96 research outputs found
Improved performance of LDPC-coded MIMO systems with EP-based soft-decisions
The proceeding at: IEEE International Symposium on Information Theory (ISIT 2014), took place 2014, June 29-July 04, in Honolulu (Hawai)Modern communications systems use efficient encoding schemes, multiple-input multiple-output (MIMO) and high-order QAM constellations for maximizing spectral efficiency. However, as the dimensions of the system grow, the design of efficient and low-complexity MIMO receivers possesses technical challenges. Symbol detection can no longer rely on conventional approaches for posterior probability computation due to complexity. Marginalization of this posterior to obtain per-antenna soft-bit probabilities to be fed to a channel decoder is computationally challenging when realistic signaling is used. In this work, we propose to use Expectation Propagation (EP) algorithm to provide an accurate low-complexity Gaussian approximation to the posterior, easily solving the posterior marginalization problem. EP soft-bit probabilities are used in an LDPC-coded MIMO system, achieving outstanding performance improvement compared to similar approaches in the literature for low-complexity LDPC MIMO decoding.This work has been partly funded by the Spanish Ministry of Science
and Innovation with the projects GRE3NSYST (TEC2011-29006-C03-03)
and ALCIT (TEC2012-38800-C03-01) and by the program CONSOLIDERINGENIO
2010 under the project COMONSENS (CSD 2008-00010).Publicad
Turbo EP-based Equalization: a Filter-Type Implementation
This manuscript has been submitted to Transactions on Communications on
September 7, 2017; revised on January 10, 2018 and March 27, 2018; and accepted
on April 25, 2018
We propose a novel filter-type equalizer to improve the solution of the
linear minimum-mean squared-error (LMMSE) turbo equalizer, with computational
complexity constrained to be quadratic in the filter length. When high-order
modulations and/or large memory channels are used the optimal BCJR equalizer is
unavailable, due to its computational complexity. In this scenario, the
filter-type LMMSE turbo equalization exhibits a good performance compared to
other approximations. In this paper, we show that this solution can be
significantly improved by using expectation propagation (EP) in the estimation
of the a posteriori probabilities. First, it yields a more accurate estimation
of the extrinsic distribution to be sent to the channel decoder. Second,
compared to other solutions based on EP the computational complexity of the
proposed solution is constrained to be quadratic in the length of the finite
impulse response (FIR). In addition, we review previous EP-based turbo
equalization implementations. Instead of considering default uniform priors we
exploit the outputs of the decoder. Some simulation results are included to
show that this new EP-based filter remarkably outperforms the turbo approach of
previous versions of the EP algorithm and also improves the LMMSE solution,
with and without turbo equalization
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 CientÃfica 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 sÃmbolos transmitidos. Los decodificadores de canal actuales se benefician enormemente de estimaciones suaves (probabilÃsticas) de cada sÃmbolo transmitido, en vez de estimaciones duras. Por este motivo, los receptores digitales deben diseñarse para proporcionar la probabilidad de cada posible sÃmbolo 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 sÃmbolos transmitidos con una distribución Gaussiana, lo cual provoca una degradación en su resultado. En esta tesis, se aplica una técnica alternativa de inferencia estadÃstica para diseñar un receptor digital probabilÃstico 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 probabilÃstico, 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 darÃan 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 artÃculos de revista (uno de ellos todavÃa bajo revisión) y dos artÃculos de conferencia. Otro artÃculo adicional se encuentra en preparación y se enviarÃa 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 CientÃfica Internacional de Radio (URSI
2018), Granada, 2018
Probabilistic MIMO symbol detection with expectation consistency approximate inference
In this paper, we explore low-complexity probabilistic algorithms for soft symbol detection in high-dimensional multiple-input multiple-output (MIMO) systems. We present a novel algorithm based on the expectation consistency (EC) framework, which describes the approximate inference problem as an optimization over a nonconvex function. EC generalizes algorithms such as belief propagation and expectation propagation. For the MIMO symbol detection problem, we discuss feasible methods to find stationary points of the EC function and explore their tradeoffs between accuracy and speed of convergence. The accuracy is studied, first in terms of input-output mutual information and show that the proposed EC MIMO detector greatly improves state-of-the-art methods, with a complexity order cubic in the number of transmitting antennas. Second, these gains are corroborated by combining the probabilistic output of the EC detector with a low-density parity-check channel code.This work has been partly supported by the Ministerio de EconomÃa of Spain jointly with the European Commission (ERDF) under projects MIMOTEX (TEC2014-61776-EXP), CIES (RTC-2015-4213-7), ELISA (TEC2014-59255-C3-3R), FLUID (TEC2016-78434-C3-3-R) and CAIMAN (TEC2017-86921-C2-2-R), by the Juan de la Cierva program (IJCI-2014-19150), and by Comunidad de Madrid (project “CASI-CAM-CM" id. S2013/ICE-2845).Publicad
Approximate inference in massive MIMO scenarios with moment matching techniques
Mención Internacional en el tÃtulo 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 probabilÃstica 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 desafÃos tecnológicos que deben ser considerados. Uno de
ellos es la detección de los sÃmbolos 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 lÃneas 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 serÃan
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 sÃmbolos 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 sÃmbolo 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 regÃmenes 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 tÃpica 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 CapÃtulo 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 capÃtulo. En los CapÃtulos II y III el estado del arte y
nuestra propuesta para detección dura son presentados, mientras que en los
CapÃtulos IV y V se presentan para detección suave. Finalmente las conclusiones
que pueden obtenerse de esta Tesis y futuras lÃneas de investigación
son expuestas en el CapÃtulo VI.Programa Oficial de Doctorado en Multimedia y ComunicacionesPresidente: Juan José Murillo Fuentes.- Secretario: Gonzalo Vázquez Vilar.- Vocal: MarÃa Isabel Valera MartÃne
Towards closing the capacity gap on multiple antenna channels
In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiple antenna systems, however, it is not clear what is the best way to obtain the soft-information required of the iterative scheme with low complexity. In this paper,
we propose a modification of the Fincke-Pohst (sphere decoder) algorithm to estimate the MAP probability of the received symbol sequence. The new algorithm solves a nonlinear integer least-squares problem and, over a wide range of rates and SNRs, has polynomial-time (often cubic) complexity. The performance of the algorithm, combined with convolutional, turbo, and LDPC codes is demonstrated on several multiple antenna channels
Polar Coding Schemes for Cooperative Transmission Systems
: In this thesis, a serially-concatenated coding scheme with a polar code as the outer code and a low density generator matrix (LDGM) code as the inner code is firstly proposed. It is shown that that the proposed scheme provides a method to improve significantly the low convergence of polar codes and the high error floor of LDGM codes while keeping the advantages of both such as the low encoding and decoding complexity. The bit error rate results show that the proposed scheme by reasonable design have the potential to approach a performance close to the capacity limit and avoid error floor effectively. Secondly, a novel transmission protocol based on polar coding is proposed for the degraded half-duplex relay channel. In the proposed protocol, the relay only needs to forward a part of the decoded source message that the destination needs according to the exquisite nested structure of polar codes. It is proved that the scheme can achieve the capacity of the half-duplex relay channel while enjoying low encoding/decoding complexity. By modeling the practical system, we verify that the proposed scheme outperforms the conventional scheme designed by low-density parity-check codes by simulations. Finally, a generalized partial information relaying protocol is proposed for degraded multiple-relay networks with orthogonal receiver components (MRN-ORCs). In such a protocol, each relay node decodes the received source message with the help of partial information from previous nodes and re-encodes part of the decoded message for transmission to satisfy the decoding requirements for the following relay node or the destination node. For the design of polar codes, the nested structures are constructed based on this protocol and the information sets corresponding to the partial messages forwarded are also calculated. It is proved that the proposed scheme achieves the theoretical capacity of the degraded MRN-ORCs while still retains the low-complexity feature of polar codes
Algorithms for Joint Phase Estimation and Decoding for MIMO Systems in the Presence of Phase Noise and Quasi-Static Fading Channels
In this work, we derive the maximum a posteriori (MAP) symbol detector for a multiple-input multiple-output system in the presence of Wiener phase noise due to noisy local oscillators. As in single-antenna systems, the computation of the optimum receiver is an analytically intractable problem and is unimplementable in practice. In this purview, we propose three suboptimal, low-complexity algorithms for approximately implementing the MAP symbol detector, which involve joint phase noise estimation and data detection. Our first algorithm is obtained by means of the sum-product algorithm, where we use the multivariate Tikhonov canonical distribution approach. In our next algorithm, we derive an approximate MAP symbol detector based on the smoother-detector framework, wherein the detector is properly designed by incorporating the phase noise statistics from the smoother. The third algorithm is derived based on the variational Bayesian framework. By simulations, we evaluate the performance of the proposed algorithms for both uncoded and coded data transmissions, and we observe that the proposed techniques significantly outperform the other important algorithms from prior works, which are considered in this work. Index Terms – Maximum a posteriori (MAP) detection, phase noise, sum-product algorithm (SPA), variational Bayesian (VB) framework, extended Kalman smoother (EKS), MIMO
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