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

Unified bit-based probabilistic data association aided MIMO detection for high-order QAM constellations

A unified Bit-based Probabilistic Data Association (B-PDA) detection approach is proposed for Multiple-Input Multiple-Output (MIMO) systems employing high-order rectangular Quadrature Amplitude Modulation (QAM). The new approach transforms the symbol detection process of QAM to a bit-based process by introducing a Unified Matrix Representation (UMR) of QAM. Both linear natural and nonlinear binary reflected Gray bit-to-symbol mappings are considered. With the aid of simulation results, we demonstrate that the linear natural mapping based B-PDA approach typically attained an improved detection performance (measured in terms of both Bit Error Ratio (BER) and Symbol Error Ratio (SER)) in comparison to the conventional symbol-based PDA aided MIMO detector, despite its dramatically reduced computational complexity. The only exception is that at low SNRs, the linear natural mapping based B-PDA is slightly inferior in terms of its BER to the conventional symbol-based PDA using binary reflected Gray mapping. Furthermore, the simulation results show that the linear natural mapping based B-PDA MIMO detector may approach the best-case performance provided by the nonlinear binary reflected Gray mapping based B-PDA MIMO detector under ideal conditions. Additionally, the implementation of the B-PDA MIMO detector is shown to be much simpler in the case of the linear natural mapping. Based on these two points, we conclude that in the context of the uncoded B-PDA MIMO detector it is preferable to use the linear natural bit-to-symbol mapping, rather than the nonlinear Gray mapping

ROBUST ITERATIVEPRUNED-TREE DETECTION ANDLDPCC DECODING

A novel sub-optimal low-complexity equalization and turbo-iterative decoding scheme based on running the sum-product algorithm on an aggressively pruned tree is proposed in this paper for use in a multiple transmit and receive antenna (MIMO) system operating over severe frequency-selective fading inter-symbol interference (ISI) channels. The receiver deals with the issue of signal processing complexity which with a full-search equalization grows with power-law. The sum-product algorithm is applied to the pruned tree which is constructed by two main operations, a sphere list detection and a threshold-based tree search algorithms. At a particular node of the tree, only a number of most probable branches in the tree of hypothetical symbols are expanded and included in the list of candidates; at a particular tree-section, all but some of most probable candidatesare pruned. This pruned tree takes the soft input and generates the soft output, and is utilized in the turbo-iterative manner with the decoder of the low-density parity check code. We oobtained the approximated error probability using the pair-wise error calculation averaged over the fading ensemble, and use it to boundour simulation results. Our current simulation results are obtained for MIMO systems up to four transmit and four receive antennas, using 4-QAM symbols. They indicate the proposed receiverperforms extremely well. The proposed transceiver system is ideal for a system of higher spectral efficiency with even larger signal constellations. Adopting Hassbi-Vikalo's framework, we provide a method which enables a quick evaluation of the signal processing complexity required in the proposed algorithm at a given set of system parameters

Linear amplification with multiple nonlinear devices

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e ComputadoresIn mobile wireless systems, where there are strict power and bandwidth constrains it is desirable to adopt energy efficient constellations combined with powerful equalizer. However, this increased spectral efficiency of multilevel modulations comes at the expense of reduced power efficiency, which is undesirable in systems where power consumption is a constraint. Hence, minimization of the transmitted energy would enable a significant reduction in the total energy consumption of the wireless mobile devices. A simple and practical constellation optimization design would optimize the transmitted energy with a minimum increase in system complexity. The constellation decomposition in terms of a sum of BPSK (Bi-Phase Shift Keying) sub-constellations, relies on an analytical characterization of the mapping rule were the constellation symbols are written as a linear function of the transmitted bits. Moreover, large constellations in general and non-uniform constellations in particular are very sensitive to interference, namely the residual ISI (Inter-Symbol Interference) at the output of a practical equalizer that does not invert completely the channel effects. IB-DFE(Iterative Block DFE) is a promising iterative frequency domain equalization technique for SC-FDE schemes (Single-Carrier with Frequency Domain Equalization) that allows excellent performance. Therefore it is possible to use the decomposition of constellations on BPSK components to define a pragmatic method for designing IB-DFE receivers that can be employed with any constellation. In this thesis we consider SC-DFE schemes based on high orderM-ary energy optimized constellations with IB-DFE receivers. It is proposed a method for designing the receiver that does not require a significant increase in system complexity and can be used for the computation of the receiver parameters for any constellation. This method is then employed to design iterative receivers, implemented in the frequency-domain, which can cope with higher sensitivity to ISI effects of the constellations resulting from the energy optimization process.Fundação para a Ciência e Tecnologia - MPSat (PTDC/EEA-TEL/099074/2008) projec

Advanced receivers and waveforms for UAV/Aircraft aeronautical communications

Nowadays, several studies are launched for the design of reliable and safe communications systems that introduce Unmanned Aerial Vehicle (UAV), this paves the way for UAV communication systems to play an important role in a lot of applications for non-segregated military and civil airspaces. Until today, rules for integrating commercial UAVs in airspace still need to be defined, the design of secure, highly reliable and cost effective communications systems still a challenging task. This thesis is part of this communication context. Motivated by the rapid growth of UAV quantities and by the new generations of UAVs controlled by satellite, the thesis aims to study the various possible UAV links which connect UAV/aircraft to other communication system components (satellite, terrestrial networks, etc.). Three main links are considered: the Forward link, the Return link and the Mission link. Due to spectrum scarcity and higher concentration in aircraft density, spectral efficiency becomes a crucial parameter for largescale deployment of UAVs. In order to set up a spectrally efficient UAV communication system, a good understanding of transmission channel for each link is indispensable, as well as a judicious choice of the waveform. This thesis begins to study propagation channels for each link: a mutipath channels through radio Line-of-Sight (LOS) links, in a context of using Meduim Altitude Long drones Endurance (MALE) UAVs. The objective of this thesis is to maximize the solutions and the algorithms used for signal reception such as channel estimation and channel equalization. These algorithms will be used to estimate and to equalize the existing muti-path propagation channels. Furthermore, the proposed methods depend on the choosen waveform. Because of the presence of satellite link, in this thesis, we consider two low-papr linear waveforms: classical Single-Carrier (SC) waveform and Extented Weighted Single-Carrier Orthogonal Frequency-Division Multiplexing (EW-SC-OFDM) waveform. channel estimation and channel equalization are performed in the time-domain (SC) or in the frequency-domain (EW-SC-OFDM). UAV architecture envisages the implantation of two antennas placed at wings. These two antennas can be used to increase diversity gain (channel matrix gain). In order to reduce channel equalization complexity, the EWSC- OFDM waveform is proposed and studied in a muti-antennas context, also for the purpose of enhancing UAV endurance and also increasing spectral efficiency, a new modulation technique is considered: Spatial Modulation (SM). In SM, transmit antennas are activated in an alternating manner. The use of EW-SC-OFDM waveform combined to SM technique allows us to propose new modified structures which exploit exces bandwidth to improve antenna bit protection and thus enhancing system performances

Capacity -based parameter optimization of bandwidth constrained CPM

Continuous phase modulation (CPM) is an attractive modulation choice for bandwidth limited systems due to its small side lobes, fast spectral decay and the ability to be noncoherently detected. Furthermore, the constant envelope property of CPM permits highly power efficient amplification. The design of bit-interleaved coded continuous phase modulation is characterized by the code rate, modulation order, modulation index, and pulse shape. This dissertation outlines a methodology for determining the optimal values of these parameters under bandwidth and receiver complexity constraints. The cost function used to drive the optimization is the information-theoretic minimum ratio of energy-per-bit to noise-spectral density found by evaluating the constrained channel capacity. The capacity can be reliably estimated using Monte Carlo integration. A search for optimal parameters is conducted over a range of coded CPM parameters, bandwidth efficiencies, and channels. Results are presented for a system employing a trellis-based coherent detector. To constrain complexity and allow any modulation index to be considered, a soft output differential phase detector has also been developed.;Building upon the capacity results, extrinsic information transfer (EXIT) charts are used to analyze a system that iterates between demodulation and decoding. Convergence thresholds are determined for the iterative system for different outer convolutional codes, alphabet sizes, modulation indices and constellation mappings. These are used to identify the code and modulation parameters with the best energy efficiency at different spectral efficiencies for the AWGN channel. Finally, bit error rate curves are presented to corroborate the capacity and EXIT chart designs