This work concentrates on the application of diversity techniques and space time block coding for future mobile wireless communications. The initial system analysis employs a space-time coded OFDM transmitter over a multipath Rayleigh channel, and a receiver which uses a selection combining diversity technique. The performance of this combined scenario is characterised in terms of the bit error rate and throughput. A novel four element QOSTBC scheme is introduced, it is created by reforming the detection matrix of the original QOSTBC scheme, for which an orthogonal channel matrix is derived. This results in a computationally less complex linear decoding scheme as compared with the original QOSTBC. Space time coding schemes for three, four and eight transmitters were also derived using a Hadamard matrix. The practical optimization of multi-antenna networks is studied for realistic indoor and mixed propagation scenarios. The starting point is a detailed analysis of the throughput and field strength distributions for a commercial dual band 802.11n MIMO radio operating indoors in a variety of line of sight and non-line of sight scenarios. The physical model of the space is based on architectural schematics, and realistic propagation data for the construction materials. The modelling is then extended and generalized to a multi-storey indoor environment, and a large mixed site for indoor and outdoor channels based on the Bradford University campus. The implications for the physical layer are also explored through the specification of antenna envelope correlation coefficients. Initially this is for an antenna module configuration with two independent antennas in close proximity. An operational method is proposed using the scattering parameters of the system and which incorporates the intrinsic power losses of the radiating elements. The method is extended to estimate the envelope correlation coefficient for any two elements in a general (N,N) MIMO antenna array. Three examples are presented to validate this technique, and very close agreement is shown to exist between this method and the full electromagnetic analysis using the far field antenna radiation patterns.

CoordenaÃÃo de AperfeiÃoamento de NÃvel Superior / Em diversas aplicaÃÃes do processamento de sinais em sistemas de comunicaÃÃo sem-fio, o sinal recebido à de natureza multidimensional, possuindo uma estrutura algÃbrica multilinear. Neste contexto, a decomposiÃÃo tensorial PARAFAC tem sido utilizada em vÃrios trabalhos ao longo dos Ãltimos seis anos. Observa-se, entretanto, que decomposiÃÃes tensoriais generalizadas sÃo necessÃrias para modelar uma classe mais ampla de sistemas de comunicaÃÃo, caracterizada pela presenÃa de estruturas de transmissÃo mais complexas, por modelos de canal mais realistas, e por tÃcnicas de processamento de sinais mais eficientes no receptor. Esta tese investiga novas abordagens tensorias e suas aplicaÃÃes em modelagem de sistemas MIMO, equalizaÃÃo, separaÃÃo de sinais e estimaÃÃo paramÃtrica de canal. Inicialmente, duas novas decomposiÃÃes tensoriais (PARAFAC em blocos com restriÃÃes e CONFAC) sÃo desenvolvidas e estudadas em termos de identificabilidade. Em uma segunda parte do trabalho, novas aplicaÃÃes destas decomposiÃÃes tensoriais sÃo propostas. A decomposiÃÃo PARAFAC em blocos com restriÃÃes à aplicada, primeiramente, Âa modelagem unificada de sistemassuperamostrados, DS-CDMA e OFDM, com aplicaÃÃo em equalizaÃÃo multiusuÃria. Em seguida, esta decomposiÃÃo à utilizada na modelagem de sistemas de transmissÃo MIMO com espalhamento espaÃo-temporal e detecÃÃo conjunta. Em seguida, a decomposiÃÃo CONFAC à explorada na concepÃÃo de uma nova arquitetura generalizada de transmissÃo MIMO/CDMA que combina diversidade e multiplexagem. As propriedades de unicidade desta decomposiÃÃo permitem o uso do processamento nÃo-supervisionado no receptor, visando a reconstruÃÃo dos sinais transmitidos e a estimaÃÃo do canal. Na terceira e Ãltima parte deste trabalho, explora-se a decomposiÃÃo PARAFAC no contexto de duas aplicaÃÃes diferentes. Na primeira, uma nova estrutura de transmissÃo espaÃo-temporal-freqÃencial à proposta para sistemas MIMO multiportadora. A segunda aplicaÃÃo consiste em um novo estimador paramÃtrico para canais multipercursos. / In several signal processing applications for wireless communications, the received signal is multidimensional in nature and may exhibit a multilinear algebraic structure. In this context, the PARAFAC tensor decomposition has been the subject of several works in the past six years. However, generalized tensor decompositions are necessary for covering a wider class of wireless communication systems with more complex transmission structures, more realistic channel models and more efficient receiver signal processing. This thesis investigates tensor modeling approaches for multiple-antenna systems, channel equalization, signal separation and parametric channel estimation. New tensor decompositions, namely, the block-constrained PARAFAC and CONFAC decompositions, are developed and studied in terms of identifiability. First, the block-constrained PARAFAC decomposition is applied for a uniÂed tensor modeling of oversampled, DS-CDMA and OFDM systems with application to blind multiuser equalization. This decomposition is also used for modeling multiple-antenna (MIMO) transmission systems with block space-time spreading and blind detection, which generalizes previous tensor-based MIMO transmission models. The CONFAC decomposition is then exploited for designing new MIMO-CDMA transmission schemes combining spatial diversity and multiplexing. Blind symbol/code/channel recovery is discussed from the uniqueness properties of this decomposition. This thesis also studies new applications of third-order PARAFAC decomposition. A new space-time-frequency spreading system is proposed for multicarrier multiple-access systems, where this decomposition is used as a joint spreading and multiplexing tool at the transmitter using tridimensional spreading code with trilinear structure. Finally, we present a PARAFAC modeling approach for the parametric estimation of SIMO and MIMO multipath wireless channels with time-varying structure.

In heterogeneous dense networks where spectrum is shared, users privacy remains one of the major challenges. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk becomes information leakage.We propose a novel and efficient secrecy rate enhancing relay strategy EFFIN for information leakage neutralization. The relay matrix is chosen such that the effective leakage channel (spectral and spatial) is zero. Thus, it ensures secrecy regardless of receive processing employed at eavesdroppers and does not rely on wiretaps codes to ensure secrecy, unlike other physical layer security techniques such as artificial noise. EFFIN achieves a higher sum secrecy rate over several state-of-the-art baseline methods.

In heterogeneous dense networks where spectrum is shared, users' privacy remains one of the major challenges. On a multi-antenna relay-assisted multi-carrier interference channel, each user shares the spectral and spatial resources with all other users. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk on the spectral and spatial channels becomes information leakage. In this paper, we propose a novel secrecy rate enhancing relay strategy that utilizes both spectral and spatial resources, termed as information leakage neutralization. To this end, the relay matrix is chosen such that the effective channel from the transmitter to the colluding eavesdropper is equal to the negative of the effective channel over the relay to the colluding eavesdropper and thus the information leakage to zero. Interestingly, the optimal relay matrix in general is not block-diagonal which encourages users' encoding over the frequency channels. We proposed two information leakage neutralization strategies, namely efficient information leakage neutralization (EFFIN) and local-optimized information leakage neutralization (LOPTIN). EFFIN provides a simple and efficient design of relay processing matrix and precoding matrices at the transmitters in the scenario of limited power and computational resources. LOPTIN, despite its higher complexity, provides a better sum secrecy rate performance by optimizing the relay processing matrix and the precoding matrices jointly. The proposed methods are shown to improve the sum secrecy rates over several state-of-the-art baseline methods.

The research reported in this thesis is concerned with robust precoder and transceiver optimization in multiuser multi-antenna wireless communication systems in the presence of imperfect channel state information(CSI). Precoding at the transmit side, which utilizes the CSI, can improve the system performance and simplify the receiver design. Transmit precoding is essential for inter-user interference cancellation in multiuser downlink where users do not cooperate. Linear and non-linear precoding have been widely investigated as low-complexity alternatives to dirty paper coding-based transmission scheme for multiuser multiple-input multiple-output(MU-MIMO)downlink. Similarly, in relay-assisted networks, precoding at the relay nodes have been shown to improve performance. The precoder and joint precoder/receive filter (transceiver) designs usually assume perfect knowledge of the CSI. In practical systems, however, the CSI will be imperfect due to estimation errors, feedback errors and feedback delays. Such imperfections in CSI will lead to deterioration of performance of the precoders/transceivers designed assuming perfect CSI. In such situations, designs which are robust to CSI errors are crucial to realize the potential of multiuser multi-antenna systems in practice. This thesis focuses on the robust designs of precoders and transceivers for MU-MIMO downlink, and for non-regenerative relay networks in the presence of errors in the CSI. We consider a norm-bounded error(NBE) model, and a stochastic error(SE) model for the CSI errors. These models are suitable for commonly encountered errors, and they allow mathematically and computationally tractable formulations for the robust designs. We adopt a statistically robust design in the case of stochastic error, and a minimax or worst-case robust design in the case of norm-bounded error. We have considered the robust precoder and transceiver designs under different performance criteria based on transmit power and quality-of-service(QoS) constraints. The work reported in this thesis can be grouped into three parts, namely,i ) robust linear pre-coder and transceiver designs for multiuser downlink, ii)robust non-linear precoder and transceiver designs for multiuser downlink, and iii)robust precoder designs for non-regenerative relay networks. Linear precoding: In this part, first, a robust precoder for multiuser multiple-input single-output(MU-MISO)downlink that minimizes the total base station(BS)transmit power with constraints on signal-to-interference-plus-noise ratio(SINR) at the user terminals is considered. We show that this problem can be reformulated as a second order cone program(SOCP) with the same order of computational complexity as that of the non-robust precoder design. Next, a robust design of linear transceiver for MU-MIMO downlink is developed. This design is based on the minimization of sum mean square error(SMSE) with a constraint on the total BS transmit power, and assumes that the error in the CSI at the transmitter(CSIT) follows the stochastic error model. For this design, an iterative algorithm based on the associated Karush-Kuhn-Tucker(KKT) conditions is proposed. Our numerical results demonstrate the robust performance of the propose designs. Non-linear precoding: In this part, we consider robust designs of Tomlinson-Harashima precoders(THP) for MU-MISO and MU-MIMO downlinks with different performance criteria and CSI error models. For MU-MISO systems with imperfect CSIT, we investigate the problem of designing robust THPs under MSE and total BS transmit power constraints. The first design is based on the minimization of total BS transmit power under constraints on the MSE at the individual user receivers. We present an iterative procedure to solve this problem, where each iteration involves the solution of a pair of convex optimization problems. The second design is based on the minimization of a stochastic function of the SMSE under a constraint on the total BS transmit power. We solve this problem efficiently by the method of alternating optimization. For MU-MIMO downlink, we propose robust THP transceiver designs that jointly optimize the TH precoder and receiver filters. We consider these transceiver designs under stochastic and norm-bounded error models for CSIT. For the SE model, we propose a minimum SMSE transceiver design. For the NBE model, we propose three robust designs, namely, minimum SMSE design, MSE-constrained design, and MSE-balancing design. Our proposed solutions to these robust design problems are based on iteratively solving a pair of sub-problems, one of which can be solved analytically, and the other can be formulated as a convex optimization problem that can be solved efficiently. Robust precoder designs for non-regenerative relay networks: In this part, we consider robust designs for two scenarios in the case of relay-assisted networks. First, we consider a non-regenerative relay network with a source-destination node pair assisted by multiple relay nodes, where each node is equipped with a single antenna. The set of the cooperating relay nodes can be considered as a distributed antenna array. For this scenario, we present a robust distributed beam former design that minimizes the total relay transmit power with a constraint on the SNR at the destination node. We show that this robust design problem can be reformulated as a semi-definite program (SDP)that can be solved efficiently. Next, we consider a non-regenerative relay network, where a set of source-destination node pairs are assisted by a MIMO-relay node, which is equipped with multiple transmit and multiple receive antennas. For this case, we consider robust designs in the presence of stochastic and norm-bounded CSI errors. We show that these problems can be reformulated as convex optimization problems. In the case of norm-bounded error, we use an approximate expression for the MSE in order to obtain a tractable solution.

In heterogeneous dense networks where spectrum is shared, users privacy remains one of the major challenges. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk becomes information leakage.We propose a novel and efficient secrecy rate enhancing relay strategy EFFIN for information leakage neutralization. The relay matrix is chosen such that the effective leakage channel (spectral and spatial) is zero. Thus, it ensures secrecy regardless of receive processing employed at eavesdroppers and does not rely on wiretaps codes to ensure secrecy, unlike other physical layer security techniques such as artificial noise. EFFIN achieves a higher sum secrecy rate over several state-of-the-art baseline methods.

In heterogeneous dense networks where spectrum is shared, users' privacy remains one of the major challenges. On a multi-antenna relay-assisted multi-carrier interference channel, each user shares the spectral and spatial resources with all other users. When the receivers are not only interested in their own signals but also in eavesdropping other users' signals, the cross talk on the spectral and spatial channels becomes information leakage. In this paper, we propose a novel secrecy rate enhancing relay strategy that utilizes both spectral and spatial resources, termed as information leakage neutralization. To this end, the relay matrix is chosen such that the effective channel from the transmitter to the colluding eavesdropper is equal to the negative of the effective channel over the relay to the colluding eavesdropper and thus the information leakage to zero. Interestingly, the optimal relay matrix in general is not block-diagonal which encourages users' encoding over the frequency channels. We proposed two information leakage neutralization strategies, namely efficient information leakage neutralization (EFFIN) and local-optimized information leakage neutralization (LOPTIN). EFFIN provides a simple and efficient design of relay processing matrix and precoding matrices at the transmitters in the scenario of limited power and computational resources. LOPTIN, despite its higher complexity, provides a better sum secrecy rate performance by optimizing the relay processing matrix and the precoding matrices jointly. The proposed methods are shown to improve the sum secrecy rates over several state-of-the-art baseline methods.

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.

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.