Abstract-We consider the block Rayleigh fading multipleinput multiple-output (MIMO) wiretap channel with no prior channel state information (CSI) available at any of the terminals. The channel gains remain constant within a coherence interval of T symbols, and then change to another independent realization in the next coherence interval. The transmitter, the legitimate receiver, and the eavesdropper have n t , n r , and n e antennas, respectively. We determine the exact secure degrees of freedom (s.d.o.f.) of this system when T ≥ 2min(n t , n r ). We show that, in this case, the s.d.o.f. is exactly equal to (min(n t , n r )−n e ) + (T −min(n t , n r ))/T . The first term in this expression can be interpreted as the eavesdropper with n e antennas taking away n e antennas from both the transmitter and the legitimate receiver. The second term can be interpreted as a fraction of the s.d.o.f. being lost due to the lack of CSI at the legitimate receiver. In particular, the fraction loss, min(n t , n r )/T , can be interpreted as the fraction of channel uses dedicated to training the legitimate receiver for it to learn its own CSI. We prove that this s.d.o.f. can be achieved by employing a constant norm channel input, which can be viewed as a generalization of discrete signalling to multiple dimensions.Index Terms-Physical layer secrecy, wiretap channel, secure degrees of freedom, multiple-input multiple-output (MIMO), Rayleigh block fading, non-coherent communications.
This work considers the joint design of training and data transmission in physical-layer secret communication systems, and examines the role of artificial noise (AN) in both of these phases. In particular, AN in the training phase is used to prevent the eavesdropper from obtaining accurate channel state information (CSI) whereas AN in the data transmission phase can be used to mask the transmission of the confidential message. By considering AN-assisted training and secrecy beamforming schemes, we first derive bounds on the achievable secrecy rate and obtain a closed-form approximation that is asymptotically tight at high SNR. Then, by maximizing the approximate achievable secrecy rate, the optimal power allocation between signal and AN in both training and data transmission phases is obtained for both conventional and AN-assisted training based schemes. We show that the use of AN is necessary to achieve a high secrecy rate at high SNR, and its use in the training phase can be more efficient than that in the data transmission phase when the coherence time is large. However, at low SNR, the use of AN provides no advantage since CSI is difficult to obtain in this case. Numerical results are presented to verify our theoretical claims.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.