Explicit Solution of Worst-Case Secrecy Rate for MISO Wiretap Channels with Spherical Uncertainty

A multiple-input single-output (MISO) wiretap channel model is considered, that includes a multi-antenna transmitter, a single-antenna legitimate receiver and a single-antenna eavesdropper. For the scenario in which spherical uncertainty for both the legitimate and the eavesdropper channels is included, the problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a power constraint, is considered, and an explicit expression for the maximum worst-case secrecy rate is provided.Comment: 1 figure

Optimal and Robust Transmit Designs for MISO Channel Secrecy by Semidefinite Programming

In recent years there has been growing interest in study of multi-antenna transmit designs for providing secure communication over the physical layer. This paper considers the scenario of an intended multi-input single-output channel overheard by multiple multi-antenna eavesdroppers. Specifically, we address the transmit covariance optimization for secrecy-rate maximization (SRM) of that scenario. The challenge of this problem is that it is a nonconvex optimization problem. This paper shows that the SRM problem can actually be solved in a convex and tractable fashion, by recasting the SRM problem as a semidefinite program (SDP). The SRM problem we solve is under the premise of perfect channel state information (CSI). This paper also deals with the imperfect CSI case. We consider a worst-case robust SRM formulation under spherical CSI uncertainties, and we develop an optimal solution to it, again via SDP. Moreover, our analysis reveals that transmit beamforming is generally the optimal transmit strategy for SRM of the considered scenario, for both the perfect and imperfect CSI cases. Simulation results are provided to illustrate the secrecy-rate performance gains of the proposed SDP solutions compared to some suboptimal transmit designs.Comment: 32 pages, 5 figures; to appear, IEEE Transactions on Signal Processing, 201

Robust Optimization of Private Communication in Multi-Antenna Systems

The thesis focuses on the privacy of communication that can be ensured by means of the physical layer, i.e., by appropriately chosen coding and resource allocation schemes. The fundamentals of physical-layer security have been already formulated in the 1970s by Wyner (1975), Csiszár and Körner (1978). But only nowadays we have the technical progress such that these ideas can find their way in current and future communication systems, which has driven the growing interest in this area of research in the last years. We analyze two physical-layer approaches that can ensure the secret transmission of private information in wireless systems in presence of an eavesdropper. One is the direct transmission of the information to the intended receiver, where the transmitter has to simultaneously ensure the reliability and the secrecy of the information. The other is a two-phase approach, where two legitimated users first agree on a common and secret key, which they use afterwards to encrypt the information before it is transmitted. In this case, the secrecy and the reliability of the transmission are managed separately in the two phases. The secrecy of the transmitted messages mainly depends on reliable information or reasonable and justifiable assumptions about the channel to the potential eavesdropper. Perfect state information about the channel to a passive eavesdropper is not a rational assumption. Thus, we introduce a deterministic model for the uncertainty about this channel, which yields a set of possible eavesdropper channels. We consider the optimization of worst-case rates in systems with multi-antenna Gaussian channels for both approaches. We study which transmit strategy can yield a maximum rate if we assume that the eavesdropper can always observe the corresponding worst-case channel that reduces the achievable rate for the secret transmission to a minimum. For both approaches, we show that the resulting max-min problem over the matrices that describe the multi-antenna system can be reduced to an equivalent problem over the eigenvalues of these matrices. We characterize the optimal resource allocation under a sum power constraint over all antennas and derive waterfilling solutions for the corresponding worst-case channel to the eavesdropper for a constraint on the sum of all channel gains. We show that all rates converge to finite limits for high signal-to-noise ratios (SNR), if we do not restrict the number of antennas for the eavesdropper. These limits are characterized by the quotients of the eigenvalues resulting from the Gramian matrices of both channels. For the low-SNR regime, we observe a rate increase that depends only on the differences of these eigenvalues for the direct-transmission approach. For the key generation approach, there exists no dependence from the eavesdropper channel in this regime. The comparison of both approaches shows that the superiority of an approach over the other mainly depends on the SNR and the quality of the eavesdropper channel. The direct-transmission approach is advantageous for low SNR and comparably bad eavesdropper channels, whereas the key generation approach benefits more from high SNR and comparably good eavesdropper channels. All results are discussed in combination with numerous illustrations.Der Fokus dieser Arbeit liegt auf der Abhörsicherheit der Datenübertragung, die auf der Übertragungsschicht, also durch geeignete Codierung und Ressourcenverteilung, erreicht werden kann. Die Grundlagen der Sicherheit auf der Übertragungsschicht wurden bereits in den 1970er Jahren von Wyner (1975), Csiszár und Körner (1978) formuliert. Jedoch ermöglicht erst der heutige technische Fortschritt, dass diese Ideen in zukünftigen Kommunikationssystemen Einzug finden können. Dies hat in den letzten Jahren zu einem gestiegenen Interesse an diesem Forschungsgebiet geführt. In der Arbeit werden zwei Ansätze zur abhörsicheren Datenübertragung in Funksystemen analysiert. Dies ist zum einen die direkte Übertragung der Information zum gewünschten Empfänger, wobei der Sender gleichzeitig die Zuverlässigkeit und die Abhörsicherheit der Übertragung sicherstellen muss. Zum anderen wird ein zweistufiger Ansatz betrachtet: Die beiden Kommunikationspartner handeln zunächst einen gemeinsamen sicheren Schlüssel aus, der anschließend zur Verschlüsselung der Datenübertragung verwendet wird. Bei diesem Ansatz werden die Abhörsicherheit und die Zuverlässigkeit der Information getrennt voneinander realisiert. Die Sicherheit der Nachrichten hängt maßgeblich davon ab, inwieweit zuverlässige Informationen oder verlässliche Annahmen über den Funkkanal zum Abhörer verfügbar sind. Die Annahme perfekter Kanalkenntnis ist für einen passiven Abhörer jedoch kaum zu rechtfertigen. Daher wird hier ein deterministisches Modell für die Unsicherheit über den Kanal zum Abhörer eingeführt, was zu einer Menge möglicher Abhörkanäle führt. Die Optimierung der sogenannten Worst-Case-Rate in einem Mehrantennensystem mit Gaußschem Rauschen wird für beide Ansätze betrachtet. Es wird analysiert, mit welcher Sendestrategie die maximale Rate erreicht werden kann, wenn gleichzeitig angenommen wird, dass der Abhörer den zugehörigen Worst-Case-Kanal besitzt, welcher die Rate der abhörsicheren Kommunikation jeweils auf ein Minimum reduziert. Für beide Ansätze wird gezeigt, dass aus dem resultierenden Max-Min-Problem über die Matrizen des Mehrantennensystems ein äquivalentes Problem über die Eigenwerte der Matrizen abgeleitet werden kann. Die optimale Ressourcenverteilung für eine Summenleistungsbeschränkung über alle Sendeantennen wird charakterisiert. Für den jeweiligen Worst-Case-Kanal zum Abhörer, dessen Kanalgewinne einer Summenbeschränkung unterliegen, werden Waterfilling-Lösungen hergeleitet. Es wird gezeigt, dass für hohen Signal-Rausch-Abstand (engl. signal-to-noise ratio, SNR) alle Raten gegen endliche Grenzwerte konvergieren, wenn die Antennenzahl des Abhörers nicht beschränkt ist. Die Grenzwerte werden durch die Quotienten der Eigenwerte der Gram-Matrizen beider Kanäle bestimmt. Für den Ratenanstieg der direkten Übertragung ist bei niedrigem SNR nur die Differenz dieser Eigenwerte maßgeblich, wohingegen für den Verschlüsselungsansatz in dem Fall keine Abhängigkeit vom Kanal des Abhörers besteht. Ein Vergleich zeigt, dass das aktuelle SNR und die Qualität des Abhörkanals den einen oder anderen Ansatz begünstigen. Die direkte Übertragung ist bei niedrigem SNR und verhältnismäßig schlechten Abhörkanälen überlegen, wohingegen der Verschlüsselungsansatz von hohem SNR und vergleichsweise guten Abhörkanälen profitiert. Die Ergebnisse der Arbeit werden umfassend diskutiert und illustriert

On Secrecy Performance of MISO SWIPT Systems With TAS and Imperfect CSI

In this paper, a multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system, including one base station (BS) equipped with multiple antennas, one desired single-antenna information receiver (IR), and N (N > 1) single-antenna energy-harvesting receivers (ERs) is considered. Assuming that the information signal to the desired IR may be eavesdropped by ERs if ERs are malicious, we investigate the secrecy performance of the target MISO SWIPT system when imperfect channel state information (CSI) is available and adopted for transmit antenna selection at the BS. Considering that each eavesdropping link experiences independent but not necessarily identically distributed Rayleigh fading, the closed-form expressions for the exact and the asymptotic secrecy outage probability, and the average secrecy capacity are derived and verified by simulations. Furthermore, the optimal power splitting factor is derived for each ER to realize the tradeoff between the energy harvesting and the information eavesdropping. Our results reveal the impact of the imperfect CSI on the secrecy performance of MISO SWIPT systems in the presence of multiple wiretap channels

Constructive interference based secure precoding:A new dimension in physical layer security

Conventionally, interference and noise are treated as catastrophic elements in wireless communications. However, it has been shown recently that exploiting known interference constructively can even contribute to signal detection ability at the receiving end. This paper exploits this concept to design artificial noise (AN) beamformers constructive to the intended receiver (IR) yet keeping AN disruptive to possible eavesdroppers (Eves). The scenario considered here is a multiple-input single-output (MISO) wiretap channel with multiple eavesdroppers. Both perfect and imperfect channel information have been considered. The main objective is to improve the receive signal-to-interference and noise ratio (SINR) at IR through exploitation of AN power in an attempt to minimize the total transmit power, while confusing the Eves. Numerical simulations demonstrate that the proposed constructive AN precoding approach yields superior performance over conventional AN schemes in terms of transmit power as well as symbol error rate (SER)

Secure SWIPT by Exploiting Constructive Interference and Artificial Noise

This paper studies interference exploitation techniques for secure beamforming design in simultaneous wireless information and power transfer (SWIPT) in multiple-input single-output (MISO) systems. In particular, multiuser interference (MUI) and artificially generated noise signals are designed as constructive to the information receivers (IRs) yet kept disruptive to potential eavesdropping by the energy receivers (ERs). The objective is to improve the received signal-to-interference and noise ratio (SINR) at the IRs by exploiting the MUI and AN power in an attempt to minimize the total transmit power. We first propose second-order cone programming based solutions for the perfect channel state information (CSI) case by defining strong upper and lower bounds on the energy harvesting (EH) constraints. We then provide semidefinite programming based solutions for the problems. In addition, we also solve the worst-case harvested energy maximization problem under the proposed bounds. Finally, robust beamforming approaches based on the above are derived for the case of imperfect CSI. Our results demonstrate that the proposed constructive interference precoding schemes yield huge saving in transmit power over conventional interference management schemes. Most importantly, they show that, while the statistical constraints of conventional approaches may lead to instantaneous SINR as well as EH outages, the instantaneous constraints of our approaches guarantee both constraints at every symbol period

A Tutorial on Interference Exploitation via Symbol-Level Precoding: Overview, State-of-the-Art and Future Directions

IEEE Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wireless communication system, by beginning with the classification of constructive interference (CI) and destructive interference (DI). The definition for CI is presented and the corresponding mathematical characterization is formulated for popular modulation types, based on which optimization-based precoding techniques are discussed. In addition, the extension of CI precoding to other application scenarios as well as for hardware efficiency is also described. Proof-of-concept testbeds are demonstrated for the potential practical implementation of CI precoding, and finally a list of open problems and practical challenges are presented to inspire and motivate further research directions in this area

Interference Exploitation via Symbol-Level Precoding: Overview, State-of-the-Art and Future Directions

Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wireless communication system, by beginning with the classification of constructive interference (CI) and destructive interference (DI). The definition for CI is presented and the corresponding mathematical characterization is formulated for popular modulation types, based on which optimization-based precoding techniques are discussed. In addition, the extension of CI precoding to other application scenarios as well as for hardware efficiency is also described. Proof-of-concept testbeds are demonstrated for the potential practical implementation of CI precoding, and finally a list of open problems and practical challenges are presented to inspire and motivate further research directions in this area