On the secrecy degress of freedom of the multi-antenna block fading wiretap channels

Mari Kobayashi (1) , Pablo Piantanida (1) , Sheng Yang (1) , S. Shamai (2)

1 E3S - Supélec Sciences des Systèmes
2 Department of Computer Science [Haifa]

We consider the multi-antenna wiretap channel in which the transmitter wishes to send a confidential message to its receiver while keeping it secret to the eavesdropper. It has been known that the secrecy capacity of such a channel does not increase with signal-to-noise ratio when the transmitter has no channel state information (CSI) under mild conditions. Motivated by Jafar's robust interference alignment technique, we study the so-called staggered multi-antenna block-fading wiretap channel where the legitimate receiver and the eavesdropper have different temporal correlation structures. Assuming no CSI at transmitter, we characterize lower and upper bounds on the secrecy degrees of freedom (s.d.o.f.) of the channel at hand. Our results show that a positive s.d.o.f. can be ensured whenever two receivers experience different fading variation. Remarkably, very simple linear precoding schemes provide the optimal s.d.o.f. in some cases of interest.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]

Mari Kobayashi, Pablo Piantanida, Sheng Yang, S. Shamai. On the secrecy degress of freedom of the multi-antenna block fading wiretap channels. 2010 IEEE International Symposium on Information Theory, Jun 2010, Austin, United States. pp.2563-2567, ⟨10.1109/ISIT.2010.5513788⟩. ⟨hal-00528209⟩