Achieving Full Secure Degrees-of-Freedom for the MISO Wiretap Channel With an Unknown Eavesdropper

Abstract

In this paper, we study the achievable secure degrees-of-freedom (sdof) for the multiple-input single-output (MISO) wiretap channel with an unknown eavesdropper. It is assumed that the eavesdropper’s (Eve’s) channel state information (CSI) is unknown to the transmitter (Alice) and legitimate receiver (Bob). Recent studies have shown that the achievable sdof in the sense of strong secrecy is zero when Eve’s number of antennas is equal to or more than Bob’s number of antennas, which is the scenario considered in this paper. To this end, we propose a novel precoding technique and a coding strategy that together achieve full sdof in the sense of strong secrecy without knowing Eve’s CSI and without using artificial noise. The proposed precoding method uses the CSI of the Alice-Bob channel in a nonlinear fashion, which makes the transmitted symbols undecodable at Eve. The proposed coding scheme is based on the channel resolvability concept and ensures strong secrecy. Achieving full sdof with an unknown Eve’s CSI is significant, because it is contrary to what is believed about the achievable sdof for the MISO wiretap channel in the sense of strong secrecy. We also show that the proposed scheme achieves near Alice-Bob’s channel capacity in the sense of strong secrecy with a probability approaching one at finite signal-to-noise ratio.