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

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

Design and optimization for wireless-powered networks

Wireless Power Transfer (WPT) opens an emerging area of Wireless-Powered Networks (WPNs). In narrowband WPNs, beamforming is recognized as a key technique for enhancing information and energy transfer. However, in multi-antenna multi-sine WPT systems, not only the beamforming gain but also the rectifier nonlinearity can be exploited by a waveform design to boost the end-to-end power transfer efficiency. This thesis proposes and optimizes novel transmission strategies for two types of WPNs: narrowband autonomous relay networks and multi-antenna multi-sine WPT systems. The thesis starts by proposing a novel Energy Flow-Assisted (EFA) relaying strategy for a one-way multi-antenna Amplify-and-Forward (AF) autonomous relay network. In contrast to state-of-the-art autonomous relaying strategies, the EFA enables the relay to simultaneously harvest power from source information signals and a dedicated Energy Flow (EF) from the destination for forwarding. As a baseline, a Non-EFA (NEFA) strategy, where the relay splits power from the source signals, is also investigated. We optimize relay strategies for EFA and NEFA, so as to maximize the end-to-end rate and gain insights into the benefit of the EF. To transmit multiple data streams, we extend the EFA and the NEFA to a Multiple-Input Multiple-Output (MIMO) relay network. A novel iterative algorithm is developed to jointly optimize source precoders and relay matrices for the EFA and the NEFA, in order to maximize the end-to-end rate. Based on a channel diagonalization method, we also propose less complex EFA and NEFA algorithms. In the study of waveform designs for multi-antenna multi-sine WPT, large-scale designs with many sinewaves and transmit antennas, computationally tractable algorithms and optimal multiuser waveforms remain open challenges. To tackle these issues, we propose efficient waveform optimization algorithms to maximize the multiuser weighted-sum/minimum rectenna DC output voltage, assuming perfect Channel State Information at the Transmitter (CSIT). An optimization framework is developed to derive these waveform algorithms. Relaxing the assumption on CSIT, we propose waveform strategies for multi-antenna multi-sine WPT based on waveform selection (WS) and waveform refinement (WR), respectively. Applying the strategies, an energy transmitter can generate preferred waveforms for WPT from predesigned codebooks of waveform precoders, according to limited feedback from an energy receiver, which carries information on the harvested energy. Although the WR-based strategy is suboptimal for maximizing the average rectenna output voltage, it causes a lower overhead than the WS-based strategy. We propose novel algorithms to optimize the codebooks for the two strategies.Open Acces

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

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

Linear Transmit-Receive Strategies for Multi-user MIMO Wireless Communications

Die Notwendigkeit zur Unterdrueckung von Interferenzen auf der einen Seite und zur Ausnutzung der durch Mehrfachzugriffsverfahren erzielbaren Gewinne auf der anderen Seite rueckte die raeumlichen Mehrfachzugriffsverfahren (Space Division Multiple Access, SDMA) in den Fokus der Forschung. Ein Vertreter der raeumlichen Mehrfachzugriffsverfahren, die lineare Vorkodierung, fand aufgrund steigender Anzahl an Nutzern und Antennen in heutigen und zukuenftigen Mobilkommunikationssystemen besondere Beachtung, da diese Verfahren das Design von Algorithmen zur Vorcodierung vereinfachen. Aus diesem Grund leistet diese Dissertation einen Beitrag zur Entwicklung linearer Sende- und Empfangstechniken fuer MIMO-Technologie mit mehreren Nutzern. Zunaechst stellen wir ein Framework zur Approximation des Datendurchsatzes in Broadcast-MIMO-Kanaelen mit mehreren Nutzern vor. In diesem Framework nehmen wir das lineare Vorkodierverfahren regularisierte Blockdiagonalisierung (RBD) an. Durch den Vergleich von Dirty Paper Coding (DPC) und linearen Vorkodieralgorithmen (z.B. Zero Forcing (ZF) und Blockdiagonalisierung (BD)) ist es uns moeglich, untere und obere Schranken fuer den Unterschied bezueglich Datenraten und bezueglich Leistung zwischen beiden anzugeben. Im Weiteren entwickeln wir einen Algorithmus fuer koordiniertes Beamforming (Coordinated Beamforming, CBF), dessen Loesung sich in geschlossener Form angeben laesst. Dieser CBF-Algorithmus basiert auf der SeDJoCo-Transformation und loest bisher vorhandene Probleme im Bereich CBF. Im Anschluss schlagen wir einen iterativen CBF-Algorithmus namens FlexCoBF (flexible coordinated beamforming) fuer MIMO-Broadcast-Kanaele mit mehreren Nutzern vor. Im Vergleich mit bis dato existierenden iterativen CBF-Algorithmen kann als vielversprechendster Vorteil die freie Wahl der linearen Sende- und Empfangsstrategie herausgestellt werden. Das heisst, jede existierende Methode der linearen Vorkodierung kann als Sendestrategie genutzt werden, waehrend die Strategie zum Empfangsbeamforming frei aus MRC oder MMSE gewaehlt werden darf. Im Hinblick auf Szenarien, in denen Mobilfunkzellen in Clustern zusammengefasst sind, erweitern wir FlexCoBF noch weiter. Hier wurde das Konzept der koordinierten Mehrpunktverbindung (Coordinated Multipoint (CoMP) transmission) integriert. Zuletzt stellen wir drei Moeglichkeiten vor, Kanalzustandsinformationen (Channel State Information, CSI) unter verschiedenen Kanalumstaenden zu erlangen. Die Qualitaet der Kanalzustandsinformationen hat einen starken Einfluss auf die Guete des Uebertragungssystems. Die durch unsere neuen Algorithmen erzielten Verbesserungen haben wir mittels numerischer Simulationen von Summenraten und Bitfehlerraten belegt.In order to combat interference and exploit large multiplexing gains of the multi-antenna systems, a particular interest in spatial division multiple access (SDMA) techniques has emerged. Linear precoding techniques, as one of the SDMA strategies, have obtained more attention due to the fact that an increasing number of users and antennas involved into the existing and future mobile communication systems requires a simplification of the precoding design. Therefore, this thesis contributes to the design of linear transmit and receive strategies for multi-user MIMO broadcast channels in a single cell and clustered multiple cells. First, we present a throughput approximation framework for multi-user MIMO broadcast channels employing regularized block diagonalization (RBD) linear precoding. Comparing dirty paper coding (DPC) and linear precoding algorithms (e.g., zero forcing (ZF) and block diagonalization (BD)), we further quantify lower and upper bounds of the rate and power offset between them as a function of the system parameters such as the number of users and antennas. Next, we develop a novel closed-form coordinated beamforming (CBF) algorithm (i.e., SeDJoCo based closed-form CBF) to solve the existing open problem of CBF. Our new algorithm can support a MIMO system with an arbitrary number of users and transmit antennas. Moreover, the application of our new algorithm is not only for CBF, but also for blind source separation (BSS), since the same mathematical model has been used in BSS application.Then, we further propose a new iterative CBF algorithm (i.e., flexible coordinated beamforming (FlexCoBF)) for multi-user MIMO broadcast channels. Compared to the existing iterative CBF algorithms, the most promising advantage of our new algorithm is that it provides freedom in the choice of the linear transmit and receive beamforming strategies, i.e., any existing linear precoding method can be chosen as the transmit strategy and the receive beamforming strategy can be flexibly chosen from MRC or MMSE receivers. Considering clustered multiple cell scenarios, we extend the FlexCoBF algorithm further and introduce the concept of the coordinated multipoint (CoMP) transmission. Finally, we present three strategies for channel state information (CSI) acquisition regarding various channel conditions and channel estimation strategies. The CSI knowledge is required at the base station in order to implement SDMA techniques. The quality of the obtained CSI heavily affects the system performance. The performance enhancement achieved by our new strategies has been demonstrated by numerical simulation results in terms of the system sum rate and the bit error rate

MIMO Systems

In recent years, it was realized that the MIMO communication systems seems to be inevitable in accelerated evolution of high data rates applications due to their potential to dramatically increase the spectral efficiency and simultaneously sending individual information to the corresponding users in wireless systems. This book, intends to provide highlights of the current research topics in the field of MIMO system, to offer a snapshot of the recent advances and major issues faced today by the researchers in the MIMO related areas. The book is written by specialists working in universities and research centers all over the world to cover the fundamental principles and main advanced topics on high data rates wireless communications systems over MIMO channels. Moreover, the book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Robust Beamforming Design for Intelligent Reflecting Surface Aided Cognitive Radio Systems with Imperfect Cascaded CSI

In this paper, intelligent reflecting surface (IRS) is introduced to enhance the network performance of cognitive radio (CR) systems. Specifically, we investigate robust beamforming design based on both bounded channel state information (CSI) error model and statistical CSI error model for primary user (PU)-related channels in IRS-aided CR systems. We jointly optimize the transmit precoding (TPC) at the secondary user (SU) transmitter (ST) and phase shifts at the IRS to minimize the ST’s total transmit power subject to the quality of service of SUs, the limited interference imposed on the PU and unit-modulus of the reflective beamforming. The successive convex approximation (SCA) method, Schur’s complement, General sign-definiteness principle, inverse Chi-square distribution and penalty convex-concave procedure are invoked for dealing with these intricate constraints. The non-convex optimization problems are transformed into several convex subproblems and efficient algorithms are proposed. Simulation results verify the efficiency of the proposed algorithms and reveal the impacts of CSI uncertainties on ST’s minimum transmit power and feasibility rate of the optimization problems. Simulation results also show that the number of transmit antennas at the ST and the number of phase shifts at the IRS should be carefully chosen to balance the channel realization feasibility rate and the total transmit power

Quality of service optimization in the Broadcast Channel with Imperfect transmit channel state information

[Resumen]Este trabajo considera un sistema Broadcast Channel (BC) que consiste en un transmisor equipado con múltiples antenas y varios usuarios con una o más antenas. Dependiendo del número de antenas en el lado receptor, tales sistemas son conocidos como Multiple-User Multiple-Input Single-Output (MU-MISO), para usuarios con una única antena, o Multiple-User Multiple-Input Multiple-Output (MU-MIMO), para usuarios con varias antenas. Este modelo es adecuado para sistemas actuales de comunicaciones inalámbricas. Respecto a la dirección del flujo de datos, diferenciamos entre el canal downlink o BC, y canal uplink o Multiple Access Channel (MAC). En el BC las señales se envían desde la estación base a los usuarios, mientras que la información perteneciente a los usuarios es transmitida a la estación base en el MAC. En este trabajo nos centramos en el BC donde la estación base aplica precodificación lineal aprovechando las múltiples antenas. La información sobre el estado del canal se asume perfecta en todos los usuarios. Sin embargo, los usuarios no cooperan, y la estación base solo tiene información de canal parcial obtenida a través de un canal de realimentación en los sistemas Frequency-Division Duplex (FDD), que tiene un ancho de banda limitado. Esta limitación fuerza a los usuarios a aplicar algunos métodos, como quantización, para reducir la cantidad de datos a enviar a la estación base. La combinación de la información proporcionada por los usuarios es interpretada en la estación base como información de canal estocástica, y constituye un factor crítico en el diseño de los precodificadores. En la literatura se han considerado varios métodos para evaluar el rendimiento del BC, a saber, Signal to Interference-plus-Noise Ratio (SINR), Minimum Mean Square Error (MMSE), y tasa. Algunos trabajos calculan las medidas correspondientes para cada usuario mientras que otros consideran la suma de todos ellos como la métrica de interés. En nuestro caso, nos centramos en la tasa como figura de mérito. En particular, estamos interesados en garantizar ciertas tasas por usuario. De esta manera, evitamos situaciones injustas que surgen de utilizar la tasa suma como criterio, en las que a los usuarios con canales pobres se les asignan tasas bajas, o incluso cero. Además, reducir la cantidad de potencia necesaria para satisfacer las restricciones de calidad de servicio mencionadas es una característica deseable en los sistemas de comunicaciones inalámbricas. Así, abordamos el problema de optimización consistente en minimizar la potencia total en el transmisor empleada para cumplir un conjunto de restricciones de calidad de servicio, expresadas como tasas por usuario. Durante los últimos años el problema de minimización de potencia ha sido estudiado ampliamente para información tanto perfecta como imperfecta de canal, en los escenarios BC. Asumir conocimiento de canal perfecto es poco realista y, por tanto, consideramos que los usuarios env´ıan la información de canal a la estación base por medio de un canal de realimentación, normalmente disponible en los est´andares de comunicación recientes. Aunque algunos autores han empleado modelos de incertidumbre limitada para el conocimiento de canal tales como rectangular, elipsoidal, o esférico, y han aprovechado esa asunción para resolver el problema de minimización de potencia, no asumimos una forma particular para esa incertidumbre sino un modelo de error estocástico. En el modelo de sistema considerado, MU-MIMO, el número de antenas en la estación base es mayor que el número de antenas en cada usuario, e.g. MU-MISO. Además, los usuarios no cooperan para separar las señales recibidas. Debido a ésto y a la falta de grados de libertad en los usuarios, es necesario el uso de filtros transmisores, también llamados precodificadores, para eliminar las interferencias entre usuarios. De este modo, en este trabajo diseñamos conjuntamente los precodificadores lineales y los filtros receptores minimizando la potencia total en el transmisor sujeta a restricciones de tasa por usuario. Esta formulación del problema no es convexa y, por tanto, es complicada de manejar. Por este motivo, aplicamos la desigualdad de Jensen a las restricciones de tasa para obtener otras basadas en el MMSE. Como consecuencia, nuestro objetivo es diseñar los precodificadores y filtros que minimizan el MMSE para todos los usuarios. Para ello, distintos tipos de dualidades basadas en SINR,Mean Square Error (MSE), o tasa, han sido empleadas para el diseño de los filtros como fórmulas para intercambiar entre el BC y el MAC por conveniencia. En particular, empleamos la dualidad de MSE con conocimiento de canal imperfecto. Además, para la distribución de potencias, explotamos el marco teórico de las standard Interference Function, planteado para resolver el algoritmo de control de potencia. De esta manera, proponemos un algoritmo para solucionar el problema de minimización de potencia en el BC. Para comprobar la factibilidad de las restricciones de calidad de servicio, proponemos un test que permite determinar si el algoritmo converge o no. Además, el algoritmo propuesto permite resolver el problema dual, ésto es, encontrar los objetivos de tasa balanceados correspondientes a una potencia total en el transmisor. Finalmente, algunas aplicaciones de la minimización de potencia surgen de diferentes escenarios y se resuelven por medio del algoritmo propuesto. Usando el lenguaje de programación MATLAB se simulan experimentos con el objetivo de mostrar el rendimiento de los métodos propuestos.[Resumo]Este traballo considera un sistema Broadcast Channel (BC) que consiste nun transmisor equipado con múltiples antenas e varios usuarios cunha ou máis antenas. Dependendo do número de antenas no lado receptor, tales sistemas son coñecidos como Multiple-User Multiple-Input Single-Output (MU-MISO), para usuarios cunha única antena, ou Multiple-User Multiple-Input Multiple-Output (MU-MIMO), para usuarios con varias antenas. Este modelo é adecuado para sistemas actuais de comunicacións sen fíos. Respecto á dirección do fluxo de datos, diferenciamos entre a canle downlink ou BC, e a canle uplink ou Multiple Access Channel (MAC). No BC os sinais env´ıanse dende a estación base aos usuarios, mentres que a información pertencente aos usuarios é transmitida á estación base no MAC. Neste traballo centrámonos no BC onde a estación base aplica precodificación lineal aproveitando as múltiples antenas. A información sobre o estado da canle asúmese perfecta en todos os usuarios. Por contra, os usuarios non cooperan e a estación base só ten información da canle parcial obtida a través dunha canle de realimentación nos sistemas Frequency-Division Duplex (FDD), que ten un ancho de banda limitado. Esta limitación forza aos usuarios a aplicar algúns métodos, como quantización, para reducir a cantidade de datos que se envían á estación base. A combinación da información proporcionada polos usuarios é interpretada na estación base como información da canle estocástica, e constitúe un factor crítico no deseño dos precodificadores. Na literatura consider´aronse varios métodos para avaliar o rendemento do BC, a saber, Signal to Interference-plus-Noise Ratio (SINR), Minimum Mean Square Error (MMSE), e taxa. Algúns traballos calculan as medidas correspondentes para cada usuario mentres que outros consideran a suma de todos eles como a métrica de interese. No noso caso, centrámonos na taxa como figura de mérito. En particular, estamos interesados en garantir certas taxas por usuario. Deste xeito evitamos situación inxustas que xurdan de utilizar a taxa suma como criterio, nas que aos usuarios con canles pobres se lles asignan tasas baixas, ou incluso cero. Ademais, reducir a cantidade de potencia necesaria para satisfacer as restricci ´ons de calidade de servizo mencionadas ´e unha característica desexable nos sistemas de comunicacións se fíos. Así, acometemos o problema de optimización consistente en minimizar a potencia total no transmisor empregada para cumprir un conxunto de restricións de calidade de servizo, expresadas como taxas por usuario. Durante os últimos anos o problema de minimización de potencia foi estudado amplamente para información tanto perfecta como imperfecta de canle, nos escenarios BC. Asumir coñecemento perfecto de canle é pouco realista e, por tanto, consideramos que os usuarios envían a información de canle á estación base por medio dunha canle de realimentación, normalmente dispoñible nos estándares de comunicación recentes. Aínda que algúns autores empregaron modelos de incerteza limitada para o coñecemento de canle tales como rectangular, elipsoidal, ou esférico, e aproveitaron esa asunción para solucionar o problema de minimización de potencia, non asumimos unha forma particular para esa incerteza sen´on un modelo de error estocástico. No modelo de sistema considerado, MU-MIMO, o número de antenas na estación base é maior que o número de antenas en cada usuario, e.g. MU-MISO. Ademais, os usuarios non cooperan para separar os sinais recibidos. Debido a isto e á falta de graos de liberdade nos usuarios, é preciso o uso de filtros transmisores, tamén chamados precodificadores, para eliminar as interferencias entre usuarios. Deste xeito, neste traballo deseñamos conxuntamente os precodificadores lineais e os filtros receptores minimizando a potencia total no transmisor suxeita a restriccións de taxa por usuario. Esta formulación do problema non é convexa e, por tanto, é complicada de manexar. Por este motivo, aplicamos a desigualdade de Jensen ´as restriccións de taxa para obter outras baseadas no MMSE. Como consecuencia, o noso obxectivo é deseñar os precodificadores e filtros que minimizan o MMSE para todos os usuarios. Para iso, distintos tipos de dualidades baseadas en SINR, Mean Square Error (MSE), ou taxa, foron empregadas para o deseño dos filtros coma fórmulas para intercambiar entre o BC e o MAC por conveniencia. En particular, empregamos a dualidade de MSE con coñecemento de canal imperfecto. Ademais, para a distribución de potencias, explotamos o marco teórico das standard Interference Function, formulado para resolver o algoritmo de control de potencia. Desta maneira, propomos un algoritmo para resolver o problema de minimización de potencia no BC. Para comprobar a factibilidade das restricci óns de calidade de servizo, propomos un test que permite determinar se o algoritmo converxe ou non. Ademais, o algoritmo proposto permite resolver o problema dual, ´ısto é, atopar os obxectivos de taxa balanceados correspondentes a unha potencia total no transmisor. Finalmente, algunhas aplicacións da minimización de potencia xorden de diferentes escenarios e resólvense por medio do algoritmo proposto. Usando a linguaxe de programación MATLAB simúlanse experimentos co obxectivo de mostrar o rendemento dos métodos propostos.[Abstract]This work considers a Broadcast Channel (BC) system, where the transmitter is equipped with multiple antennas and each user at the receiver side could have one or more antennas. Depending on the number of antennas at the receiver side, such a system is known as Multiple-User Multiple-Input Single-Output (MU-MISO), for single antenna users, orMultiple-UserMultiple-InputMultiple-Output (MU-MIMO), for several antenna users. This model is suitable for current wireless communication systems. Regarding the direction of the data flow, we differentiate between downlink channel or BC, and uplink channel or Multiple Access Channel (MAC). In the BC the signals are sent from the Base Station (BS) to the users, whereas the information from the users is sent to the BS in the MAC. In this work we focus on the BC where the BS applies linear precoding taking advantage of multiple antennas. The Channel State Information (CSI) is assumed to be perfectly known at each user. However, the users do not cooperate, and the BS only has partial CSI obtained via a feedback link in Frequency-Division Duplex (FDD) systems, which is bandwidth limited. This limitation forces the users to apply some methods, like quantization, to reduce the amount of data to be sent to the BS. The combination of the information provided by the users is interpreted as stochastic CSI at the BS, so that the partial CSI is critical for the design of the precoders. Several criteria have been considered to evaluate the BC performance in the literature, namely, Signal to Interference-plus-Noise Ratio (SINR), Minimum Mean Square Error (MMSE), and rate. While some works compute the corresponding metric for each of the users, others consider the sum of all of them as the value of interest. In our case, we concentrate on rate as figure of merit. In particular, we are interested in guarantying certain per-user rates. That way, we avoid unfair situations of the sum rate criterion arising when the channels for some of the users are poor with assigned low, even zero, rates. Moreover, reducing the amount of power required to fulfill the mentioned Qualityof- Service (QoS) restrictions is a desirable feature for a wireless communication system. Thus, we address the optimization problem consisting on minimizing the total transmit power employed at the BS to fulfill a set of given QoS constraints, expressed as per-user rates. The power minimization problem has been widely studied during the last years for both perfect and imperfect CSI at the BS scenarios. The assumption of perfect CSI is rather unrealistic so that, as we mentioned previously, we consider that the users send the channel information to the BS by means of the feedback channel, usually available in recent wireless communication standards. Although some authors have employed XIV bounded uncertainty models for the CSI such as rectangular, ellipsoidal, or spherical, and have taken advantage of that assumption to solve the power minimization problem, we do not assume a particular shape for that uncertainty, but is modeled as a stochastic error. In the considered MU-MIMO system model the number of antennas at the BS is larger than the number of antennas at each user, e.g. MU-MISO. Moreover, the users do not cooperate to separate the received signals. Due to that and to the lack of degrees of freedom at the users, it makes necessary the use of transmit filters, also denoted as precoders, to remove inter-user interference. Thus, in this work we jointly design the linear precoders and receive filters minimizing the total transmit power subject to per-user rate constraints. This problem formulation is non-convex. As a consequence, it is difficult to deal with. For such a reason, we apply the Jensen’s inequality to the rate constraints to obtain a MMSE based restrictions. Consequently, our aim is to find the precoders and the filters that minimize the MMSE for all the users. To that end, several types of dualities based on SINR, Mean Square Error (MSE), or rate have been employed for the design of the filters as conversion formulas that allow to switch between the BC and the MAC for convenience. We employ the MSE BC/MAC duality for imperfect Channel State Information at the Transmitter (CSIT). Furthermore, for the power allocation design, we take advantage of the standard Interference Function (IF) framework, proposed to solve the power control algorithm. In such a way, an algorithm is proposed to solve the power minimization problem in the BC. To check the feasibility of the QoS constraints, we propose a test that allows to determine the convergence of the algorithm. Additionally, the proposed algorithm can be employed to solve the dual problem, i.e., find the balanced targets for given total transmit power. Finally, some applications of the power minimization problem arising from different scenarios are studied and solved by means of the proposed algorithm. Simulation experiments are carried out using the technical programming language MATLAB in order to show the performance of the proposed methods