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Free probability theory as a main branch of random matrix theory is a valuable tool for describing the asymptotic behavior of multiple systems, especially for those with large random matrices. But classical freeness results mainly focus on random matrices with independent and identically distributed (i.i.d.) entries. In this paper, by using the latest research results of random Vandermonde matrix (a class of matrix that does not satisfy the i.i.d. condition) in free probability theory, a new spectrum sensing scheme is proposed, which shows how the asymptotic behavior of random Vandermonde matrices can be used to assist spectrum sensing for cognitive radio.
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