Low-complexity soft-decision feedback turbo equalization for multilevel modulations

This dissertation proposes two new decision feedback equalization schemes suitable for multilevel modulation systems employing turbo equalization. One is soft-decision feedback equalization (SDFE) that takes into account the reliability of both soft a priori information and soft decisions of the data symbols. The proposed SDFE exhibits lower signal to noise ratio (SNR) threshold that is required for water fall bit error rate (BER) and much faster convergence than the near-optimal exact minimum mean square error linear equalizer (Exact-MMSE-LE) for high-order constellation modulations. The proposed SDFE also offers a low computational complexity compared to the Exact-MMSE-LE. The drawback of the SDFE is that its coefficients cannot reach the matched filter bound (MFB) and therefore after a large number of iterations (e.g. 10), its performance becomes inferior to that of the Exact-MMSE-LE. Therefore, soft feedback intersymbol interference (ISI) canceller-based (SIC) structure is investigated. The SIC structure not only exhibits the same low complexity, low SNR threshold and fast convergence as the SDFE but also reaches the MFB after a large number of iterations. Both theoretical analysis and numerical simulations demonstrate why the SIC achieves MFB while the SDFE cannot. These two turbo equalization structures are also extended from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and applied in high data-rate underwater acoustic (UWA) communications --Abstract, page iv

Coded Modulation Assisted Radial Basis Function Aided Turbo Equalisation for Dispersive Rayleigh Fading Channels

In this contribution a range of Coded Modulation (CM) assisted Radial Basis Function (RBF) based Turbo Equalisation (TEQ) schemes are investigated when communicating over dispersive Rayleigh fading channels. Specifically, 16QAM based Trellis Coded Modulation (TCM), Turbo TCM (TTCM), Bit-Interleaved Coded Modulation (BICM) and iteratively decoded BICM (BICM-ID) are evaluated in the context of an RBF based TEQ scheme and a reduced-complexity RBF based In-phase/Quadrature-phase (I/Q) TEQ scheme. The Least Mean Square (LMS) algorithm was employed for channel estimation, where the initial estimation step-size used was 0.05, which was reduced to 0.01 for the second and the subsequent TEQ iterations. The achievable coding gain of the various CM schemes was significantly increased, when employing the proposed RBF-TEQ or RBF-I/Q-TEQ rather than the conventional non-iterative Decision Feedback Equaliser - (DFE). Explicitly, the reduced-complexity RBF-I/Q-TEQ-CM achieved a similar performance to the full-complexity RBF-TEQ-CM, while attaining a significant complexity reduction. The best overall performer was the RBF-I/Q-TEQ-TTCM scheme, requiring only 1.88~dB higher SNR at BER=10-5, than the identical throughput 3~BPS uncoded 8PSK scheme communicating over an AWGN channel. The coding gain of the scheme was 16.78-dB

MIMO-aided near-capacity turbo transceivers: taxonomy and performance versus complexity

In this treatise, we firstly review the associated Multiple-Input Multiple-Output (MIMO) system theory and review the family of hard-decision and soft-decision based detection algorithms in the context of Spatial Division Multiplexing (SDM) systems. Our discussions culminate in the introduction of a range of powerful novel MIMO detectors, such as for example Markov Chain assisted Minimum Bit-Error Rate (MC-MBER) detectors, which are capable of reliably operating in the challenging high-importance rank-deficient scenarios, where there are more transmitters than receivers and hence the resultant channel-matrix becomes non-invertible. As a result, conventional detectors would exhibit a high residual error floor. We then invoke the Soft-Input Soft-Output (SISO) MIMO detectors for creating turbo-detected two- or three-stage concatenated SDM schemes and investigate their attainable performance in the light of their computational complexity. Finally, we introduce the powerful design tools of EXtrinsic Information Transfer (EXIT)-charts and characterize the achievable performance of the diverse near- capacity SISO detectors with the aid of EXIT charts

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Turbo equalization for multiple-input multiple-output (MIMO) wireless communication systems

This dissertation investigates both of the frequency domain and time domain turbo equalization with multiple-input multiple-output (MIMO) fading channels for radio frequency and underwater acoustic communications. First, a low complexity frequency domain turbo equalization (FDTE) is proposed for the MIMO systems with zero padding (ZP) or cyclic prefix (CP) inserted between the transmitted data blocks and its performance is tested on the real-world UWA communications experiments. Second, as high speed communication system requires efficient bandwidth usage and power consumption, CP or ZP is not transmitted as auxiliary information. An inter-block interference cancelation and CP reconstruction algorithm is developed to re-arrange the channel matrix into a block diagonal one. This improvement makes the FDTE effectively detects the continuous data stream from the high speed UWA communications and its performance has been verified by processing data collected from the UWA communications experiment. Finally, a low complexity soft interference cancelation (SIC) time domain turbo equalizer for MIMO systems with high level modulation is proposed. Compared with the conventional linear or nonlinear turbo equalizers, the proposed SIC turbo equalizer can theoretically reach the bound set up by the ideal match filter and its bit error rate (BER) performance from Monte Carlo simulation achieves a lower error floor as well as a more rapid convergence speed. --Abstract, page iv

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

Adaptive iterative decoding : block turbo codes and multilevel codes

New adaptive, iterative approaches to the decoding of block Turbo codes and multilevel codes are developed. Block Turbo codes are considered as they can readily provide high data rates, low decoding complexity and good performance. Multilevel codes are considered as they provide a moderate complexity approach to a high complexity code and can provide codes with good bandwidth efficiency. The work develops two adaptive sub-optimal soft output decoding algorithms for block Turbo codes. One is based on approximation and the other on the distance properties of the component codes. They can be used with different codes, modulation schemes, channel conditions and in different applications without modification. Both approaches provide improved performance compared to previous approaches on the additive white Gaussian noise (AWGN) channel. The approximation based adaptive algorithm is also investigated on the uncorrelated Rayleigh fiat fading channel and is shown to improve performance over previous approaches. Multilevel codes are typically decoded using a multistage decoder (MSD) for complexity reasons. Each level passes hard decisions to subsequent levels. If the approximation based adaptive algorithm is used to decode component codes in a traditional MSD it improves performance significantly. Performance can be improved further by passing reliability (extrinsic) information to all previous and subsequent levels using an iterative MSD. A new iterative multistage decoding algorithm for multilevel codes is developed by treating the extrinsic information as a Gaussian random variable. If the adaptive algorithms are used in conjunction with iterative multistage decoding on the AWGN channel, then a significant improvement in performance is obtained compared to results using a traditional MSD

Improved timing recovery in wireless mobile receivers

The problem of timing recovery in wireless mobile receiver systems is critical. This is partly because timing recovery functions must follow rapid parameter changes inherent in mobile systems and partly because both bandwidth and power must be conserved in low signal to noise ratio communication channels. The ultimate goal is therefore to achieve a low bit error rate on the recovered information for improving QoS provisioning to terminal mobile users. Traditional timing recovery methods have over-relied on phase-locked loops for timing information adjustment. However, associated schemes do not exploit code properties. This leads to synchronization difficulties in digital receivers separated from transmitters by lossy channels. In this paper we present a soft timing phase estimation algorithm for wireless mobile receivers in low signal to noise ratios. In order to develop a bandwidth and power efficient timing recovery method for wireless mobile receivers, a raised cosine filter and a multilevel phase shift keying modulation scheme are implemented and no clock signals are transmitted to the receiver. In the proposed method, the receiver exploits the soft decisions computed at each turbo decoding iteration to provide reliable estimates of a soft timing signal, which in turn, improves the decoding time. The derived method, based on sequential minimization techniques, approaches the theoretical Cramer-Rao bound with unbiased estimates within a few iterations.Key Words: discrete polyphase matched filters, maximum likelihood estimators, iterative turbo receivers, log-MAP b