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Source And Channel Coding Techniques for The MIMO Reverse-link ChannelGanesan, T January 2014 (has links) (PDF)
In wireless communication systems, the use of multiple antennas, also known as Multiple-Input Multiple-Output(MIMO) communications, is now a widely accepted and important technology for improving their reliability and throughput performance. However, in order to achieve the performance gains predicted by the theory, the transmitter and receiver need to have accurate and up-to-date Channel State Information(CSI) to overcome the vagaries of the fading environment. Traditionally, the CSI is obtained at the receiver by sending a known training sequence in the forward-link direction. This CSI has to be conveyed to the transmitter via a low-rate, low latency and noisy feedback channel in the reverse-link direction. This thesis addresses three key challenges in sending the CSI to the transmitter of a MIMO communication system over the reverse-link channel, and provides novel solutions to them.
The first issue is that the available CSI at the receiver has to be quantized to a finite number of bits, sent over a noisy feedback channel, reconstructed at the transmitter, and used by the transmitter for precoding its data symbols. In particular, the CSI quantization technique has to be resilient to errors introduced by the noisy reverse-link channel, and it is of interest to design computationally simple, linear filters to mitigate these errors. The second issue addressed is the design of low latency and low decoding complexity error correction codes to provide protection against fading conditions and noise in the reverse-link channel. The third issue is to improve the resilience of the reverse-link channel to fading.
The solution to the first problem is obtained by proposing two classes of receive filtering techniques, where the output of the source decoder is passed through a filter designed to reduce the overall distortion including the effect of the channel noise. This work combines the high resolution quantization theory and the optimal Minimum Mean Square Error(MMSE) filtering formulation to analyze, and optimize, the total end-to-end distortion. As a result, analytical expressions for the linear receive filters are obtained that minimize the total end-to-end distortion, given the quantization scheme and source(channel state) distribution. The solution to the second problem is obtained by proposing a new family of error correction codes, termed trellis coded block codes, where a trellis code and block code are concatenated in order to provide good coding gain as well as low latency and low complexity decoding. This code construction is made possible due to the existence of a uniform partitioning of linear block codes. The solution to the third problem is obtained by proposing three novel transmit precoding methods that are applicable to time-division-duplex systems, where the channel reciprocity can be exploited in designing the precoding scheme. The proposed precoding methods convert the Rayleigh fading MIMO channel into parallel Additive White Gaussian Noise(AWGN) channels with fixed gain, while satisfying an average transmit power constraint. Moreover, the receiver does not need to have knowledge of the CSI in order to decode the received data. These precoding methods are also extended to Rayleigh fading multi-user MIMO channels.
Finally, all the above methods are applied to the problem of designing a low-rate, low-latency code for the noisy and fading reverse-link channel that is used for sending the CSI. Simulation results are provided to demonstrate the improvement in the forward-link data rate due to the proposed methods. Note that, although the three solutions are presented in the context of CSI feedback in MIMO communications, their development is fairly general in nature, and, consequently, the solutions are potentially applicable in other communication systems also.
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Beamforming and Protection Strategies in Gaussian MISO Wiretap Systems with Partial Channel State InformationEngelmann, Sabrina 29 June 2015 (has links)
Within this thesis, we investigate the possibilities of physical layer secrecy for two special system models. In detail, we study beamforming and protection strategies in the Multiple-Input Single-Output (MISO) Gaussian Wiretap Channel (WTC) and the Gaussian two-hop relay WTC with multiple antennas at transmitter and receiver. In both system models, we examine the influence of partial Channel State Information (CSI) on the link to the eavesdropper and compare the achievable secrecy rates with the case of full CSI.
We show for the MISO WTC that in the fast fading scenario the Beamforming Vector (BV) can be optimized such that the ergodic secrecy rate is maximized with regard to the degree of channel knowledge. Further we show that the ergodic secrecy rate can be significantly increased by usage of Artificial Noise (AN), if applied in a smart way. This means that the degree of channel knowledge on the link to the eavesdropper influences the portion of power that is spent for AN at the transmitter as well as the direction, in which the AN signal is sent. In addition, we apply the same beamforming and protection strategies to the slow fading scenario and find that these techniques also reduce the secrecy outage probability.
For the two-hop relay WTC, we introduce Information Leakage Neutralization (IN) as a new protection strategy. If applied to a system model, where the transmitter has full CSI, the instantaneous secrecy rate performs almost as well as the instantaneous capacity of the peaceful system without an eavesdropper. The IN protected scheme outperforms the AN protected approach and performs much better than any beamforming scheme without additional protection mechanism. Another positive aspect of the IN protected scheme in the case of full CSI is that conventional channel codes can be applied instead of wiretap codes. For the case of partial CSI, where the transmitter has only an outdated estimate on the channel between relay and the eavesdropper, we show that the IN protected scheme can also be applied. Here, it strongly depends on the channel realizations and the delay of the estimate, whether the IN or the AN protection scheme should be applied. / In dieser Arbeit wird das Leistungsvermögen der Sicherheit auf der physikalischen Schicht anhand von zwei speziellen Systemmodellen untersucht. Im Detail werden Beamforming- und Absicherungsstrategien im gaußschen Multiple-Input Single-Output (MISO) Wiretap Channel (WTC) und dem gaußschen Two-hop Relay WTC mit mehreren Antennen am Sender und Empfänger studiert. In beiden Systemmodellen wird der Einfluss von partieller Kanalkenntnis zum Abhörer betrachtet und die so erreichbaren Sicherheitsraten mit denen verglichen, die bei voller Kanalkenntnis erreichbar sind.
Für den MISO WTC kann gezeigt werden, dass für Kanäle mit schnellem Schwund der Beamforming-Vektor in Hinblick auf die ergodische Sicherheitsrate unter Berücksichtigung des Grades der Kanalkenntnis optimiert werden kann. Zudem kann durch die intelligente Verwendung von künstlichem Rauschen (Artificial Noise, AN) die ergodische Sicherheitsrate signifikant erhöht werden. Hierbei nimmt der Grad der Kanalkenntnis direkt Einfluss auf die Aufteilung der Leistung zwischen Daten- und AN-Signal am Sender sowie auch auf die Richtung, in der das AN-Signal gesendet wird. Zudem kann gezeigt werden, dass dieselben Beamforming- und Absicherungsstrategien ebenfalls die Sicherheitsausfallwahrscheinlichkeit für Kanäle mit langsamem Schwund minimieren.
Im gaußschen Two-hop Relay WTC wird Information Leakage Neutralization (IN) als neuartige Absicherungsstrategie eingeführt. Diese Absicherungsstrategie erreicht nahezu dieselben instantanen Raten wie ein friedvolles System ohne Abhörer, wenn es bei voller Kanalkenntnis am Sender eingesetzt wird. Weiterhin sind durch die IN-Absicherungsstrategie höhere Raten erreichbar als durch den Einsatz von AN. Zusätzlich kann im Fall von voller Kanalkenntnis auf den Einsatz von Wiretap-Codes verzichtet werden. Auch im Fall partieller Kanalkenntnis, wo der Sender nur eine veraltete Schätzung des Kanals zwischen Relay und Abhörer besitzt, kann gezeigt werden, dass die IN-Absicherungsstrategie angewendet werden kann. Hierbei hängt es jedoch stark von den Kanalrealisierungen und dem Alter der Kanalschätzung ab, ob die IN- oder die AN-Absicherungsstrategie bessere Ergebnisse bringt und daher angewandt werden sollte.
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Interference Leakage Neutralization in Two-Hop Wiretap Channels with Partial CSIEngelmann, Sabrina, Ho, Zuleita K.-M., Jorswieck, Eduard A. January 2013 (has links)
In this paper, we analyze the four-node relay wiretap channel, where the relay performs amplify-and-forward. There is no direct link between transmitter and receiver available. The transmitter has multiple antennas, which assist in securing the transmission over both phases. In case of full channel state information (CSI), the transmitter can apply information leakage neutralization in order to prevent the eavesdropper from obtaining any information about the signal sent. This gets more challenging, if the transmitter has only an outdated estimate of the channel from the relay to the eavesdropper. For this case, we optimize the worst case secrecy rate by choosing intelligently the beamforming vectors and the power allocation at the transmitter and the relay.
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Authentication Techniques Based on Physical Layer Attributes / Autentisering tekniker baserade på fysiska lager attributLiang, Xintai January 2022 (has links)
Authentication is an indispensable part of information security. It serves to distinguish legitimate users from unauthorized ones. With the rapid growth of Internet of Things (IoT) devices, authentication of wireless communication is gathering more and more attention. Traditional authentication methods using cryptography, such as Hash-based Message Authentication Codes (HMACs) or digital signature, demand significant computational power and hardware resources, especially for low-end platforms. Spoofing attackers take advantage of trust relationships, trying to impersonate legitimate entities the wireless Access Point (AP) trusts. To tackle this issue, physical layer authentication methods are proposed. Using a fast and lightweight implementation, authentication based on physical layer attributes has the chance to improve the security performance of the authentication in the wireless network and protect it from spoofing attacks. It takes advantage of the uniqueness and inimitability of physical layer attributes by using them as identifying information. In this project, one of the physical layer attributes, Channel State Information (CSI), is utilized as the identifying information of devices. CSI samples from different wireless devices are collected by a wireless monitor. Features on amplitude and phase are extracted from raw CSI samples through data processing algorithms. For every device, a corresponding feature profile is pre-built so that authentication can be accomplished by matching the CSI profile. One-Class Support Vector Machine (OCSVM), a machine learning technique, which has a satisfying performance in novel discrimination, is used for profile building and profile matching algorithms so that the physical layer identities from various devices can be distinguished effectively. Our study aims to prove the feasibility of the authentication using CSI identity is conducted and the authentication and spoofer detection accuracy is calculated. With the profile matching algorithm based on OCSVM, the authentication accuracy and the spoofer detection accuracy remains around 98% and 100% respectively. Finally, to address the limitations in related work, such as the phase error fingerprinting which is not effective across all the bands, and the instability of the authentication results, a combined authentication method is designed and implemented successfully. The new method is based on both the traditional cryptographic authentication and CSI-based authentication. The implementation is accomplished by using the data processing methods and discrimination techniques mentioned above. The basic functions, such as detecting CSI variance and switching between CSI and cryptographic authentication, and the CPU computing performance under different authentication modes are observed. The performance of the new method is analyzed and evaluated under different potential attack scenarios. The evaluation shows that the basic functions and defense ability are valid and satisfying under different scenarios. The computing resource saves at least 36.92% and at most 79.73% compared to various traditional cryptographic authentication. / Autentisering är en oumbärlig del av informationssäkerheten, eftersom den särskiljer legitima användare och motståndare i nätverk. Med den snabba tillväxten av trådlösa IoT-enheter får säker autentisering inom trådlös kommunikation mer och mer uppmärksamhet. Traditionell trådlös autentisering metoder har en enorm efterfrågan på beräkningskraft och hårdvaruresurser, samtidigt som de är sårbara för vissa attacker. Spoofing-attack, som drar fördel av pålitliga relationer genom att imitera en person eller organisation som den trådlösa AP litar på, är en av de svåraste säkerheterna problem med trådlös autentisering. För att lösa detta problem föreslås autentiseringsmetoder för fysiska lager. Genom att använda en snabb och lätt implementering har autentiseringen baserad på fysiska lagerattribut möjlighet att förbättra säkerhetsprestandan för autentiseringen i det trådlösa nätverket och skydda den från spoofing attacker. Eftersom det tar fördelen av det unika och oefterhärmlighet av fysiska lagerattribut genom att använda dem som identitetsinformation som ska autentiseras. I detta projekt används ett av attributen för fysiskt lager, CSI som enhetsidentitet för att studera prestandan för trådlös autentisering under det nya överföringsprotokollet 802.11ac.CSI-prov från olika trådlösa enheter samlas in från den trådlösa monitorn. Funktioner på Amplitude och Phase extraheras från råa CSI-prover genom respektive dataförbehandlingsalgoritmer. För varje enhet är en motsvarande funktionsprofil förbyggd så att autentiseringen kan utföras genom att matcha CSI-profilen. Maskininlärningsteknik, OCSVM, som har en tillfredsställande prestanda i den nya diskrimineringen, används i profilbyggande och profilmatchningsalgoritmer så att de fysiska lagrets identiteter från olika enheter effektivt kan särskiljas. En studie syftar till att bevisa genomförbarheten av autentisering med CSI-identitet genomförs och noggrannheten för autentisering och spooferdetektering beräknas. Med profilmatchningsalgoritmen bas ed på OCSVM förblir autentiseringsnoggrannheten och spooferdetekteringsnoggrannheten runt 98% till 99% respektive 100%. Slutligen, med ovanstående metoder och tekniker och övervägandet av begränsningar i relaterat arbete, som fasfelsfingeravtrycksfelet som inte är tillräckligt effektivt över alla band, och instabiliteten i autentiseringsresultaten, ett lättviktigt och flexibelt autentiseringsschema baserat på kombination av traditionell kryptoautentisering och CSI-autentisering designas och implementeras framgångsrikt. Grundfunktionen och datorprestanda observeras och prestandan för den nya metoden analyseras under olika potentiella attackscenarier. Efter experimenten kan datorresurser sparas åtminstone 36,92% och som mest 79,73% jämfört med olika traditionella kryptoautentiseringar. Dessutom är den grundläggande funktionen och försvarsförmågan giltig och tillfredsställande under olika scenarier.
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Scheduling in Wireless Networks with Limited and Imperfect Channel KnowledgeOuyang, Wenzhuo 18 August 2014 (has links)
No description available.
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Opportunistic Scheduling Using Channel Memory in Markov-modeled Wireless NetworksMurugesan, Sugumar 26 October 2010 (has links)
No description available.
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Random matrix theory for advanced communication systems. / Matrices aléatoires pour les futurs systèmes de communicationHoydis, Jakob 05 April 2012 (has links)
Les futurs systèmes de communication mobile sont caractérisés par un déploiement de plus en plus dense de différents types de points d'accès sans fil. Afin d’atténuer les interférences dans ces systèmes, les techniques aux entrées multiples-sorties multiples (MIMO) ainsi que la coopération entre les émetteurs et/ou les récepteurs sont nécessaires. Les systèmes de communication mobile en deviennent plus complexes, ce qui impose une évolution des outils mathématiques permettant leur analyse. Ceux-ci doivent être capables de prendre en compte les caractéristiques les plus importantes du système, telles que l'affaiblissement de propagation, les interférences et l'information imparfaite d'état du canal. Le but de cette thèse est de développer de tels outils basés sur la théorie des grandes matrices aléatoires et de démontrer leur utilité à l'aide de plusieurs applications pratiques, telles que l'analyse des performances des systèmes « network MIMO » et des systèmes MIMO à grande échelle, la conception de détecteurs de faible complexité à expansion polynomiale, l'étude des techniques de précodage unitaire aléatoire, ainsi que l'analyse de canaux à relais multiples et de canaux à double diffusion. En résumé, les méthodes développées dans ce travail fournissent des approximations déterministes de la performance du système qui deviennent exactes en régime asymptotique avec un nombre illimité d'émetteurs et de récepteurs. Cette approche conduit souvent à des approximations de la performance du système étonnamment simples et précises et permet de tirer d’importantes conclusions sur les paramètres les plus pertinents. / Advanced mobile communication systems are characterized by a dense deployment of different types of wireless access points. Since these systems are primarily limited by interference, multiple-input multiple-output (MIMO) techniques as well as coordinated transmission and detection schemes are necessary to mitigate this limitation. Thus, mobile communication systems become more complex which requires that also the mathematical tools for their theoretical analysis must evolve. These must be able to take the most important system characteristics into account, such as fading, path loss, and interference. The aim of this thesis is to develop such tools based on large random matrix theory and to demonstrate their usefulness with the help of several practical applications, such as the performance analysis of network MIMO and large-scale MIMO systems, the design of low-complexity polynomial expansion detectors, and the study of random beamforming techniques as well as multi-hop relay and double-scattering channels. The methods developed in this work provide deterministic approximations of the system performance which become arbitrarily tight in the large system regime with an unlimited number of transmitting and receiving devices. This leads in many cases to simple and close approximations of the finite-size system performance and allows one to draw relevant conclusions about the most significant parameters. One can think of these methods as a way to provide a deterministic abstraction of the physical layer which substantially reduces the system complexity. Due to this complexity reduction, it is possible to carry out a system optimization which would be otherwise intractable.
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Utilizing Channel State Information for Enhancement of Wireless Communication SystemsHeidari, Abdorreza January 2007 (has links)
One of the fundamental limitations of mobile radio
communications is their time-varying fading channel. This
thesis addresses the efficient use of channel state information
to improve the communication systems, with a particular
emphasis on practical issues such as compatibility with the
existing wireless systems and low complexity implementation.
The closed-loop transmit diversity technique is used to improve
the performance of the downlink channel in MIMO communication
systems. For example, the WCDMA standard endorsed by 3GPP
adopts a mode of downlink closed-loop scheme based on partial
channel state information known as mode 1 of
3GPP. Channel state information is fed back
from the mobile unit to the base station through a low-rate
uncoded feedback bit stream. In these closed-loop systems,
feedback error and feedback delay, as well as the sub-optimum
reconstruction of the quantized feedback data, are the usual
sources of deficiency.
In this thesis, we address the efficient reconstruction of the
beamforming weights in the presence of the feedback
imperfections, by exploiting the residual redundancies in the
feedback stream. We propose a number of algorithms for
reconstruction of beamforming weights at the base-station, with
the constraint of a constant transmit power. The issue of the
decoding at the receiver is also addressed. In one of the
proposed algorithms, channel fading prediction is utilized to
combat the feedback delay. We introduce the concept of Blind
Antenna Verification which can substitute the conventional
Antenna Weight Verification process without the need for any
training data. The closed-loop mode 1 of 3GPP is used as a
benchmark, and the performance is examined within a WCDMA
simulation framework. It is demonstrated that the proposed
algorithms have substantial gain over the conventional method
at all mobile speeds, and are suitable for the implementation
in practice. The proposed approach is applicable to other
closed-loop schemes as well.
The problem of (long-range) prediction of the fading channel is
also considered, which is a key element for many
fading-compensation techniques. A linear approach, usually used
to model the time evolution of the fading process, does not
perform well for long-range prediction applications. We propose
an adaptive algorithm using a state-space approach for the
fading process based on the sum-sinusoidal model. Also to
enhance the widely-used linear approach, we propose a tracking
method for a multi-step linear predictor. Comparing the two
methods in our simulations shows that the proposed algorithm
significantly outperforms the linear method, for both
stationary and non-stationary fading processes, especially for
long-range predictions. The robust structure, as well as the
reasonable computational complexity, makes the proposed
algorithm appealing for practical applications.
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Utilizing Channel State Information for Enhancement of Wireless Communication SystemsHeidari, Abdorreza January 2007 (has links)
One of the fundamental limitations of mobile radio
communications is their time-varying fading channel. This
thesis addresses the efficient use of channel state information
to improve the communication systems, with a particular
emphasis on practical issues such as compatibility with the
existing wireless systems and low complexity implementation.
The closed-loop transmit diversity technique is used to improve
the performance of the downlink channel in MIMO communication
systems. For example, the WCDMA standard endorsed by 3GPP
adopts a mode of downlink closed-loop scheme based on partial
channel state information known as mode 1 of
3GPP. Channel state information is fed back
from the mobile unit to the base station through a low-rate
uncoded feedback bit stream. In these closed-loop systems,
feedback error and feedback delay, as well as the sub-optimum
reconstruction of the quantized feedback data, are the usual
sources of deficiency.
In this thesis, we address the efficient reconstruction of the
beamforming weights in the presence of the feedback
imperfections, by exploiting the residual redundancies in the
feedback stream. We propose a number of algorithms for
reconstruction of beamforming weights at the base-station, with
the constraint of a constant transmit power. The issue of the
decoding at the receiver is also addressed. In one of the
proposed algorithms, channel fading prediction is utilized to
combat the feedback delay. We introduce the concept of Blind
Antenna Verification which can substitute the conventional
Antenna Weight Verification process without the need for any
training data. The closed-loop mode 1 of 3GPP is used as a
benchmark, and the performance is examined within a WCDMA
simulation framework. It is demonstrated that the proposed
algorithms have substantial gain over the conventional method
at all mobile speeds, and are suitable for the implementation
in practice. The proposed approach is applicable to other
closed-loop schemes as well.
The problem of (long-range) prediction of the fading channel is
also considered, which is a key element for many
fading-compensation techniques. A linear approach, usually used
to model the time evolution of the fading process, does not
perform well for long-range prediction applications. We propose
an adaptive algorithm using a state-space approach for the
fading process based on the sum-sinusoidal model. Also to
enhance the widely-used linear approach, we propose a tracking
method for a multi-step linear predictor. Comparing the two
methods in our simulations shows that the proposed algorithm
significantly outperforms the linear method, for both
stationary and non-stationary fading processes, especially for
long-range predictions. The robust structure, as well as the
reasonable computational complexity, makes the proposed
algorithm appealing for practical applications.
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Robust Precoder And Transceiver Optimization In Multiuser Multi-Antenna SystemsUbaidulla, P 09 1900 (has links) (PDF)
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.
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