A determinant representation for the distribution of quadratic forms in complex normal vectors
Journal of Multivariate Analysis
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Eigenvalues and Condition Numbers of Complex Random Matrices
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Tails of Condition Number Distributions
SIAM Journal on Matrix Analysis and Applications
Condition Numbers of Gaussian Random Matrices
SIAM Journal on Matrix Analysis and Applications
Random matrix theory and wireless communications
Communications and Information Theory
Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in Wishart matrices
IEEE Communications Letters
On the marginal distribution of the eigenvalues ofWishart matrices
IEEE Transactions on Communications
Eigenvalue-based spectrum sensing algorithms for cognitive radio
IEEE Transactions on Communications
IEEE Transactions on Signal Processing
On analytical derivations of the condition number distributions of dual non-central Wishart matrices
IEEE Transactions on Wireless Communications
CFAR matched direction detector
IEEE Transactions on Signal Processing
Characterizing the statistical properties of mutual information in MIMO channels
IEEE Transactions on Signal Processing
Efficient detection algorithms for MIMO channels: a geometrical approach to approximate ML detection
IEEE Transactions on Signal Processing
IEEE Transactions on Wireless Communications
Capacity of MIMO Rician channels
IEEE Transactions on Wireless Communications
On the capacity of doubly correlated MIMO channels
IEEE Transactions on Wireless Communications
IEEE Transactions on Wireless Communications
Impact of Correlation on the Capacity of Multiple Access and Broadcast Channels with MIMO-MRC
IEEE Transactions on Wireless Communications
Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels
IEEE Transactions on Information Theory
On the capacity of spatially correlated MIMO Rayleigh-fading channels
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Capacity of MIMO systems with semicorrelated flat fading
IEEE Transactions on Information Theory
Impact of antenna correlation on the capacity of multiantenna channels
IEEE Transactions on Information Theory
General Capacity Bounds for Spatially Correlated Rician MIMO Channels
IEEE Transactions on Information Theory
High-SNR power offset in multiantenna communication
IEEE Transactions on Information Theory
Largest eigenvalue of complex Wishart matrices and performance analysis of MIMO MRC systems
IEEE Journal on Selected Areas in Communications
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This paper investigates the distribution of the condition number of complex Wishart matrices. Two closely related measures are considered: the standard condition number (SCN) and the Demmel condition number (DCN), both of which have important applications in the context of multiple-input multiple-output (MIMO) communication systems, as well as in various branches of mathematics. We first present a novel generic framework for the SCN distribution which accounts for both central and non-central Wishart matrices of arbitrary dimension. This result is a simple unified expression which involves only a single scalar integral, and therefore allows for fast and efficient computation. For the case of dual Wishart matrices, we derive new exact polynomial expressions for both the SCN and DCN distributions. We also formulate a new closed-form expression for the tail SCN distribution which applies for correlated central Wishart matrices of arbitrary dimension and demonstrates an interesting connection to the maximum eigenvalue moments of Wishart matrices of smaller dimension. Based on our analytical results, we gain valuable insights into the statistical behavior of the channel conditioning for various MIMO fading scenarios, such as uncorrelated/semi-correlated Rayleigh fading and Ricean fading.