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

IST-2000-30148 I-METRA: D3.2 Implementation of relevant algorithms

This deliverable provides a high level description of the software developed within the I-METRA project following the selection reported in D3.1 "Design, Analysis and Selection of Suitable Algorithms".Preprin

Doctor of Philosophy

dissertationMultiple-input and multiple-output (MIMO) technique has emerged as a key feature for future generations of wireless communication systems. It increases the channel capacity proportionate to the minimum number of transmit and receive antennas. This dissertation addresses the receiver design for high-rate MIMO communications in at fading environments. The emphasis of the thesis is on the cases where channel state information (CSI) is not available and thus, clever channel estimation algorithms have to be developed to bene t from the maximum available channel capacity. The thesis makes four distinct novel contributions. First, we note that the conventional MCMC-MIMO detector presented in the prior work may deteriorate as SNR increases. We suggest and show through computer simulations that this problem to a great extent can be solved by initializing the MCMC detector with regulated states which are found through linear detectors. We also introduce the novel concept of staged-MCMC in a turbo receiver, where we start the detection process at a lower complexity and increase complexity only if the data could not be correctly detected in the present stage of data detection. Second, we note that in high-rate MIMO communications, joint data detection and channel estimation poses new challenges when a turbo loop is used to improve the quality of the estimated channel and the detected data. Erroneous detected data may propagate in the turbo loop and, thus, degrade the performance of the receiver signi cantly. This is referred to as error propagation. We propose a novel receiver that decorrelates channel estimation and the detected data to avoid the detrimental e ect of error propagation. Third, the dissertation studies joint channel estimation and MIMO detection over a continuously time-varying channel and proposes a new dual-layer channel estimator to overcome the complexity of optimal channel estimators. The proposed dual-layer channel estimator reduces the complexity of the MIMO detector with optimal channel estimator by an order of magnitude at a cost of a negligible performance degradation, on the order of 0.1 to 0.2 dB. The fourth contribution of this dissertation is to note that the Wiener ltering techniques that are discussed in this dissertation and elsewhere in the literature assume that channel (time-varying) statistics are available. We propose a new method that estimates such statistics using the coarse channel estimates obtained through pilot symbols. The dissertation also makes an additional contribution revealing di erences between the MCMC-MIMO and LMMSE-MIMO detectors. We nd that under the realistic condition where CSI has to be estimated, hence the available channel estimate will be noisy, the MCMC-MIMO detector outperforms the LMMSE-MIMO detector with a signi cant margin

Joint Channel Estimation and Detection for Multi-Carrier MIMO Communications

In MIMO OFDM systems, channel estimation and detection are very important. Pilot-based channel estimation using BEMs is widely used for approximating time-frequency variations of doubly-selective channels. BEMs can provide high estimation performance with low computational load. Data-aided channel estimation outperforms the pilot-based estimation. The data-aided estimation iteratively improves estimates using tentative data symbols and corresponding adaptive weights (reweighted channel estimation). These weights are computed assuming Gaussian data errors, which is inapplicable to OFDM. In this thesis, this assumption is however shown to improve the channel estimation performance. The reweighted channel estimation is shown to significantly outperform the unweighted estimation. Most often used mismatched receivers assume perfect channel estimates when detecting data symbols. However, due to limited pilot symbols and data errors, the channel estimates are imperfect, resulting in a degraded detection performance. The optimal receiver without explicit channel estimation significantly outperform mismatched receivers. However, its complexity is high. To reduce the complexity, a receiver that combines mismatched and optimal detection is proposed. The optimal detection is only applied to data symbols unreliably detected by the mismatched detector, identified using weights computed in the reweighted estimator. The channel estimator and the optimal receiver require the knowledge of channel statistics, which are unavailable and difficult to acquire. To overcome this, an adaptive regularization using the cross-validation criterion is introduced, which finds a regularization matrix providing best channel estimates. The proposed receiver has a reduced complexity than the optimal receiver and provides close-to-optimal detection performance without the knowledge of channel PDP. The adaptive regularization is extended to joint estimation of the Doppler-delay spread and channel. The Doppler and delay spread corresponding to the optimal regularization are selected as their estimates. This approach outperforms other known techniques and provides channel estimation performance close to that obtained with perfect channel statistics

Low-complexity iterative receiver algorithms for multiple-input multiple-output underwater wireless communications

This dissertation proposes three low-complexity iterative receiver algorithms for multiple-input multiple-output (MIMO) underwater acoustic (UWA) communications. First is a bidirectional soft-decision feedback Turbo equalizer (Bi-SDFE) which harvests the time-reverse diversity in severe multipath MIMO channels. The Bi-SDFE outperforms the original soft-decision feedback Turbo equalizer (SDFE) while keeping its total computational complexity similar to that of the SDFE. Second, this dissertation proposes an efficient direct adaptation Turbo equalizer for MIMO UWA communications. Benefiting from the usage of soft-decision reference symbols for parameter adaptation as well as the iterative processing inside the adaptive equalizer, the proposed algorithm is efficient in four aspects: robust performance in tough channels, high spectral efficiency with short training overhead, time efficient with fast convergence and low complexity in hardware implementation. Third, a frequency-domain soft-decision block iterative equalizer combined with iterative channel estimation is proposed for the uncoded single carrier MIMO systems with high data efficiency. All the three new algorithms are evaluated by data recorded in real world ocean experiment or pool experiment. Finally, this dissertation also compares several Turbo equalizers in single-input single-output (SISO) UWA channels. Experimental results show that the channel estimation based Turbo equalizers are robust in SISO underwater transmission under harsh channel conditions --Abstract, page iv

An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin