QoS-Based Transmit Beamforming in the Presence of Eavesdroppers: An Optimized Artificial-Noise-Aided Approach

Secure transmission techniques have been receiving growing attention in recent years, as a viable, powerful alternative to blocking eavesdropping attempts in an open wireless medium. This paper proposes a secret transmit beamforming approach using a quality-of-service (QoS)-based perspective. Specifically, we establish design formulations that: i) constrain the maximum allowable signal-to-interference-and-noise ratios (SINRs) of the eavesdroppers, and that ii) provide the intended receiver with a satisfactory SINR through either a guaranteed SINR constraint or SINR maximization. The proposed designs incorporate a relatively new idea called artificial noise (AN), where a suitable amount of AN is added in the transmitted signal to confuse the eavesdroppers. Our designs advocate joint optimization of the transmit weights and AN spatial distribution in accordance with the channel state information (CSI) of the intended receiver and eavesdroppers. Our formulated design problems are shown to be NP-hard in general. We deal with this difficulty by using semidefinite relaxation (SDR), an approximation technique based on convex optimization. Interestingly, we prove that SDR can exactly solve the design problems for a practically representative class of problem instances; e.g., when the intended receiver's instantaneous CSI is known. Extensions to the colluding-eavesdropper scenario and the multi-intended-receiver scenario are also examined. Extensive simulation results illustrate that the proposed AN-aided designs can yield significant power savings or SINR enhancement compared to some other methods.

I. Introduction

Transmit beamforming designs through quality-of-service (QoS) optimizations have recently flourished as an important class of multi-antenna transmission techniques. QoS-based transmit beamforming has proven to be a viable, versatile approach to a variety of communication scenarios, such as downlink unicast [2]–[5], downlink multicast [6], and multi-group multicast (a combination of unicast and multicast) [7]. In this topic, the challenges usually lie in the optimization of a desired, possibly nonconvex, design formulation; and convex optimization has been playing a significant role in this aspect, providing tractable solutions that can either exactly solve or well approximate the considered design formulation. For a general coverage of convex optimization for transmit beamforming, readers are referred to the magazine article [8] and the book chapter [9]; see also [10]–[13] for some further studies on the capability of convex optimization, and [14], [15] for some emerging applications.