Dimension Boundary Between Finite and Infinite Random Matrices in Cognitive Radio Networks

The dimension boundary between finite random matrices and infinite random matrices is originally defined in this letter. The proposed boundary provides a theoretical approach to classify random matrices based on their dimensions. Two methods are proposed to determine the dimension boundary. One is based on the eigenvalue distribution and the other is based on the eigenvalue interval. In particular, a boundary-based threshold generation scheme in cognitive radio networks is studied. The theoretical analysis and numerical results verify the proposed dimension boundary and the corresponding boundary decision methods.

[1]  C. Tracy,et al.  Mathematical Physics © Springer-Verlag 1996 On Orthogonal and Symplectic Matrix Ensembles , 1995 .

[2]  Marco Chiani,et al.  On the Probability That All Eigenvalues of Gaussian, Wishart, and Double Wishart Random Matrices Lie Within an Interval , 2015, IEEE Transactions on Information Theory.

[3]  Debashis Paul,et al.  No eigenvalues outside the support of the limiting empirical spectral distribution of a separable covariance matrix , 2009, J. Multivar. Anal..

[4]  Josef A. Nossek,et al.  On the condition number distribution of complex wishart matrices , 2010, IEEE Transactions on Communications.

[5]  V. Marčenko,et al.  DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES , 1967 .

[6]  Marco Chiani,et al.  On the probability that all eigenvalues of Gaussian and Wishart random matrices lie within an interval. , 2015 .

[7]  Ranjan K. Mallik,et al.  Analysis of transmit-receive diversity in Rayleigh fading , 2003, IEEE Trans. Commun..

[8]  Lu Bai,et al.  Recent advances and future challenges for massive MIMO channel measurements and models , 2016, Science China Information Sciences.

[9]  Moe Z. Win,et al.  On the capacity of spatially correlated MIMO Rayleigh-fading channels , 2003, IEEE Trans. Inf. Theory.

[10]  A. James.  Distributions of Matrix Variates and Latent Roots Derived from Normal Samples , 1964 .

[11]  Wensheng Zhang,et al.  Spectrum Sensing Algorithms via Finite Random Matrices , 2012, IEEE Transactions on Communications.

[12]  Yonghong Zeng,et al.  Eigenvalue-based spectrum sensing algorithms for cognitive radio , 2008, IEEE Transactions on Communications.

[13]  Caijun Zhong,et al.  Distribution of the Demmel Condition Number of Wishart Matrices , 2011, IEEE Transactions on Communications.