Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel

Filterbank optimization with convex objectives and the optimality of principal component forms

This paper proposes a general framework for the optimization of orthonormal filterbanks (FBs) for given input statistics. This includes as special cases, many previous results on FB optimization for compression. It also solves problems that have not been considered thus far. FB optimization for coding gain maximization (for compression applications) has been well studied before. The optimum FB has been known to satisfy the principal component property, i.e., it minimizes the mean-square error caused by reconstruction after dropping the P weakest (lowest variance) subbands for any P. We point out a much stronger connection between this property and the optimality of the FB. The main result is that a principal component FB (PCFB) is optimum whenever the minimization objective is a concave function of the subband variances produced by the FB. This result has its grounding in majorization and convex function theory and, in particular, explains the optimality of PCFBs for compression. We use the result to show various other optimality properties of PCFBs, especially for noise-suppression applications. Suppose the FB input is a signal corrupted by additive white noise, the desired output is the pure signal, and the subbands of the FB are processed to minimize the output noise. If each subband processor is a zeroth-order Wiener filter for its input, we can show that the expected mean square value of the output noise is a concave function of the subband signal variances. Hence, a PCFB is optimum in the sense of minimizing this mean square error. The above-mentioned concavity of the error and, hence, PCFB optimality, continues to hold even with certain other subband processors such as subband hard thresholds and constant multipliers, although these are not of serious practical interest. We prove that certain extensions of this PCFB optimality result to cases where the input noise is colored, and the FB optimization is over a larger class that includes biorthogonal FBs. We also show that PCFBs do not exist for the classes of DFT and cosine-modulated FBs

Optimizing the capacity of orthogonal and biorthogonal DMT channels

The uniform DFT filter bank has been used routinely in discrete multitone modulation (DMT) systems because of implementation efficiency. It has recently been shown that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT communication. In this paper we show that such filter banks are optimal even when scalar prefilters and postfilters are used around the channel. We show that the theoretically optimum scalar prefilter is the half-whitening solution, well known in data compression theory. We conclude with the observation that the PCFB continues to be optimal for the maximization of theoretical capacity as well

Nonuniform principal component filter banks: definitions, existence, and optimality

The optimality of principal component filter banks (PCFBs) for data compression has been observed in many works to varying extents. Recent work by the authors has made explicit the precise connection between the optimality of uniform orthonormal filter banks (FBs) and the principal component property: The PCFB is optimal whenever the minimization objective is a concave function of the subband variances of the FB. This gives a unified explanation of PCFB optimality for compression, denoising and progressive transmission. However not much is known for the case when the optimization is over a class of nonuniform Fbs. In this paper we first define the notion of a PCFB for a class of nonuniform orthonormal Fbs. We then show how it generalizes the uniform PCFBs by being optimal for a certain family of concave objectives. Lastly, we show that existence of nonuniform PCFBs could imply severe restrictions on the input power spectrum. For example, for the class of unconstrained orthonormal nonuniform Fbs with any given set of decimators that are not all equal, there is no PCFB if the input spectrum is strictly monotone

On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Doctor of Philosophy

dissertationWireless communications pervade all avenues of modern life. The rapid expansion of wireless services has increased the need for transmission schemes that are more spectrally efficient. Dynamic spectrum access (DSA) systems attempt to address this need by building a network where the spectrum is used opportunistically by all users based on local and regional measurements of its availability. One of the principal requirements in DSA systems is to initialize and maintain a control channel to link the nodes together. This should be done even before a complete spectral usage map is available. Additionally, with more users accessing the spectrum, it is important to maintain a stable link in the presence of significant interference in emergency first-responders, rescue, and defense applications. In this thesis, a new multicarrier spread spectrum (MC-SS) technique based on filter banks is presented. The new technique is called filter bank multicarrier spread spectrum (FB-MC-SS). A detailed theory of the underlying properties of this signal are given, with emphasis on the properties that lend themselves to synchronization at the receiver. Proposed algorithms for synchronization, channel estimation, and detection are implemented on a software-defined radio platform to complete an FB-MC-SS transceiver and to prove the practicality of the technique. FB-MC-SS is shown through physical experimentation to be significantly more robust to partial band interference compared to direct sequence spread spectrum. With a higher power interfering signal occupying 90% of its band, FB-MC-SS maintains a low bit error rate. Under the same interference conditions, DS-SS fails completely. This experimentation leads to a theoretical analysis that shows in a frequency selective channel with additive white noise, the FB-MC-SS system has performance that equals that obtained by a DS-SS system employing an optimal rake receiver. This thesis contains a detailed chapter on implementation and design, including lessons learned while prototyping the system. This is to assist future system designers to quickly gain proficiency in further development of this technology

Spectrum Adaptation in Cognitive Radio Systems with Operating Constraints

The explosion of high-data-rate-demanding wireless applications such as smart-phones and wireless Internet access devices, together with growth of existing wireless services, are creating a shortage of the scarce Radio Frequency (RF) spectrum. However, several spectrum measurement campaigns revealed that current spectrum usage across time and frequency is inefficient, creating the artificial shortage of the spectrum because of the traditional exclusive command-and-control model of using the spectrum. Therefore, a new concept of Cognitive Radio (CR) has been emerging recently in which unlicensed users temporarily borrow spectrum from the licensed Primary Users (PU) based on the Dynamic Spectrum Access (DSA) technique that is also known as the spectrum sharing concept. A CR is an intelligent radio system based on the Software Defined Radio platform with artificial intelligence capability which can learn, adapt, and reconfigure through interaction with the operating environment. A CR system will revolutionize the way people share the RF spectrum, lowering harmful interference to the licensed PU of the spectrum, fostering innovative DSA technology and giving people more choices when it comes to using the wireless-communication-dependent applications without having any spectrum congestion problems. A key technical challenge for enabling secondary access to the licensed spectrum adaptation is to ensure that the CR does not interfere with the licensed incumbent users. However, incumbent user behavior is dynamic and requires CR systems to adapt this behavior in order to maintain smooth information transmission. In this context, the objective of this dissertation is to explore design issues for CR systems focusing on adaptation of physical layer parameters related to spectrum sensing, spectrum shaping, and rate/power control. Specifically, this dissertation discusses dynamic threshold adaptation for energy detector spectrum sensing, spectrum allocation and power control in Orthogonal Frequency Division Multiplexing-(OFDM-)based CR with operating constraints, and adjacent band interference suppression techniques in turbo-coded OFDM-based CR systems

Resource Management in Multicarrier Based Cognitive Radio Systems

The ever-increasing growth of the wireless application and services affirms the importance of the effective usage of the limited radio spectrum. Existing spectrum management policies have led to significant spectrum under-utilization. Recent measurements showed that large range of the spectrum is sparsely used in both temporal and spatial manner. This conflict between the inefficient usage of the spectrum and the continuous evolution in the wireless communication calls upon the development of more flexible management policies. Cognitive radio (CR) with the dynamic spectrum access (DSA) is considered to be a key technology in making the best solution of this conflict by allowing a group of secondary users (SUs) to share the radio spectrum originally allocated to the primary user (PUs). The operation of CR should not negatively alter the performance of the PUs. Therefore, the interference control along with the highly dynamic nature of PUs activities open up new resource allocation problems in CR systems. The resource allocation algorithms should ensure an effective share of the temporarily available frequency bands and deliver the solutions in timely fashion to cope with quick changes in the network. In this dissertation, the resource management problem in multicarrier based CR systems is considered. The dissertation focuses on three main issues: 1) design of efficient resource allocation algorithms to allocate subcarriers and powers between SUs such that no harmful interference is introduced to PUs, 2) compare the spectral efficiency of using different multicarrier schemes in the CR physical layer, specifically, orthogonal frequency division multiplexing (OFDM) and filter bank multicarrier (FBMC) schemes, 3) investigate the impact of the different constraints values on the overall performance of the CR system. Three different scenarios are considered in this dissertation, namely downlink transmission, uplink transmission, and relayed transmission. For every scenario, the optimal solution is examined and efficient sub-optimal algorithms are proposed to reduce the computational burden of obtaining the optimal solution. The suboptimal algorithms are developed by separate the subcarrier and power allocation into two steps in downlink and uplink scenarios. In the relayed scenario, dual decomposition technique is used to obtain an asymptotically optimal solution, and a joint heuristic algorithm is proposed to find the suboptimal solution. Numerical simulations show that the proposed suboptimal algorithms achieve a near optimal performance and perform better than the existing algorithms designed for cognitive and non-cognitive systems. Eventually, the ability of FBMC to overcome the OFDM drawbacks and achieve more spectral efficiency is verified which recommends the consideration of FBMC in the future CR systems.El crecimiento continuo de las aplicaciones y servicios en sistemas inal´ambricos, indica la importancia y necesidad de una utilizaci´on eficaz del espectro radio. Las pol´ıticas actuales de gesti´on del espectro han conducido a una infrautilizaci´on del propio espectro radioel´ectrico. Recientes mediciones en diferentes entornos han mostrado que gran parte del espectro queda poco utilizado en sus ambas vertientes, la temporal, y la espacial. El permanente conflicto entre el uso ineficiente del espectro y la evoluci´on continua de los sistemas de comunicaci´on inal´ambrica, hace que sea urgente y necesario el desarrollo de esquemas de gesti´on del espectro m´as flexibles. Se considera el acceso din´amico (DSA) al espectro en los sistemas cognitivos como una tecnolog´ıa clave para resolver este conflicto al permitir que un grupo de usuarios secundarios (SUs) puedan compartir y acceder al espectro asignado inicialmente a uno o varios usuarios primarios (PUs). Las operaciones de comunicaci´on llevadas a cabo por los sistemas radio cognitivos no deben en ning´un caso alterar (interferir) los sistemas primarios. Por tanto, el control de la interferencia junto al gran dinamismo de los sistemas primarios implica nuevos retos en el control y asignaci´on de los recursos radio en los sistemas de comunicaci´on CR. Los algoritmos de gesti´on y asignaci´on de recursos (Radio Resource Management-RRM) deben garantizar una participaci´on efectiva de las bandas con frecuencias disponibles temporalmente, y ofrecer en cada momento oportunas soluciones para hacer frente a los distintos cambios r´apidos que influyen en la misma red. En esta tesis doctoral, se analiza el problema de la gesti´on de los recursos radio en sistemas multiportadoras CR, proponiendo varias soluciones para su uso eficaz y coexistencia con los PUs. La tesis en s´ı, se centra en tres l´ıneas principales: 1) el dise˜no de algoritmos eficientes de gesti´on de recursos para la asignaci´on de sub-portadoras y distribuci´on de la potencia en sistemas segundarios, evitando asi cualquier interferencia que pueda ser perjudicial para el funcionamiento normal de los usuarios de la red primaria, 2) analizar y comparar la eficiencia espectral alcanzada a la hora de utilizar diferentes esquema de transmisi´on multiportadora en la capa f´ısica del sistema CR, espec´ıficamente en sistemas basados en OFDM y los basados en banco de filtros multiportadoras (Filter bank Multicarrier-FBMC), 3) investigar el impacto de las diferentes limitaciones en el rendimiento total del sistema de CR. Los escenarios considerados en esta tesis son tres, es decir; modo de transmisi´on descendente (downlink), modo de transmisi´on ascendente (uplink), y el modo de transmisi´on ”Relay”. En cada escenario, la soluci´on ´optima es examinada y comparada con algoritmos sub- ´optimos que tienen como objetivo principal reducir la carga computacional. Los algoritmos sub-´optimos son llevados a cabo en dos fases mediante la separaci´on del propio proceso de distribuci´on de subportadoras y la asignaci´on de la potencia en los modos de comunicaci´on descendente (downlink), y ascendente (uplink). Para los entornos de tipo ”Relay”, se ha utilizado la t´ecnica de doble descomposici´on (dual decomposition) para obtener una soluci´on asint´oticamente ´optima. Adem´as, se ha desarrollado un algoritmo heur´ıstico para poder obtener la soluci´on ´optima con un reducido coste computacional. Los resultados obtenidos mediante simulaciones num´ericas muestran que los algoritmos sub-´optimos desarrollados logran acercarse a la soluci´on ´optima en cada uno de los entornos analizados, logrando as´ı un mayor rendimiento que los ya existentes y utilizados tanto en entornos cognitivos como no-cognitivos. Se puede comprobar en varios resultados obtenidos en la tesis la superioridad del esquema multiportadora FBMC sobre los sistemas basados en OFDM para los entornos cognitivos, causando una menor interferencia que el OFDM en los sistemas primarios, y logrando una mayor eficiencia espectral. Finalmente, en base a lo analizado en esta tesis, podemos recomendar al esquema multiportadora FBMC como una id´onea y potente forma de comunicaci´on para las futuras redes cognitivas

Discrete Time Systems

Discrete-Time Systems comprehend an important and broad research field. The consolidation of digital-based computational means in the present, pushes a technological tool into the field with a tremendous impact in areas like Control, Signal Processing, Communications, System Modelling and related Applications. This book attempts to give a scope in the wide area of Discrete-Time Systems. Their contents are grouped conveniently in sections according to significant areas, namely Filtering, Fixed and Adaptive Control Systems, Stability Problems and Miscellaneous Applications. We think that the contribution of the book enlarges the field of the Discrete-Time Systems with signification in the present state-of-the-art. Despite the vertiginous advance in the field, we also believe that the topics described here allow us also to look through some main tendencies in the next years in the research area