Research Article
On the limiting moments of Vandermonde random matrices
@INPROCEEDINGS{10.4108/ICST.WIOPT2008.3231, author={\`{U}yvind Ryan and Merouane Debbah}, title={On the limiting moments of Vandermonde random matrices}, proceedings={1st International ICST Workshop on Physics Inspired Paradigms for Wireless Communications and Network}, publisher={IEEE}, proceedings_a={PHYSCOMNET}, year={2008}, month={8}, keywords={Array signal processing Biomedical signal processing Deconvolution Direction of arrival estimation Eigenvalues and eigenfunctions Finance Limiting Signal processing Signal sampling Veins}, doi={10.4108/ICST.WIOPT2008.3231} }- Øyvind Ryan
Merouane Debbah
Year: 2008
On the limiting moments of Vandermonde random matrices
PHYSCOMNET
IEEE
DOI: 10.4108/ICST.WIOPT2008.3231
Abstract
In this paper, analytical methods for finding moments of random Vandermonde matrices are developed. Vandermonde Matrices play an important role in signal processing and communication applications such as direction of arrival estimation, sampling theory or precoding. Within this framework, we extend classical freeness results on random matrices with i.i.d entries and show that Vandermonde structured matrices can be treated in the same vein with different tools. We focus on various types of Vandermonde matrices, namely Vandermonde matrices with or without uniformly distributed phases. In each case, we provide explicit expressions of the moments of the associated Gram matrix, as well as more advanced models involving the Vandermonde matrix. Comparisons with classical i.i.d. random matrix theory are provided and free deconvolution results are also discussed.