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Eigenvalues and Singular Values of Random Matrices: Theory and Applications

Communication Sciences Institute Seminar: Eigenvalues and Singular Values of Random Matrices: Theory and ApplicationsAntonia Tulino (University of Naples)Abstract:
Of late, random matrices have attracted great interest in the engineering community because of their applications to the communications and information theory on the fundamental limits of wireless communication noisy vector channels. The purpose of this talk is to illustrate this synergy between random matrix theory and information theory through several classes of channels that arise in wireless communications. These channels are characterized by random matrices that admit various statistical descriptions depending on the actual application. Motivated by the intuition drawn from various applications in communications, the _ and Shannon transforms turn out to be quite helpful at clarifying the exposition as well as the statement of many results. In this talk we revisit in terms of _- and Shannon-transform some of the main results in random matrix theory from the work of Mar_enko-Pastur in 1967 to the most recent asymptotic results in the contest of free probability theory and we give an extended summary of their main recent applications to wireless communication problems.In addition, recent results on the speed of convergence to the asymptotic limits are visited and used
to evaluate the probability density function of the mutual informationThroughout the talk, we apply the various findings to the fundamental limits of wireless communication with focus on several classes of vector channels that arise in wireless communications: • Code-division multiple-access (CDMA), with and without fading (both frequency-flat and frequency-selective) and with single and multiple receive antennas. • Multi-carrier code-division multiple access (MC-CDMA), which is the time-frequency dual of CDMA • Channels with multiple receive and transmit antennas, incorporating features such as antenna correlation, polarization, and line-of-sight components.For each of these channels, we analyze two performance measures of engineering interest: the average mutual information (highest data rate that can be conveyed reliably per unit bandwidth) and minimum mean-square error (smallest mean-square error that can be incurred estimating the channel input based on its noisy received observations), which are determined by the distribution of the singular values of the channel matrix.Bio:
Antonia Maria Tulino was born in Napoli, Italy, on September 12, 1971. She received the Dr. Engr. degree (summa cum laude) from the Università degli Studi di Napoli Federico II, Napoli, Italy, in 1995 and the Ph.D. degree in electronic engineering from the Seconda Università degli Studi di Napoli, Napoli, Italy, in 1999. In 1999, she was a Research Scientist at the Center for Wireless Communications (CWC), Oulu, Finland. From January 2000 to February 2001, she was a post-doctoral visitor with Princeton University, Princeton, NJ. From February 2001 to November to 2002, she was Assistant Professor with the Dipartmento di Ingegneria delle Telecomunicazioni, Università degli Studi del Sannio, Benevento, Italy. From Novembre to 2002 she has been Associate Professor with the Dipartmento di Ingegneria Elettronica e delle Telecomunicazioni, Università degli Studi di Napoli "Federico II", Napoli, Italy. She is periodically appointed as visiting research staff member at the Department of Electrical Engineering, Princeton University. Her current research interests are in the area of statistical signal processing, information theory, random matrix theory.

Location: Hughes Aircraft Electrical Engineering Center (EEB) - 248

Audiences: Everyone Is Invited

Contact: michael neely