Approximate inference in massive MIMO scenarios with moment matching techniques

Mención Internacional en el título de doctorThis Thesis explores low-complexity inference probabilistic algorithms in high-dimensional Multiple-Input Multiple-Output (MIMO) systems and high order M-Quadrature Amplitude Modulation (QAM) constellations. Several modern communications systems are using more and more antennas to maximize spectral efficiency, in a new phenomena call Massive MIMO. However, as the number of antennas and/or the order of the constellation grow several technical issues have to be tackled, one of them is that the symbol detection complexity grows fast exponentially with the system dimension. Nowadays the design of massive MIMO low-complexity receivers is one important research line in MIMO because symbol detection can no longer rely on conventional approaches such as Maximum a Posteriori (MAP) due to its exponential computation complexity. This Thesis proposes two main results. On one hand a hard decision low-complexity MIMO detector based on Expectation Propagation (EP) algorithm which allows to iteratively approximate within polynomial cost the posterior distribution of the transmitted symbols. The receiver is named Expectation Propagation Detector (EPD) and its solution evolves from Minimum Mean Square Error (MMSE) solution and keeps per iteration the MMSE complexity which is dominated by a matrix inversion. Hard decision Symbol Error Rate (SER) performance is shown to remarkably improve state-of-the-art solutions of similar complexity. On the other hand, a soft-inference algorithm, more suitable to modern communication systems with channel codification techniques such as Low- Density Parity-Check (LDPC) codes, is also presented. Modern channel decoding techniques need as input Log-Likehood Ratio (LLR) information for each coded bit. In order to obtain that information, firstly a soft bit inference procedure must be performed. In low-dimensional scenarios, this can be done by marginalization over the symbol posterior distribution. However, this is not feasible at high-dimension. While EPD could provide this probabilistic information, it is shown that its probabilistic estimates are in general poor in the low Signal-to-Noise Ratio (SNR) regime. In order to solve this inconvenience a new algorithm based on the Expectation Consistency (EC) algorithm, which generalizes several algorithms such as Belief. Propagation (BP) and EP itself, was proposed. The proposed algorithm called Expectation Consistency Detector (ECD) maps the inference problem as an optimization over a non convex function. This new approach allows to find stationary points and tradeoffs between accuracy and convergence, which leads to robust update rules. At the same complexity cost than EPD, the new proposal achieves a performance closer to channel capacity at moderate SNR. The result reveals that the probabilistic detection accuracy has a relevant impact in the achievable rate of the overall system. Finally, a modified ECD algorithm is presented, with a Turbo receiver structure where the output of the decoder is fed back to ECD, achieving performance gains in all block lengths simulated. The document is structured as follows. In Chapter I an introduction to the MIMO scenario is presented, the advantages and challenges are exposed and the two main scenarios of this Thesis are set forth. Finally, the motivation behind this work, and the contributions are revealed. In Chapters II and III the state of the art and our proposal are presented for Hard Detection, whereas in Chapters IV and V are exposed for Soft Inference Detection. Eventually, a conclusion and future lines can be found in Chapter VI.Esta Tesis aborda algoritmos de baja complejidad para la estimación probabilística en sistemas de Multiple-Input Multiple-Output (MIMO) de grandes dimensiones con constelaciones M-Quadrature Amplitude Modulation (QAM) de alta dimensionalidad. Son diversos los sistemas de comunicaciones que en la actualidad están utilizando más y más antenas para maximizar la eficiencia espectral, en un nuevo fenómeno denominado Massive MIMO. Sin embargo los incrementos en el número de antenas y/o orden de la constelación presentan ciertos desafíos tecnológicos que deben ser considerados. Uno de ellos es la detección de los símbolos transmitidos en el sistema debido a que la complejidad aumenta más rápido que las dimensiones del sistema. Por tanto el diseño receptores para sistemas Massive MIMO de baja complejidad es una de las importantes líneas de investigación en la actualidad en MIMO, debido principalmente a que los métodos tradicionales no se pueden implementar en sistemas con decenas de antenas, cuando lo deseable serían centenas, debido a que su coste es exponencial. Los principales resultados en esta Tesis pueden clasificarse en dos. En primer lugar un receptor MIMO para decisión dura de baja complejidad basado en el algoritmo Expectation Propagation (EP) que permite de manera iterativa, con un coste computacional polinómico por iteración, aproximar la distribución a posteriori de los símbolos transmitidos. El algoritmo, denominado Expectation Propagation Detector (EPD), es inicializado con la solución del algoritmo Minimum Mean Square Error (MMSE) y mantiene el coste de este para todas las iteraciones, dominado por una inversión de matriz. El rendimiento del decisor en probabilidad de error de símbolo muestra ganancias remarcables con respecto a otros métodos en la literatura con una complejidad similar. En segundo lugar, un algoritmo que provee una estimación blanda, información que es más apropiada para los actuales sistemas de comunicaciones que utilizan codificación de canal, como pueden ser códigos Low-Density Parity-Check (LDPC). La información necesaria para estos decodificadores de canal es Log-Likehood Ratio (LLR) para cada uno de los bits codificados. En escenarios de bajas dimensiones se pueden calcular las marginales de la distribución a posteriori, pero en escenarios de grandes dimensiones no es viable, aunque EPD puede proporcionar este tipo de información a la entrada del decodificador, dicha información no es la mejor al estar el algoritmo pensado para detección dura, sobre todo se observa este fenómeno en el rango de baja Signal-to-Noise Ratio (SNR). Para solucionar este problema se propone un nuevo algoritmo basado en Expectation Consistency (EC) que engloba diversos algoritmos como pueden ser Belief Propagation (BP) y el algoritmo EP propuesto con anterioridad. El nuevo algoritmo llamado Expectation Consistency Detector (ECD), trata el problema como una optimización de una función no convexa. Esta aproximación permite encontrar los puntos estacionarios y la relación entre precisión y convergencia, que permitirán reglas de actualización más robustas y eficaces. Con la misma compleja que el algoritmo propuesto inicialmente, ECD permite rendimientos más próximos a la capacidad del canal en regímenes moderados de SNR. Los resultados muestran que la precisión tiene un gran efecto en la tasa que alcanza el sistema. Finalmente una versión modificada de ECD es propuesta en una arquitectura típica de los Turbo receptores, en la que la salida del decodificador es la entrada del receptor, y que permite ganancias en el rendimiento en todas las longitudes de código simuladas. El presente documento está estructurado de la siguiente manera. En el primer Capítulo I, se realiza una introducción a los sistemas MIMO, presentando sus ventajas, desventajas, problemas abiertos. Los modelos que se utilizaran en la tesis y la motivación con la que se inició esta tesis son expuestos en este primer capítulo. En los Capítulos II y III el estado del arte y nuestra propuesta para detección dura son presentados, mientras que en los Capítulos IV y V se presentan para detección suave. Finalmente las conclusiones que pueden obtenerse de esta Tesis y futuras líneas de investigación son expuestas en el Capítulo VI.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Gonzalo Vázquez Vilar.- Vocal: María Isabel Valera Martíne

Performance Evaluation of Encrypted Text Message Transmission in 5G Compatible Frequency-domain Subband Superposed Scheme Implemented MIMO OFDM Wireless Communication System

In this paper, an investigative study has been made on the performance evaluation of encrypted text message transmission in 5G compatible multiuser frequency-domainsubband superposed (FDSS) scheme implemented MIMO OFDM wireless communication system. The 2D7;2 multiantenna configured simulated system under consideration incorporates modern channel coding (LDPC and Repeat and Accumulate (RA)) and signal detection (Cholesky decomposition based ZF detection, Group Detection (GD) approach aided Efficient Zero-Forcing (ZF) and Lanczos method based efficient signal detection) techniques. In the scenario of transmitting encrypted text message over AWGN and Rayleigh fading channels, it is noticeable that implementation of Repeat and Accumulate channel coding and Group Detection (GD) approach aided Efficient Zero- Forcing (ZF) signal detection techniques is very much robust and effective in retrieving transmitted text messages for all users

Gradient-Based Markov Chain Monte Carlo for MIMO Detection

Accurately detecting symbols transmitted over multiple-input multiple-output (MIMO) wireless channels is crucial in realizing the benefits of MIMO techniques. However, optimal MIMO detection is associated with a complexity that grows exponentially with the MIMO dimensions and quickly becomes impractical. Recently, stochastic sampling-based Bayesian inference techniques, such as Markov chain Monte Carlo (MCMC), have been combined with the gradient descent (GD) method to provide a promising framework for MIMO detection. In this work, we propose to efficiently approach optimal detection by exploring the discrete search space via MCMC random walk accelerated by Nesterov's gradient method. Nesterov's GD guides MCMC to make efficient searches without the computationally expensive matrix inversion and line search. Our proposed method operates using multiple GDs per random walk, achieving sufficient descent towards important regions of the search space before adding random perturbations, guaranteeing high sampling efficiency. To provide augmented exploration, extra samples are derived through the trajectory of Nesterov's GD by simple operations, effectively supplementing the sample list for statistical inference and boosting the overall MIMO detection performance. Furthermore, we design an early stopping tactic to terminate unnecessary further searches, remarkably reducing the complexity. Simulation results and complexity analysis reveal that the proposed method achieves near-optimal performance in both uncoded and coded MIMO systems, adapts to realistic channel models, and scales well to large MIMO dimensions.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

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

Récepteur itératif pour les systèmes MIMO-OFDM basé sur le décodage sphérique : convergence, performance et complexité

Recently, iterative processing has been widely considered to achieve near-capacity performance and reliable high data rate transmission, for future wireless communication systems. However, such an iterative processing poses significant challenges for efficient receiver design. In this thesis, iterative receiver combining multiple-input multiple-output (MIMO) detection with channel decoding is investigated for high data rate transmission. The convergence, the performance and the computational complexity of the iterative receiver for MIMO-OFDM system are considered. First, we review the most relevant hard-output and soft-output MIMO detection algorithms based on sphere decoding, K-Best decoding, and interference cancellation. Consequently, a low-complexity K-best (LCK- Best) based decoder is proposed in order to substantially reduce the computational complexity without significant performance degradation. We then analyze the convergence behaviors of combining these detection algorithms with various forward error correction codes, namely LTE turbo decoder and LDPC decoder with the help of Extrinsic Information Transfer (EXIT) charts. Based on this analysis, a new scheduling order of the required inner and outer iterations is suggested. The performance of the proposed receiver is evaluated in various LTE channel environments, and compared with other MIMO detection schemes. Secondly, the computational complexity of the iterative receiver with different channel coding techniques is evaluated and compared for different modulation orders and coding rates. Simulation results show that our proposed approaches achieve near optimal performance but more importantly it can substantially reduce the computational complexity of the system. From a practical point of view, fixed-point representation is usually used in order to reduce the hardware costs in terms of area, power consumption and execution time. Therefore, we present efficient fixed point arithmetic of the proposed iterative receiver based on LC-KBest decoder. Additionally, the impact of the channel estimation on the system performance is studied. The proposed iterative receiver is tested in a real-time environment using the MIMO WARP platform.Pour permettre l’accroissement de débit et de robustesse dans les futurs systèmes de communication sans fil, les processus itératifs sont de plus considérés dans les récepteurs. Cependant, l’adoption d’un traitement itératif pose des défis importants dans la conception du récepteur. Dans cette thèse, un récepteur itératif combinant les techniques de détection multi-antennes avec le décodage de canal est étudié. Trois aspects sont considérés dans un contexte MIMOOFDM: la convergence, la performance et la complexité du récepteur. Dans un premier temps, nous étudions les différents algorithmes de détection MIMO à décision dure et souple basés sur l’égalisation, le décodage sphérique, le décodage K-Best et l’annulation d’interférence. Un décodeur K-best de faible complexité (LC-K-Best) est proposé pour réduire la complexité sans dégradation significative des performances. Nous analysons ensuite la convergence de la combinaison de ces algorithmes de détection avec différentes techniques de codage de canal, notamment le décodeur turbo et le décodeur LDPC en utilisant le diagramme EXIT. En se basant sur cette analyse, un nouvel ordonnancement des itérations internes et externes nécessaires est proposé. Les performances du récepteur ainsi proposé sont évaluées dans différents modèles de canal LTE, et comparées avec différentes techniques de détection MIMO. Ensuite, la complexité des récepteurs itératifs avec différentes techniques de codage de canal est étudiée et comparée pour différents modulations et rendement de code. Les résultats de simulation montrent que les approches proposées offrent un bon compromis entre performance et complexité. D’un point de vue implémentation, la représentation en virgule fixe est généralement utilisée afin de réduire les coûts en termes de surface, de consommation d’énergie et de temps d’exécution. Nous présentons ainsi une représentation en virgule fixe du récepteur itératif proposé basé sur le décodeur LC K-Best. En outre, nous étudions l’impact de l’estimation de canal sur la performance du système. Finalement, le récepteur MIMOOFDM itératif est testé sur la plateforme matérielle WARP, validant le schéma proposé

A Performance comparision of polar codes with convolutional turbo codes

Ankara : Department of Electrical and Electronic Engineering and the Institute of Engineering and Sciences of Bilkent University, 2009.Thesis (Master's) -- Bilkent University, 2009.Includes bibliographical references leaves 134-136.Polar codes introduced recently by Arıkan are the first low-complexity codes achieving symmetric capacity for arbitrary binary-input discrete memoryless channels (B-DMCs). Although being theoretically significant, their practical significance is an issue that has not yet been fully explored. Previous studies have compared polar codes with Reed-Muller codes, where it was found that polar codes can outperform them. In this thesis, to investigate how polar codes perform against state-of-the-art forward error correction (FEC) codes used in practice, we implement a IEEE 802.16 based link-level Worldwide Interoperability for Microwave Access (WiMAX) simulator which incorporates several WiMAX FEC options, and polar codes. IEEE 802.16 standards family define standards for current and next generation broadband wireless access, which will make high data rate multimedia applications in mobile environments a reality. Next generation broadband access standard, pursued by the IEEE 802.16 Task Group m is a work in progress, and requires even more sophisticated error correction schemes so that higher throughput, better QOS, higher mobilities, wider ranges and lower latencies are supported. We perform performance comparison simulations with the convolutional turbo codes (CTC) configurations defined in IEEE 802.16e to see how much of a performance gap exists between polar codes and CTCs. The main findings of the thesis are that, although the polar codes achieve capacity for specific conditions, as expected, for the code lengths and channel conditions we have simulated, the performance of them cannot compete with that of the CTCs with equivalent rates and lengths. It remains a task to see whether polar codes can achieve similar performances with CTCs when used as component codes in other configurations and aid in the advancement of new communication technologies.Özgür, ÜstünM.S

Expectation propagation as a solution for digital communication systems.

In the context of digital communications, a digital receiver is required to provide an estimation of the transmitted symbols. Nowadays channel decoders highly benefit from soft (probabilistic) estimates for each transmitted symbol rather than from hard decisions. For this reason, digital receivers must be designed to provide the probability that each possible symbol was transmitted based on the received corrupted signal. Since exact inference might be unfeasible in terms of complexity for high-order scenarios, it is necessary to resort to approximate inference, such as the linear minimum mean square error (LMMSE) criterion. The LMMSE approximates the discrete prior information of the transmitted symbols with a Gaussian distribution, which causes a degradation in its performance. In this thesis, an alternative approximate statistical technique is applied to the design of a digital probabilistic receiver in digital communications. Specifically, the expectation propagation (EP) algorithm is investigated to find the Gaussian posterior probability density function (pdf) that minimizes the Kullback-Leibler (KL) divergence with respect to the true posterior pdf. Two different communication system scenarios are studied: a single-input singleoutput (SISO) digital communication system with memory channel and a multipleinput multiple-output (MIMO) system with memoryless channel. In the SISO scenario, three different designs of a soft standalone and turbo equalizer based on the EP algorithm are developed: the block or batch approach, the filter-type version that emulates theWiener filter behavior and the smoothing equalizer which proceeds similarly to a Kalman smoother. Finally, the block EP implementation is also adapted to MIMO scenarios with feedback from the decoder. In both scenarios, the EP is applied iteratively, including a damping mechanism and a control to avoid negative values of variances, which would lead to instabilities (specially for high-order constellations). Experimental results included through the thesis show that the EP algorithm applied to communication systems greatly improves the performance of previous approaches found in the literature with a complexity slightly increased but still proportional to that of the LMMSE. These results also show the robustness of the algorithm even for high-order modulations, large memory channels and high number of antennas. Major contributions of this dissertation have been published in four journal (one of them is still under review) and two conference papers. One more paper will be submitted to a journal soon. All these papers are listed below: • Irene Santos, Juan José Murillo-Fuentes, Rafael Boloix-Tortosa, Eva Arias de Reyna and Pablo M. Olmos, "Expectation Propagation as Turbo Equalizer in ISI Channels," IEEE Transactions on Communications, vol. 65, no.1, pp. 360-370, Jan 2017. • Irene Santos, Juan José Murillo-Fuentes, Eva Arias de Reyna and Pablo M. Olmos, "Turbo EP-based Equalization: a Filter-Type Implementation," IEEE Transactions on Communications, Sep 2017, Accepted. [Online] Available: https://ieeexplore.ieee.org/document/8353388/ • Irene Santos, Juan José Murillo-Fuentes, Eva Arias-de-Reyna and Pablo M. Olmos, "Probabilistic Equalization With a Smoothing Expectation Propagation Approach," IEEE Transactions on Wireless Communications, vol. 16, no. 5, pp. 2950-2962, May 2017. • Irene Santos, Juan José Murillo-Fuentes and Eva Arias-de-Reyna, "Equalization with Expectation Propagation at Smoothing Level," To be submitted. [Online] Available: https://arxiv.org/abs/1809.00806 • Irene Santos and Juan José Murillo-Fuentes, "EP-based turbo detection for MIMO receivers and large-scale systems," IEEE Transactions on Vehicular Technology, May 2018, Under review. [Online] Available: https://arxiv.org/abs/1805.05065 • Irene Santos, Juan José Murillo-Fuentes, and Pablo M. Olmos, "Block expectation propagation equalization for ISI channels," 23rd European Signal Processing Conference (EUSIPCO 2015), Nice, 2015, pp. 379-383. • Irene Santos, and Juan José Murillo-Fuentes, "Improved probabilistic EPbased receiver for MIMO systems and high-order modulations," XXXIII Simposium Nacional de la Unión Científica Internacional de Radio (URSI 2018), Granada, 2018.En el ámbito de las comunicaciones digitales, es necesario un receptor digital que proporcione una estimación de los símbolos transmitidos. Los decodificadores de canal actuales se benefician enormemente de estimaciones suaves (probabilísticas) de cada símbolo transmitido, en vez de estimaciones duras. Por este motivo, los receptores digitales deben diseñarse para proporcionar la probabilidad de cada posible símbolo que fue transmitido en base a la señal recibida y corrupta. Dado que la inferencia exacta puede no ser posible en términos de complejidad para escenarios de alto orden, es necesario recurrir a inferencia aproximada, como por ejemplo el criterio de linear minimum-mean-square-error (LMMSE). El LMMSE aproxima la información a priori discreta de los símbolos transmitidos con una distribución Gaussiana, lo cual provoca una degradación en su resultado. En esta tesis, se aplica una técnica alternativa de inferencia estadística para diseñar un receptor digital probabilístico de comunicaciones digitales. En concreto, se investiga el algoritmo expectation propagation (EP) con el objetivo de encontrar la función densidad de probabilidad (pdf) a posteriori Gaussiana que minimiza la divergencia de Kullback-Leibler (KL) con respecto a la pdf a posteriori verdadera. Se estudian dos escenarios de comunicaciones digitales diferentes: un sistema de comunicaciones single-input single-output (SISO) con canales con memoria y un sistema multiple-input multiple-output (MIMO) con canales sin memoria. Para el escenario SISO se proponen tres diseños diferentes para un igualador probabilístico, tanto simple como turbo, que está basado en el algoritmo EP: una versión bloque, una versión filtrada que emula el comportamiento de un filtroWiener y una versión smoothing que funciona de forma similar a un Kalman smoother. Finalmente, la implementación del EP en bloque se adapta también para escenarios MIMO con realimentación desde el decodificador. En ambos escenarios, el EP se aplica de forma iterativa, incluyendo un mecanismo de damping y un control para evitar valores de varianzas negativas, que darían lugar a inestabilidades (especialmente, en constelaciones de alto orden). Los resultados experimentales que se incluyen en la tesis muestran que, cuando el algoritmo EP se aplica a sistemas de comunicaciones, se mejora notablemente el resultado de otras propuestas anteriores que existen en la literatura, con un pequeño incremento de la complejidad que es proporcional a la carga del LMMSE. Estos resultados también demuestran la robustez del algoritmo incluso para modulaciones de alto orden, canales con bastante memoria y un gran número de antenas. Las principales contribuciones de esta tesis se han publicado en cuatro artículos de revista (uno de ellos todavía bajo revisión) y dos artículos de conferencia. Otro artículo adicional se encuentra en preparación y se enviaría próximamente a una revista. Estos se citan a continuación: • Irene Santos, Juan José Murillo-Fuentes, Rafael Boloix-Tortosa, Eva Arias de Reyna and Pablo M. Olmos, "Expectation Propagation as Turbo Equalizer in ISI Channels," IEEE Transactions on Communications, vol. 65, no.1, pp. 360-370, Jan 2017. • Irene Santos, Juan José Murillo-Fuentes, Eva Arias de Reyna and Pablo M. Olmos, "Turbo EP-based Equalization: a Filter-Type Implementation," IEEE Transactions on Communications, Sep 2017, Aceptado. [Online] Disponible: https://ieeexplore.ieee.org/document/8353388/ • Irene Santos, Juan José Murillo-Fuentes, Eva Arias-de-Reyna and Pablo M. Olmos, "Probabilistic Equalization With a Smoothing Expectation Propagation Approach," IEEE Transactions on Wireless Communications, vol. 16, no. 5, pp. 2950-2962, May 2017. • Irene Santos, Juan José Murillo-Fuentes and Eva Arias-de-Reyna, "Equalization with Expectation Propagation at Smoothing Level," En preparación. [Online] Disponible: https://arxiv.org/abs/1809.00806 • Irene Santos and Juan José Murillo-Fuentes, "EP-based turbo detection for MIMO receivers and large-scale systems," IEEE Transactions on Vehicular Technology, May 2018, En revisión. [Online] Disponible: https://arxiv.org/abs/1805.05065 • Irene Santos, Juan José Murillo-Fuentes, and Pablo M. Olmos, "Block expectation propagation equalization for ISI channels," 23rd European Signal Processing Conference (EUSIPCO 2015), Nice, 2015, pp. 379-383. • Irene Santos, and Juan José Murillo-Fuentes, "Improved probabilistic EPbased receiver for MIMO systems and high-order modulations," XXXIII Simposium Nacional de la Unión Científica Internacional de Radio (URSI 2018), Granada, 2018