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

Robust massive MIMO Equilization for mmWave systems with low resolution ADCs

Leveraging the available millimeter wave spectrum will be important for 5G. In this work, we investigate the performance of digital beamforming with low resolution ADCs based on link level simulations including channel estimation, MIMO equalization and channel decoding. We consider the recently agreed 3GPP NR type 1 OFDM reference signals. The comparison shows sequential DCD outperforms MMSE-based MIMO equalization both in terms of detection performance and complexity. We also show that the DCD based algorithm is more robust to channel estimation errors. In contrast to the common believe we also show that the complexity of MMSE equalization for a massive MIMO system is not dominated by the matrix inversion but by the computation of the Gram matrix.Comment: submitted to WCNC 2018 Workshop

A blind decision feedback equalizer incorporating fixed lag smoothing

Copyright © 2000 IEEEA new type of blind decision feedback equalizer (DFE) incorporating fixed lag smoothing is developed in this paper. The structure is motivated by the fact that if we make full use of the dependence of the observed data on a given transmitted symbol, delayed decisions may produce better estimates of that symbol. To this end, we use a hidden Markov model (HMM) suboptimal formulation that offers a good tradeoff between computational complexity and bit error rate (BER) performance. The proposed equalizer also provides estimates of the channel coefficients and operates adaptively (so that it can adapt to a fading channel for instance) by means of an online version of the expectation-maximization (EM) algorithm. The resulting equalizer structure takes the form of a linear feedback system including a quantizer, and hence, it is easily implemented. In fact, because of its feedback structure, the proposed equalizer shows some similarities with the well-known DFE. A full theoretical analysis of the initial version of the algorithm is not available, but a characterization of a simplified version is provided. We demonstrate that compared to the zero-forcing DFE (ZF-DFE), the algorithm yields many improvements. A large range of simulations on finite impulse response (FIR) channels and on typical fading GSM channel models illustrate the potential of the proposed equalizer.Sylvie Perreau, Langford B. White and Pierre Duhame

Semi-blind Channel Estimation and Data Detection for Multi-cell Massive MIMO Systems on Time-Varying Channels

We study the problem of semi-blind channel estimation and symbol detection in the uplink of multi-cell massive MIMO systems with spatially correlated time-varying channels. An algorithm based on expectation propagation (EP) is developed to iteratively approximate the joint a posteriori distribution of the unknown channel matrix and the transmitted data symbols with a distribution from an exponential family. This distribution is then used for direct estimation of the channel matrix and detection of data symbols. A modified version of the popular Kalman filtering algorithm referred to as KF-M emerges from our EP derivation and it is used to initialize the EP-based algorithm. Performance of the Kalman smoothing algorithm followed by KF-M is also examined. Simulation results demonstrate that channel estimation error and the symbol error rate (SER) of the semi-blind KF-M, KS-M, and EP-based algorithms improve with the increase in the number of base station antennas and the length of the transmitted frame. It is shown that the EP-based algorithm significantly outperforms KF-M and KS-M algorithms in channel estimation and symbol detection. Finally, our results show that when applied to time-varying channels, these algorithms outperform the algorithms that are developed for block-fading channel models.Comment: 28 pages, 13 figures, Submitted to IEEE Trans. on Vehicular Technolog

Estimation and tracking of rapidly time-varying broadband acoustic communication channels

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 2006This thesis develops methods for estimating wideband shallow-water acoustic communication channels. The very shallow water wideband channel has three distinct features: large dimension caused by extensive delay spread; limited number of degrees of freedom (DOF) due to resolvable paths and inter-path correlations; and rapid fluctuations induced by scattering from the moving sea surface. Traditional LS estimation techniques often fail to reconcile the rapid fluctuations with the large dimensionality. Subspace based approaches with DOF reduction are confronted with unstable subspace structure subject to significant changes over a short period of time. Based on state-space channel modeling, the first part of this thesis develops algorithms that jointly estimate the channel as well as its dynamics. Algorithms based on the Extended Kalman Filter (EKF) and the Expectation Maximization (EM) approach respectively are developed. Analysis shows conceptual parallels, including an identical second-order innovation form shared by the EKF modification and the suboptimal EM, and the shared issue of parameter identifiability due to channel structure, reflected as parameter unobservability in EKF and insufficient excitation in EM. Modifications of both algorithms, including a two-model based EKF and a subspace EM algorithm which selectively track dominant taps and reduce prediction error, are proposed to overcome the identifiability issue. The second part of the thesis develops algorithms that explicitly find the sparse estimate of the delay-Doppler spread function. The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.Financial support for this thesis research was provided by the Office of Naval Research and the WHOI Academic Program Office

Fiscal policy and intranational risk-sharing

A general feature of national fiscal systems is that they provide buffers against regional fluctuations in output and employment by redistributing income between the different regions of a country. Recent literature in connection with European monetary integration has stressed the insurance aspect of this function: Through the fiscal system, regions obtain insurance against asymmetric shocks. In this paper, we review the literature on risk-sharing through fiscal mechanisms. While consumption smoothing would call for full risk-sharing among regions, moral hazard problems, political economy problems and considerations of macro economic stabilization reduce the optimal degree of risk sharing. This may explain why empirical research generally finds that intranational risk-sharing based on fiscal policy seems rather modest. --