Review of Recent Trends

This work was partially supported by the European Regional Development Fund (FEDER), through the Regional Operational Programme of Centre (CENTRO 2020) of the Portugal 2020 framework, through projects SOCA (CENTRO-01-0145-FEDER-000010) and ORCIP (CENTRO-01-0145-FEDER-022141). Fernando P. Guiomar acknowledges a fellowship from “la Caixa” Foundation (ID100010434), code LCF/BQ/PR20/11770015. Houda Harkat acknowledges the financial support of the Programmatic Financing of the CTS R&D Unit (UIDP/00066/2020).MIMO-OFDM is a key technology and a strong candidate for 5G telecommunication systems. In the literature, there is no convenient survey study that rounds up all the necessary points to be investigated concerning such systems. The current deeper review paper inspects and interprets the state of the art and addresses several research axes related to MIMO-OFDM systems. Two topics have received special attention: MIMO waveforms and MIMO-OFDM channel estimation. The existing MIMO hardware and software innovations, in addition to the MIMO-OFDM equalization techniques, are discussed concisely. In the literature, only a few authors have discussed the MIMO channel estimation and modeling problems for a variety of MIMO systems. However, to the best of our knowledge, there has been until now no review paper specifically discussing the recent works concerning channel estimation and the equalization process for MIMO-OFDM systems. Hence, the current work focuses on analyzing the recently used algorithms in the field, which could be a rich reference for researchers. Moreover, some research perspectives are identified.publishersversionpublishe

Multipacket reception in LTE femtocell networks

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de ComputadoresDriven by the growing demand for high-speed broadband wireless services, LTE technology has emerged and evolve, promising high data rates to the demanding mobile users. Based on the 3rd Generation Partnership Project (3GPP) speci cations,Long Term Evo- lution Advanced (LTE-A) telecommunication services predict the existence of macro base stations, Enhanced Node B (eNB) and micro stations HeNB with low power that complements the network's coverage. This dissertation studies the complementary use of HeNBs (femtocells 3GPP terminology) to provide broadband services. It is essential to maintain the networks performance with the network densi cation phenomenon, which brings signi cant interference problems and consequently more collisions and lost packets. The use of SC-FDE in the downlink of a LTE-A femtocell network - speci cally multipacket reception (MPR), with an IB-DFE receiver employing Multipacket Detection (MPD) and SIC techniques is proposed. A new telecommunications concept named GC emerged with the increasing environmental concerns. This dissertation shows the performance results of an iterative MPR and proposes a green association algorithm to change the network layout according to the mobile users demands reducing the Base Station (BS)'s negative contribution to the network total energy consumption. The overall results show that the technologies employed are a solution to achieve a favorable trade-o between performance and Energy E ciency (EE), responding to the global demands (high data rates) and concerns (low energy consumption and carbon footprint reduction). Keywords: Long Term Evolution(LTE), Single Carrier with Frequency Domain Equalization (SC-FDE), Iterative Block-Decision Feedback Equalizer (IB-DFE), Home enhanced Node B (HeNB), Successive Interference Cancellation(SIC),Multipacket Reception(MPR), Green Communications (GC)FCT/MEC Femtocells(PTDC/EEATEL/120666/2010), OPPORTUNISTIC CR(PTDC/EEA-TEL/115981/2009) and ADIN(PTDC/EEI-TEL/2990/2012) project

Transmission strategies for broadband wireless systems with MMSE turbo equalization

This monograph details efficient transmission strategies for single-carrier wireless broadband communication systems employing iterative (turbo) equalization. In particular, the first part focuses on the design and analysis of low complexity and robust MMSE-based turbo equalizers operating in the frequency domain. Accordingly, several novel receiver schemes are presented which improve the convergence properties and error performance over the existing turbo equalizers. The second part discusses concepts and algorithms that aim to increase the power and spectral efficiency of the communication system by efficiently exploiting the available resources at the transmitter side based upon the channel conditions. The challenging issue encountered in this context is how the transmission rate and power can be optimized, while a specific convergence constraint of the turbo equalizer is guaranteed.Die vorliegende Arbeit beschäftigt sich mit dem Entwurf und der Analyse von effizienten Übertragungs-konzepten für drahtlose, breitbandige Einträger-Kommunikationssysteme mit iterativer (Turbo-) Entzerrung und Kanaldekodierung. Dies beinhaltet einerseits die Entwicklung von empfängerseitigen Frequenzbereichs-entzerrern mit geringer Komplexität basierend auf dem Prinzip der Soft Interference Cancellation Minimum-Mean Squared-Error (SC-MMSE) Filterung und andererseits den Entwurf von senderseitigen Algorithmen, die durch Ausnutzung von Kanalzustandsinformationen die Bandbreiten- und Leistungseffizienz in Ein- und Mehrnutzersystemen mit Mehrfachantennen (sog. Multiple-Input Multiple-Output (MIMO)) verbessern. Im ersten Teil dieser Arbeit wird ein allgemeiner Ansatz für Verfahren zur Turbo-Entzerrung nach dem Prinzip der linearen MMSE-Schätzung, der nichtlinearen MMSE-Schätzung sowie der kombinierten MMSE- und Maximum-a-Posteriori (MAP)-Schätzung vorgestellt. In diesem Zusammenhang werden zwei neue Empfängerkonzepte, die eine Steigerung der Leistungsfähigkeit und Verbesserung der Konvergenz in Bezug auf existierende SC-MMSE Turbo-Entzerrer in verschiedenen Kanalumgebungen erzielen, eingeführt. Der erste Empfänger - PDA SC-MMSE - stellt eine Kombination aus dem Probabilistic-Data-Association (PDA) Ansatz und dem bekannten SC-MMSE Entzerrer dar. Im Gegensatz zum SC-MMSE nutzt der PDA SC-MMSE eine interne Entscheidungsrückführung, so dass zur Unterdrückung von Interferenzen neben den a priori Informationen der Kanaldekodierung auch weiche Entscheidungen der vorherigen Detektions-schritte berücksichtigt werden. Durch die zusätzlich interne Entscheidungsrückführung erzielt der PDA SC-MMSE einen wesentlichen Gewinn an Performance in räumlich unkorrelierten MIMO-Kanälen gegenüber dem SC-MMSE, ohne dabei die Komplexität des Entzerrers wesentlich zu erhöhen. Der zweite Empfänger - hybrid SC-MMSE - bildet eine Verknüpfung von gruppenbasierter SC-MMSE Frequenzbereichsfilterung und MAP-Detektion. Dieser Empfänger besitzt eine skalierbare Berechnungskomplexität und weist eine hohe Robustheit gegenüber räumlichen Korrelationen in MIMO-Kanälen auf. Die numerischen Ergebnisse von Simulationen basierend auf Messungen mit einem Channel-Sounder in Mehrnutzerkanälen mit starken räumlichen Korrelationen zeigen eindrucksvoll die Überlegenheit des hybriden SC-MMSE-Ansatzes gegenüber dem konventionellen SC-MMSE-basiertem Empfänger. Im zweiten Teil wird der Einfluss von System- und Kanalmodellparametern auf die Konvergenzeigenschaften der vorgestellten iterativen Empfänger mit Hilfe sogenannter Korrelationsdiagramme untersucht. Durch semi-analytische Berechnungen der Entzerrer- und Kanaldecoder-Korrelationsfunktionen wird eine einfache Berechnungsvorschrift zur Vorhersage der Bitfehlerwahrscheinlichkeit von SC-MMSE und PDA SC-MMSE Turbo Entzerrern für MIMO-Fadingkanäle entwickelt. Des Weiteren werden zwei Fehlerschranken für die Ausfallwahrscheinlichkeit der Empfänger vorgestellt. Die semi-analytische Methode und die abgeleiteten Fehlerschranken ermöglichen eine aufwandsgeringe Abschätzung sowie Optimierung der Leistungsfähigkeit des iterativen Systems. Im dritten und abschließenden Teil werden Strategien zur Raten- und Leistungszuweisung in Kommunikationssystemen mit konventionellen iterativen SC-MMSE Empfängern untersucht. Zunächst wird das Problem der Maximierung der instantanen Summendatenrate unter der Berücksichtigung der Konvergenz des iterativen Empfängers für einen Zweinutzerkanal mit fester Leistungsallokation betrachtet. Mit Hilfe des Flächentheorems von Extrinsic-Information-Transfer (EXIT)-Funktionen wird eine obere Schranke für die erreichbare Ratenregion hergeleitet. Auf Grundlage dieser Schranke wird ein einfacher Algorithmus entwickelt, der für jeden Nutzer aus einer Menge von vorgegebenen Kanalcodes mit verschiedenen Codierraten denjenigen auswählt, der den instantanen Datendurchsatz des Mehrnutzersystems verbessert. Neben der instantanen Ratenzuweisung wird auch ein ausfallbasierter Ansatz zur Ratenzuweisung entwickelt. Hierbei erfolgt die Auswahl der Kanalcodes für die Nutzer unter Berücksichtigung der Einhaltung einer bestimmten Ausfallwahrscheinlichkeit (outage probability) des iterativen Empfängers. Des Weiteren wird ein neues Entwurfskriterium für irreguläre Faltungscodes hergeleitet, das die Ausfallwahrscheinlichkeit von Turbo SC-MMSE Systemen verringert und somit die Zuverlässigkeit der Datenübertragung erhöht. Eine Reihe von Simulationsergebnissen von Kapazitäts- und Durchsatzberechnungen werden vorgestellt, die die Wirksamkeit der vorgeschlagenen Algorithmen und Optimierungsverfahren in Mehrnutzerkanälen belegen. Abschließend werden außerdem verschiedene Maßnahmen zur Minimierung der Sendeleistung in Einnutzersystemen mit senderseitiger Singular-Value-Decomposition (SVD)-basierter Vorcodierung untersucht. Es wird gezeigt, dass eine Methode, welche die Leistungspegel des Senders hinsichtlich der Bitfehlerrate des iterativen Empfängers optimiert, den konventionellen Verfahren zur Leistungszuweisung überlegen ist

Towards low-cost gigabit wireless systems at 60 GHz

The world-wide availability of the huge amount of license-free spectral space in the 60 GHz band provides wide room for gigabit-per-second (Gb/s) wireless applications. A commercial (read: low-cost) 60-GHz transceiver will, however, provide limited system performance due to the stringent link budget and the substantial RF imperfections. The work presented in this thesis is intended to support the design of low-cost 60-GHz transceivers for Gb/s transmission over short distances (a few meters). Typical applications are the transfer of high-definition streaming video and high-speed download. The presented work comprises research into the characteristics of typical 60-GHz channels, the evaluation of the transmission quality as well as the development of suitable baseband algorithms. This can be summarized as follows. In the first part, the characteristics of the wave propagation at 60 GHz are charted out by means of channel measurements and ray-tracing simulations for both narrow-beam and omni-directional configurations. Both line-of-sight (LOS) and non-line-of-sight (NLOS) are considered. This study reveals that antennas that produce a narrow beam can be used to boost the received power by tens of dBs when compared with omnidirectional configurations. Meanwhile, the time-domain dispersion of the channel is reduced to the order of nanoseconds, which facilitates Gb/s data transmission over 60-GHz channels considerably. Besides the execution of measurements and simulations, the influence of antenna radiation patterns is analyzed theoretically. It is indicated to what extent the signal-to-noise ratio, Rician-K factor and channel dispersion are improved by application of narrow-beam antennas and to what extent these parameters will be influenced by beam pointing errors. From both experimental and analytical work it can be concluded that the problem of the stringent link-budget can be solved effectively by application of beam-steering techniques. The second part treats wideband transmission methods and relevant baseband algorithms. The considered schemes include orthogonal frequency division multiplexing (OFDM), multi-carrier code division multiple access (MC-CDMA) and single carrier with frequency-domain equalization (SC-FDE), which are promising candidates for Gb/s wireless transmission. In particular, the optimal linear equalization in the frei quency domain and associated implementation issues such as synchronization and channel estimation are examined. Bit error rate (BER) expressions are derived to evaluate the transmission performance. Besides the linear equalization techniques, a low-complexity inter-symbol interference cancellation technique is proposed to achieve much better performance of code-spreading systems such as MC-CDMA and SC-FDE. Both theoretical analysis and simulations demonstrate that the proposed scheme offers great advantages as regards both complexity and performance. This makes it particularly suitable for 60-GHz applications in multipath environments. The third part treats the influence of quantization and RF imperfections on the considered transmission methods in the context of 60-GHz radios. First, expressions for the BER are derived and the influence of nonlinear distortions caused by the digital-to-analog converters, analog-to-digital converters and power amplifiers on the BER performance is examined. Next, the BER performance under the influence of phase noise and IQ imbalance is evaluated for the case that digital compensation techniques are applied in the receiver as well as for the case that such techniques are not applied. Finally, a baseline design of a low-cost Gb/s 60-GHz transceiver is presented. It is shown that, by application of beam-steering in combination with SC-FDE without advanced channel coding, a data rate in the order of 2 Gb/s can be achieved over a distance of 10 meters in a typical NLOS indoor scenario

Pré-codificação e equalização para sistemas SC-FDMA heterogéneos

Mestrado em Engenharia Electrónica e TelecomunicaçõesMobile traffic in cellular networks is increasing exponentially. Small-cells are considered as a key solution to meet these requirements. Under the same spectrum the small-cells and the associated macro-cell (forming the so called heterogeneous systems) must cooperate so that one system can adapt to the other. If no cooperation is considered then the small-cells will generate harmful interference at the macro-cell. Interference alignment (IA) is a precoding technique that is able to achieve the maximum degrees of freedom of the interference channel, and can efficiently deal with inter-systems interference. Single carrier frequency division multiple access (SC-FDMA) is a promising solution technique for high data rate uplink communications in future cellular systems. Conventional linear equalizers are not efficient to remove the residual inter-carrier interference of the SC-FDMA systems. For this reason, there has been significant interest in the design of nonlinear frequency domain equalizers in general and decision feedback equalizers in particular, with the iterative block decision feedback equalizer (IB-DFE) being the most promising nonlinear equalizer. In this dissertation we propose and evaluate joint interference alignment precoding at the small cell user terminals with iterative non-linear frequency domain equalizer at the receivers (macro base station and central unit) for SC-FDMA based heterogeneous networks. The small-cell precoders are designed by enforcing that all generated interference at the macro-cell is aligned in an orthogonal subspace to the macro-cell received signal subspace. This enforces that no performance degradation is observed at the macro cell. Then, we design an iterative nonlinear frequency domain equalizer at the macro-cell receiver that is able to recover the macro-cell spatial streams, in the presence of both small-cell and inter-carrier interferences. The results show that the proposed transmitter and receiver structures are robust to the inter-system interferences and at the same time are able to efficient separate the macro and small cells spatial streams.O trafego móvel nas redes celulares tem aumentado exponencialmente. As pico- células são consideradas como a solução chave para cumprir estes requisitos. Dentro do mesmo espectro, as pico-células e as macro-células (formando os chamados sistemas heterogéneos) precisam de colaborar de modo a que um sistema possa adaptar-se ao outro. Se não for considerada a cooperação, então as pico-células irão gerar interferência prejudicial na macro-célula. Interference alignment (IA) é uma técnica de précodificação que é capaz de atingir o grau máximo de liberdade do canal de interferência, e consegue lidar eficazmente com interferência entre sistemas. Single carrier frequency division multiple access (SC-FDMA) é uma solução técnica promissora para transmissão de dados em uplink, para sistemas celulares futuros. Equalizadores lineares convencionais não são eficientes a remover a interferência residual entre portadoras dos sistemas SC-FDMA. Por este motivo, tem havido interesse significativo no desenho de equalizadores não lineares no domínio da frequência em geral e em equalizadores baseados em decisão por feedback em particular, tendo o iterative block decision feedback equalizer (IB-DFE) como o equalizador não linear mais promissor. Nesta dissertação propomos e avaliamos précodificação de alinhamento de interferência nos terminais das pico-células em conjunto com equalizadores não lineares no domínio da frequência nos recetores (estação base da macro-célula e unidade central de processamento) para redes heterogéneas baseadas em SC-FDMA. Os précodificadores das pico-células são desenhados de maneira a obrigar a que toda a interferência gerada na macro-célula esteja alinhada num subespaço ortogonal em relação ao subespaço do sinal recebido na macro- célula. Isto obriga a que não seja observada degradação de desempenho na macro-célula. Em seguida, desenhamos um equalizador não linear no domínio da frequência no recetor da macro-célula capaz de recuperar os fluxos de dados da macro-célula, na presença de interferência tanto entre portadoras como das pico-células. Os resultados mostram que as estruturas de transmissão e receção propostas são robustas contra a interferência entre sistemas e ao mesmo tempo capaz de separar eficientemente os dados da macro e das pico células

Técnicas de igualização adaptativas com estimativas imperfeitas do canal para os futuros sistemas 5G

Wireless communication networks have been continuously experiencing an exponential growth since their inception. The overwhelming demand for high data rates, support of a large number of users while mitigating disruptive interference are the constant research focus and it has led to the creation of new technologies and efficient techniques. Orthogonal frequency division multiplexing (OFDM) is the most common example of a technology that has come to the fore in this past decade as it provided a simple and generally ideal platform for wireless data transmission. It’s drawback of a rather high peak-to-average power ratio (PAPR) and sensitivity to phase noise, which in turn led to the adoption of alternative techniques, such as the single carrier systems with frequency domain equalization (SC-FDE) or the multi carrier systems with code division multiple access (MC-CDMA), but the nonlinear Frequency Domain Equalizers (FDE) have been of special note due to their improved performance. From these, the Iterative Block Decision Feedback Equalizer (IB-DFE) has proven itself especially promising due to its compatibility with space diversity, MIMO systems and CDMA schemes. However, the IB-DFE requires the system to have constant knowledge of the communication channel properties, that is, to have constantly perfect Channel State Information (CSI), which is both unrealistic and impractical to implement. In this dissertation we shall design an altered IB-DFE receiver that is able to properly detect signals from SC-FDMA based transmitters, even with constantly erroneous channel states. The results shall demonstrate that the proposed equalization scheme is robust to imperfect CSI (I-CSI) situations, since its performance is constantly close to the perfect CSI case, within just a few iterations.Redes sem fios têm crescido de maneira contínua e exponencial desde a sua incepção. A tremenda exigência para altas taxas de dados e o suporte para um elevado número de utilizadores sem aumentar a interferência disruptiva originada por estes são alguns dos focos que levaram ao desenvolvimento de técnicas de compensação e novas tecnologias. “Orthogonal frequency division multiplexing” (OFDM) é um dos exemplos de tecnologias que se destacaram nesta última década, visto ter fornecido uma plataforma para transmissão de dados sem-fio eficaz e simples. O seu maior problema é a alta “peak-to-average power ratio” (PAPR) e a sua sensibilidade a ruído de fase que deram motivo à adoção de técnicas alternativas, tais como os sistemas “single carrier” com “frequency domain equalization” (SC-FDE) ou os sistemas “multi-carrier” com “code division multiple access” (MC-CDMA), mas equalizadores não lineares no domínio de frequência têm sido alvo de especial atenção devido ao seu melhor desempenho. Destes, o “iterative block decision feedback equalizer” (IB-DFE) tem-se provado especialmente promissor devido à sua compatibilidade com técnicas de diversidade no espaço, sistemas MIMO e esquemas CDMA. No entanto, IB-DFE requer que o sistema tenha constante conhecimento das propriedades dos canais usados, ou seja, necessita de ter perfeito “channel state information” (CSI) constantemente, o que é tanto irrealista como impossível de implementar. Nesta dissertação iremos projetar um recetor IB-DFE alterado de forma a conseguir detetar sinais dum transmissor baseado em tecnologia SC-FDMA, mesmo com a informação de estado de canal errada. Os resultados irão então demonstrar que o novo esquema de equalização proposto é robusto para situações de CSI imperfeito (I-CSI), visto que o seu desempenho se mantém próximo dos valores esperados para CSI perfeito, em apenas algumas iterações.Mestrado em Engenharia Eletrónica e Telecomunicaçõe

Nouvelles Techniques de Précodage et d Égalisation pour les Systèmes Multiporteuses

Dans cette thèse, de nouvelles techniques d'égalisation et de précodage pour des systèmes multiporteuses ont été proposées et analysées. D'abord, la performance d'erreur des systèmes multiporteuses à base de bancs de filtres (FBMC) précodées a été analysée. Il a été découvert que cette performance est très sensible à l'égalisation complète des sous-canaux. Quand il y a de l'interference inter-symbole residuel qui vient de l'égalisation imparfaite du sous-canaux, il y a une perte de diversité; cette diversité peut être recuperée avec l'adoption d'un nombre de sous-canaux assez grand pour que chaque sous-canaux subisse de l'évanouissement plat ou avec l'utilisation d'un égaliseur de sous-canaux avec une longueur assez suffisante pour compenser cette réponse en fréquence. Après, une approximation pour la distribution du rapport signal/bruit-plus-interfèrence (SINR) des systèmes SC-FDE qui utilisent égalisation MMSE linéaire a été proposée. Cette approximation utilise la distribution lognormal avec la plus petit distance de Kullback-Leibler vers la vraie distribution, et il s'est révélé qu'elle est precise dans la performance d'erreur; elle sert aussi comme une abstraction de cette système. Avec cette abstraction, une méthode précise pour obtenir la performance d'erreur analytique codée de ces systèmes a été proposée. Finalement, des précodeurs Tomlinson-Harashima (THP) et égaliseurs (linéaires et à retour de décision) largement linéaires pour des systèmes SC-FDE ont été proposés. Ces précodeurs et égaliseurs ont une performance d'erreur mieux quand comparés avec ses versions strictement linéaires si des signaux de constellations impropres sont transmises. Aussi, la performance d'erreur quand des égaliseurs à retour de décision sont utilisés est moins sensible au longueur du filtre de retour. Quand des précodeurs largement linéaires sont utilisés, cette performance devient moins sensible à des erreurs d'estimation du canaux.In this thesis, new precoding and equalization techniques for multicarrier systems were proposed and analyzed.First, the error performance of precoded filterbank multicarrier (FBMC) systems was analyzed. It was found out that this performance is highly sensitive to complete subchannel equalization. When there is residual intersymbol interference (ISI) stemming from imperfect subchannel equalization there is a loss of diversity; this loss can be prevented with the adoption of a number of subchannels large enough so that each subchannel suffers flat fading or with the utilization of a subchannel equalizer with sufficient length to compensate the subchannel frequency response.After that, an approximation for the signal to interference-plus-noise ratio (SINR) distribution of SC-FDE systems using linear MMSE equalization was proposed. This approximation uses the lognormal distribution with the smallest Kullback-Leibler distance to the true distribution, and was shown to be precise in the error performance sense; it serves as a system abstraction. With this abstraction, a precise method to obtain the analytical coded error performance of these systems was proposed.Finally, widely linear Tomlinson-Harashima precoders and equalizers (linear and decision-feedback) for SC-FDE systems were proposed. These precoders and equalizers have better error performance when compared to their strictly linear versions if signals coming from an improper constellation are transmitted. Their error performance when decision-feedback equalizers are used is less sensitive to the length of the feedback filter. When widely linear precoders are used, this error performance becomes less sensitive to channel estimation errors.PARIS-CNAM (751032301) / SudocSudocFranceF

Novas técnicas de précodificação e equalização para sistemas multiportadoras

Tese [doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica.Nesta tese, novas técnicas de equalização e précodificação para sistemas multiportadora foram propostas e analisadas. Primeiramente, foi analisado o desempenho de erro dos sistemas multiportadoras baseados em bancos de filtros (FBMC) précodificados. Foi descoberto que este desempenho é altamente sensível à completa equalização dos subcanais. Quando há interferência intersimbólica residual proveniente de equalização imperfeita do subcanal, há uma perda de diversidade; esta diversidade pode ser restaurada adotando um número de subcanais suficiente para que o subcanal sofra desvanecimento plano ou utilizando um equalizador de subcanal com comprimento suficiente para compensar a resposta em frequência deste. Após isto, uma aproximação para a distribuição para a relação sinal/ruído+interferência (SINR) de sistemas SC-FDE utilizando equalização linear MMSE foi proposta. Esta aproximação usa a distribuição lognormal com a menor distância de Kullback-Leibler para a verdadeira distribuição, e se mostrou precisa no desempenho de erro; ela serve como uma abstração do sistema. Com esta abstração, foi proposto um método preciso para obter o desempenho de erro codificado analítico desses sistemas. Finalmente, précodificadores Tomlinson-Harashima (THP) e equalizadores (lineares e de decisão realimentada) utilizando o processamento largamente linear para sistemas SC-FDE foram propostos. Estes précodificadores e equalizadores têm um desempenho de erro melhor quando comparados com suas versões estritamente lineares se sinais provenientes de uma constelação imprópria são transmitidos. Além disso, o desempenho de erro quando equalizadores com realimentação de decisão são utilizados é menos sensível ao comprimento do filtro realimentado. Quando précodificadores largamente lineares são utilizados, este desempenho torna-se menos sensível a erros de estimação do cana