FIXED-RATE POWER ALLOCATION STRATEGIES FOR ENHANCED SECRECY IN MIMO WIRETAP CHANNELS Amitav Mukherjee and A. Lee Swindlehurst Dept. of Electrical Engineering & Computer Science University of California, Irvine Irvine, CA 92697 email: {a.mukherjee;swindle}@uci.edu ABSTRACT This paper studies the use of artiﬁcial interference in reduc- ing the likelihood that a conﬁdential message transmitted be- tween two multi-antenna nodes is intercepted by a passive eavesdropper. A portion of the transmit power is used to broadcast the information signal with just enough power to guarantee a certain data rate for the intended receiver, and the remainder of the power is used to broadcast artiﬁcial noise in order to mask the desired signal from a potential eaves- dropper. The interference is designed to be orthogonal to the multiple-stream information signal when it reaches the de- sired receiver. A modiﬁed water-ﬁlling algorithm is proposed that balances the required transmit power with the number of spatial dimensions available for jamming the eavesdropper. Numerical results verify the increase in secrecy capacity un- der the proposed transmission scheme. 1. INTRODUCTION Wireless communications are inherently insecure due to the broadcast nature of the wireless medium. A passive eaves- dropper in the vicinity of a wireless transmission has the abil- ity to obtain information about the transmitted signal without risk of detection, since it never transmits itself. The information- theoretic aspects of this scenario, referred to as the wiretap channel, have been explored in some detail [1–3]. In partic- ular, this work led to the development of the notion of se- crecy capacity, which quantiﬁes the rate at which a transmit- ter can reliably send a secret message to the receiver, without the eavesdropper being able to decode it. Ultimately, it was shown that a non-zero secrecy capacity can only be obtained if the eavesdropper’s channel is of lower quality than that of the intended recipient. The work cited above assumes single an- tenna nodes; secrecy capacity for the multiple-input multiple- output (MIMO) wiretap channel, where all nodes may pos- sess multiple antennas, has been studied in [4,5], for example. Note that much of this information theoretic work is based on This work was supported by the U.S. Army Research Ofﬁce under the Multi-University Research Initiative (MURI) grant W911NF-07-1-0318. the assumption that the eavesdropper’s channel is known to the transmitter, which is hard to justify if the eavesdropper is truly passive. While encryption at the network layer can be used to en- sure conﬁdential wireless communications, its computational cost may be prohibitive and there are difﬁculties and vulner- abilities associated with key distribution and management. Even when encryption is available, it is often still desirable to augment the security of the link and prevent its detection or interception. Consequently, there has recently been con- siderable interest in the use of physical layer mechanisms to increase the security of wireless communications links via ar- tiﬁcial interference. The idea is to increase the interference seen by the eavesdropper in such a way that her channel is degraded while the channel of the receiver is not. For ex- ample, assuming that the transmitter has more antennas than the intended recipient so that the corresponding channel has a non-trivial nullspace, one of the approaches taken in [6] is to broadcast artiﬁcial interference using transmit beamform- ers in this nullspace. Such interference will have no impact on the receiver, but will in general degrade the eavesdropper’s channel since its nullspace (if any) will be different. The high-SNR performance of this type of technique was studied in [7]. While [6] studied the case where only the distribution of the eavesdropper’s channel was known, [7,8] focused on the situation where the eavesdropper’s instanta- neous channel is known to the transmitter, and developed an algorithm to optimally exploit such information for the case where the intended recipient has a single antenna. A different but related approach can be found in [9], where the channel nullspace is exploited to design time-varying transmit beam- formers that result in a constant channel to the receiver, but a random time-varying channel for the eavesdropper. The use of relays or neighboring nodes in implementing artiﬁcial in- terference was examined in [10, 11]. In [12], a scalar secret message-transmission scheme with the aid of artiﬁcial inter- ference was examined with the relative SINR of the eaves- dropper and intended receiver as the performance criterion. In this paper, we study the MIMO wiretap problem in 978-1-4244-3696-5/09/$25.00 © 2009 IEEE 344 Authorized licensed use limited to: IEEE Editors in Chief. Downloaded on August 17, 2009 at 19:48 from IEEE Xplore. Restrictions apply.