On the Secrecy Degress of Freedom of the Multi-Antenna Block Fading Wiretap Channels

TL;DR

This paper investigates the secrecy degrees of freedom in multi-antenna block-fading wiretap channels with no transmitter channel state information, revealing conditions for positive secrecy capacity and proposing simple optimal schemes.

Contribution

It characterizes bounds on the secrecy degrees of freedom for staggered multi-antenna block-fading channels without CSI, highlighting the impact of different fading structures.

Findings

Positive s.d.o.f. achievable with different fading variations

Simple linear precoding schemes can be optimal in some scenarios

Secrecy capacity does not increase with SNR without CSI

Abstract

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.