic Form
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Related Publications
(4)
Capacity of correlated MIMO Rayleigh channels
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Quadratic forms on complex random matrices and multipleantenna systems
Quadratic forms on complex random matrices and multipleantenna systems,10.1109/TIT.2005.851778,IEEE Transactions on Information Theory,Tharmalingam R
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Quadratic forms on complex random matrices and multipleantenna systems
(
Citations: 30
)
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Tharmalingam Ratnarajah
,
Remi Vaillancourt
In this correspondence, the densities of quadratic forms on complex
random matrices
and their joint eigenvalue densities are derived for applications to information theory. These densities are represented by complex hypergeometric functions of matrix arguments, which can be expressed in terms of complex zonal polynomials. The derived densities are used to evaluate the two most important informationtheoretic measures, the socalled ergodic
channel capacity
and capacity versus outage of multipleinput multipleoutput (MIMO) spatially correlated Rayleighdistributed
wireless communication
channels. We also derive the
probability density function
of the
mutual information
between transmitted and received complex signals of MIMO systems with a finite number of transmit and receive antennas. Numerical results show how channel correlation degrades the capacity of MIMO communication systems.
Journal:
IEEE Transactions on Information Theory  TIT
, vol. 51, no. 8, pp. 29762984, 2005
DOI:
10.1109/TIT.2005.851778
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Citation Context
(22)
...The estimation of eigenvalue distributions with finite sample sizes has been elucidated in recent years, thanks to the work on estimating the exact eigenvalue distributions of complex Wishart matrix with finite sizes which is expressed in terms of complex hypergeometric function by one of the authors of this article Ratnarajah et.al [8] [
9
] and provided an excellent framework to the recent exact threshold formulation of MME detection in ...
...2) Exact Threshold for Correlated Noise: The distribution of complex central Wishart matrix �� is denoted by �� ∼ ���� �� (��, Σ)(�� ≥ �� ). For the largest eigenvalue �� ������ of �� , the cumulative distribution function is given in [
9
] by...
Ayse Kortun
,
et al.
Exact performance analysis of blindly combined energy detection for sp...
...which contains a nonanalytical Dirac delta function, see [
21
]...
Zhiguo Ding
,
et al.
A Relay Assisted Cooperative Transmission Protocol for Wireless Multip...
...<{[SECTION]}>ity density function (PDF) of the variable �� = ∏ 2 =1 �� �� �� �� can be first calculated as [
11
]...
Faheem A. Khan
,
et al.
Outage analysis of cognitive Zinterference channel with twopath cogn...
...Most of these works deal with the joint pdf of the ordered eigenvalues [17]–[24], [30], [39], [46], [
49
]–[52], the marginal distribution of an unordered eigenvalue [4], [25]–[29], or the distribution of the smallest eigenvalue [32], [45] to evaluate the...
L. G. Ordoez
,
et al.
Ordered Eigenvalues of a General Class of Hermitian Random Matrices Wi...
...in any instantiation of channels from the ensemble, we shall obtain a mutual information I less than Iout with probability Pout [
9
]...
...Then the probability density function of mutual information Ic is obtained as [
9
]...
Faheem A. Khan
,
et al.
Outage analysis of causal cognitive radio channel
References
(26)
Complex random matrices and Rician channel capacity
(
Citations: 31
)
T. Ratnarajah
,
R. Vaillancourt
,
M. Alvo
Journal:
Problems of Information Transmission  PROBL INF TRANSM
, vol. 41, no. 1, pp. 122, 2005
Complex singular wishart matrices and applications
(
Citations: 14
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T. Ratnarajah
,
R. Vaillancourt
Journal:
Computers & Mathematics With Applications  COMPUT MATH APPL
, vol. 50, no. 3, pp. 399411, 2005
Eigenvalue Density of Correlated Complex Random Wishart Matrices
(
Citations: 17
)
Steven H. Simon
,
Aris L. Moustakas
Journal:
Bell Labs Technical Journal  BLTJ
A Determinant Representation for the Distribution of Quadratic Forms in Complex Normal Vectors
(
Citations: 33
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Hongsheng Gao
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Peter J. Smith
Journal:
Journal of Multivariate Analysis  MA
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The CalogeroSutherland Model and Generalized Classical Polynomials
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Citations: 102
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P. J. Forrester
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 188, no. 1, pp. 175216, 1997
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Citations
(30)
Effective Capacity of Correlated MISO Channels
Caijun Zhong
,
Tharm Ratnarajah
,
KaiKit Wong
,
MohamedSlim Alouini
Published in 2011.
Outage performance of causal cognitive radio Zinterference fading channel with cognitive relaying
(
Citations: 1
)
Faheem A. Khan
,
T. Ratnarajah
,
S. Prakriya
Conference:
International Conference on Signal Processing and Communications  SPCOM
, 2010
Exact performance analysis of blindly combined energy detection for spectrum sensing
(
Citations: 1
)
Ayse Kortun
,
Tharmalingam Ratnarajah
,
Mathini Sellathurai
Conference:
IEEE International Symposium on Personal, Indoor and Mobile Radio Communications  PIMRC
, pp. 560563, 2010
A Relay Assisted Cooperative Transmission Protocol for Wireless Multiple Access Systems
Zhiguo Ding
,
Kin K. Leung
,
Dennis L. Goeckel
,
Donald F. Towsley
Journal:
IEEE Transactions on Communications  TCOM
, vol. 58, no. 8, pp. 24252435, 2010
Multisource multidestination relay network: constrained optimisation for higher diversity
S. Zhu
,
Z. Ding
,
K. Markarian
Journal:
Iet Communications  IET COMMUN
, vol. 4, no. 12, 2010