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We consider three channel models: 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 channel state information (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 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 fromK . For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases fromin 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. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modification of the achievable schemes as demonstrated in this paper.

We consider 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. We consider an average power constraint on the input, and assume that no channel state information (CSI) is available to 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.

Abstract-

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.