Asymptotic Behavior of Random Vandermonde Matrices With Entries on the Unit Circle
Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name...
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| Veröffentlicht in: | IEEE transactions on information theory 2009-07, Vol.55 (7), p.3115-3147 |
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| creator | Ryan, O. Debbah, M. |
| description | Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent and identically distributed (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 matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. 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 deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications. |
| doi_str_mv | 10.1109/TIT.2009.2021317 |
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Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent and identically distributed (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 matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. 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 deconvolution results are discussed. 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Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent and identically distributed (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 matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. 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 deconvolution results are discussed. We review some applications of the results to the fields of signal processing and wireless communications.</description><subject>Antennas</subject><subject>Applied sciences</subject><subject>Array signal processing</subject><subject>Asymptotic properties</subject><subject>Biomedical signal processing</subject><subject>Coding, codes</subject><subject>Communications networks</subject><subject>Computer Science</subject><subject>Deconvolution</subject><subject>Direction of arrival estimation</subject><subject>Eigenvalues and eigenfunctions</subject><subject>Exact sciences and technology</subject><subject>Fast Fourier transforms</subject><subject>Information theory</subject><subject>Information, signal and communications theory</subject><subject>limiting eigenvalue distribution</subject><subject>Mathematical analysis</subject><subject>Matrices</subject><subject>Matrix</subject><subject>Matrix methods</subject><subject>Matrix theory</subject><subject>Methods</subject><subject>MIMO</subject><subject>Miscellaneous</subject><subject>multiple-input multiple-output (MIMO)</subject><subject>Networking and Internet Architecture</subject><subject>Radiocommunications</subject><subject>random matrices</subject><subject>Sampling</subject><subject>Signal and communications theory</subject><subject>Signal processing</subject><subject>Signal sampling</subject><subject>Sparse matrices</subject><subject>Telecommunications</subject><subject>Telecommunications and information theory</subject><subject>Vandermonde matrices</subject><subject>Veins</subject><subject>Wireless communication</subject><subject>Wireless communications</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkUFrGzEQhUVpoW7ae6AXUSilh001K41XOromaQIuheA0RyFrtVhhd-VK60D-fcbY-NDLjJ70vRHDY-wSxBWAMD_Wd-urWghDpQYJzRs2A8SmMnNUb9lMCNCVUUq_Zx9KeSKpEOoZu1-Ul2E3pSl6_jNs3XNMmaeO37uxTQP_Sy3kIVHlv92Uow-FP8Zpy69HUiTSyKdt4A9jnPgyZt-Hj-xd5_oSPp36BXu4uV4vb6vVn193y8Wq8krKqQptixrdZoONQY-ogqyN3rgOlJaAbaO6GvQG6ka2zjRemdZIDXQyVB3KC_b9OHfrervLcXD5xSYX7e1iZQ93QijRkOcZiP12ZHc5_duHMtkhFh_63o0h7YvVc6OVNmCI_PIf-ZT2eaRFLBg0UhnUBIkj5HMqJYfu_D8Ie4jDUhz2EIc9xUGWr6e5rnjXd9mNPpazj1at5wIVcZ-PXAwhnJ9RNKiNlK9P5pBR</recordid><startdate>20090701</startdate><enddate>20090701</enddate><creator>Ryan, O.</creator><creator>Debbah, M.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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Vandermonde matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with independent and identically distributed (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 matrices, such as Vandermonde matrices with and without uniform phase distributions, as well as generalized Vandermonde matrices. 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 deconvolution results are discussed. 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| subjects | Antennas Applied sciences Array signal processing Asymptotic properties Biomedical signal processing Coding, codes Communications networks Computer Science Deconvolution Direction of arrival estimation Eigenvalues and eigenfunctions Exact sciences and technology Fast Fourier transforms Information theory Information, signal and communications theory limiting eigenvalue distribution Mathematical analysis Matrices Matrix Matrix methods Matrix theory Methods MIMO Miscellaneous multiple-input multiple-output (MIMO) Networking and Internet Architecture Radiocommunications random matrices Sampling Signal and communications theory Signal processing Signal sampling Sparse matrices Telecommunications Telecommunications and information theory Vandermonde matrices Veins Wireless communication Wireless communications |
| title | Asymptotic Behavior of Random Vandermonde Matrices With Entries on the Unit Circle |
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