Analytical Characterization and Optimum Detection of Nonlinear Multicarrier Schemes

It is widely recognized that multicarrier systems such as orthogonal frequency division multiplexing (OFDM) are suitable for severely time-dispersive channels. However, it is also recognized that multicarrier signals have high envelope fluctuations which make them especially sensitive to nonlinear distortion effects. In fact, it is almost unavoidable to have nonlinear distortion effects in the transmission chain. For this reason, it is essential to have a theoretical, accurate characterization of nonlinearly distorted signals not only to evaluate the corresponding impact of these distortion effects on the system’s performance, but also to develop mechanisms to combat them. One of the goals of this thesis is to address these challenges and involves a theoretical characterization of nonlinearly distorted multicarrier signals in a simple, accurate way. The other goal of this thesis is to study the optimum detection of nonlinearly distorted, multicarrier signals. Conventionally, nonlinear distortion is seen as a noise term that degrades the system’s performance, leading even to irreducible error floors. Even receivers that try to estimate and cancel it have a poor performance, comparatively to the performance associated to a linear transmission, even with perfect cancellation of nonlinear distortion effects. It is shown that the nonlinear distortion should not be considered as a noise term, but instead as something that contains useful information for detection purposes. The adequate receiver to take advantage of this information is the optimum receiver, since it makes a block-by-block detection, allowing us to exploit the nonlinear distortion which is spread along the signal’s band. Although the optimum receiver for nonlinear multicarrier schemes is too complex, due to its necessity to compare the received signal with all possible transmitted sequences, it is important to study its potential performance gains. In this thesis, it is shown that the optimum receiver outperforms the conventional detection, presenting gains not only relatively to conventional receivers that deal with nonlinear multicarrier signals, but also relatively to conventional receivers that deal with linear, multicarrier signals. We also present sub-optimum receivers which are able to approach the performance gains associated to the optimum detection and that can even outperform the conventional linear, multicarrier schemes

Performance limits in optical communications due to fiber nonlinearity

In this paper, we review the historical evolution of predictions of the performance of optical communication systems. We will describe how such predictions were made from the outset of research in laser based optical communications and how they have evolved to their present form, accurately predicting the performance of coherently detected communication systems

Simultaneous Wireless Information and Power Transfer in 5G communication

Green communication technology is expected to be widely adopted in future generation networks to improve energy efficiency and reliability of wireless communication network. Among the green communication technologies,simultaneous wireless information and power transfer (SWIPT) is adopted for its flexible energy harvesting technology through the radio frequency (RF) signa lthati sused for information transmission. Even though existing SWIPT techniques are flexible and adoptable for the wireless communication networks, the power and time resources of the signal need to be shared between infor- mation transmission and RF energy harvesting, and this compromises the quality of the signal. Therefore,SWIP Ttechniques need to be designed to allow an efficient resource allocation for communication and energy harvesting. The goal oft his thesisis to design SWIP Ttechniques that allow efficient,reliable and secure joint communications and power transference. A problem associated to SWIPT techniques combined with multi carrier signals is that the increased power requirements inherent to energy harvesting purposes can exacerbate nonlinear distortion effects at the transmitter. Therefore, we evaluate nonlinear distortion and present feasible solutions to mitigate the impact of nonlinear distortion effects on the performance.Another goal of the thesisis to take advantage of the energy harvesting signals in SWIP Ttechniques for channel estimation and security purposes.Theperformance of these SWIPT techniques is evaluated analytically, and those results are validated by simulations. It is shownthatthe proposed SWIPT schemes can have excellent performance, out performing conventional SWIPT schemes.Espera-se que aschamadas tecnologiasde green communications sejam amplamente ado- tadas em futuras redes de comunicação sem fios para melhorar a sua eficiência energética a fiabilidade.Entre estas,encontram-se as tecnologias SWIPT (Simultaneous Wireless Information and Power Transference), nas quais um sinal radio é usado para transferir simultaneamente potência e informações.Embora as técnicas SWIPT existentes sejam fle- xíveis e adequadas para as redes de comunicações sem fios, os recursos de energia e tempo do sinal precisam ser compartilhados entre a transmissão de informações e de energia, o que pode comprometer a qualidade do sinal. Deste modo,as técnicas SWIPT precisam ser projetadas para permitir uma alocação eficiente de recursos para comunicação e recolha de energia. O objetivo desta tese é desenvolver técnicas SWIPT que permitam transferência de energia e comunicações eficientes,fiáveis e seguras.Um problema associado às técnicas SWIPT combinadas com sinais multi-portadora são as dificuldades de amplificação ine- rentes à combinação de sinais de transmissão de energia com sinais de transferência de dados, que podem exacerbar os efeitos de distorção não-linear nos sinais transmitidos. Deste modo, um dos objectivos desta tese é avaliar o impacto da distorção não-linear em sinais SWIPT, e apresentar soluções viáveis para mitigar os efeitos da distorção não-linear no desempenho da transmissão de dados.Outro objetivo da tese é aproveitar as vantagens dos sinais de transferência de energia em técnicas SWIPT para efeitos de estimação de canal e segurança na comunicação.Os desempenhos dessas técnicas SWIPT são avaliados analiticamente,sendo os respectivos resultados validados por simulações.É mostrado que os esquemas SWIPT propostos podem ter excelente desempenho, superando esquemas SWIPT convencionais

Analysis and power diversity-based cancellation of nonlinear distortions in OFDM systems

International audienceOne of the main drawbacks of orthogonal frequency division multiplexing (OFDM) systems is the high peak-to-average power ratio (PAPR) of the transmitted signals, which can cause the introduction of inter-carrier interference (ICI) due to the presence of nonlinear power amplifiers (PAs). In this paper, a theoretical analysis of ICI in nonlinear OFDM systems with polynomial PAs is made. Contrarily to other works, this analysis provides an exact description of nonlinear ICI. Moreover, three receivers for channel estimation and ICI cancellation in OFDM systems with polynomial PAs are proposed, based on the concept of power diversity that consists in re-transmitting the information symbols several times with a different transmission power each time. The transmission powers that minimize the sum of the residual mean square errors (MSEs) provided by the proposed receivers are derived in the case of a third-degree polynomial PA. An important advantage of the proposed receivers is that the optimal transmission powers do not depend on the channel nor the PA coefficients

Design and implementation of an ETSI-SDR OFDM transmitter with power amplifier linearizer

Satellite radio has attained great popularity because of its wide range of geographical coverage and high signal quality as compared to the terrestrial broadcasts. Most Satellite Digital Radio (SDR) based systems favor multi-carrier transmission schemes, especially, orthogonal frequency division multiplexing (OFDM) transmission because of high data transfer rate and spectral efficiency. It is a challenging task to find a suitable platform that supports fast data rates and superior processing capabilities required for the development and deployment of the new SDR standards. Field programmable gate array (FPGA) devices have the potential to become suitable development platform for such standards. Another challenging factor in SDR systems is the distortion of variable envelope signals used in OFDM transmission by the nonlinear RF power amplifiers (PA) used in the base station transmitters. An attractive option is to use a linearizer that would compensate for the nonlinear effects of the PA. In this research, an OFDM transmitter, according to European Telecommunications Standard Institute (ETSI) SDR Technical Specifications 2007-2008, was designed and implemented on a low-cost Xilinx FPGA platform. A weakly nonlinear PA, operating in the L-band SDR frequency (1.450-1.490GHz), was used for signal transmission. An FPGA-based, low-cost, adaptive linearizer was designed and implemented based on the digital predistortion (DPD) reference design from Xilinx, to correct the distortion effects of the PA on the transmitted signal

mm-Wave Data Transmission and Measurement Techniques: A Holistic Approach

The ever-increasing demand on data services places unprecedented technical requirements on networks capacity. With wireless systems having significant roles in broadband delivery, innovative approaches to their development are imperative. By leveraging new spectral resources available at millimeter-wave (mm-wave) frequencies, future systems can utilize new signal structures and new system architectures in order to achieve long-term sustainable solutions.This thesis proposes the holistic development of efficient and cost-effective techniques and systems which make high-speed data transmission at mm-wave feasible. In this paradigm, system designs, signal processing, and measurement techniques work toward a single goal; to achieve satisfactory system level key performance indicators (KPIs). Two intimately-related objectives are simultaneously addressed: the realization of efficient mm-wave data transmission and the development of measurement techniques to enable and assist the design and evaluation of mm-wave circuits.The standard approach to increase spectral efficiency is to increase the modulation order at the cost of higher transmission power. To improve upon this, a signal structure called spectrally efficient frequency division multiplexing (SEFDM) is utilized. SEFDM adds an additional dimension of continuously tunable spectral efficiency enhancement. Two new variants of SEFDM are implemented and experimentally demonstrated, where both variants are shown to outperform standard signals.A low-cost low-complexity mm-wave transmitter architecture is proposed and experimentally demonstrated. A simple phase retarder predistorter and a frequency multiplier are utilized to successfully generate spectrally efficient mm-wave signals while simultaneously mitigating various issues found in conventional mm-wave systems.A measurement technique to characterize circuits and components under antenna array mutual coupling effects is proposed and demonstrated. With minimal setup requirement, the technique effectively and conveniently maps prescribed transmission scenarios to the measurement environment and offers evaluations of the components in terms of relevant KPIs in addition to conventional metrics.Finally, a technique to estimate transmission and reflection coefficients is proposed and demonstrated. In one variant, the technique enables the coefficients to be estimated using wideband modulated signals, suitable for implementation in measurements performed under real usage scenarios. In another variant, the technique enhances the precision of noisy S-parameter measurements, suitable for characterizations of wideband mm-wave components

Design of communication systems based on broadband sources for fiber and free space optical links

[ES] Las comunicaciones ópticas inalámbricas (OWC) constituyen una tecnología muy prometedora para el desarrollo de futuras comunicaciones inalámbricas. De hecho, ha despertado un interés creciente entre los investigadores y varias empresas de todo el mundo trabajan actualmente en el desarrollo de redes inalámbricas de muy alta velocidad. Las comunidades científica e industrial consideran la OWC como una tecnología complementaria en sus diversas formas: comunicaciones ópticas en el espacio libre (FSO), comunicaciones de luz visible (VLC) o fidelidad de la luz (Li-Fi). El espectro óptico ha sido considerado durante muchos años como una gran oportunidad para las comunicaciones inalámbricas, especialmente debido a la saturación del espectro de radiofrecuencia (RF). Esta disertación trata del uso de fuentes de banda ancha en sistemas de transmisión de luz visible (VLC), así como en sistemas de transmisión en el espectro infrarrojo por fibra óptica. En el trabajo de investigación realizado se pueden distinguir tres partes: En la primera parte, se considera el estudio y la simulación de componentes de Diodos Emisores de Luz (LED) con el software WIEN2k centrándose en las propiedades ópticas y eléctricas de los elementos II-VI. La segunda parte trata del diseño, la implementación y las pruebas de diferentes prototipos de comunicación VLC para la transmisión analógica y digital en modo simplex y semidúplex. Hemos demostrado un sistema OWC empleando una fuente de banda ancha (LED) para la transmisión no sólo de datos, sino también para la transmisión inalámbrica de energía. Además, se aborda el problema de la sincronización y la detección del nivel "1" o "0" de un bit en los sistemas de comunicación inalámbrica óptica implementados que surge como consecuencia de la atenuación de la luz a lo largo de la distancia y al problema de la pérdida de línea de visión (NLOS) entre el emisor y el receptor. Para hacer frente a este problema, se ha proporcionado un protocolo de comunicación que garantiza la transmisión fiable de datos digitales con un algoritmo de detección de nivel de bits adaptativo y se ha demostrado su eficacia mediante la transmisión de textos e imágenes. Además, esta tesis aporta una solución para la implementación de transmisores multiplexados en redes con división de longitud de onda (WDM) para formatos de modulación con multiplexación por división de frecuencia ortogonal (OFDM) basados en el uso de fuentes de banda ancha en el espectro infrarrojo para redes de fibra bidireccionales centralizadas. A pesar de las limitaciones impuestas por la dispersión cromática en el uso de este tipo de fuentes ópticas, la inclusión de ciertas estructuras antes de la detección permite la transmisión de señales OFDM en enlaces ópticos. En este trabajo se ha demostrado experimentalmente la reutilización de portadoras, la asignación dinámica de ancho de banda y la transmisión de señales OFDM multibanda mediante el uso de fuentes ópticas de banda ancha en redes WDM. Los principales resultados obtenidos en cada parte de esta tesis doctoral muestran los procedimientos de estudio, la eficacia de las soluciones propuestas y las limitaciones encontradas.[CA] Les comunicacions òptiques sense fils (OWC) constitueixen una tecnologia molt prometedora per al desenvolupament de futures comunicacions sense fils. De fet, ha despertat un interés creixent entre els investigadors i diverses empreses de tot el món treballen actualment en el desenvolupament de xarxes sense fils de molt alta velocitat. Les comunitats científica i industrial consideren la OWC com una tecnologia complementària en les seues diverses formes: comunicacions òptiques en l'espai lliure (FSO), comunicacions de llum visible (VLC) o fidelitat de la llum (Li-Fi). L'espectre òptic ha sigut considerat durant molts anys com una gran oportunitat per a les comunicacions sense fils, especialment a causa de la saturació de l'espectre de radiofreqüència (RF). Aquesta dissertació tracta de l'ús de fonts de banda ampla en sistemes de transmissió de llum visible (VLC), així com en sistemes de transmissió en l'espectre infraroig per fibra òptica. En el treball de recerca realitzat es poden distingir tres parts: ¿ En la primera part, es considera l'estudi i la simulació de components de Díodes Emissors de Llum (LED) amb el software WIEN2k centrant-se en les propietats òptiques i elèctriques dels elements II-VI. ¿ La segona part tracta del disseny, la implementació i les proves de diferents prototips de comunicació VLC per a la transmissió analògica i digital de manera simplex i semidúplex. Hem demostrat un sistema OWC emprant una font de banda ampla (LED) per a la transmissió no sols de dades, sinó també per a la transmissió sense fil d'energia. A més, s'aborda el problema de la sincronització i la detecció del nivell "1" o "0" d'un bit en els sistemes de comunicació sense fil òptica implementats, que sorgeix a conseqüència de l'atenuació de la llum al llarg de la distància i al problema de la pèrdua de línia de visió (NLOS) entre l'emissor i el receptor. Per a fer front a aquest problema, s'ha proporcionat un protocol de comunicació que garanteix la transmissió fiable de dades digitals amb un algorisme de detecció de nivell de bits adaptatiu i s'ha demostrat la seua eficàcia mitjançant la transmissió de textos i imatges. ¿ A més, aquesta tesi aporta una solució per a la implementació de transmissors multiplexats en xarxes amb divisió de longitud d'ona (WDM) per a formats de modulació amb multiplexació per divisió de freqüència ortogonal (OFDM) basats en l'ús de fonts de banda ampla en l'espectre infraroig per a xarxes de fibra bidireccionals centralitzades. Malgrat les limitacions imposades per la dispersió cromàtica en l'ús d'aquest tipus de fonts òptiques, la inclusió d'unes certes estructures abans de la detecció permet la transmissió de senyals OFDM en enllaços òptics. En aquest treball s'ha demostrat experimentalment la reutilització de portadores, l'assignació dinàmica d'amplada de banda i la transmissió de senyals OFDM multibanda mitjançant l'ús de fonts òptiques de banda ampla en xarxes WDM. Els principals resultats obtinguts en cada part d'aquesta tesi doctoral mostren els procediments d'estudi, l'eficàcia de les solucions proposades i les limitacions trobades.[EN] Optical wireless communication (OWC) is a very promising technology for future wireless communications developments. It has attracted increasing interest from researchers and several companies around the world are currently working on the development of very high-speed wireless networks. The scientific and industrial communities believe that OWC will be a complementary technology in its various forms: Free Space Optical communications (FSO), Visible Light Communications (VLC), Light Fidelity (Li-Fi). In fact, the optical spectrum has been considered for many years as a great opportunity for wireless communications especially due to the saturation of the radio frequency (RF) spectrum. This dissertation deals with the use of broadband sources in visible light transmission systems (VLC) as well as fiber optic systems. To carry out the research, three parts can be distinguished: In the first part, we consider the study and simulation of Light Emitting Diode (LED) components with the WIEN2k software by focusing on the optical and electrical properties of elements II-VI. The second part deals with the design, implementation and testing of different VLC communication prototypes for analog and digital transmission in simplex and half-duplex mode. We have demonstrated that an OWC system using a broadband source (i.e. an LED) can be used not only for data transmission, but also for wireless power transmission. Moreover, the synchronization problem and the detection of level "1" or "0" of a bit often arise in the optical wireless communication systems. This is a result of the attenuation nature of the light over the distance and the problem of Non Line-Of-Sight (NLOS) between the emitter and the receiver. To deal with this problem, a communication protocol ensuring reliable digital data transmission with an adaptive bit level detection algorithm has been provided and its effectiveness has been demonstrated by the transmission of texts and images. In addition, this thesis provides a solution for the implementation of wavelength division multiplexed - orthogonal frequency division multiplexed (WDM-OFDM) transmitters based on the use of broadband sources in the infrared spectrum for centralized bidirectional fiber networks. Despite the chromatic dispersion that avoids the use of this type of optical sources, the inclusion of certain structures before detection allows the transmission of OFDM signals in optical links. Carrier reuse, dynamic bandwidth allocation and multiband OFDM signals transmission will be experimentally demonstrated by using optical broadband sources in WDM networks. The main results obtained during this thesis work demonstrate the study procedures, for each part, the effectiveness of the proposed solutions as well as the constraints encountered.Sekkiou, I. (2021). Design of communication systems based on broadband sources for fiber and free space optical links [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/172542TESI

Optics for AI and AI for Optics

Artificial intelligence is deeply involved in our daily lives via reinforcing the digital transformation of modern economies and infrastructure. It relies on powerful computing clusters, which face bottlenecks of power consumption for both data transmission and intensive computing. Meanwhile, optics (especially optical communications, which underpin today’s telecommunications) is penetrating short-reach connections down to the chip level, thus meeting with AI technology and creating numerous opportunities. This book is about the marriage of optics and AI and how each part can benefit from the other. Optics facilitates on-chip neural networks based on fast optical computing and energy-efficient interconnects and communications. On the other hand, AI enables efficient tools to address the challenges of today’s optical communication networks, which behave in an increasingly complex manner. The book collects contributions from pioneering researchers from both academy and industry to discuss the challenges and solutions in each of the respective fields

Ultra-wideband indoor communications using optical technology

La communication ultra large bande (UWB) a attiré une énorme quantité de recherches ces dernières années, surtout après la présentation du masque spectral de US Federal Communications Commission (FCC). Les impulsions ultra-courtes permettent de très hauts débits de faible puissance tout en éliminant les interférences avec les systèmes existants à bande étroite. La faible puissance, cependant, limite la portée de propagation des radios UWB à quelques mètres pour la transmission sans fil à l’intérieur d’une pièce. En outre, des signaux UWB reçu sont étendus dans le temps en raison de la propagation par trajet multiple qui résulte en beaucoup d’interférence inter-symbole (ISI) à haut débit. Le monocycle Gaussien, l’impulsion la plus commune dans UWB, a une mauvaise couverture sous le masque de la FCC. Dans cette thèse, nous démontrons des transmet- teurs qui sont capables de générer des impulsions UWB avec une efficacité de puissance élevée. Une impulsion efficace résulte dans un rapport de signal à bruit (SNR) supérieur au récepteur en utilisant plus de la puissance disponible sous le masque spectral de la FCC. On produit les impulsions dans le domaine optique et utilise la fibre optique pour les transporter sur plusieurs kilomètres pour la distribution dans un réseau optique pas- sif. La fibre optique est très fiable pour le transport des signaux radio avec une faible consommation de puissance. On utilise les éléments simples comme un modulateur Mach-Zehnder ou un résonateur en anneau pour générer des impulsions, ce qui permet l’intégration dans le silicium. Compatible avec la technologie CMOS, la photonique sur silicium a un potentiel énorme pour abaisser le coût et l’encombrement des systèmes optiques. La photodétection convertit les impulsions optiques en impulsions électriques avant la transmission sur l’antenne du côté de l’utilisateur. La réponse fréquentielle de l’antenne déforme la forme d’onde de l’impulsion UWB. Nous proposons une technique d’optimisation non-linéaire qui prend en compte la distorsion d’antenne pour trouver des impulsions qui maximisent la puissance transmise, en respectant le masque spectral de la FCC. Nous travaillons avec trois antennes et concevons une impulsion unique pour chacune d’entre elle. L’amélioration de l’énergie des impulsions UWB améliore directement la SNR au récepteur. Les résultats de simulation montrent que les impulsions optimisées améliorent considérablement le taux d’erreur (BER) par rapport au monocycle Gaussien sous propagation par trajet multiple. Notre autre contribution est l’évaluation d’un filtre adapté pour recevoir efficacement des impulsions UWB. Le filtre adapté est synthétisé et fabriqué en technologie microstrip, en collaboration avec l’Université McGill comme un dispositif de bande interdite électromagnétique. La réponse fréquentielle du filtre adapté montre une ex- cellente concordance avec le spectre ciblé de l’impulsion UWB. Les mesures de BER confirment la performance supérieure du filtre adapté par rapport à un récepteur à conversion directe. Le canal UWB est très riche en trajet multiple conduisant à l’ISI à haut débit. Notre dernière contribution est l’étude de performance des récepteurs en simulant un système avec des conditions de canaux réalistes. Les résultats de la simulation montrent que la performance d’un tel système se dégrade de façon significative pour les hauts débits. Afin de compenser la forte ISI dans les taux de transfert de données en Gb/s, nous étudions l’algorithme de Viterbi (VA) avec un nombre limité d’états et un égaliseur DFE (decision feedback equalizer). Nous examinons le nombre d’états requis dans le VA, et le nombre de coefficients du filtre dans le DFE pour une transmission fiable de UWB en Gb/s dans les canaux en ligne de vue. L’évaluation par simulation de BER confirme que l’égalisation améliore considérablement les performances par rapport à la détection de symbole. La DFE a une meilleure performance par rapport à la VA en utilisant une complexité comparable. La DFE peut couvrir une plus grande mémoire de canal avec un niveau de complexité relativement réduit.Ultra-wideband (UWB) communication has attracted an enormous amount of research in recent years, especially after the introduction of the US Federal Communications Commission (FCC) spectral mask. Ultra-short pulses allow for very high bit-rates while low power eliminates interference with existing narrowband systems. Low power, however, limits the propagation range of UWB radios to a few meters for indoors wireless transmission. Furthermore, received UWB signals are spread in time because of multipath propagation which results in high intersymbol interference at high data rates. Gaussian monocycle, the most commonly employed UWB pulse, has poor coverage under the FCC mask. In this thesis we demonstrate transmitters capable of generating UWB pulses with high power efficiency at Gb/s bit-rates. An efficient pulse results in higher signal-to-noise ratio (SNR) at the receiver by utilizing most of the available power under the FCC spectral mask. We generate the pulses in the optical domain and use optical fiber to transport the pulses over several kilometers for distribution in a passive optical network. Optical fiber is very reliable for transporting radio signals with low power consumption. We use simple elements such as a Mach Zehnder modulator or a ring resonator for pulse shaping, allowing for integration in silicon. Being compatible with CMOS technology, silicon photonics has huge potential for lowering the cost and bulkiness of optical systems. Photodetection converts the pulses to the electrical domain before antenna transmission at the user side. The frequency response of UWB antennas distorts the UWB waveforms. We pro- pose a nonlinear optimization technique which takes into account antenna distortion to find pulses that maximize the transmitted power, while respecting the FCC spectral mask. We consider three antennas and design a unique pulse for each. The energy improvement in UWB pulses directly improves the receiver SNR. Simulation results show that optimized pulses have a significant bit error rate (BER) performance improvement compared to the Gaussian monocycle under multipath propagation. Our other contribution is evaluating a matched filter to receive efficiently designed UWB pulses. The matched filter is synthesized and fabricated in microstrip technology in collaboration with McGill University as an electromagnetic bandgap device. The frequency response of the matched filter shows close agreement with the target UWB pulse spectrum. BER measurements confirm superior performance of the matched filter compared to a direct conversion receiver. The UWB channel is very rich in multipath leading to ISI at high bit rates. Our last contribution is investigating the performance of receivers by simulating a system employing realistic channel conditions. Simulation results show that the performance of such system degrades significantly for high data rates. To compensate the severe ISI at gigabit rates, we investigate the Viterbi algorithm (VA) with a limited number of states and the decision feedback equalizer (DFE). We examine the required number of states in the VA, and the number of taps in the DFE for reliable Gb/s UWB trans- mission for line-of-sight channels. Non-line-of-sight channels were also investigated at lower speeds. BER simulations confirm that equalization considerably improves the performance compared to symbol detection. The DFE results in better performance compared to the VA when using comparable complexity as the DFE can cover greater channel memory with a relatively low complexity level