Modeling and equalization of nonlinear bandlimited satellite channels

The problem of modeling and equalization of a nonlinear satellite channel is considered. The channel is assumed to be bandlimited and exhibits both amplitude and phase nonlinearities. A discrete time satellite link is modeled under both uplink and downlink white Gaussian noise. Under conditions of practical interest, a simple and computationally efficient design technique for the minimum mean square error linear equalizer is presented. The bit error probability and some numerical results for a binary phase shift keyed (BPSK) system demonstrate that the proposed equalization technique outperforms standard linear receiver structures

A survey of the state of the art and focused research in range systems, task 2

Contract generated publications are compiled which describe the research activities for the reporting period. Study topics include: equivalent configurations of systolic arrays; least squares estimation algorithms with systolic array architectures; modeling and equilization of nonlinear bandlimited satellite channels; and least squares estimation and Kalman filtering by systolic arrays

Electronic equalization for advanced modulation formats in dispersion-limited systems

We investigate in this letter the use of electronic equalization on dispersion limited systems for different modulation formats. Besides analyzing equalization on standard NRZ intensity modulation as a reference, we focus on two advanced modulation formats, Duobinary and Differential Phase Shift Keying (DPSK) which are recently gaining large attention. We demonstrate that the introduction of an electronic equalizer strongly improves standard NRZ performance, whereas it has a limited effect on Duobinary and DPSK formats. Moreover, we give rules for the optimal choice of the equalizer transversal filter parameters, i.e., the number of taps and the delay between taps

Equalization and detection for digital communication over nonlinear bandlimited satellite communication channels

This dissertation evaluates receiver-based methods for mitigating the effects due to nonlinear bandlimited signal distortion present in high data rate satellite channels. The effects of the nonlinear bandlimited distortion is illustrated for digitally modulated signals. A lucid development of the low-pass Volterra discrete time model for a nonlinear communication channel is presented. In addition, finite-state machine models are explicitly developed for a nonlinear bandlimited satellite channel. A nonlinear fixed equalizer based on Volterra series has previously been studied for compensation of noiseless signal distortion due to a nonlinear satellite channel. This dissertation studies adaptive Volterra equalizers on a downlink-limited nonlinear bandlimited satellite channel. We employ as figure of merits performance in the mean-square error and probability of error senses. In addition, a receiver consisting of a fractionally-spaced equalizer (FSE) followed by a Volterra equalizer (FSE-Volterra) is found to give improvement beyond that gained by the Volterra equalizer. Significant probability of error performance improvement is found for multilevel modulation schemes. Also, it is found that probability of error improvement is more significant for modulation schemes, constant amplitude and multilevel, which require higher signal to noise ratios (i.e., higher modulation orders) for reliable operation. The maximum likelihood sequence detection (MLSD) receiver for a nonlinear satellite channel, a bank of matched filters followed by a Viterbi detector, serves as a probability of error lower bound for the Volterra and FSE-Volterra equalizers. However, this receiver has not been evaluated for a specific satellite channel. In this work, an MLSD receiver is evaluated for a specific downlink-limited satellite channel. Because of the bank of matched filters, the MLSD receiver may be high in complexity. Consequently, the probability of error performance of a more practical suboptimal MLSD receiver, requiring only a single receive filter, is evaluated

Formes d'ondes avancées et traitements itératifs pour les canaux non linéaires satellites

L'augmentation de l'efficacité spectrale des transmissions mono-porteuses sur un lien de diffusion par satellite est devenu un défi d'envergure afin de pallier la demande croissante en débits de transmission. Si des techniques émergentes de transmissions encouragent l'utilisation de modulations à ordre élevé telles que les modulations de phase et d'amplitude (APSK), certaines dégradations sont encourues lors du traitement à bord du satellite. En effet, en raison de l'utilisation d'amplificateurs de puissance ainsi que de filtres à mémoires, les modulations d'ordre élevé subissent des distorsions non-linéaires dues à la fluctuation de leur enveloppe, ce qui nécessite des traitements au sein de l'émetteur ou bien au sein du récepteur. Dans cette thèse, nous nous intéressons au traitement de l'interférence non-linéaire au sein du récepteur, avec une attention particulière aux égaliseurs itératifs qui améliorent les performances du système au prix d'une complexité élevée. A partir du modèle temporel des interférences non-linéaires induites par l'amplificateur de puissance, des algorithmes de réception optimaux et sous optimaux sont dérivés, et leurs performances comparées. Des égaliseurs à complexité réduite sont aussi étudiés dans le but d'atteindre un compromis performances-complexité satisfaisant. Ensuite, un modèle des non-linéarités est dérivé dans le domaine fréquentiel, et les égaliseurs correspondants sont présentés. Dans un second temps, nous analysons et dérivons des récepteurs itératifs pour l'interférence entre symboles non linéaire. L'objectif est d'optimiser les polynômes de distributions d'un code externe basé sur les codes de contrôle de parité à faible densité (LDPC) afin de coller au mieux à la sortie de l'égaliseur. Le récepteur ainsi optimisé atteint de meilleures performances comparé à un récepteur non optimisé pour le canal non-linéaire. Finalement, nous nous intéressons à une classe spécifique de techniques de transmissions mono-porteuse basée sur le multiplexage par division de fréquence (SC-OFDM) pour les liens satellites. L'avantage de ces formes d'ondes réside dans l'efficacité de leur égaliseur dans le domaine fréquentiel. Des formules analytiques de la densité spectrale de puissance et du rapport signal sur bruit et interférence sont dérivées et utilisées afin de prédire les performances du système. ABSTRACT : Increasing both the data rate and power efficiency of single carrier transmissions over broadcast satellite links has become a challenging issue to comply with the urging demand of higher transmission rates. If emerging transmission techniques encourage the use of high order modulations such as Amplitude and Phase Shift Keying (APSK) and Quadrature Amplitude Modulation (QAM), some channel impairments arise due to onboard satellite processing. Indeed, due to satellite transponder Power Amplifiers (PA) as well as transmission filters, high order modulations incur non linear distortions due to their high envelope fluctuations which require specific processing either at the transmitter or at the receiver. In this thesis, we investigate on non linear interference mitigation at the receiver with a special focus on iterative equalizers which dramatically enhance the performance at the cost of additional complexity. Based on the time domain model of the non linear interference induced by the PA, optimal and sub-optimal receiving algorithms are proposed and their performance compared. Low complexity implementations are also investigated for the sake of a better complexity-performance trade-off. Then, a non linear frequency domain model is derived and the corresponding frequency equalizers are investigated. In the second part, we analyse and design an iterative receiver for the non linear Inter Symbol Interference (ISI) channel. The objective is to optimize an outer Low Density Parity Check (LDPC) code distribution polynomials so as to best fit the inner equalizer Extrinsic information. The optimized receiver is shown to achieve better performance compared to a code only optimized for linear ISI channel. Finally, we investigate on a specific class of single carrier transmissions relying on Single Carrier Orthogonal Frequency Division Multiplexing (SCO-FDM) for satellite downlink. The advantage of such waveforms lies in their practical receiver implementation in the frequency domain. General analytical formulas of the power spectral density and signal to noise and interference ratio are derived and used to predict the bit error rate for frequency selective multiplexers

A variable-rate modulation and coding scheme for low earth orbit satellites

Low Earth Orbit (LEO) satellites are increasingly being used for a wide variety of communications applications. These satellites have to operate in widely varying channel conditions. These conditions are often significantly better than the 'worst case' situations that are experienced and thus a single rate transmission scheme is clearly suboptimal. The objective of the thesis is to suggest and test a method of modulation/coding that can take advantage of better signal strength conditions in order to improve data transmission rates. In order to provide the goal of approximately 50kbps transmission in a 10kHz Frequency Division Multiple Access (FDMA) channel it was necessary to consider spectrally efficient, rather than power efficient, modulations. The proposed modulation scheme makes use of an eight-dimensional trellis coded modulation system. Multiple signal constellation sets are used in conjunction with this coding in order to provide different transmission rates, depending on the signal to noise ratio and the channel state. To enhance the suitability of the modulation scheme for the channel, it was combined with Reed-Solomon Coding and interleaving in an inner/outer code arrangement. Various means of determining when to switch between coding rates were discussed briefly, but an in-depth treatment of the subject fell outside of the scope of the thesis. Various combinations of these codes were tested in gaussian noise conditions and various degrees of Rician and Rayleigh fading. In order to make use of the higher rate QAM constellations, it was necessary to provide the decoder with channel state information. The tested system achieved its purpose of providing a variable rate coding scheme resulting in good performance over a range of channel conditions. It is fairly flexible and can be adapted to specific channel requirements

Voronoi Constellations for Coherent Fiber-Optic Communication Systems

The increasing demand for higher data rates is driving the adoption of high-spectral-efficiency (SE) transmission in communication systems. The well-known 1.53 dB gap between Shannon\u27s capacity and the mutual information (MI) of uniform quadrature amplitude modulation (QAM) formats indicates the importance of power efficiency, particularly in high-SE transmission scenarios, such as fiber-optic communication systems and wireless backhaul links. Shaping techniques are the only way to close this gap, by adapting the uniform input distribution to the capacity-achieving distribution. The two categories of shaping are probabilistic shaping (PS) and geometric shaping (GS). Various methods have been proposed for performing PS and GS, each with distinct implementation complexity and performance characteristics. In general, the complexity of these methods grows dramatically with the SE and number of dimensions.Among different methods, multidimensional Voronoi constellations (VCs) provide a good trade-off between high shaping gains and low-complexity encoding/decoding algorithms due to their nice geometric structures. However, VCs with high shaping gains are usually very large and the huge cardinality makes system analysis and design cumbersome, which motives this thesis.In this thesis, we develop a set of methods to make VCs applicable to communication systems with a low complexity. The encoding and decoding, labeling, and coded modulation schemes of VCs are investigated. Various system performance metrics including uncoded/coded bit error rate, MI, and generalized mutual information (GMI) are studied and compared with QAM formats for both the additive white Gaussian noise channel and nonlinear fiber channels. We show that the proposed methods preserve high shaping gains of VCs, enabling significant improvements on system performance for high-SE transmission in both the additive white Gaussian noise channel and nonlinear fiber channel. In addition, we propose general algorithms for estimating the MI and GMI, and approximating the log-likelihood ratios in soft-decision forward error correction codes for very large constellations

Fifty Years of Noise Modeling and Mitigation in Power-Line Communications.

Building on the ubiquity of electric power infrastructure, power line communications (PLC) has been successfully used in diverse application scenarios, including the smart grid and in-home broadband communications systems as well as industrial and home automation. However, the power line channel exhibits deleterious properties, one of which is its hostile noise environment. This article aims for providing a review of noise modeling and mitigation techniques in PLC. Specifically, a comprehensive review of representative noise models developed over the past fifty years is presented, including both the empirical models based on measurement campaigns and simplified mathematical models. Following this, we provide an extensive survey of the suite of noise mitigation schemes, categorizing them into mitigation at the transmitter as well as parametric and non-parametric techniques employed at the receiver. Furthermore, since the accuracy of channel estimation in PLC is affected by noise, we review the literature of joint noise mitigation and channel estimation solutions. Finally, a number of directions are outlined for future research on both noise modeling and mitigation in PLC

Neural-Kalman Schemes for Non-Stationary Channel Tracking and Learning

This Thesis focuses on channel tracking in Orthogonal Frequency-Division Multiplexing (OFDM), a widely-used method of data transmission in wireless communications, when abrupt changes occur in the channel. In highly mobile applications, new dynamics appear that might make channel tracking non-stationary, e.g. channels might vary with location, and location rapidly varies with time. Simple examples might be the di erent channel dynamics a train receiver faces when it is close to a station vs. crossing a bridge vs. entering a tunnel, or a car receiver in a route that grows more tra c-dense. Some of these dynamics can be modelled as channel taps dying or being reborn, and so tap birth-death detection is of the essence. In order to improve the quality of communications, we delved into mathematical methods to detect such abrupt changes in the channel, such as the mathematical areas of Sequential Analysis/ Abrupt Change Detection and Random Set Theory (RST), as well as the engineering advances in Neural Network schemes. This knowledge helped us nd a solution to the problem of abrupt change detection by informing and inspiring the creation of low-complexity implementations for real-world channel tracking. In particular, two such novel trackers were created: the Simpli- ed Maximum A Posteriori (SMAP) and the Neural-Network-switched Kalman Filtering (NNKF) schemes. The SMAP is a computationally inexpensive, threshold-based abrupt-change detector. It applies the three following heuristics for tap birth-death detection: a) detect death if the tap gain jumps into approximately zero (memoryless detection); b) detect death if the tap gain has slowly converged into approximately zero (memory detection); c) detect birth if the tap gain is far from zero. The precise parameters for these three simple rules can be approximated with simple theoretical derivations and then ne-tuned through extensive simulations. The status detector for each tap using only these three computationally inexpensive threshold comparisons achieves an error reduction matching that of a close-to-perfect path death/birth detection, as shown in simulations. This estimator was shown to greatly reduce channel tracking error in the target Signal-to-Noise Ratio (SNR) range at a very small computational cost, thus outperforming previously known systems. The underlying RST framework for the SMAP was then extended to combined death/birth and SNR detection when SNR is dynamical and may drift. We analyzed how di erent quasi-ideal SNR detectors a ect the SMAP-enhanced Kalman tracker's performance. Simulations showed SMAP is robust to SNR drift in simulations, although it was also shown to bene t from an accurate SNR detection. The core idea behind the second novel tracker, NNKFs, is similar to the SMAP, but now the tap birth/death detection will be performed via an arti cial neuronal network (NN). Simulations show that the proposed NNKF estimator provides extremely good performance, practically identical to a detector with 100% accuracy. These proposed Neural-Kalman schemes can work as novel trackers for multipath channels, since they are robust to wide variations in the probabilities of tap birth and death. Such robustness suggests a single, low-complexity NNKF could be reusable over di erent tap indices and communication environments. Furthermore, a di erent kind of abrupt change was proposed and analyzed: energy shifts from one channel tap to adjacent taps (partial tap lateral hops). This Thesis also discusses how to model, detect and track such changes, providing a geometric justi cation for this and additional non-stationary dynamics in vehicular situations, such as road scenarios where re ections on trucks and vans are involved, or the visual appearance/disappearance of drone swarms. An extensive literature review of empirically-backed abrupt-change dynamics in channel modelling/measuring campaigns is included. For this generalized framework of abrupt channel changes that includes partial tap lateral hopping, a neural detector for lateral hops with large energy transfers is introduced. Simulation results suggest the proposed NN architecture might be a feasible lateral hop detector, suitable for integration in NNKF schemes. Finally, the newly found understanding of abrupt changes and the interactions between Kalman lters and neural networks is leveraged to analyze the neural consequences of abrupt changes and brie y sketch a novel, abrupt-change-derived stochastic model for neural intelligence, extract some neuro nancial consequences of unstereotyped abrupt dynamics, and propose a new portfolio-building mechanism in nance: Highly Leveraged Abrupt Bets Against Failing Experts (HLABAFEOs). Some communication-engineering-relevant topics, such as a Bayesian stochastic stereotyper for hopping Linear Gauss-Markov (LGM) models, are discussed in the process. The forecasting problem in the presence of expert disagreements is illustrated with a hopping LGM model and a novel structure for a Bayesian stereotyper is introduced that might eventually solve such problems through bio-inspired, neuroscienti cally-backed mechanisms, like dreaming and surprise (biological Neural-Kalman). A generalized framework for abrupt changes and expert disagreements was introduced with the novel concept of Neural-Kalman Phenomena. This Thesis suggests mathematical (Neural-Kalman Problem Category Conjecture), neuro-evolutionary and social reasons why Neural-Kalman Phenomena might exist and found signi cant evidence for their existence in the areas of neuroscience and nance. Apart from providing speci c examples, practical guidelines and historical (out)performance for some HLABAFEO investing portfolios, this multidisciplinary research suggests that a Neural- Kalman architecture for ever granular stereotyping providing a practical solution for continual learning in the presence of unstereotyped abrupt dynamics would be extremely useful in communications and other continual learning tasks.Programa de Doctorado en Multimedia y Comunicaciones por la Universidad Carlos III de Madrid y la Universidad Rey Juan CarlosPresidente: Luis Castedo Ribas.- Secretaria: Ana García Armada.- Vocal: José Antonio Portilla Figuera