Event
Ph.D. Dissertation Defense; Pritam Mukherjee
Wednesday, August 24, 2016
3:00 p.m.
Room 2168 AVW Bldg.
Maria Hoo
301 405 3681
mch@umd.edu
NAME: Pritam Mukherjee
Advisory Committee:
Professor Sennur Ulukus, Chair/Advisor
Professor Prakash Narayan
Professor Alexander Barg
Professor Charalampos Papamanthou
Professor Lawrence C. Washington, Dean's representative
Date/Time: Wednesday, August 24, 2016 at 3:00 p.m.
Place: Room 2168 A.V. Williams Building
Title: SECURITY UNDER IMPERFECT CHANNEL KNOWLEDGE IN WIRELESS NETWORKS
Abstract: This dissertation studies physical layer security in wireless networks using an information theoretic framework. The central theme of this work is exploring the effect of delayed or no channel state information (CSI) on physical layer security in various wireless channel models.
We begin with the fast Rayleigh fading wiretap channel, over which a legitimate transmitter wishes to have secure communication with a legitimate receiver in the presence of an eavesdropper. Subject to an average power constraint on the input, and with no CSI at any user, we show that the input distribution that achieves the secrecy capacity for this wiretap channel is discrete with a finite number of mass points. This enables us to evaluate the exact secrecy capacity of this channel numerically.
Next, we consider multi-user models, specifically, the wiretap channel with $M$ helpers, the $K$-user multiple access wiretap channel, and the K-user interference channel with an external eavesdropper, when no eavesdropper's CSI is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSI at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the $K$-user multiple access wiretap channel reduces to a wiretap channel with $(K-1)$ helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K-1)/(K(K-1)+1) to (K-1)/K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K-1)/(2K-1) to (K-1)/2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large.
In line with the theme of this dissertation, we next consider the MIMO wiretap channel with one helper and the two-user MIMO multiple access channel when no eavesdropper CSIT is available. In each case, the eavesdropper has K antennas while the remaining terminals have N antennas. We determine the optimal sum s.d.o.f. for each channel model for the regime K N.
