16 research outputs found

    Coordinated Beamforming with Relaxed Zero Forcing: The Sequential Orthogonal Projection Combining Method and Rate Control

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    In this paper, coordinated beamforming based on relaxed zero forcing (RZF) for K transmitter-receiver pair multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) interference channels is considered. In the RZF coordinated beamforming, conventional zero-forcing interference leakage constraints are relaxed so that some predetermined interference leakage to undesired receivers is allowed in order to increase the beam design space for larger rates than those of the zero-forcing (ZF) scheme or to make beam design feasible when ZF is impossible. In the MISO case, it is shown that the rate-maximizing beam vector under the RZF framework for a given set of interference leakage levels can be obtained by sequential orthogonal projection combining (SOPC). Based on this, exact and approximate closed-form solutions are provided in two-user and three-user cases, respectively, and an efficient beam design algorithm for RZF coordinated beamforming is provided in general cases. Furthermore, the rate control problem under the RZF framework is considered. A centralized approach and a distributed heuristic approach are proposed to control the position of the designed rate-tuple in the achievable rate region. Finally, the RZF framework is extended to MIMO interference channels by deriving a new lower bound on the rate of each user.Comment: Lemma 1 proof corrected; a new SOPC algorithm invented; K > N case considere

    Advanced Signal Processing Techniques for Two-Way Relaying Networks and Full-Duplex Communication Systems

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    Sehr hohe Datenraten und ständig verfügbare Netzabdeckung in zukünftigen drahtlosen Netzwerken erfordern neue Algorithmen auf der physischen Schicht. Die Nutzung von Relais stellt ein vielversprechendes Verfahren dar, da die Netzabdeckung gesteigert werden kann. Zusätzlich steht hierdurch im Vergleich zu Kupfer- oder Glasfaserleitungen eine preiswerte Lösung zur Anbindung an die Netzinfrastruktur zur Verfügung. Traditionelle Einwege-Relais-Techniken (One-Way Relaying [OWR]) nutzen Halbduplex-Verfahren (HD-Verfahren), welche das Übertragungssystem ausbremst und zu spektralen Verlusten führt. Einerseits erlauben es Zweiwege-Relais-Techniken (Two-Way Relaying [TWR]), simultan sowohl an das Relais zu senden als auch von diesem zu empfangen, wodurch im Vergleich zu OWR das Spektrum effizienter genutzt wird. Aus diesem Grunde untersuchen wir Zweiwege-Relais und im Speziellen TWR-Systeme für den Mehrpaar-/Mehrnutzer-Betrieb unter Nutzung von Amplify-and-forward-Relais (AF-Relais). Derartige Szenarien leiden unter Interferenzen zwischen Paaren bzw. zwischen Nutzern. Um diesen Interferenzen Herr zu werden, werden hochentwickelte Signalverarbeitungsalgorithmen – oder in anderen Worten räumliche Mehrfachzugriffsverfahren (Spatial Division Multiple Access [SDMA]) – benötigt. Andererseits kann der spektrale Verlust durch den HD-Betrieb auch kompensiert werden, wenn das Relais im Vollduplexbetrieb arbeitet. Nichtsdestotrotz ist ein FD-Gerät in der Praxis aufgrund starker interner Selbstinterferenz (SI) und begrenztem Dynamikumfang des Tranceivers schwer zu realisieren. Aus diesem Grunde sollten fortschrittliche Verfahren zur SI-Ünterdrückung entwickelt werden. Diese Dissertation trägt diesen beiden Zielen Rechnung, indem optimale und/oder effiziente algebraische Lösungen entwickelt werden, welche verschiedenen Nutzenfunktionen, wie Summenrate und minimale Sendeleistung, maximieren.Im ersten Teil studieren wir zunächst Mehrpaar-TWR-Netzwerke mit einem einzelnen Mehrantennen-AF-Relais. Dieser Anwendungsfall kann auch so betrachtet werden, dass sich mehrere verschiedene Dienstoperatoren Relais und Spektrum teilen, wobei verschiedene Nutzerpaare zu verschiedenen Dienstoperatoren gehören. Aktuelle Ansätzen zielen auf Interferenzunterdrückung ab. Wir schlagen ein auf Projektion basiertes Verfahren zur Trennung mehrerer Dienstoperatoren (projection based separation of multiple operators [ProBaSeMO]) vor. ProBaSeMO ist leicht anpassbar für den Fall, dass jeder Nutzer mehrere Antennen besitzt oder unterschiedliche Systemdesignkriterien angewendet werden müssen. Als Bewertungsmaßstab für ProBaSeMO entwickeln wir optimale Algorithmen zur Maximierung der Summenrate, zur Minimierung der Sendeleistung am Relais oder zur Maximierung des minimalen Signal-zu-Interferenz-und-Rausch-Verhältnisses (Signal to Interference and Noise Ratio [SINR]) am Nutzer. Zur Maximierung der Summenrate wurden spezifische gradientenbasierte Methoden entwickelt, die unabhängig davon sind, ob ein Nutzer mit einer oder mehr Antennen ausgestattet ist. Um im Falle eines „Worst-Case“ immer noch eine polynomielle Laufzeit zu garantieren, entwickelten wir einen Algorithmus mit polynomieller Laufzeit. Dieser ist inspiriert von der „Polynomial Time Difference of Convex Functions“-Methode (POTDC-Methode). Bezüglich der Summenrate des Systems untersuchen wir zuletzt, welche Bedingungen erfüllt sein müssen, um einen Gewinn durch gemeinsames Nutzen zu erhalten. Hiernach untersuchen wir die Maximierung der Summenrate eines Mehrpaar-TWR-Netzwerkes mit mehreren Einantennen-AF-Relais und Einantennen-Nutzern. Das daraus resultierende Problem der Summenraten-Maximierung, gebunden an eine bestimmte Gesamtsendeleistung aller Relais im Netzwerk, ist ähnlich dem des vorangegangenen Szenarios. Dementsprechend kann eine optimale Lösung für das eine Szenario auch für das jeweils andere Szenario genutzt werden. Weiterhin werden basierend auf dem Polynomialzeitalgorithmus global optimale Lösungen entwickelt. Diese Lösungen sind entweder an eine maximale Gesamtsendeleistung aller Relais oder an eine maximale Sendeleistung jedes einzelnen Relais gebunden. Zusätzlich entwickeln wir suboptimale Lösungen, die effizient in ihrer Laufzeit sind und eine Approximation der optimalen Lösung darstellen. Hiernach verlegen wir unser Augenmerk auf ein Mehrpaar-TWR-Netzwerk mit mehreren Mehrantennen-AF-Relais und mehreren Repeatern. Solch ein Szenario ist allgemeiner, da die vorherigen beiden Szenarien als spezielle Realisierungen dieses Szenarios aufgefasst werden können. Das Interferenz-Management in diesem Szenario ist herausfordernder aufgrund der vorhandenen Repeater. Interferenzneutralisierung (IN) stellt eine Lösung dar, um diese Art Interferenz zu handhaben. Im Zuge dessen werden notwendige und ausreichende Bedingungen zur Aufhebung der Interferenz hergeleitet. Weiterhin wird ein Framework entwickelt, dass verschiedene Systemnutzenfunktionen optimiert, wobei IN im jeweiligen Netzwerk vorhanden sein kann oder auch nicht. Dies ist unabhängig davon, ob die Relais einer maximalen Gesamtsendeleistung oder einer individuellen maximalen Sendeleistung unterliegen. Letztendlich entwickeln wir ein Übertragungsverfahren sowie ein Vorkodier- und Dekodierverfahren für Basisstationen (BS) in einem TWR-assistierten Mehrbenutzer-MIMO-Downlink-Kanal. Im Vergleich mit dem Mehrpaar-TWR-Netzwerk leidet dieses Szenario unter Interferenzen zwischen den Kanälen. Wir entwickeln drei suboptimale Algorithmen, welche auf Kanalinversion basieren. ProBaSeMO und „Zero-Forcing Dirty Paper Coding“ (ZFDPC), welche eine geringe Zeitkomplexität aufweisen, schaffen eine Balance zwischen Leistungsfähigkeit und Komplexität. Zusätzlich gibt es jeweils nur geringe Einbrüche in stark beanspruchten Kommunikationssystemen.Im zweiten Teil untersuchen wir Techniken zur SI-Unterdrückung, um den FD-Gewinn in einem Punkt-zu-Punkt-System auszunutzen. Zunächst entwickeln wir ein Übertragungsverfahren, dass auf SI Rücksicht nimmt und die SI-Unterdrückung gegen den Multiplexgewinn abwägt. Die besten Ergebnisse werden durch die perfekte Kenntnis des Kanals erzielt, was praktisch nicht genau der Fall ist. Aus diesem Grund werden Übertragungstechniken für den „Worst Case“ entwickelt, die den Kanalschätzfehlern Rechnung tragen. Diese Fehler werden deterministisch modelliert und durch Ellipsoide beschränkt. In praktischen Szenarien ist der HF-Schaltkreise nicht perfekt. Dies hat Einfluss auf die Verfahren zur SI-Unterdrückung und führt zu einer Restselbstinterferenz. Wir entwickeln effiziente Übertragungstechniken mittels Beamforming, welche auf dem Signal-zu-Verlust-und-Rausch-Verhältnis (signal to leakage plus noise ratio [SLNR]) aufbauen, um Unvollkommenheiten der HF-Schaltkreise auszugleichen. Zusätzlich können alle Designkonzepte auf FD-OWR-Systeme erweitert werden.To enable ultra-high data rate and ubiquitous coverage in future wireless networks, new physical layer techniques are desired. Relaying is a promising technique for future wireless networks since it can boost the coverage and can provide low cost wireless backhauling solutions, as compared to traditional wired backhauling solutions via fiber and copper. Traditional one-way relaying (OWR) techniques suffer from the spectral loss due to the half-duplex (HD) operation at the relay. On one hand, two-way relaying (TWR) allows the communication partners to transmit to and/or receive from the relay simultaneously and thus uses the spectrum more efficiently than OWR. Therefore, we study two-way relays and more specifically multi-pair/multi-user TWR systems with amplify-and-forward (AF) relays. These scenarios suffer from inter-pair or inter-user interference. To deal with the interference, advanced signal processing algorithms, in other words, spatial division multiple access (SDMA) techniques, are desired. On the other hand, if the relay is a full-duplex (FD) relay, the spectral loss due to a HD operation can also be compensated. However, in practice, a FD device is hard to realize due to the strong loop-back self-interference and the limited dynamic range at the transceiver. Thus, advanced self-interference suppression techniques should be developed. This thesis contributes to the two goals by developing optimal and/or efficient algebraic solutions for different scenarios subject to different utility functions of the system, e.g., sum rate maximization and transmit power minimization. In the first part of this thesis, we first study a multi-pair TWR network with a multi-antenna AF relay. This scenario can be also treated as the sharing of the relay and the spectrum among multiple operators assuming that different pairs of users belong to different operators. Existing approaches focus on interference suppression. We propose a projection based separation of multiple operators (ProBaSeMO) scheme, which can be easily extended when each user has multiple antennas or when different system design criteria are applied. To benchmark the ProBaSeMO scheme, we develop optimal relay transmit strategies to maximize the system sum rate, minimize the required transmit power at the relay, or maximize the minimum signal to interference plus noise ratio (SINR) of the users. Specifically for the sum rate maximization problem, gradient based methods are developed regardless whether each user has a single antenna or multiple antennas. To guarantee a worst-case polynomial time solution, we also develop a polynomial time algorithm which has been inspired by the polynomial time difference of convex functions (POTDC) method. Finally, we analyze the conditions for obtaining the sharing gain in terms of the sum rate. Then we study the sum rate maximization problem of a multi-pair TWR network with multiple single antenna AF relays and single antenna users. The resulting sum rate maximization problem, subject to a total transmit power constraint of the relays in the network, yields a similar problem structure as in the previous scenario. Therefore the optimal solution for one scenario can be used for the other. Moreover, a global optimal solution, which is based on the polyblock approach, and several suboptimal solutions, which are more computationally efficient and approximate the optimal solution, are developed when there is a total transmit power constraint of the relays in the network or each relay has its own transmit power constraint. We then shift our focus to a multi-pair TWR network with multiple multi-antenna AF relays and multiple dumb repeaters. This scenario is more general because the previous two scenarios can be seen as special realizations of this scenario. The interference management in this scenario is more challenging due to the existence of the repeaters. Interference neutralization (IN) is a solution for dealing with this kind of interference. Thereby, necessary and sufficient conditions for neutralizing the interference are derived. Moreover, a general framework to optimize different system utility functions in this network with or without IN is developed regardless whether the AF relays in the network have a total transmit power limit or individual transmit power limits. Finally, we develop the relay transmit strategy as well as base station (BS) precoding and decoding schemes for a TWR assisted multi-user MIMO (MU-MIMO) downlink channel. Compared to the multi-pair TWR network, this scenario suffers from the co-channel interference. We develop three suboptimal algorithms which are based on channel inversion, ProBaSeMO and zero-forcing dirty paper coding (ZFDPC), which has a low computational complexity, provides a balance between the performance and the complexity, and suffers only a little when the system is heavily loaded, respectively.In the second part of this thesis, we investigate self-interference (SI) suppression techniques to exploit the FD gain for a point-to-point MIMO system. We first develop SI aware transmit strategies, which provide a balance between the SI suppression and the multiplexing gain of the system. To get the best performance, perfect channel state information (CSI) is needed, which is imperfect in practice. Thus, worst case transmit strategies to combat the imperfect CSI are developed, where the CSI errors are modeled deterministically and bounded by ellipsoids. In real word applications, the RF chain is imperfect. This affects the performance of the SI suppression techniques and thus results in residual SI. We develop efficient transmit beamforming techniques, which are based on the signal to leakage plus noise ratio (SLNR) criterion, to deal with the imperfections in the RF chain. All the proposed design concepts can be extended to FD OWR systems

    Multiantenna Downlink Interference Management for Next Generation Mobile Networks

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    Department of Electrical EngineeringIn downlink multi-input single-output (MISO) networks, achieving optimal sum-rate with limited channel state information (CSI) is still a challenge even with a single user per cell. In this dissertation, three cooperative downlink multicell MISO beamforming schemes are proposed with highly limited information exchange among the base stations (BSs) to maximize the sum-rate. In the proposed schemes, each BS can design its beamforming vector with only local CSI based on limited information exchange on CSI. Unlike previous studies, the proposed beamforming designs are non-iterative and do not require any vector or matrix feedback but require only quantized scalar information. In the first work, the beamforming vector at each BS is designed to minimize the sum of its weighted generating-interference (WGI) with local CSI and the aid of information exchange between the BSs. The generating-interference weight coefficients are designed in pursuit of increasing the sum-rate. Simulation results show that the proposed scheme outperforms the existing scheme in the mid to high signal-to-noise ratio (SNR) regime even with much reduced amount of information exchange via backhaul. In the second work, the proposed beamforming design is based on the combination of the maximization of weighted signal-to-leakage-plus-noise ratio (WSLNR) and WGI. The weights in WSLNR and WGI are designed via choosing a proper set of users who shall be interference-free, which has never been endeavored in the literature. Though there have been extensive studies on downlink multicell beamforming, the proposed scheme closely achieves the optimal sum-rate bound in almost all SNR regime based on non-iterative optimization with lower amount of information exchange than existing schemes, which is justified by numerical simulations. In addition, the proposed scheme achieves a better trade-off between the amount of the information exchange and the sum-rate than existing schemes. In the third work, a beamforming vector design based on a deep neural network (DNN) is proposed for multicell multi-input single-output channels with scalar information exchange and local CSI. The beamforming vectors are designed making zero generating-interference to the selected interference-free users (IFUs). The set of IFUs is chosen from the DNN based on supervised learning where the inputs can be obtained with only local CSI and limited scalar information exchange. Simulation results show that the DNN is well-trained in estimating the unknown CSI from the inputs with only local CSI in multicell networks.clos

    Energy-aware resource allocation in next generation wireless networks : application in large-scale MIMO Systems

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    In this thesis, we investigate the resource allocation problem for wireless networks that incorporate large-scale multiple-input multiple-output (MIMO) systems. These systems are considered as key technologies for future 5G wireless networks and are based on using few hundreds of antennas simultaneously to serve tens of users in the same time-frequency resource. The gains obtained by large-scale MIMO systems cannot be fully exploited without adequate resource allocation strategies. Hence, the aim of this thesis is to develop energy-aware resource allocation solutions for large-scale MIMO systems that take into consideration network power cost. Firstly, this thesis investigates the downlink of a base station equipped with large-scale MIMO system while taking into account a non-negligible transmit circuit power consumption. This consumption involves that activating all RF chains does not always necessarily achieve the maximum sum-rate. Thus, we derive the optimal number of activated RF chains. In addition, efficient antenna selection, user scheduling and power allocation algorithms in term of instantaneous sum-rate are proposed and compared. Also, fairness is investigated by considering equal receive power among users. Secondly, this thesis investigates a large-scale MIMO system that incorporates energy harvesting that is a promising key technology for greening future wireless networks since it reduces network operation costs and carbon footprints. Hence, we consider distributed large-scale MIMO systems made up of a set of remote radio heads (RRHs), each of which is powered by both an independent energy harvesting source and the grid. The grid energy source allows to compensate for the randomness and intermittency of the harvested energy. Optimal on-line and off-line energy management strategies are developed. In addition, on-line energy management algorithm based on energy prediction is devised. The feasibility problem is addressed by proposing an efficient link removal algorithm and for better energy efficiency, RRH on/off operation is investigated. Thirdly, wireless backhauling was proposed as an alternative solution that enable low-cost connection between the small base stations and the macro base station in heterogeneous networks (HetNets). The coexistence of massive MIMO, HetNets and wireless backhauling is a promising research direction since massive MIMO is a suitable solution to enable wireless backhauling. Thus, we propose a new transmission technique that is able to efficiently manage the interference in heterogeneous networks with massive MIMO wireless backhaul. The optimal time splitting parameter and the allocated transmit power are derived. The proposed transmission technique is shown to be more efficient in terms of transmit power consumption than the conventional reverse time division duplex with bandwidth splitting. In this thesis, we developed efficient resource allocation solutions related to system power for wireless networks that incorporate large-scale MIMO systems under different assumptions and network architectures. The results in this thesis can be expanded by investigating the research problems given at the end of the dissertation

    D 3. 3 Final performance results and consolidated view on the most promising multi -node/multi -antenna transmission technologies

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    This document provides the most recent updates on the technical contributions and research challenges focused in WP3. Each Technology Component (TeC) has been evaluated under possible uniform assessment framework of WP3 which is based on the simulation guidelines of WP6. The performance assessment is supported by the simulation results which are in their mature and stable state. An update on the Most Promising Technology Approaches (MPTAs) and their associated TeCs is the main focus of this document. Based on the input of all the TeCs in WP3, a consolidated view of WP3 on the role of multinode/multi-antenna transmission technologies in 5G systems has also been provided. This consolidated view is further supported in this document by the presentation of the impact of MPTAs on METIS scenarios and the addressed METIS goals.Aziz, D.; Baracca, P.; De Carvalho, E.; Fantini, R.; Rajatheva, N.; Popovski, P.; Sørensen, JH.... (2015). D 3. 3 Final performance results and consolidated view on the most promising multi -node/multi -antenna transmission technologies. http://hdl.handle.net/10251/7675

    Performance Analysis of Directional Modulation With Finite-Quantized RF Phase Shifters in Analog Beamforming Structure

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    The radio frequency (RF) phase shifter with finite quantization bits in analog beamforming (AB) structure forms quantization error (QE) and causes a performance loss of received signal to interference plus noise ratio (SINR) at the receiver (called Bob). By using the law of large numbers in probability theory, the closed-form expression of the SINR performance loss is derived to be inversely proportional to the square of Sinc (or sin(x)/x) function. Here, a phase alignment method is applied in the directional modulation transmitter with the AB structure. Also, the secrecy rate (SR) expression is derived with the QE. From the numerical simulation results, we find that the SINR performance loss gradually decreases as the number L of quantization bits increases. This loss is less than 0.3 dB when L is larger than or equal to three. As L exceeds five, the SINR performance loss at Bob can be approximately trivial. Similarly, the SR performance loss gradually reduces as L increases. In particular, the SR performance loss is about 0.1 bits/s/Hz for L = 3 at signal-to-noise ratio of 15 dB

    Alocação de recursos para sistemas móveis multi-utilizador e multi-antena

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    Doutoramento em Engenharia ElectrotécnicaThe thesis addresses the sum rate or spectral e ciency maximization problem in cellular systems with two main components, multiple antennas and multiple users. In order to solve such a problem, several resource allocation techniques are studied and developed for di erent cellular scenarios. The antennas at the transmitters are arranged in several con gurations, i.e., co-located or distributed and for such arrangements di erent levels of coordination and cooperation between transmitters are investigated. Accounting for more receiver antennas than transmitter antennas implies that system optimization must select the best transmitter-receiver match (combinatorial problem) which can be solved with di erent degrees of cooperation between transmitters. The system models studied can be classi ed either as interference limited or as power limited systems. In interference limited systems the resource allocation is carried out independently by each transmitter which yield power leakage to unintended receivers. For this kind of systems, the access network using distributed antenna architectures is examined. The properties of distributed antenna in cellular systems as well as the gains they provide in terms of frequency reuse and throughput are assessed. Accounting for multiple user scenarios, several techniques and algorithms for transmitter-receiver assignment, power allocation, and rate allocation are developed in order to maximize the spectral e ciency. In power limited systems the transmitters jointly allocate resources among transmit and receive antennas. The transmitters are equipped with multiple antennas and signal processing is implemented in order to suppress inter-user interference. Single-cell and multi-cell systems are studied and the problem of sum rate maximization is tackled by decoupling the user selection and the resource allocation (power and precoding) processes. The user selection is a function of the type of precoding technique that is implemented and the level of information that can be processed at the transmitter. The developed user selection algorithms exploit information provided by novel channel metrics which establish the spatial compatibility between users. Each metric provides a di erent trade-o between the accuracy to identify compatible users, and the complexity required to compute it. Numerical simulations are used to assess the performance of the proposed user selection techniques (metrics and algorithms) whose performance are compared to state-of-the-art techniques.Esta tese descreve o problema da maximização da taxa de transmissão ou e ciência espectral em sistemas moveis tomando em atenção duas características fundamentais destes, o número de antenas e utilizadores. A fim de resolver este tipo de problema, várias técnicas de alocação de recursos foram estudadas e propostas para diferentes cenários. As antenas nos transmissores estão organizadas em diferentes configurações, podendo ser localizadas ou distribuídas e para estes esquemas, diferentes níveis de cooperação e coordenação entre transmissores foram investigados. Assumindo mais antenas receptoras do que antenas transmissoras, implica que a otimização do sistema seleccione as melhores combinações de transmissor-receptor (problema combinatório), o que pode ser concretizado usando diferentes graus de cooperação entre transmissores. Os modelos de sistemas estudados, podem ser classificados como sistemas limitados por interferência ou sistemas limitados por potência. Em sistemas limitados por interferência a alocação de recursos e feita independentemente para cada transmissor o que resulta em perda de energia para os receptores não tomados em consideração. Para este tipo de sistemas, e considerado o caso em que a rede de acesso e constituída por antenas distribuídas. Os ganhos obtidos devido ao uso de antenas distribuídas, quer em termos do planeamento de frequências quer da maximização da taxa de transmissão são considerados. Assumindo esquemas multi-utilizador, várias técnicas e algoritmos de transmissão-recepção, alocação de potência e de taxa de transmissão foram desenvolvidos para maximizar a e ciência espectral. Para sistemas limitados em potência os transmissores alocam os recursos quer de antenas de transmissão quer de recepção conjuntamente. Os transmissores estão equipados com várias antenas e o processamento de sinal e implementado de modo a eliminar a interferência entre utilizadores. Sistemas de célula única e de múltiplas células foram estudados. Para estes foi considerado o problema da maximização de taxa de transmissão o qual foi resolvido heuristicamente, através do desacoplamento do problema em duas partes, uma onde se efectua a seleção de utilizadores e outra onde se considera a alocação de recursos. A seleção de utilizadores e feita em função do tipo de técnicas de pré-codificação implementadas e do nível de informação que o transmissor possui. Os algoritmos de seleção de utilizadores desenvolvidos verificam a compatibilidade espacial entre utilizadores, usando para tal métricas propostas. Cada uma das métricas oferece um trade-off diferente entre a precisão para identificar um utilizador compatível e a complexidade necessária para a implementar. Foram usadas simulações numéricas para avaliar a performance das técnicas de seleção de utilizadores propostas (métricas e algoritmos), performance que foi comparada com as técnicas mais inovadoras

    Joint beamforming design for secure RIS-assisted IoT networks

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    This paper studies secure communication in an internet-of-things (IoT) network, where the confidential signal is sent by an active refracting reconfigurable intelligent surface (RIS)-based transmitter, and a passive reflective RIS is utilized to improve the secrecy performance of users in the presence of multiple eavesdroppers. Specifically, we aim to maximize the weighted sum secrecy rate by jointly designing the power allocation, transmit beamforming (BF) of the refracting RIS, and the phase shifts of the reflective RIS. To solve the non-convex optimization problem, we propose a linearization method to approximate the objective function into a linear form. Then, an alternating optimization (AO) scheme is proposed to jointly optimize the power allocation factors, BF vector and phase shifts, where the first one is found using the Lagrange dual method, while the latter two are obtained by utilizing the penalty dual decomposition method. Moreover, considering the demands of green and secure communications, by applying the Dinkelbach’s method, we extend our proposed scheme to solving a secrecy energy maximization problem. Finally, simulation results demonstrate the effectiveness of the proposed design
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