Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling

Orthogonal or superimposed pilots? A rate-efficient channel estimation strategy for stationary MIMO fading channels

©IEEE, 2017This paper considers channel estimation for multiple-input multiple-output (MIMO) channels and revisits two competing concepts of including training data into the transmit signal, namely orthogonal pilot (OP) that periodically transmits alternating pilot-data symbols, and superimposed pilot (SP) that overlays pilot-data symbols over time. We investigate rates achievable by both schemes when the channel undergoes time-selective bandlimited fading and analyze their behaviors with respect to the MIMO dimension and fading speed. By incorporating the multiple-antenna factors, we demonstrate that the widely-known trend, in which the OP is superior to the SP in the regimes of high signal-to-noise ratio (SNR) and slow-fading, and vice-versa, does not hold in general. As the number of transmit antennas (nt) increases, the range of operable fading speeds for the OP is significantly narrowed due to limited time resources for channel estimation and insufficient fading samples, which results in the SP being competitive in wider speed and SNR ranges. For a sufficiently small nt, we demonstrate thatas the fading variation becomes slower, the estimation quality for the SP can be superior to that for the OP. In this case, the SP outperforms the OP in the slow-fading regime due to full utilization of time for data transmission

Advanced interference management techniques for future wireless networks

In this thesis, we design advanced interference management techniques for future wireless networks under the availability of perfect and imperfect channel state information (CSI). We do so by considering a generalized imperfect CSI model where the variance of the channel estimation error depends on the signal-to-noise ratio (SNR). First, we analyze the performance of standard linear precoders, namely channel inversion (CI) and regularized CI (RCI), in downlink of cellular networks by deriving the received signal-to-interference-plus-noise ratio (SINR) of each user subject to both perfect and imperfect CSI. In this case, novel bounds on the asymptotic performance of linear precoders are derived, which determine howmuch accurate CSI should be to achieve a certain quality of service (QoS). By relying on the knowledge of error variance in advance, we propose an adaptive RCI technique to further improve the performance of standard RCI subject to CSI mismatch. We further consider transmit-power efficient design of wireless cellular networks. We propose two novel linear precoding techniques which can notably decrease the deployed power at transmit side in order to secure the same average output SINR at each user compared to standard linear precoders like CI and RCI. We also address a more sophisticated interference scenario, i.e., wireless interference networks, wherein each of the K transmitters communicates with its corresponding receiver while causing interference to the others. The most representative interference management technique in this case is interference alignment (IA). Unlike standard techniques like time division multiple access (TDMA) and frequency division multiple access (FDMA) where the achievable degrees of freedom (DoF) is one, with IA, the achievable DoF scales up with the number of users. Therefore, in this thesis, we quantify the asymptotic performance of IA under a generalized CSI mismatch model by deriving novel bounds on asymptotic mean loss in sum rate and the achievable DoF. We also propose novel least squares (LS) and minimum mean square error (MMSE) based IA techniques which are able to outperform standard IA schemes under perfect and imperfect CSI. Furthermore, we consider the implementation of IA in coordinated networks which enable us to decrease the number of deployed antennas in order to secure the same achievable DoF compared to standard IA techniques

Distributed Quasi-Orthogonal Space-Time coding in wireless cooperative relay networks

Cooperative diversity provides a new paradigm in robust wireless re- lay networks that leverages Space-Time (ST) processing techniques to combat the effects of fading. Distributing the encoding over multiple relays that potentially observe uncorrelated channels to a destination terminal has demonstrated promising results in extending range, data- rates and transmit power utilization. Specifically, Space Time Block Codes (STBCs) based on orthogonal designs have proven extremely popular at exploiting spatial diversity through simple distributed pro- cessing without channel knowledge at the relaying terminals. This thesis aims at extending further the extensive design and analysis in relay networks based on orthogonal designs in the context of Quasi- Orthogonal Space Time Block Codes (QOSTBCs). The characterization of Quasi-Orthogonal MIMO channels for cooper- ative networks is performed under Ergodic and Non-Ergodic channel conditions. Specific to cooperative diversity, the sub-channels are as- sumed to observe different shadowing conditions as opposed to the traditional co-located communication system. Under Ergodic chan- nel assumptions novel closed-form solutions for cooperative channel capacity under the constraint of distributed-QOSTBC processing are presented. This analysis is extended to yield closed-form approx- imate expressions and their utility is verified through simulations. The effective use of partial feedback to orthogonalize the QOSTBC is examined and significant gains under specific channel conditions are demonstrated. Distributed systems cooperating over the network introduce chal- lenges in synchronization. Without extensive network management it is difficult to synchronize all the nodes participating in the relaying between source and destination terminals. Based on QOSTBC tech- niques simple encoding strategies are introduced that provide compa- rable throughput to schemes under synchronous conditions with neg- ligible overhead in processing throughout the protocol. Both mutli- carrier and single-carrier schemes are developed to enable the flexi- bility to limit Peak-to-Average-Power-Ratio (PAPR) and reduce the Radio Frequency (RF) requirements of the relaying terminals. The insights gained in asynchronous design in flat-fading cooperative channels are then extended to broadband networks over frequency- selective channels where the novel application of QOSTBCs are used in distributed-Space-Time-Frequency (STF) coding. Specifically, cod- ing schemes are presented that extract both spatial and mutli-path diversity offered by the cooperative Multiple-Input Multiple-Output (MIMO) channel. To provide maximum flexibility the proposed schemes are adapted to facilitate both Decode-and-Forward (DF) and Amplify- and-Forward (AF) relaying. In-depth Pairwise-Error-Probability (PEP) analysis provides distinct design specifications which tailor the distributed- STF code to maximize the diversity and coding gain offered under the DF and AF protocols. Numerical simulation are used extensively to confirm the validity of the proposed cooperative schemes. The analytical and numerical re- sults demonstrate the effective use of QOSTBC over orthogonal tech- niques in a wide range of channel conditions

Capacity of interference networks : achievable regions and outer bounds

textIn an interference network, multiple transmitters communicate with multiple receivers using the same communication channel. The capacity region of an interference network is defined as the set of data rates that can be simultaneously achieved by the users of the network. One of the most important example of an interference network is the wireless network, where the communication channel is the wireless channel. Wireless interference networks are known to be interference limited rather than noise limited since the interference power level at the receivers (caused by other user's transmissions) is much higher than the noise power level. Most wireless communication systems deployed today employ transmission strategies where the interfering signals are treated in the same manner as thermal noise. Such strategies are known to be suboptimal (in terms of achieving higher data rates), because the interfering signals generated by other transmitters have a structure to them that is very different from that of random thermal noise. Hence, there is a need to design transmission strategies that exploit this structure of the interfering signals to achieve higher data rates. However, determining optimal strategies for mitigating interference has been a long standing open problem. In fact, even for the simplest interference network with just two users, the capacity region is unknown. In this dissertation, we will investigate the capacity region of several models of interference channels. We will derive limits on achievable data rates and design effective transmission strategies that come close to achieving the limits. We will investigate two kinds of networks - "small" (usually characterized by two transmitters and two receivers) and "large" where the number of users is large.Electrical and Computer Engineerin

Radio Communications

In the last decades the restless evolution of information and communication technologies (ICT) brought to a deep transformation of our habits. The growth of the Internet and the advances in hardware and software implementations modified our way to communicate and to share information. In this book, an overview of the major issues faced today by researchers in the field of radio communications is given through 35 high quality chapters written by specialists working in universities and research centers all over the world. Various aspects will be deeply discussed: channel modeling, beamforming, multiple antennas, cooperative networks, opportunistic scheduling, advanced admission control, handover management, systems performance assessment, routing issues in mobility conditions, localization, web security. Advanced techniques for the radio resource management will be discussed both in single and multiple radio technologies; either in infrastructure, mesh or ad hoc networks

Intelligent Reflecting Surface Enhanced Wireless Network: Two-timescale Beamforming Optimization

Intelligent reflecting surface (IRS) has drawn a lot of attention recently as a promising new solution to achieve high spectral and energy efficiency for future wireless networks. By utilizing massive low-cost passive reflecting elements, the wireless propagation environment becomes controllable and thus can be made favorable for improving the communication performance. Prior works on IRS mainly rely on the instantaneous channel state information (I-CSI), which, however, is practically difficult to obtain for IRS-associated links due to its passive operation and large number of elements. To overcome this difficulty, we propose in this paper a new two-timescale (TTS) transmission protocol to maximize the achievable average sum-rate for an IRS-aided multiuser system under the general correlated Rician channel model. Specifically, the passive IRS phase-shifts are first optimized based on the statistical CSI (S-CSI) of all links, which varies much slowly as compared to their I-CSI, while the transmit beamforming/precoding vectors at the access point (AP) are then designed to cater to the I-CSI of the users' effective channels with the optimized IRS phase-shifts, thus significantly reducing the channel training overhead and passive beamforming complexity over the existing schemes based on the I-CSI of all channels. For the single-user case, a novel penalty dual decomposition (PDD)-based algorithm is proposed, where the IRS phase-shifts are updated in parallel to reduce the computational time. For the multiuser case, we propose a general TTS optimization algorithm by constructing a quadratic surrogate of the objective function, which cannot be explicitly expressed in closed-form. Simulation results are presented to validate the effectiveness of our proposed algorithms and evaluate the impact of S-CSI and channel correlation on the system performance.Comment: 15 pages, 12 figures, accepted for publication in IEEE Transactions on Wireless Communication

Advanced wireless communications using large numbers of transmit antennas and receive nodes

The concept of deploying a large number of antennas at the base station, often called massive multiple-input multiple-output (MIMO), has drawn considerable interest because of its potential ability to revolutionize current wireless communication systems. Most literature on massive MIMO systems assumes time division duplexing (TDD), although frequency division duplexing (FDD) dominates current cellular systems. Due to the large number of transmit antennas at the base station, currently standardized approaches would require a large percentage of the precious downlink and uplink resources in FDD massive MIMO be used for training signal transmissions and channel state information (CSI) feedback. First, we propose practical open-loop and closed-loop training frameworks to reduce the overhead of the downlink training phase. We then discuss efficient CSI quantization techniques using a trellis search. The proposed CSI quantization techniques can be implemented with a complexity that only grows linearly with the number of transmit antennas while the performance is close to the optimal case. We also analyze distributed reception using a large number of geographically separated nodes, a scenario that may become popular with the emergence of the Internet of Things. For distributed reception, we first propose coded distributed diversity to minimize the symbol error probability at the fusion center when the transmitter is equipped with a single antenna. Then we develop efficient receivers at the fusion center using minimal processing overhead at the receive nodes when the transmitter with multiple transmit antennas sends multiple symbols simultaneously using spatial multiplexing

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