Secret-key agreement over spatially correlated multiple-antenna channels in the low-SNR regime

Marwen Zorgui, Zouheir Rezki, Basel Alomair, Eduard A. Jorswieck, Mohamed-Slim Alouini

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


We consider secret-key agreement with public discussion over Rayleigh fast-fading channels with transmit, receive and eavesdropper correlation. The legitimate receiver along with the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the correlation matrices. We analyze the secret-key capacity in the low signal-to-noise ratio (SNR) regime. We derive closed-form expressions for the first and the second derivatives of the secret-key capacity with respect to SNR at SNR= 0, for arbitrary correlation matrices and number of transmit, receive and eavesdropper antennas. Moreover, we identify optimal transmission strategies achieving these derivatives. For instance, we prove that achieving the first and the second derivatives requires a uniform power distribution between the eigenvectors spanning the maximal-eigenvalue eigenspace of the transmit correlation matrix. We also compare the optimal transmission scheme to a simple uniform power allocation. Finally, we express the minimum energy required for sharing a secret-key bit as well as the wideband slope in terms of the system parameters.
Original languageEnglish (US)
Title of host publication2015 IEEE Conference on Communications and Network Security (CNS)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Number of pages2
ISBN (Print)9781467378765
StatePublished - Dec 8 2015


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