Channel equalization to achieve high bit rates in discrete multitone systems

textMulticarrier modulation (MCM) techniques such as orthogonal frequency division multiplexing (OFDM) and discrete multi-tone (DMT) modulation are attractive for high-speed data communications due to the ease with which MCM can combat channel dispersion. With all the benefits MCM could give, DMT modulation has an extra ability to perform dynamic bit loading, which has the potential to exploit fully the available bandwidth in a slowly time-varying channel. In broadband wireline communications, DMT modulation is standardized for asymmetric digital subscribe line (ADSL) and very-high-bit-rate digital subscriber line (VDSL) modems. ADSL and VDSL standards are used by telephone companies to provide high speed data service to residences and offices. In an ADSL receiver, an equalizer is required to compensate for the channel’s dispersion in the time domain and the channel’s distortion in the frequency domain of the transmitted waveform. This dissertation proposes design methods for linear equalizers to increase the bit rate of the connection. The methods are amenable to implementation on programmable fixed-point digital signal processors, which are employed in ADSL/VDSL transceivers. A conventional ADSL equalizer consists of a time-domain equalizer, a fast Fourier transform, and a frequency domain equalizer. The time domain equalizer (TEQ) is a finite impulse response filter that when coupled with a discretized channel produces an equivalent channel whose impulse response is shorter than that of the discretized channel. This channel shortening is required by the ADSL standards. In this dissertation, I first propose a linear phase TEQ design that exploits symmetry in existing eigen-filter approaches such as minimum mean square error(MMSE), maximum shortening signal to noise ratio (MSSNR) and minimum intersymbol interference (Min-ISI) equalizers. TEQs with symmetric coefficients can reach the same performance as non-symmetric ones with much lower training complexity. Second, I improve Min-ISI design. I reformulate the cost function to make long TEQs design feasible. I remove the dependency of transmission delay in order to reduce the complexity associated with delay optimization. The quantized weighting is introduced to further lower the complexity. I also propose an iterative optimization procedure of Min-ISI that completely avoids Cholesky decomposition hence is better suited for a fixed-point implementation. Finally I propose a dual-path TEQ structure, which designs a standard singleFIR TEQ to achieve good bit rate over the entire transmission bandwidth, and designs another FIR TEQ to improve the bit rate over a subset of subcarriers. Dualpath TEQ can be viewed as a special case of a complex valued filter bank structure that delivers the best bit rate of existing DMT equalizers. However, dual-path TEQ provides a very good tradeoff between achievable bit rate vs. implementation complexity on a programmable digital signal processor.Electrical and Computer Engineerin

Spectrum optimization in multi-user multi-carrier systems with iterative convex and nonconvex approximation methods

Several practical multi-user multi-carrier communication systems are characterized by a multi-carrier interference channel system model where the interference is treated as noise. For these systems, spectrum optimization is a promising means to mitigate interference. This however corresponds to a challenging nonconvex optimization problem. Existing iterative convex approximation (ICA) methods consist in solving a series of improving convex approximations and are typically implemented in a per-user iterative approach. However they do not take this typical iterative implementation into account in their design. This paper proposes a novel class of iterative approximation methods that focuses explicitly on the per-user iterative implementation, which allows to relax the problem significantly, dropping joint convexity and even convexity requirements for the approximations. A systematic design framework is proposed to construct instances of this novel class, where several new iterative approximation methods are developed with improved per-user convex and nonconvex approximations that are both tighter and simpler to solve (in closed-form). As a result, these novel methods display a much faster convergence speed and require a significantly lower computational cost. Furthermore, a majority of the proposed methods can tackle the issue of getting stuck in bad locally optimal solutions, and hence improve solution quality compared to existing ICA methods.Comment: 33 pages, 7 figures. This work has been submitted for possible publicatio

Dynamic Resource Allocation in Cognitive Radio Networks: A Convex Optimization Perspective

This article provides an overview of the state-of-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks. Focusing on the interference-power/interference-temperature (IT) constraint approach for CRs to protect primary radio transmissions, many new and challenging problems regarding the design of CR systems are formulated, and some of the corresponding solutions are shown to be obtainable by restructuring some classic results known for traditional (non-CR) wireless networks. It is demonstrated that convex optimization plays an essential role in solving these problems, in a both rigorous and efficient way. Promising research directions on interference management for CR and other related multiuser communication systems are discussed.Comment: to appear in IEEE Signal Processing Magazine, special issue on convex optimization for signal processin

Physical Layer Techniques for High Frequency Wireline Broadband Systems

This thesis collects contributions to wireline and wireless communication systems with an emphasis on multiuser and multicarrier physical layer technology. To deliver increased capacity, modern wireline access systems such as G.fast extend the signal bandwidth up from tens to hundreds of MHz. This ambitious development revealed a number of unforeseen hurdles such as the impact of impedance changes in various forms. Impedance changes have a strong effect on the performance of multi-user crosstalk mitigation techniques such as vectoring. The first part of the thesis presents papers covering the identification of one of these problems, a model describing why it occurs and a method to mitigate its effects, improving line stability for G.fast systems.A second part of the thesis deals with the effects of temperature changes on wireline channels. When a vectored (MIMO) wireline system is initialized, channel estimates need to be obtained. This thesis presents contributions on the feasibility of re-using channel coefficients to speed up the vectoring startup procedures, even after the correct coefficients have changed, e.g., due to temperature changes. We also present extensive measurement results showing the effects of temperature changes on copper channels using a temperature chamber and British cables. The last part of the thesis presents three papers on the convergence of physical layer technologies, more specifically the deployment of OFDM-based radio systems using twisted pairs in different ways. In one proposed scenario, the idea of using the access copper lines to deploy small cells inside users' homes is explored. The feasibility of the concept, the design of radio-heads and a practical scheme for crosstalk mitigation are presented in three contributions

Analysis of the impact of impulse noise in digital subscriber line systems

In recent years, Digital subscriber line (DSL) technology has been gaining popularity as a high speed network access technology, capable of the delivery of multimedia services. A major impairment for DSL is impulse noise in the telephone line. However, evaluating the data errors caused by this noise is not trivial due to its complex statistical nature, which until recently had not been well understood, and the complicated error mitigation and framing techniques used in DSL systems. This thesis presents a novel analysis of the impact of impulse noise and the DSL framing parameters on transmission errors, building on a recently proposed impulse noise model. It focuses on errors at higher protocol layers, such as asynchronous transfer mode (ATM), in the most widely used DSL version, namely Asymmetric DSL (ADSL). The impulse noise is characterised statistically through its amplitudes, duration, inter-arrival times, and frequency spectrum, using the British Telecom / University of Edinburgh / Deutsche Telekom (BT/UE/DT) model. This model is broadband, considers both the time and the frequency domains, and accounts for the impulse clustering. It is based on recent measurements in two different telephone networks (the UK and Germany) and therefore is the most complete model available to date and suited for DSL analysis. A new statistical analysis of impulse noise spectra from DT measurements shows that impulse spectra can be modelled with three spectral components with similar bandwidth statistical distributions. Also, a novel distribution of the impulse powers is derived from the impulse amplitude statistics. The performance of a generic ADSL modem is investigated in an impulse noise and crosstalk environment for different bit rates and framing parameters. ATM cell and ADSL frame error rates, and subjective MPEG2 video quality are used as performance metrics. A new modification of a bit loading algorithm is developed to enable stable convergence of the algorithm with trellis coding and restricted subtone constellation size. It is shown that while interleaving brings improvement if set at its maximum depth, at intermediate depths it actually worsens the performance of all considered metrics in comparison with no interleaving. No such performance degradation is caused by combining several symbols in a forward error correction (FEC) codeword, but this burst error mitigation technique is only viable at low bit rates. Performance improvement can also be achieved by increasing the strength of FEC, especially if combined with interleaving. In contrast, trellis coding is ineffective against the long impulse noise error bursts. Alien as opposed to kindred crosstalk degrades the error rates and this is an important issue in an unbundled network environment. It is also argued that error free data units is a better performance measure from a user perspective than the commonly used error free seconds. The impact of impulse noise on the errors in DSL systems has also been considered analytically. A new Bernoulli-Weibull impulse noise model at symbol level is proposed and it is shown that other models which assume Gaussian distributed impulse amplitudes or Rayleigh distributed impulse powers give overly optimistic error estimates in DSL systems. A novel bivariate extension of the Weibull impulse amplitudes is introduced to enable the analysis of orthogonal signals. Since an exact closed-form expression for the symbol error probability of multi-carrierQAM assuming Bernoulli-Weibull noise model does not exist, this problem has been solved numerically. Multi-carrier QAM is shown to perform better at high signal-to-noise ratio (SNR), but worse at low SNR than single carrier QAM, in both cases because of the spreading of noise power between subcarriers. Analytical expressions for errors up to frame level in the specific case of ADSL are then derived from the impulse noise model, with good agreement with simulation results. The Bernoulli-Weibull model is applied to study the errors in single-pair highspeed DSL (SHDSL). The performance of ADSL is found to be better when the burst error mitigation techniques are used, but SHDSL has advantages if low bit error rate and low latency are required

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