CLT for eigen-inference methods in cognitive radios

This article provides a central limit theorem for a consistent estimator of the population eigenvalues of a class of sample covariance matrices. An exact expression as well as an empirical and asymptotically accurate approximation of the limiting variance is also derived. These results are applied in a cognitive radio context featuring an orthogonal-CDMA primary network and a secondary network whose objective is to maximise the coverage of secondary transmissions under low probability of interference with primary users.

[1]  R. Couillet,et al.  Random Matrix Methods for Wireless Communications , 2011 .

[2]  Z. Bai,et al.  CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data , 2017, Statistical Papers.

[3]  W. Rudin.  Real and complex analysis, 3rd ed. , 1987 .

[4]  Mérouane Debbah,et al.  Eigen-Inference for Energy Estimation of Multiple Sources , 2010, IEEE Transactions on Information Theory.

[5]  B. Achiriloaie,et al.  VI REFERENCES , 1961 .

[6]  Noureddine El Karoui.  Spectrum estimation for large dimensional covariance matrices using random matrix theory , 2006, math/0609418.

[7]  R. Bass,et al.  Review: P. Billingsley, Convergence of probability measures , 1971 .

[8]  Philippe Loubaton,et al.  Improved subspace DoA estimation methods with large arrays: The deterministic signals case , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[9]  R. Cooke.  Real and Complex Analysis , 2011 .

[10]  Patrick L. Combettes,et al.  Signal detection via spectral theory of large dimensional random matrices , 1992, IEEE Trans. Signal Process..

[11]  Feng Luo,et al.  Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory , 2007, BMC Bioinformatics.

[12]  Mérouane Debbah,et al.  Free deconvolution for OFDM multicell SNR detection , 2008, 2008 IEEE 19th International Symposium on Personal, Indoor and Mobile Radio Communications.

[13]  V. Plerou,et al.  Random matrix approach to cross correlations in financial data. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Mérouane Debbah,et al.  Free Deconvolution for Signal Processing Applications , 2007, 2007 IEEE International Symposium on Information Theory.

[15]  Xavier Mestre,et al.  Improved Estimation of Eigenvalues and Eigenvectors of Covariance Matrices Using Their Sample Estimates , 2008, IEEE Transactions on Information Theory.

[16]  M. J. Gans,et al.  On Limits of Wireless Communications in a Fading Environment when Using Multiple Antennas , 1998, Wirel. Pers. Commun..

[17]  J. W. Silverstein,et al.  On the empirical distribution of eigenvalues of a class of large dimensional random matrices , 1995 .