Design and Analysis of GFDM-Based Wireless Communication Systems

Le multiplexage généralisé par répartition en fréquence (GFDM), une méthode de traitement par blocs de modulation multiporteuses non orthogonales, est une candidate prometteuse pour les technologies de forme d'onde pour les systèmes sans fil au-delà de la cinquième génération (5G). La capacité du GFDM à ajuster de manière flexible la taille du bloc et le type de filtres de mise en forme des impulsions en fait une méthode appropriée pour répondre à plusieurs exigences importantes, comme une faible latence, un faible rayonnement hors bande (OOB) et des débits de données élevés. En appliquant aux systèmes GFDM la technique des systèmes à entrées multiples et sorties multiples (MIMO), la technique de MIMO massif ou des codes de contrôle de parité à faible densité (LDPC), il est possible d'améliorer leurs performances. Par conséquent, l'étude de ces systèmes combinés sont d'une grande importance théorique et pratique. Dans cette thèse, nous étudions les systèmes de communication sans fil basés sur le GFDM en considérant trois aspects. Tout d'abord, nous dérivons une borne d'union sur le taux d'erreur sur les bits (BER) pour les systèmes MIMO-GFDM, technique qui est basée sur des probabilités d'erreur par paires exactes (PEP). La PEP exacte est calculée en utilisant la fonction génératrice de moments(MGF) pour les détecteurs à maximum de vraisemblance (ML). La corrélation spatiale entre les antennes et les erreurs d'estimation de canal sont prises en compte dans l'environnement de canal étudié. Deuxièmement, les estimateurs et les précodeurs de canal de faible complexité basés sur une expansion polynomiale sont proposés pour les systèmes MIMO-GFDM massifs. Des pilotes sans interférence sont utilisés pour l'estimation du canal basée sur l'erreur quadratique moyenne minimale(MMSE) pour lutter contre l'influence de la non-orthogonalité entre les sous-porteuses dans le GFDM. La complexité de calcul cubique peut être réduite à une complexité d'ordre au carré en utilisant la technique d'expansion polynomiale pour approximer les inverses de matrices dans l'estimation MMSE conventionnelle et le précodage. De plus, nous calculons les limites de performance en termes d'erreur quadratique moyenne (MSE) pour les estimateurs proposés, ce qui peut être un outil utile pour prédire la performance des estimateurs dans la région de Eₛ/N₀ élevé. Une borne inférieure de Cramér-Rao(CRLB) est dérivée pour notre modèle de système et agit comme une référence pour les estimateurs. La complexité de calcul des estimateurs de canal proposés et des précodeurs et les impacts du degré du polynôme sont également étudiés. Enfin, nous analysons les performances de la probabilité d'erreur des systèmes GFDM combinés aux codes LDPC. Nous dérivons d'abord les expressions du ratio de vraisemblance logarithmique (LLR) initiale qui sont utilisées dans le décodeur de l'algorithme de somme de produits (SPA). Ensuite, basé sur le seuil de décodage, nous estimons le taux d'erreur de trame (FER) dans la région de bas E[indice b]/N₀ en utilisant le BER observé pour modéliser les variations du canal. De plus, une borne inférieure du FER du système est également proposée basée sur des ensembles absorbants. Cette borne inférieure peut agir comme une estimation du FER dans la région de E[indice b]/N₀ élevé si l'ensemble absorbant utilisé est dominant et que sa multiplicité est connue. La quantification a également un impact important sur les performances du FER et du BER. Des codes LDPC basés sur un tableau et construit aléatoirement sont utilisés pour supporter les analyses de performances. Pour ces trois aspects, des simulations et des calculs informatiques sont effectués pour obtenir des résultats numériques connexes, qui vérifient les méthodes proposées.8 372162\u a Generalized frequency division multiplexing (GFDM) is a block-processing based non-orthogonal multi-carrier modulation scheme, which is a promising candidate waveform technology for beyond fifth-generation (5G) wireless systems. The ability of GFDM to flexibly adjust the block size and the type of pulse-shaping filters makes it a suitable scheme to meet several important requirements, such as low latency, low out-of-band (OOB) radiation and high data rates. Applying the multiple-input multiple-output (MIMO) technique, the massive MIMO technique, or low-density parity-check (LDPC) codes to GFDM systems can further improve the systems performance. Therefore, the investigation of such combined systems is of great theoretical and practical importance. This thesis investigates GFDM-based wireless communication systems from the following three aspects. First, we derive a union bound on the bit error rate (BER) for MIMO-GFDM systems, which is based on exact pairwise error probabilities (PEPs). The exact PEP is calculated using the moment-generating function (MGF) for maximum likelihood (ML) detectors. Both the spatial correlation between antennas and the channel estimation errors are considered in the investigated channel environment. Second, polynomial expansion-based low-complexity channel estimators and precoders are proposed for massive MIMO-GFDM systems. Interference-free pilots are used in the minimum mean square error (MMSE) channel estimation to combat the influence of non-orthogonality between subcarriers in GFDM. The cubic computational complexity can be reduced to square order by using the polynomial expansion technique to approximate the matrix inverses in the conventional MMSE estimation and precoding. In addition, we derive performance limits in terms of the mean square error (MSE) for the proposed estimators, which can be a useful tool to predict estimators performance in the high Eₛ/N₀ region. A Cramér-Rao lower bound (CRLB) is derived for our system model and acts as a benchmark for the estimators. The computational complexity of the proposed channel estimators and precoders, and the impacts of the polynomial degree are also investigated. Finally, we analyze the error probability performance of LDPC coded GFDM systems. We first derive the initial log-likelihood ratio (LLR) expressions that are used in the sum-product algorithm (SPA) decoder. Then, based on the decoding threshold, we estimate the frame error rate (FER) in the low E[subscript b]/N₀ region by using the observed BER to model the channel variations. In addition, a lower bound on the FER of the system is also proposed based on absorbing sets. This lower bound can act as an estimate of the FER in the high E[subscript b]/N₀ region if the absorbing set used is dominant and its multiplicity is known. The quantization scheme also has an important impact on the FER and BER performances. Randomly constructed and array-based LDPC codes are used to support the performance analyses. For all these three aspects, software-based simulations and calculations are carried out to obtain related numerical results, which verify our proposed methods

Enhanced Air-Interfaces for Fifth Generation Mobile Broadband Communication

In broadband wireless multicarrier communication systems, intersymbol interference (ISI) and intercarrier interference (ICI) should be reduced. In orthogonal frequency division multiplexing (OFDM), the cyclic prefix (CP) guarantees to reduce the ISI interference. However, the CP reduces spectral and power efficiency. In this thesis, iterative interference cancellation (IIC) with iterative decoding is used to reduce ISI and ICI from the received signal in multicarrier modulation (MCM) systems. Alternative schemes as well as OFDM with insufficient CP are considered; filter bank multicarrier (FBMC/Offset QAM) and discrete wavelet transform based multicarrier modulation (DWT-MCM). IIC is applied in these different schemes. The required components are calculated from either the hard decision of the demapper output or the estimated decoded signal. These components are used to improve the received signal. Channel estimation and data detection are very important parts of the receiver design of the wireless communication systems. Iterative channel estimation using Wiener filter channel estimation with known pilots and IIC is used to estimate and improve data detection. Scattered and interference approximation method (IAM) preamble pilot are using to calculate the estimated values of the channel coefficients. The estimated soft decoded symbols with pilot are used to reduce the ICI and ISI and improve the channel estimation. The combination of Multi-Input Multi-Output MIMO and OFDM enhances the air-interface for the wireless communication system. In a MIMO-MCM scheme, IIC and MIMO-IIC-based successive interference cancellation (SIC) are proposed to reduce the ICI/ISI and cross interference to a given antenna from the signal transmitted from the target and the other antenna respectively. The number of iterations required can be calculated by analysing the convergence of the IIC with the help of EXtrinsic Information Transfer (EXIT) charts. A new EXIT approach is proposed to provide a means to define performance for a given outage probability on quasi-static channels

LDPC-coded modulation for transmission over AWGN and flat rayleigh fading channels

La modulation codée est une technique de transmission efficace en largeur de bande qui intègre le codage de canal et la modulation en une seule entité et ce, afin d'améliorer les performances tout en conservant la même efficacité spectrale comparé à la modulation non codée. Les codes de parité à faible densité (low-density parity-check codes, LDPC) sont les codes correcteurs d'erreurs les plus puissants et approchent la limite de Shannon, tout en ayant une complexité de décodage relativement faible. L'idée de combiner les codes LDPC et la modulation efficace en largeur de bande a donc été considérée par de nombreux chercheurs. Dans ce mémoire, nous étudions une méthode de modulation codée à la fois puissante et efficace en largeur de bande, ayant d'excellentes performances de taux d'erreur binaire et une complexité d'implantation faible. Ceci est réalisé en utilisant un encodeur rapide, un décoder de faible complexité et aucun entrelaceur. Les performances du système proposé pour des transmissions sur un canal additif gaussien blanc et un canal à évanouissements plats de Rayleigh sont évaluées au moyen de simulations. Les résultats numériques montrent que la méthode de modulation codée utilisant la modulation d'amplitude en quadrature à M niveaux (M-QAM) peut atteindre d'excellentes performances pour toute une gamme d'efficacité spectrale. Une autre contribution de ce mémoire est une méthode simple pour réaliser une modulation codée adaptative avec les codes LDPC pour la transmission sur des canaux à évanouissements plats et lents de Rayleigh. Dans cette méthode, six combinaisons de paires encodeur modulateur sont employées pour une adaptation trame par trame. L'efficacité spectrale moyenne varie entre 0.5 et 5 bits/s/Hz lors de la transmission. Les résultats de simulation montrent que la modulation codée adaptative avec les codes LDPC offre une meilleure efficacité spectrale tout en maintenant une performance d'erreur acceptable

Non-binary LDPC coded STF-MIMO-OFDM with an iterative joint receiver structure

The aim of the dissertation was to design a realistic, low-complexity non-binary (NB) low density parity check (LDPC) coded space-time-frequency (STF) coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with an iterative joint decoder and detector structure at the receiver. The goal of the first part of the dissertation was to compare the performance of different design procedures for NB-LDPC codes on an additive white Gaussian noise (AWGN) channel, taking into account the constraint on the code length. The effect of quantisation on the performance of the code was also analysed. Different methods for choosing the NB elements in the parity check matrix were compared. For the STF coding, a class of universal STF codes was used. These codes use linear pre-coding and a layering approach based on Diophantine numbers to achieve full diversity and a transmission rate (in symbols per channel use per frequency) equal to the number of transmitter antennas. The study of the system considers a comparative performance analysis of di erent ST, SF and STF codes. The simulations of the system were performed on a triply selective block fading channel. Thus, there was selectivity in the fading over time, space and frequency. The effect of quantisation at the receiver on the achievable diversity of linearly pre-coded systems (such as the STF codes used) was mathematically derived and verified with simulations. A sphere decoder (SD) was used as a MIMO detector. The standard method used to create a soft-input soft output (SISO) SD uses a hard-to-soft process and the max-log-map approximation. A new approach was developed which combines a Hopfield network with the SD. This SD-Hopfield detector was connected with the fast Fourier transform belief propagation (FFT-BP) algorithm in an iterative structure. This iterative system was able to achieve the same bit error rate (BER) performance as the original SISO-SD at a reduced complexity. The use of the iterative Hopfield-SD and FFT-BP decoder system also allows performance to be traded off for complexity by varying the number of decoding iterations. The complete system employs a NB-LDPC code concatenated with an STF code at the transmitter with a SISO-SD and FFT-BP decoder connected in an iterative structure at the receiver. The system was analysed in varying channel conditions taking into account the effect of correlation and quantisation. The performance of different SF and STF codes were compared and analysed in the system. An analysis comparing different numbers of FFT-BP and outer iterations was also done. AFRIKAANS : Die doel van die verhandeling was om ’n realistiese, lae-kompleksiteit nie-binˆere (NB) LDPC gekodeerde ruimte-tyd-frekwensie-gekodeerde MIMO-OFDM-sisteem met iteratiewe gesamentlike dekodeerder- en detektorstrukture by die ontvanger te ontwerp. Die eerstem deel van die verhandeling was om die werkverrigting van verskillende ontwerpprosedures vir NB-LDPC kodes op ’n gesommeerde wit Gausruiskanaal te vergelyk met inagneming van die beperking op die lengte van die kode. Verskillende metodes om die nie-bineêre elemente in die pariteitstoetsmatriks te kies, is gebruik. Vir die ruimte-tyd-frekwensiekodering is ’n klas universele ruimte-tyd-frekwensiekodes gebruik. Hierdie kodes gebruik lineêre pre-kodering en ’n laagbenadering gebaseer op Diofantiese syfers om volle diversiteit te bereik en ’n oordragtempo (in simbole per kanaalgebruik per frekwensie) gelyk aan die aantal senderantennes. Die studie van die sisteem oorweeg ’n vergelykende werkverrigtinganalisie van verskillende ruimte-tyd-, ruimte-freksensie- en ruimte-tyd-frekwensiekodes. Die simulasies van die sisteem is gedoen op ’n drievoudig selektiewe blokwegsterwingskanaal. Daar was dus selektiwiteit in die wegsterwing oor tyd, ruimte en frekwensie. Die effek van kwantisering by die ontvanger op die bereikbare diversiteit van lineêr pre-gekodeerde sisteme (soos die ruimte-tyd-frekwensiekodes wat gebruik is) is matematies afgelei en bevestig deur simulasies. ’n Sfeerdekodeerder (SD) is gebruik as ’n MIMO-detektor. Die standaardmetode wat gebuik is om ’n sagte-inset-sagte-uitset (SISO) SD te skep, gebruik ’n harde-na-sagte proses en die maksimum logaritmiese afbeelding-benadering. ’n Nuwe benadering wat ’n Hopfield-netwerk met die SD kombineer, is ontwikkel. Hierdie SD-Hopfield-detektor is verbind met die FFT-BP-algoritme in iteratiewe strukture. Hierdie iteratiewe sisteem was in staat om dieselfde bisfouttempo te bereik as die oorspronklike SISO-SD, met laer kompleksiteit. Die gebruik van die iteratiewe Hopfield-SD en FFT-BP-dekodeerdersisteem maak ook daarvoor voorsiening dat werkverrigting opgeweeg kan word teen kompleksiteit deur die aantal dekodering-iterasies te varieer. Die volledige sisteem maak gebruik van ’n QC-NB-LDPC-kode wat met ’n ruimte-tyd-frekwensiekode by die sender aaneengeskakel is met ’n SISO-SD en FFT-BP-dekodeerder wat in ’n iteratiewe struktuur by die ontvanger gekoppel is. Die sisteem is onder ’n verskeidenheid kanaalkondisies ge-analiseer met inagneming van die effek van korrelasie en kwantisering. Die werkverrigting van verskillende ruimte-frekwensie- en ruimte-tyd-frekwensiekodes is vergelyk en in die sisteem ge-analiseer. ’n Analise om ’n wisselende aantal FFT-BP en buite-iterasies te vergelyk, is ook gedoen. CopyrightDissertation (MEng)--University of Pretoria, 2010.Electrical, Electronic and Computer Engineeringunrestricte

Algorithm Development and VLSI Implementation of Energy Efficient Decoders of Polar Codes

With its low error-floor performance, polar codes attract significant attention as the potential standard error correction code (ECC) for future communication and data storage. However, the VLSI implementation complexity of polar codes decoders is largely influenced by its nature of in-series decoding. This dissertation is dedicated to presenting optimal decoder architectures for polar codes. This dissertation addresses several structural properties of polar codes and key properties of decoding algorithms that are not dealt with in the prior researches. The underlying concept of the proposed architectures is a paradigm that simplifies and schedules the computations such that hardware is simplified, latency is minimized and bandwidth is maximized. In pursuit of the above, throughput centric successive cancellation (TCSC) and overlapping path list successive cancellation (OPLSC) VLSI architectures and express journey BP (XJBP) decoders for the polar codes are presented. An arbitrary polar code can be decomposed by a set of shorter polar codes with special characteristics, those shorter polar codes are referred to as constituent polar codes. By exploiting the homogeneousness between decoding processes of different constituent polar codes, TCSC reduces the decoding latency of the SC decoder by 60% for codes with length n = 1024. The error correction performance of SC decoding is inferior to that of list successive cancellation decoding. The LSC decoding algorithm delivers the most reliable decoding results; however, it consumes most hardware resources and decoding cycles. Instead of using multiple instances of decoding cores in the LSC decoders, a single SC decoder is used in the OPLSC architecture. The computations of each path in the LSC are arranged to occupy the decoder hardware stages serially in a streamlined fashion. This yields a significant reduction of hardware complexity. The OPLSC decoder has achieved about 1.4 times hardware efficiency improvement compared with traditional LSC decoders. The hardware efficient VLSI architectures for TCSC and OPLSC polar codes decoders are also introduced. Decoders based on SC or LSC algorithms suffer from high latency and limited throughput due to their serial decoding natures. An alternative approach to decode the polar codes is belief propagation (BP) based algorithm. In BP algorithm, a graph is set up to guide the beliefs propagated and refined, which is usually referred to as factor graph. BP decoding algorithm allows decoding in parallel to achieve much higher throughput. XJBP decoder facilitates belief propagation by utilizing the specific constituent codes that exist in the conventional factor graph, which results in an express journey (XJ) decoder. Compared with the conventional BP decoding algorithm for polar codes, the proposed decoder reduces the computational complexity by about 40.6%. This enables an energy-efficient hardware implementation. To further explore the hardware consumption of the proposed XJBP decoder, the computations scheduling is modeled and analyzed in this dissertation. With discussions on different hardware scenarios, the optimal scheduling plans are developed. A novel memory-distributed micro-architecture of the XJBP decoder is proposed and analyzed to solve the potential memory access problems of the proposed scheduling strategy. The register-transfer level (RTL) models of the XJBP decoder are set up for comparisons with other state-of-the-art BP decoders. The results show that the power efficiency of BP decoders is improved by about 3 times

Advanced Coding And Modulation For Ultra-wideband And Impulsive Noises

The ever-growing demand for higher quality and faster multimedia content delivery over short distances in home environments drives the quest for higher data rates in wireless personal area networks (WPANs). One of the candidate IEEE 802.15.3a WPAN proposals support data rates up to 480 Mbps by using punctured convolutional codes with quadrature phase shift keying (QPSK) modulation for a multi-band orthogonal frequency-division multiplexing (MB-OFDM) system over ultra wideband (UWB) channels. In the first part of this dissertation, we combine more powerful near-Shannon-limit turbo codes with bandwidth efficient trellis coded modulation, i.e., turbo trellis coded modulation (TTCM), to further improve the data rates up to 1.2 Gbps. A modified iterative decoder for this TTCM coded MB-OFDM system is proposed and its bit error rate performance under various impulsive noises over both Gaussian and UWB channel is extensively investigated, especially in mismatched scenarios. A robust decoder which is immune to noise mismatch is provided based on comparison of impulsive noises in time domain and frequency domain. The accurate estimation of the dynamic noise model could be very difficult or impossible at the receiver, thus a significant performance degradation may occur due to noise mismatch. In the second part of this dissertation, we prove that the minimax decoder in \cite, which instead of minimizing the average bit error probability aims at minimizing the worst bit error probability, is optimal and robust to certain noise model with unknown prior probabilities in two and higher dimensions. Besides turbo codes, another kind of error correcting codes which approach the Shannon capacity is low-density parity-check (LDPC) codes. In the last part of this dissertation, we extend the density evolution method for sum-product decoding using mismatched noises. We will prove that as long as the true noise type and the estimated noise type used in the decoder are both binary-input memoryless output symmetric channels, the output from mismatched log-likelihood ratio (LLR) computation is also symmetric. We will show the Shannon capacity can be evaluated for mismatched LLR computation and it can be reduced if the mismatched LLR computation is not an one-to-one mapping function. We will derive the Shannon capacity, threshold and stable condition of LDPC codes for mismatched BIAWGN and BIL noise types. The results show that the noise variance estimation errors will not affect the Shannon capacity and stable condition, but the errors do reduce the threshold. The mismatch in noise type will only reduce Shannon capacity when LLR computation is based on BIL

Algorithm Development and VLSI Implementation of Energy Efficient Decoders of Polar Codes

With its low error-floor performance, polar codes attract significant attention as the potential standard error correction code (ECC) for future communication and data storage. However, the VLSI implementation complexity of polar codes decoders is largely influenced by its nature of in-series decoding. This dissertation is dedicated to presenting optimal decoder architectures for polar codes. This dissertation addresses several structural properties of polar codes and key properties of decoding algorithms that are not dealt with in the prior researches. The underlying concept of the proposed architectures is a paradigm that simplifies and schedules the computations such that hardware is simplified, latency is minimized and bandwidth is maximized. In pursuit of the above, throughput centric successive cancellation (TCSC) and overlapping path list successive cancellation (OPLSC) VLSI architectures and express journey BP (XJBP) decoders for the polar codes are presented. An arbitrary polar code can be decomposed by a set of shorter polar codes with special characteristics, those shorter polar codes are referred to as constituent polar codes. By exploiting the homogeneousness between decoding processes of different constituent polar codes, TCSC reduces the decoding latency of the SC decoder by 60% for codes with length n = 1024. The error correction performance of SC decoding is inferior to that of list successive cancellation decoding. The LSC decoding algorithm delivers the most reliable decoding results; however, it consumes most hardware resources and decoding cycles. Instead of using multiple instances of decoding cores in the LSC decoders, a single SC decoder is used in the OPLSC architecture. The computations of each path in the LSC are arranged to occupy the decoder hardware stages serially in a streamlined fashion. This yields a significant reduction of hardware complexity. The OPLSC decoder has achieved about 1.4 times hardware efficiency improvement compared with traditional LSC decoders. The hardware efficient VLSI architectures for TCSC and OPLSC polar codes decoders are also introduced. Decoders based on SC or LSC algorithms suffer from high latency and limited throughput due to their serial decoding natures. An alternative approach to decode the polar codes is belief propagation (BP) based algorithm. In BP algorithm, a graph is set up to guide the beliefs propagated and refined, which is usually referred to as factor graph. BP decoding algorithm allows decoding in parallel to achieve much higher throughput. XJBP decoder facilitates belief propagation by utilizing the specific constituent codes that exist in the conventional factor graph, which results in an express journey (XJ) decoder. Compared with the conventional BP decoding algorithm for polar codes, the proposed decoder reduces the computational complexity by about 40.6%. This enables an energy-efficient hardware implementation. To further explore the hardware consumption of the proposed XJBP decoder, the computations scheduling is modeled and analyzed in this dissertation. With discussions on different hardware scenarios, the optimal scheduling plans are developed. A novel memory-distributed micro-architecture of the XJBP decoder is proposed and analyzed to solve the potential memory access problems of the proposed scheduling strategy. The register-transfer level (RTL) models of the XJBP decoder are set up for comparisons with other state-of-the-art BP decoders. The results show that the power efficiency of BP decoders is improved by about 3 times