Reduced Complexity Super-Trellis Decoding for Convolutionally Encoded Transmission Over ISI-Channels

In this paper we propose a matched encoding (ME) scheme for convolutionally encoded transmission over intersymbol interference (usually called ISI) channels. A novel trellis description enables to perform equalization and decoding jointly, i.e., enables efficient super-trellis decoding. By means of this matched non-linear trellis description we can significantly reduce the number of states needed for the receiver-side Viterbi algorithm to perform maximum-likelihood sequence estimation. Further complexity reduction is achieved using the concept of reduced-state sequence estimation.Comment: 6 pages, 8 figures, accepted for ICNC'13. (see also: arXiv:1205.7031

Advanced Signal Processing for Pulse-Amplitude Modulation Optical Transmission Systems

[ES] Los sistemas de transmisión óptica no-coherente se emplean actualmente en las redes ópticas de corto alcance (< 80 km), como son las redes de ámbito metropolitano. La implementación más común en el estado del arte se basa en sistemas que emplean multiplexación por división en longitud de onda (WDM, wavelength division multiplexing) de cuatro longitudes de onda (¿) proporcionando un régimen binario de 100 Gbps (4¿×25 Gbps). En los últimos años, los sistemas de transmisión ópticos no-coherentes están evolucionando desde 100 Gbps a 400 Gbps (4¿×100 Gbps). Dado que este mercado comprende un gran número de sistemas, el coste es un parámetro importante que debe ser lo más bajo posible. El objetivo de esta tesis es investigar distintos aspectos del procesado de señal en general y, específicamente, investigar nuevas técnicas de procesado digital de señal (DSP, digital signal processing) que puedan ser utilizadas en sistemas de transmisión óptica no-coherentes empleando la modulación por amplitud de pulsos (PAM, pulse-amplitude modulation). Para que una técnica DSP sea interesante en el contexto de una red óptica WDM no-coherente, esta debe mitigar de manera efectiva al menos una de las tres limitaciones principales que afectan a estos sistemas: limitaciones de ancho de banda, limitaciones por dispersión cromática (CD), y el ruido. En esta tesis se proponen y examinan una serie de algoritmos cuyo su rendimiento es analizado mediante simulación y experimentalmente en laboratorio: - Feed-forward equalizer (FFE): este es el esquema de ecualización más común que se emplea principalmente en las transmisiones ópticas no-coherentes de alto régimen binario. Puede compensar grandes limitaciones en el ancho de banda. - Estimación de la secuencia de máxima verosimilitud (MLSE): el MLSE es un detector óptimo y, por lo tanto, proporciona las mejores prestaciones en detección cuando se abordan las limitaciones por CD y de ancho de banda. - Conformación geométrica de la constelación: en los esquemas de modulación de intensidad óptica multinivel, la distancia entre los niveles de amplitud puede ajustarse adecuadamente (de manera que no son equidistantes) a fin de aumentar la tolerancia de la señal frente al ruido. - Conformación probabilística: técnica diseñada específicamente para esquemas de modulación multinivel. Esta técnica ajusta la probabilidad de cada nivel de amplitud de modo que se incrementa la tolerancia al ruido óptico. - Señalización de respuesta parcial (PRS, partial signaling response): este es un enfoque basado en DSP donde una interferencia entre símbolos (ISI, inter-symbol interference) controlada es introducida intencionalmente de tal manera que la señal resultante requiere menos ancho de banda. La técnica PRS puede adaptarse para combatir también el efecto de CD. - Pre-énfasis digital (DPE, digital pre-emphasis): esta técnica consiste en aplicar el inverso de la función de transferencia del sistema a la señal en el transmisor, lo que reduce el impacto de las limitaciones de ancho de banda en el receptor. - Modulación con codificación Trellis (TCM, Trellis-coded modulation): esquema de modulación que combina elementos de corrección de errores (FEC, forward error correction) con técnicas de partición en conjuntos y modulación multidimensional para generar una señal más resistente al ruido. - Modulación multidimensional por partición en conjuntos: muy similar a TCM, pero sin ningún elemento FEC. Tiene menos ganancias que TCM en términos de tolerancia al ruido, pero no es tan sensible al ISI. Utilizando estas técnicas, esta tesis demuestra que es posible lograr una transmisión óptica con régimen binario de 100 Gbps/¿ empleando componentes de bajo coste. En esta tesis también demuestra regímenes binarios de más de 200 Gbps, lo que indica que la transmisión óptica no-coherente con modulación PAM puede ser una solución viable y eficiente en coste[CA] Actualment, s'utilitzen sistemes òptics no coherents en xarxes òptiques de curt abast ( < 80 km), com són les xarxes d'àmbit metropolità. La implementació més comuna que podem trobar en l'estat de l'art es correspon amb sistemes emplenant multiplexació per divisió en longitud d'ona (WDM, wavelength division multiplexing) de quatre longituds d'ona (¿) proporcionant un règim binari de 100 Gbps (4¿×25 Gbps). En els últims anys, els sistemes de transmissió òptica no-coherents han evolucionat des de 100 Gbps cap a 400 Gbps (100 Gbps/¿). Atès que el mercat de sistemes de curt abast compren un gran volum de dispositius òptics instal·lats, el cost unitari és molt important i ha de ser el més baix possible. L'objectiu d'aquesta tesi és analitzar aspectes del processament de senyal en general i, específicament, investigar noves tècniques de processament digital de senyal (DSP, digital signal processing) que puguen ser utilitzades en sistemes de transmissió òptica no-coherent que utilitzen la modulació per amplitud d'impulsos (PAM, pulse-amplitude modulation). Per tal que una tècnica DSP es considere interessant per a una xarxa òptica WDM no-coherent, aquesta ha de mitigar efectivament almenys una de les tres principals limitacions que afecten aquests sistemes: limitacions d'ample de banda, limitacions per dispersió cromàtica (CD), i el soroll. En aquesta tesi s'examinen una sèrie d'algoritmes, el seu rendiment s'analitza per simulació i experimentalment en laboratori: - Feed-forward equalizer (FFE): aquest és l'esquema d'equalització més comú i s'utilitza bàsicament en les transmissions òptiques no coherents d'alt règim binari. Pot compensar grans quantitats de limitacions d'ample de banda. - Estimació de la seqüència de probabilitat màxima (MLSE): el MLSE és un detector òptim i, per tant, proporciona el millor rendiment quan es tracta de limitacions d'ample de banda i de CD. - Conformació geomètrica de la constel·lació: en esquemes de modulació òptica d'intensitat multinivell es pot ajustar la distància entre els nivells d'amplitud (de manera que ja no són equidistants) per augmentar la tolerància del senyal al soroll. - Conformació probabilística: una tècnica dissenyada específicament per als esquemes de modulació multinivell; ajusta la probabilitat de cada nivell d'amplitud de manera que augmenta la tolerància al soroll òptic. - Senyalització de resposta parcial (PRS, partial signaling response): és un enfocament basat en DSP on la interferència entre símbols (ISI, inter-symbol interference) controlada s'introdueix intencionalment de manera que el senyal resultant requereix menys ample de banda. La tècnica PRS es pot adaptar per combatre els efectes del CD. - Pre-èmfasi digital (DPE, digital pre-emphasis): aquesta tècnica consisteix a aplicar la inversió de la funció de transferència del sistema a la senyal en el transmissor de manera que es redueix l'impacte de les limitacions d'ample de banda en la senyal en el receptor. - Modulació amb codificació Trellis (TCM, Trellis-coded modulation): esquema de modulació que combina els elements de correcció d'errors avançats (FEC, forward error correction) amb tècniques de partionament de conjunts i modulació multidimensional per generar un senyal més resistent al soroll. - Modulació multidimensional per partició en conjuntes: molt similar a TCM però sense elements FEC. Té guanys menors que TCM en termes de tolerància al soroll, però no és tan sensible a l'ISI. Mitjançant l'ús d'aquestes tècniques, aquesta tesi demostra que és possible aconseguir una transmissió òptica amb un règim binari de 100 Gbps/¿ utilitzant components de baix cost. Esta tesi també demostra règims binaris de més de 200 Gbps, el que indica que la tecnologia no-coherent amb modulació PAM és una solució viable i eficient en cost per a una nova generació de sistemes transceptors òptics WDM funcionant a 800 Gbps (4¿×200 G[EN] Non-coherent optical transmission systems are currently employed in short-reach optical networks (reach shorter than 80 km), like metro networks. The most common implementation in the state-of-the-art is the four wavelength (¿) 100 Gbps (4¿×25 Gbps) wavelength division multiplexing (WDM) transceiver. In recent years non-coherent optical transmissions are evolving from 100 Gbps to 400 Gbps (4¿×100 Gbps). Since in the short-reach market the volume of optical devices being deployed is very large, the cost-per-unit of the devices is very important, and it should be as low as possible. The goal of this thesis is to investigate some general signal processing aspects and, specifically, digital signal processing (DSP) techniques required in non-coherent pulse-amplitude modulation (PAM) optical transmission, and also to investigate novel algorithms which could be applied to this application scenario. In order for a DSP technique to be considered an interesting solution for non-coherent WDM optical networks it has to effectively mitigate at least one of the three main impairments affecting such systems: bandwidth limitations, chromatic dispersion (CD) and noise (in optical or electrical domain). A series of algorithms are proposed and examined in this thesis, and their performance is analyzed by simulation and also experimentally in the laboratory: - Feed-forward equalization (FFE): this is the most common equalizer and it is basically employed in every high-speed non-coherent optical transmission. It can compensate high bandwidth limitations. - Maximum likelihood sequence estimation (MLSE): the MLSE is the optimum detector and thus provides the best performance when it comes to dealing with CD and bandwidth limitations. - Geometrical constellation shaping: in multilevel optical intensity modulation schemes the distance between amplitude levels can be adjusted (such that they are no longer equidistant) in order to increase the signal's tolerance to noise. - Probabilistic shaping: another technique designed specifically for multilevel modulation schemes; it adjusts the probability of each amplitude level such that the tolerance to optical noise is increased. - Partial response signaling (PRS): this is a DSP-based approach where a controlled inter-symbol interference (ISI) is intentionally introduced in such a way that the resulting signal requires less bandwidth. PRS can be customized to also mitigate CD impairment, effectively increasing transmission distances up to three times. - Digital pre-emphasis (DPE): this technique consists in applying the inverse of the transfer function of the system to the signal at the transmitter side which reduces the impact of bandwidth limitations on the signal at the receiver side. - Trellis-coded modulation (TCM): a modulation scheme that combines forward error correction (FEC) elements with set-partitioning techniques and multidimensional modulation to generate a signal that is more resistant to noise. - Multidimensional set-partitioned modulation: very similar with TCM but without any FEC elements. It has lower gains than TCM in terms of noise tolerance but is not so sensitive to ISI. By using the techniques enumerated above, this thesis demonstrates that is possible to achieve 100 Gbps/¿ optical transmission bitrate employing cost-effective components. Even more, bitrates higher than 200 Gbps are also demonstrated, indicating that non-coherent PAM is a viable cost-effective solution for next-generation 800 Gbps (4¿×200 Gbps) WDM transceivers.Prodaniuc, C. (2019). Advanced Signal Processing for Pulse-Amplitude Modulation Optical Transmission Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/117315TESI

Reduced Receivers for Faster-than-Nyquist Signaling and General Linear Channels

Fast and reliable data transmission together with high bandwidth efficiency are important design aspects in a modern digital communication system. Many different approaches exist but in this thesis bandwidth efficiency is obtained by increasing the data transmission rate with the faster-than-Nyquist (FTN) framework while keeping a fixed power spectral density (PSD). In FTN consecutive information carrying symbols can overlap in time and in that way introduce a controlled amount of intentional intersymbol interference (ISI). This technique was introduced already in 1975 by Mazo and has since then been extended in many directions. Since the ISI stemming from practical FTN signaling can be of significant duration, optimum detection with traditional methods is often prohibitively complex, and alternative equalization methods with acceptable complexity-performance tradeoffs are needed. The key objective of this thesis is therefore to design reduced-complexity receivers for FTN and general linear channels that achieve optimal or near-optimal performance. Although the performance of a detector can be measured by several means, this thesis is restricted to bit error rate (BER) and mutual information results. FTN signaling is applied in two ways: As a separate uncoded narrowband communication system or in a coded scenario consisting of a convolutional encoder, interleaver and the inner ISI mechanism in serial concatenation. Turbo equalization where soft information in the form of log likelihood ratios (LLRs) is exchanged between the equalizer and the decoder is a commonly used decoding technique for coded FTN signals. The first part of the thesis considers receivers and arising stability problems when working within the white noise constraint. New M-BCJR algorithms for turbo equalization are proposed and compared to reduced-trellis VA and BCJR benchmarks based on an offset label idea. By adding a third low-complexity M-BCJR recursion, LLR quality is improved for practical values of M. M here measures the reduced number of BCJR computations for each data symbol. An improvement of the minimum phase conversion that sharpens the focus of the ISI model energy is proposed. When combined with a delayed and slightly mismatched receiver, the decoding allows a smaller M without significant loss in BER. The second part analyzes the effect of the internal metric calculations on the performance of Forney- and Ungerboeck-based reduced-complexity equalizers of the M-algorithm type for both ISI and multiple-input multiple-output (MIMO) channels. Even though the final output of a full-complexity equalizer is identical for both models, the internal metric calculations are in general different. Hence, suboptimum methods need not produce the same final output. Additionally, new models working in between the two extremes are proposed and evaluated. Note that the choice of observation model does not impact the detection complexity as the underlying algorithm is unaltered. The last part of the thesis is devoted to a different complexity reducing approach. Optimal channel shortening detectors for linear channels are optimized from an information theoretical perspective. The achievable information rates of the shortened models as well as closed form expressions for all components of the optimal detector of the class are derived. The framework used in this thesis is more general than what has been previously used within the area

Neural networks for optical channel equalization in high speed communication systems

La demande future de bande passante pour les données dépassera les capacités des systèmes de communication optique actuels, qui approchent de leurs limites en raison des limitations de la bande passante électrique des composants de l’émetteur. L’interférence intersymbole (ISI) due à cette limitation de bande est le principal facteur de dégradation pour atteindre des débits de données élevés. Dans ce mémoire, nous étudions plusieurs techniques de réseaux neuronaux (NN) pour combattre les limites physiques des composants de l’émetteur pilotés à des débits de données élevés et exploitant les formats de modulation avancés avec une détection cohérente. Notre objectif principal avec les NN comme égaliseurs de canaux ISI est de surmonter les limites des récepteurs optimaux conventionnels, en fournissant une complexité évolutive moindre et une solution quasi optimale. Nous proposons une nouvelle architecture bidirectionnelle profonde de mémoire à long terme (BiLSTM), qui est efficace pour atténuer les graves problèmes d’ISI causés par les composants à bande limitée. Pour la première fois, nous démontrons par simulation que notre BiLSTM profonde proposée atteint le même taux d’erreur sur les bits(TEB) qu’un estimateur de séquence à maximum de vraisemblance (MLSE) optimal pour la modulation MDPQ. Les NN étant des modèles pilotés par les données, leurs performances dépendent fortement de la qualité des données d’entrée. Nous démontrons comment les performances du BiLSTM profond réalisable se dégradent avec l’augmentation de l’ordre de modulation. Nous examinons également l’impact de la sévérité de l’ISI et de la longueur de la mémoire du canal sur les performances de la BiLSTM profonde. Nous étudions les performances de divers canaux synthétiques à bande limitée ainsi qu’un canal optique mesuré à 100 Gbaud en utilisant un modulateur photonique au silicium (SiP) de 35 GHz. La gravité ISI de ces canaux est quantifiée grâce à une nouvelle vue graphique des performances basée sur les écarts de performance de base entre les solutions optimales linéaires et non linéaires classiques. Aux ordres QAM supérieurs à la QPSK, nous quantifions l’écart de performance BiLSTM profond par rapport à la MLSE optimale à mesure que la sévérité ISI augmente. Alors qu’elle s’approche des performances optimales de la MLSE à 8QAM et 16QAM avec une pénalité, elle est capable de dépasser largement la solution optimale linéaire à 32QAM. Plus important encore, l’avantage de l’utilisation de modèles d’auto-apprentissage comme les NN est leur capacité à apprendre le canal pendant la formation, alors que la MLSE optimale nécessite des informations précises sur l’état du canal.The future demand for the data bandwidth will surpass the capabilities of current optical communication systems, which are approaching their limits due to the electrical bandwidth limitations of the transmitter components. Inter-symbol interference (ISI) due to this band limitation is the major degradation factor to achieve high data rates. In this thesis, we investigate several neural network (NN) techniques to combat the physical limits of the transmitter components driven at high data rates and exploiting the advanced modulation formats with coherent detection. Our main focus with NNs as ISI channel equalizers is to overcome the limitations of conventional optimal receivers, by providing lower scalable complexity and near optimal solution. We propose a novel deep bidirectional long short-term memory (BiLSTM) architecture, that is effective in mitigating severe ISI caused by bandlimited components. For the first time, we demonstrate via simulation that our proposed deep BiLSTM achieves the same bit error rate (BER) performance as an optimal maximum likelihood sequence estimator (MLSE) for QPSK modulation. The NNs being data-driven models, their performance acutely depends on input data quality. We demonstrate how the achievable deep BiLSTM performance degrades with the increase in modulation order. We also examine the impact of ISI severity and channel memory length on deep BiLSTM performance. We investigate the performances of various synthetic band-limited channels along with a measured optical channel at 100 Gbaud using a 35 GHz silicon photonic(SiP) modulator. The ISI severity of these channels is quantified with a new graphical view of performance based on the baseline performance gaps between conventional linear and nonlinear optimal solutions. At QAM orders above QPSK, we quantify deep BiLSTM performance deviation from the optimal MLSE as ISI severity increases. While deep BiLSTM approaches the optimal MLSE performance at 8QAM and 16QAM with a penalty, it is able to greatly surpass the linear optimal solution at 32QAM. More importantly, the advantage of using self learning models like NNs is their ability to learn the channel during the training, while the optimal MLSE requires accurate channel state information

Iterative receivers and multichannel equalisation for time division multiple access systems

The thesis introduces receiver algorithms improving the performance of TDMA mobile radio systems. Particularly, we consider receivers utilising side information, which can be obtained from the error control coding or by having a priori knowledge of interference sources. Iterative methods can be applied in the former case and interference suppression techniques in the latter. Convolutional coding adds redundant information into the signal and thereby protects messages transmitted over a radio channel. In the coded systems the receiver is usually comprised of separate channel estimation, detection and channel decoding tasks due to complexity restrictions. This suboptimal solution suffers from performance degradation compared to the optimal solution achieved by optimising the joint probability of information bits, transmitted symbols and channel impulse response. Conventional receiver utilises estimated channel state information in the detection and detected symbols in the channel decoding to finally obtain information bits. However, the channel decoder provides also extrinsic information on the bit probabilities, which is independent of the received information at the equaliser input. Therefore it is beneficial to re-perform channel estimation and detection using this new extrinsic information together with the original input signal. We apply iterative receiver techniques mainly to Enhanced General Packet Radio System (EGPRS) using GMSK modulation for iterative channel estimation and 8-PSK modulation for iterative detection scheme. Typical gain for iterative detection is around 2 dB and for iterative channel estimation around 1 dB. Furthermore, we suggest two iteration rounds as a reasonable complexity/performance trade-off. To obtain further complexity reduction we introduce the soft trellis decoding technique that reduces the decoder complexity significantly in the iterative schemes. Cochannel interference (CCI) originates from the nearby cells that are reusing the same transmission frequency. In this thesis we consider CCI suppression by joint detection (JD) technique, which detects simultaneously desired and interfering signals. Because of the complexity limitations we only consider JD for two binary modulated signals. Therefore it is important to find the dominant interfering signal (DI) to achieve the best performance. In the presence of one strong DI, the JD provides major improvement in the receiver performance. The JD requires joint channel estimation (JCE) for the two signals. However, the JCE makes the implementation of the JD more difficult, since it requires synchronised network and unique training sequences with low cross-correlation for the two signals.reviewe

Adaptive equalisation for fading digital communication channels

This thesis considers the design of new adaptive equalisers for fading digital communication channels. The role of equalisation is discussed in the context of the functions of a digital radio communication system and both conventional and more recent novel equaliser designs are described. The application of recurrent neural networks to the problem of equalisation is developed from a theoretical study of a single node structure to the design of multinode structures. These neural networks are shown to cancel intersymbol interference in a manner mimicking conventional techniques and simulations demonstrate their sensitivity to symbol estimation errors. In addition the error mechanisms of conventional maximum likelihood equalisers operating on rapidly time-varying channels are investigated and highlight the problems of channel estimation using delayed and often incorrect symbol estimates. The relative sensitivity of Bayesian equalisation techniques to errors in the channel estimate is studied and demonstrates that the structure's equalisation capability is also susceptible to such errors. Applications of multiple channel estimator methods are developed, leading to reduced complexity structures which trade performance for a smaller computational load. These novel structures are shown to provide an improvement over the conventional techniques, especially for rapidly time-varying channels, by reducing the time delay in the channel estimation process. Finally, the use of confidence measures of the equaliser's symbol estimates in order to improve channel estimation is studied and isolates the critical areas in the development of the technique — the production of reliable confidence measures by the equalisers and the statistics of symbol estimation error bursts