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.