Secure Transmission with Multiple Antennas: The MISOME Wiretap Channel

TL;DR

This paper analyzes the secrecy capacity of a MISO wiretap channel with multiple antennas, showing beamforming strategies are capacity-achieving and how the number of eavesdropper antennas impacts secure communication.

Contribution

It characterizes the secrecy capacity using generalized eigenvalues and demonstrates the effectiveness of beamforming and secure space-time codes in different antenna regimes.

Findings

Beamforming is capacity-achieving for the MISO wiretap channel.

The secrecy capacity depends on the ratio of eavesdropper to sender antennas.

Eavesdropper's effectiveness increases with more antennas, potentially nullifying secure communication.

Abstract

The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we show that in the high signal-to-noise (SNR) ratio regime the penalty for not knowing eavesdropper's channel is small--a simple ``secure space-time code'' that can be thought of as masked beamforming and radiates power isotropically attains near-optimal performance. In the limit of large number of antennas, we obtain a realization-independent characterization of the secrecy capacity as a function of the number $\beta$: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when $\beta<1$, but that for $\beta\ge2$ the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.