A Closed-Form Approximated Expression for the Residual ISI Obtained by Blind Adaptive Equalizers with Gain Equal or Less than One

In this paper we propose for the real and two independent quadrature carrier case, a closed-form approximated expression for the achievable residual Inter-Symbol Interference (ISI) that depends on the step-size parameter, equalizer’s tap length, equalized output gain, input signal statistics, channel power and SNR. This expression is valid for blind adaptive equalizers, where the error that is fed into the adaptive mechanism which updates the equalizer‘s taps can be expressed as a polynomial function of order three of the equalized output and where the gain between the input and equalized output signal is less than or equal to one, as is in the case of Godard (gain = 1) and WNEW (gain < 1) algorithm. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need to carry out simulation with various step-size parameters in order to reach the required residual ISI. In addition, we show two new equalization methods (gain dependent), which have shown to have improved equalization performance compared to Godard and WNEW

Edgeworth Expansion Based Model for the Convolutional Noise pdf

Recently, the Edgeworth expansion up to order 4 was used to represent the convolutional noise probability density function (pdf) in the conditional expectation calculations where the source pdf was modeled with the maximum entropy density approximation technique. However, the applied Lagrange multipliers were not the appropriate ones for the chosen model for the convolutional noise pdf. In this paper we use the Edgeworth expansion up to order 4 and up to order 6 to model the convolutional noise pdf. We derive the appropriate Lagrange multipliers, thus obtaining new closed-form approximated expressions for the conditional expectation and mean square error (MSE) as a byproduct. Simulation results indicate hardly any equalization improvement with Edgeworth expansion up to order 4 when using optimal Lagrange multipliers over a nonoptimal set. In addition, there is no justification for using the Edgeworth expansion up to order 6 over the Edgeworth expansion up to order 4 for the 16QAM and easy channel case. However, Edgeworth expansion up to order 6 leads to improved equalization performance compared to the Edgeworth expansion up to order 4 for the 16QAM and hard channel case as well as for the case where the 64QAM is sent via an easy channel

Machine Learning in Digital Signal Processing for Optical Transmission Systems

The future demand for digital information will exceed the capabilities of current optical communication systems, which are approaching their limits due to component and fiber intrinsic non-linear effects. Machine learning methods are promising to find new ways of leverage the available resources and to explore new solutions. Although, some of the machine learning methods such as adaptive non-linear filtering and probabilistic modeling are not novel in the field of telecommunication, enhanced powerful architecture designs together with increasing computing power make it possible to tackle more complex problems today. The methods presented in this work apply machine learning on optical communication systems with two main contributions. First, an unsupervised learning algorithm with embedded additive white Gaussian noise (AWGN) channel and appropriate power constraint is trained end-to-end, learning a geometric constellation shape for lowest bit-error rates over amplified and unamplified links. Second, supervised machine learning methods, especially deep neural networks with and without internal cyclical connections, are investigated to combat linear and non-linear inter-symbol interference (ISI) as well as colored noise effects introduced by the components and the fiber. On high-bandwidth coherent optical transmission setups their performances and complexities are experimentally evaluated and benchmarked against conventional digital signal processing (DSP) approaches. This thesis shows how machine learning can be applied to optical communication systems. In particular, it is demonstrated that machine learning is a viable designing and DSP tool to increase the capabilities of optical communication systems

Investigation of coding and equalization for the digital HDTV terrestrial broadcast channel

Includes bibliographical references (p. 241-248).Supported by the Advanced Telecommunications Research Program.Julien J. Nicolas

Adaptive equalizers for multipath compensation in digital microwave communications

SIGLEAvailable from British Library Document Supply Centre- DSC:D82998 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Machine Learning Techniques To Mitigate Nonlinear Impairments In Optical Fiber System

The upcoming deployment of 5/6G networks, online services like 4k/8k HDTV (streamers and online games), the development of the Internet of Things concept, connecting billions of active devices, as well as the high-speed optical access networks, impose progressively higher and higher requirements on the underlying optical networks infrastructure. With current network infrastructures approaching almost unsustainable levels of bandwidth utilization/ data traffic rates, and the electrical power consumption of communications systems becoming a serious concern in view of our achieving the global carbon footprint targets, network operators and system suppliers are now looking for ways to respond to these demands while also maximizing the returns of their investments. The search for a solution to this predicted ªcapacity crunchº led to a renewed interest in alternative approaches to system design, including the usage of high-order modulation formats and high symbol rates, enabled by coherent detection, development of wideband transmission tools, new fiber types (such as multi-mode and ±core), and finally, the implementation of advanced digital signal processing (DSP) elements to mitigate optical channel nonlinearities and improve the received SNR. All aforementioned options are intended to boost the available optical systems’ capacity to fulfill the new traffic demands. This thesis focuses on the last of these possible solutions to the ªcapacity crunch," answering the question: ªHow can machine learning improve existing optical communications by minimizing quality penalties introduced by transceiver components and fiber media nonlinearity?". Ultimately, by identifying a proper machine learning solution (or a bevy of solutions) to act as a nonlinear channel equalizer for optical transmissions, we can improve the system’s throughput and even reduce the signal processing complexity, which means we can transmit more using the already built optical infrastructure. This problem was broken into four parts in this thesis: i) the development of new machine learning architectures to achieve appealing levels of performance; ii) the correct assessment of computational complexity and hardware realization; iii) the application of AI techniques to achieve fast reconfigurable solutions; iv) the creation of a theoretical foundation with studies demonstrating the caveats and pitfalls of machine learning methods used for optical channel equalization. Common measures such as bit error rate, quality factor, and mutual information are considered in scrutinizing the systems studied in this thesis. Based on simulation and experimental results, we conclude that neural network-based equalization can, in fact, improve the channel quality of transmission and at the same time have computational complexity close to other classic DSP algorithms

Channel Estimation Architectures for Mobile Reception in Emerging DVB Standards

Throughout this work, channel estimation techniques have been analyzed and proposed for moderate and very high mobility DVB (digital video broadcasting) receivers, focusing on the DVB-T2 (Digital Video Broadcasting - Terrestrial 2) framework and the forthcoming DVB-NGH (Digital Video Broadcasting - Next Generation Handheld) standard. Mobility support is one of the key features of these DVB specifications, which try to deal with the challenge of enabling HDTV (high definition television) delivery at high vehicular speed. In high-mobility scenarios, the channel response varies within an OFDM (orthogonal frequency-division multiplexing) block and the subcarriers are no longer orthogonal, which leads to the so-called ICI (inter-carrier interference), making the system performance drop severely. Therefore, in order to successfully decode the transmitted data, ICI-aware detectors are necessary and accurate CSI (channel state information), including the ICI terms, is required at the receiver. With the aim of reducing the number of parameters required for such channel estimation while ensuring accurate CSI, BEM (basis expansion model) techniques have been analyzed and proposed for the high-mobility DVB-T2 scenario. A suitable clustered pilot structure has been proposed and its performance has been compared to the pilot patterns proposed in the standard. Different reception schemes that effectively cancel ICI in combination with BEM channel estimation have been proposed, including a Turbo scheme that includes a BP (belief propagation) based ICI canceler, a soft-input decision-directed BEM channel estimator and the LDPC (low-density parity check) decoder. Numerical results have been presented for the most common channel models, showing that the proposed receiver schemes allow good reception, even in receivers with extremely high mobility (up to 0.5 of normalized Doppler frequency).Doktoretza tesi honetan, hainbat kanal estimazio teknika ezberdin aztertu eta proposatu dira mugikortasun ertain eta handiko DVB (Digital Video Broadcasting) hartzaileentzat, bigarren belaunaldiko Lurreko Telebista Digitalean DVB-T2 (Digital Video Broadcasting - Terrestrial 2 ) eta hurrengo DVB-NGH (Digital Video Broadcasting - Next Generation Handheld) estandarretan oinarrututa. Mugikortasuna bigarren belaunaldiko telebista estandarrean funtsezko ezaugarri bat da, HDTV (high definition television) zerbitzuak abiadura handiko hartzaileetan ahalbidetzeko erronkari aurre egiteko nahian. Baldintza horietan, kanala OFDM (ortogonalak maiztasun-zatiketa multiplexing ) sinbolo baten barruan aldatzen da, eta subportadorak jada ez dira ortogonalak, ICI-a (inter-carrier interference) sortuz, eta sistemaren errendimendua hondatuz. Beraz, transmititutako datuak behar bezala deskodeatzeko, ICI-a ekiditeko gai diren detektagailuak eta CSI-a (channel state information) zehatza, ICI osagaiak barne, ezinbestekoak egiten dira hartzailean. Kanalaren estimazio horretarako beharrezkoak diren parametro kopurua murrizteko eta aldi berean CSI zehatza bermatzeko, BEM (basis expansion model) teknika aztertu eta proposatu da ICI kanala identifikatzeko mugikortasun handiko DVB-T2 eszenatokitan. Horrez gain, pilotu egitura egokia proposatu da, estandarrean proposatutako pilotu ereduekin alderatuz BEM estimazioan oinarritua. ICI-a baliogabetzen duten hartzaile sistema ezberdin proposatu dira, Turbo sistema barne, non BP (belief propagation) detektagailua, soft BEM estimazioa eta LDPC (low-density parity check ) deskodetzailea uztartzen diren. Ohiko kanal ereduak erabilita, simulazio emaitzak aurkeztu dira, proposatutako hartzaile sistemak mugikortasun handiko kasuetan harrera ona dutela erakutsiz, 0.5 Doppler maiztasun normalizaturaino.Esta tesis doctoral analiza y propone diferentes técnicas de estimación de canal para receptores DVB (Digital Video Broadcasting) con movilidad moderada y alta, centrándose en el estándar de segunda generación DVB-T2 (Digital Video Broadcasting - Terrestrial 2 ) y en el próximó estándar DVB-NGH (Digital Video Broadcasting - Next Generation Handheld ). La movilidad es una de las principales claves de estas especificaciones, que tratan de lidiar con el reto de permitir la recepción de señal HDTV (high definition television) en receptores móviles. En escenarios de alta movilidad, la respuesta del canal varía dentro de un símbolo OFDM (orthogonal frequency-division multiplexing ) y las subportadoras ya no son ortogonales, lo que genera la llamada ICI (inter-carrier interference), deteriorando el rendimiento de los receptores severamente. Por lo tanto, con el fin de decodificar correctamente los datos transmitidos, detectores capaces de suprimir la ICI y una precisa CSI (channel state information), incluyendo los términos de ICI, son necesarios en el receptor. Con el objetivo de reducir el número de parámetros necesarios para dicha estimación de canal, y al mismo tiempo garantizar una CSI precisa, la técnica de estimación BEM (basis expansion model) ha sido analizada y propuesta para identificar el canal con ICI en receptores DVB-T2 de alta movilidad. Además se ha propuesto una estructura de pilotos basada en clústers, comparando su rendimiento con los patrones de pilotos establecidos en el estándar. Se han propuesto diferentes sistemas de recepción que cancelan ICI en combinación con la estimación BEM, incluyendo un esquema Turbo que incluye un detector BP (belief propagation), un estimador BEM soft y un decodificador LDPC (low-density parity check). Se han presentado resultados numéricos para los modelos de canal más comunes, demostrando que los sistemas de recepción propuestos permiten la decodificación correcta de la señal incluso en receptores con movilidad muy alta (hasta 0,5 de frecuencia de Doppler normalizada)