90 research outputs found

    On the Exact BER of Bit-Wise Demodulators for One-Dimensional Constellations

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    The optimal bit-wise demodulator for M-ary pulse amplitude modulation (PAM) over the additive white Gaussian noise channel is analyzed in terms of uncoded bit-error rate (BER). New closed-form BER expressions for 4-PAM with any labeling are developed. Moreover, closed-form BER expressions for 11 out of 23 possible bit patterns for 8-PAM are presented, which enable us to obtain the BER for 8-PAM with some of the most popular labelings, including the binary reflected Gray code and the natural binary code. Numerical results show that, regardless of the labeling, there is no difference between the optimal demodulator and the symbol-wise demodulator for any BER of practical interest (below 0.1)

    General BER Expression for One-Dimensional Constellations

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    A novel general ready-to-use bit-error rate (BER) expression for one-dimensional constellations is developed. The BER analysis is performed for bit patterns that form a labeling. The number of patterns for equally spaced M-PAM constellations with different BER is analyzed.Comment: To appear in the Proceedings of the IEEE Global Communications Conference (GLOBECOM) 2012. Remark 3 modifie

    Replacing the Soft FEC Limit Paradigm in the Design of Optical Communication Systems

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    The FEC limit paradigm is the prevalent practice for designing optical communication systems to attain a certain bit-error rate (BER) without forward error correction (FEC). This practice assumes that there is an FEC code that will reduce the BER after decoding to the desired level. In this paper, we challenge this practice and show that the concept of a channel-independent FEC limit is invalid for soft-decision bit-wise decoding. It is shown that for low code rates and high order modulation formats, the use of the soft FEC limit paradigm can underestimate the spectral efficiencies by up to 20%. A better predictor for the BER after decoding is the generalized mutual information, which is shown to give consistent post-FEC BER predictions across different channel conditions and modulation formats. Extensive optical full-field simulations and experiments are carried out in both the linear and nonlinear transmission regimes to confirm the theoretical analysis

    On the Information Loss of the Max-Log Approximation in BICM Systems

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    We present a comprehensive study of the information rate loss of the max-log approximation for MM-ary pulse-amplitude modulation (PAM) in a bit-interleaved coded modulation (BICM) system. It is widely assumed that the calculation of L-values using the max-log approximation leads to an information loss. We prove that this assumption is correct for all MM-PAM constellations and labelings with the exception of a symmetric 4-PAM constellation labeled with a Gray code. We also show that for max-log L-values, the BICM generalized mutual information (GMI), which is an achievable rate for a standard BICM decoder, is too pessimistic. In particular, it is proved that the so-called "harmonized" GMI, which can be seen as the sum of bit-level GMIs, is achievable without any modifications to the decoder. We then study how bit-level channel symmetrization and mixing affect the mutual information (MI) and the GMI for max-log L-values. Our results show that these operations, which are often used when analyzing BICM systems, preserve the GMI. However, this is not necessarily the case when the MI is considered. Necessary and sufficient conditions under which these operations preserve the MI are provided

    A Simple Approximation for the Bit-Interleaved Coded Modulation Capacity

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    The generalized mutual information (GMI) is an achievable rate for bit-interleaved coded modulation (BICM) and is highly dependent on the binary labeling of the constellation. The BICM-GMI, sometimes called the BICM capacity, can be evaluated numerically. This approach, however, becomes impractical when the number of constellation points and/or the constellation dimensionality grows, or when many different labelings are considered. A simple approximation for the BICM-GMI based on the area theorem of the demapper's extrinsic information transfer (EXIT) function is proposed. Numerical results show the proposed approximation gives good estimates of the BICM-GMI for labelings with close to linear EXIT functions, which includes labelings of common interest, such as the natural binary code, binary reflected Gray code, etc. This approximation is used to optimize the binary labeling of the 32-APSK constellation defined in the DVB-S2 standard. Gains of approximately 0.15 dB are obtained

    Transmit and Receive Signal Processing for MIMO Terrestrial Broadcast Systems

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    [EN] Multiple-Input Multiple-Output (MIMO) technology in Digital Terrestrial Television (DTT) networks has the potential to increase the spectral efficiency and improve network coverage to cope with the competition of limited spectrum use (e.g., assignment of digital dividend and spectrum demands of mobile broadband), the appearance of new high data rate services (e.g., ultra-high definition TV - UHDTV), and the ubiquity of the content (e.g., fixed, portable, and mobile). It is widely recognised that MIMO can provide multiple benefits such as additional receive power due to array gain, higher resilience against signal outages due to spatial diversity, and higher data rates due to the spatial multiplexing gain of the MIMO channel. These benefits can be achieved without additional transmit power nor additional bandwidth, but normally come at the expense of a higher system complexity at the transmitter and receiver ends. The final system performance gains due to the use of MIMO directly depend on physical characteristics of the propagation environment such as spatial correlation, antenna orientation, and/or power imbalances experienced at the transmit aerials. Additionally, due to complexity constraints and finite-precision arithmetic at the receivers, it is crucial for the overall system performance to carefully design specific signal processing algorithms. This dissertation focuses on transmit and received signal processing for DTT systems using MIMO-BICM (Bit-Interleaved Coded Modulation) without feedback channel to the transmitter from the receiver terminals. At the transmitter side, this thesis presents investigations on MIMO precoding in DTT systems to overcome system degradations due to different channel conditions. At the receiver side, the focus is given on design and evaluation of practical MIMO-BICM receivers based on quantized information and its impact in both the in-chip memory size and system performance. These investigations are carried within the standardization process of DVB-NGH (Digital Video Broadcasting - Next Generation Handheld) the handheld evolution of DVB-T2 (Terrestrial - Second Generation), and ATSC 3.0 (Advanced Television Systems Committee - Third Generation), which incorporate MIMO-BICM as key technology to overcome the Shannon limit of single antenna communications. Nonetheless, this dissertation employs a generic approach in the design, analysis and evaluations, hence, the results and ideas can be applied to other wireless broadcast communication systems using MIMO-BICM.[ES] La tecnología de múltiples entradas y múltiples salidas (MIMO) en redes de Televisión Digital Terrestre (TDT) tiene el potencial de incrementar la eficiencia espectral y mejorar la cobertura de red para afrontar las demandas de uso del escaso espectro electromagnético (e.g., designación del dividendo digital y la demanda de espectro por parte de las redes de comunicaciones móviles), la aparición de nuevos contenidos de alta tasa de datos (e.g., ultra-high definition TV - UHDTV) y la ubicuidad del contenido (e.g., fijo, portable y móvil). Es ampliamente reconocido que MIMO puede proporcionar múltiples beneficios como: potencia recibida adicional gracias a las ganancias de array, mayor robustez contra desvanecimientos de la señal gracias a la diversidad espacial y mayores tasas de transmisión gracias a la ganancia por multiplexado del canal MIMO. Estos beneficios se pueden conseguir sin incrementar la potencia transmitida ni el ancho de banda, pero normalmente se obtienen a expensas de una mayor complejidad del sistema tanto en el transmisor como en el receptor. Las ganancias de rendimiento finales debido al uso de MIMO dependen directamente de las características físicas del entorno de propagación como: la correlación entre los canales espaciales, la orientación de las antenas y/o los desbalances de potencia sufridos en las antenas transmisoras. Adicionalmente, debido a restricciones en la complejidad y aritmética de precisión finita en los receptores, es fundamental para el rendimiento global del sistema un diseño cuidadoso de algoritmos específicos de procesado de señal. Esta tesis doctoral se centra en el procesado de señal, tanto en el transmisor como en el receptor, para sistemas TDT que implementan MIMO-BICM (Bit-Interleaved Coded Modulation) sin canal de retorno hacia el transmisor desde los receptores. En el transmisor esta tesis presenta investigaciones en precoding MIMO en sistemas TDT para superar las degradaciones del sistema debidas a diferentes condiciones del canal. En el receptor se presta especial atención al diseño y evaluación de receptores prácticos MIMO-BICM basados en información cuantificada y a su impacto tanto en la memoria del chip como en el rendimiento del sistema. Estas investigaciones se llevan a cabo en el contexto de estandarización de DVB-NGH (Digital Video Broadcasting - Next Generation Handheld), la evolución portátil de DVB-T2 (Second Generation Terrestrial), y ATSC 3.0 (Advanced Television Systems Commitee - Third Generation) que incorporan MIMO-BICM como clave tecnológica para superar el límite de Shannon para comunicaciones con una única antena. No obstante, esta tesis doctoral emplea un método genérico tanto para el diseño, análisis y evaluación, por lo que los resultados e ideas pueden ser aplicados a otros sistemas de comunicación inalámbricos que empleen MIMO-BICM.[CA] La tecnologia de múltiples entrades i múltiples eixides (MIMO) en xarxes de Televisió Digital Terrestre (TDT) té el potencial d'incrementar l'eficiència espectral i millorar la cobertura de xarxa per a afrontar les demandes d'ús de l'escàs espectre electromagnètic (e.g., designació del dividend digital i la demanda d'espectre per part de les xarxes de comunicacions mòbils), l'aparició de nous continguts d'alta taxa de dades (e.g., ultra-high deffinition TV - UHDTV) i la ubiqüitat del contingut (e.g., fix, portàtil i mòbil). És àmpliament reconegut que MIMO pot proporcionar múltiples beneficis com: potència rebuda addicional gràcies als guanys de array, major robustesa contra esvaïments del senyal gràcies a la diversitat espacial i majors taxes de transmissió gràcies al guany per multiplexat del canal MIMO. Aquests beneficis es poden aconseguir sense incrementar la potència transmesa ni l'ample de banda, però normalment s'obtenen a costa d'una major complexitat del sistema tant en el transmissor com en el receptor. Els guanys de rendiment finals a causa de l'ús de MIMO depenen directament de les característiques físiques de l'entorn de propagació com: la correlació entre els canals espacials, l'orientació de les antenes, i/o els desequilibris de potència patits en les antenes transmissores. Addicionalment, a causa de restriccions en la complexitat i aritmètica de precisió finita en els receptors, és fonamental per al rendiment global del sistema un disseny acurat d'algorismes específics de processament de senyal. Aquesta tesi doctoral se centra en el processament de senyal tant en el transmissor com en el receptor per a sistemes TDT que implementen MIMO-BICM (Bit-Interleaved Coded Modulation) sense canal de tornada cap al transmissor des dels receptors. En el transmissor aquesta tesi presenta recerques en precoding MIMO en sistemes TDT per a superar les degradacions del sistema degudes a diferents condicions del canal. En el receptor es presta especial atenció al disseny i avaluació de receptors pràctics MIMO-BICM basats en informació quantificada i al seu impacte tant en la memòria del xip com en el rendiment del sistema. Aquestes recerques es duen a terme en el context d'estandardització de DVB-NGH (Digital Video Broadcasting - Next Generation Handheld), l'evolució portàtil de DVB-T2 (Second Generation Terrestrial), i ATSC 3.0 (Advanced Television Systems Commitee - Third Generation) que incorporen MIMO-BICM com a clau tecnològica per a superar el límit de Shannon per a comunicacions amb una única antena. No obstant açò, aquesta tesi doctoral empra un mètode genèric tant per al disseny, anàlisi i avaluació, per la qual cosa els resultats i idees poden ser aplicats a altres sistemes de comunicació sense fils que empren MIMO-BICM.Vargas Paredero, DE. (2016). Transmit and Receive Signal Processing for MIMO Terrestrial Broadcast Systems [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/66081TESISPremiad

    COMPARATIVE ANALYSIS OF ML AND MAP DETECTORS FOR PAM CONSTELLATIONS IN AWGN CHANNEL

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    In this paper we perform a comparative performances analysis of “maximum a posteriori” (MAP) and “maximum likelihood” (ML) detectors for one-dimensional constellation in the adaptive white Gaussian noise (AWGN) channel. More precisely, error probabilities per symbol for the aforementioned detectors are compared for the case when the pulse amplitude modulation (PAM) constellation with the equidistant and non-equiprobable constellation points is used as one-dimensional constellation. We perform analysis for different distributions of the constellation point probabilities and different values of the signal-to-noise ratio (SNR). The analysis indicates which detector can be adequate choice for the certain distribution of constellation point probabilities and the SNR. Besides this, for the straightforward performance assessment of the MAP detector we derive a formula for the symbol error probability. Our analysis also points out that the nonuniform distribution of the constellation points probabilities does not necessarily improve the symbol error probability. With the aim to decrease the symbol error probability we propose a method for defining constellation point probabilities. The presented results show that PAM constellation designed by utilizing the method we propose significantly outperforms the conventional PAM constellation in terms to the symbol error probability

    Performance Prediction Recipes for Optical Links

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    Although forward error-correction (FEC) coding is an essential part of modern fiber-optic communication systems, it is impractical to implement and evaluate FEC in transmission experiments and simulations. Therefore, it is desirable to accurately predict the end-to-end link performance including FEC from transmission data recorded without FEC. In this tutorial, we provide ready-to-implement "recipes" for such prediction techniques, which apply to arbitrary channels and require no knowledge of information or coding theory. The appropriate choice of recipe depends on properties of the FEC encoder and decoder. The covered metrics include bit error rate, symbol error rate, achievable information rate, and asymptotic information, in all cases computed using a mismatched receiver. Supplementary software implementations are available

    Exploiting diversity in wireless channels with bit-interleaved coded modulation and iterative decoding (BICM-ID)

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    This dissertation studies a state-of-the-art bandwidth-efficient coded modulation technique, known as bit interleaved coded modulation with iterative decoding (BICM-ID), together with various diversity techniques to dramatically improve the performance of digital communication systems over wireless channels. For BICM-ID over a single-antenna frequency non-selective fading channel, the problem of mapping over multiple symbols, i.e., multi-dimensional (multi-D) mapping, with 8-PSK constellation is investigated. An explicit algorithm to construct a good multi-D mapping of 8-PSK to improve the asymptotic performance of BICM-ID systems is introduced. By comparing the performance of the proposed mapping with an unachievable lower bound, it is conjectured that the proposed mapping is the global optimal mapping. The superiority of the proposed mapping over the best conventional (1-dimensional complex) mapping and the multi-D mapping found previously by computer search is thoroughly demonstrated. In addition to the mapping issue in single-antenna BICM-ID systems, the use of signal space diversity (SSD), also known as linear constellation precoding (LCP), is considered in BICM-ID over frequency non-selective fading channels. The performance analysis of BICM-ID and complex N-dimensional signal space diversity is carried out to study its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. Based on the design criterion obtained from a tight error bound, the optimality of the rotation matrix is established. It is shown that using the class of optimal rotation matrices, the performance of BICM-ID systems over a frequency non-selective Rayleigh fading channel approaches that of the BICM-ID systems over an additive white Gaussian noise (AWGN) channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary quadrature amplitude modulation (QAM) constellation, a very simple sub-optimal, yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity. The application of BICM-ID with SSD is then extended to the case of cascaded Rayleigh fading, which is more suitable to model mobile-to-mobile communication channels. By deriving the error bound on the asymptotic performance, it is first illustrated that for a small modulation constellation, a cascaded Rayleigh fading causes a much more severe performance degradation than a conventional Rayleigh fading. However, BICM-ID employing SSD with a sufficiently large constellation can close the performance gap between the Rayleigh and cascaded Rayleigh fading channels, and their performance can closely approach that over an AWGN channel. In the next step, the use of SSD in BICM-ID over frequency selective Rayleigh fading channels employing a multi-carrier modulation technique known as orthogonal frequency division multiplexing (OFDM) is studied. Under the assumption of correlated fading over subcarriers, a tight bound on the asymptotic error performance for the general case of applying SSD over all N subcarriers is derived and used to establish the best achievable asymptotic performance by SSD. It is then shown that precoding over subgroups of at least L subcarriers per group, where L is the number of channel taps, is sufficient to obtain this best asymptotic error performance, while significantly reducing the receiver complexity. The optimal joint subcarrier grouping and rotation matrix design is subsequently determined by solving the Vandermonde linear system. Illustrative examples show a good agreement between various analytical and simulation results. Further, by combining the ideas of multi-D mapping and subcarrier grouping, a novel power and bandwidth-efficient bit-interleaved coded modulation with OFDM and iterative decoding (BI-COFDM-ID) in which multi-D mapping is performed over a group of subcarriers for broadband transmission in a frequency selective fading environment is proposed. A tight bound on the asymptotic error performance is developed, which shows that subcarrier mapping and grouping have independent impacts on the overall error performance, and hence they can be independently optimized. Specifically, it is demonstrated that the optimal subcarrier mapping is similar to the optimal multi-D mapping for BICM-ID in frequency non-selective Rayleigh fading environment, whereas the optimal subcarrier grouping is the same with that of OFDM with SSD. Furthermore, analytical and simulation results show that the proposed system with the combined optimal subcarrier mapping and grouping can achieve the full channel diversity without using SSD and provide significant coding gains as compared to the previously studied BI-COFDM-ID with the same power, bandwidth and receiver complexity. Finally, the investigation is extended to the application of BICM-ID over a multiple-input multiple-output (MIMO) system equipped with multiple antennas at both the transmitter and the receiver to exploit both time and spatial diversities, where neither the transmitter nor the receiver knows the channel fading coefficients. The concentration is on the class of unitary constellation, due to its advantages in terms of both information-theoretic capacity and error probability. The tight error bound with respect to the asymptotic performance is also derived for any given unitary constellation and mapping rule. Design criteria regarding the choice of unitary constellation and mapping are then established. Furthermore, by using the unitary constellation obtained from orthogonal design with quadrature phase-shift keying (QPSK or 4-PSK) and 8-PSK, two different mapping rules are proposed. The first mapping rule gives the most suitable mapping for systems that do not implement iterative processing, which is similar to a Gray mapping in coherent channels. The second mapping rule yields the best mapping for systems with iterative decoding. Analytical and simulation results show that with the proposed mappings of the unitary constellations obtained from orthogonal designs, the asymptotic error performance of the iterative systems can closely approach a lower bound which is applicable to any unitary constellation and mapping

    High-SNR Asymptotics of Mutual Information for Discrete Constellations

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    The high-signal-to-noise ratio (SNR) asymptotic behavior of the mutual information (MI) for discrete constellations over the scalar additive white Gaussian noise channel is studied. Exact asymptotic expressions for the MI for arbitrary one-dimensional constellations and input distributions are presented in the limit as the SNR tends to infinity. Using the relationship between the MI and the minimum mean-square error (MMSE), asymptotics of the MMSE are also developed. It is shown that for any input distribution, the MI and the MMSE have an asymptotic behavior proportional to a Gaussian Q-function, whose argument depends only on the minimum Euclidean distance of the constellation and the SNR. Closed-form expressions for the coefficients of these Q-functions are calculated
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