Secret-key Agreement over Spatially Correlated Fast-Fading Multiple-Antenna Channels with Public Discussion

by Marwen Zorgui, Zouheir Rezki, Basel Alomair, Mohamed-Slim Alouini
Conference Proceedings Year: 2015


Marwen Zorgui, Zouheir Rezki, Basel Alomair and Mohamed-Slim Alouini, Secret-key Agreement over Spatially Correlated Fast-Fading Multiple-Antenna Channels with Public Discussion, accepted in IEEE International Symposium on Information Theory ( ISIT'2015), Hong Kong, Hong Kong, June, 2015.


We consider secret-key agreement with public dis- cussion over multiple-input multiple-output (MIMO) Rayleigh fast-fading channels under correlated environment. We assume that transmit, legitimate receiver and eavesdropper antennas are correlated. The legitimate receiver and the eavesdropper are assumed to have perfect channel knowledge while the transmitter has only knowledge of the correlation matrices. First, we derive the expression of the secret-key capacity under the considered setup. Then, we prove that the optimal transmit strategy achiev- ing the secret-key capacity consists in transmitting independent Gaussian signals along the eingenvectors of the transmit cor- relation matrix. The powers allocated to each channel mode are determined as the solution to a numerical optimization problem that we derive. A necessary and sufficient condition for beamforming (i.e., transmitting along the strongest channel mode) to be capacity-achieving is derived. Finally, we analyze the impact of correlation matrices on the system performance and provide closed-form expressions of the gain/loss due to correlation in the high power regime.​ 



Secret-key agreement MIMO systems optimal signaling correlation beamforming high power regime