Broadband wireless access systems deployed in residential and business environments are likely to face hostile radio propagation environments, with multipath delay spread extending over tens or hundreds of bit intervals. Orthogonal frequency-division multiplex (OFDM) is a recognized multicarrier solution to combat the effects of such multipath conditions. This article surveys frequency domain equalization (FDE) applied to single-carrier (SC) modulation solutions. SC radio modems with frequency domain equalization have similar performance, efficiency, and low signal processing complexity advantages as OFDM, and in addition are less sensitive than OFDM to RF impairments such as power amplifier nonlinearities. We discuss similarities and differences of SC and OFDM systems and coexistence possibilities, and present examples of SC-FDE performance capabilities.

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Frequency domain equalization for single-carrier broadband wireless systems

Bandwidth-efficient data transmission over telephone and radio channels is made possible by the use of adaptive equalization to compensate for the time dispersion introduced by the channel Spurred by practical applications, a steady research effort over the last two decades has produced a rich body of literature in adaptive equalization and the related more general fields of reception of digital signals, adaptive filtering, and system identification. This tutorial paper gives an overview of the current state of the art in adaptive equalization. In the first part of the paper, the problem of intersymbol interference (ISI) and the basic concept of transversal equalizers are introduced followed by a simplified description of some practical adaptive equalizer structures and their properties. Related applications of adaptive filters and implementation approaches are discussed. Linear and nonlinear receiver structures, their steady-state performance and sensitivity to timing phase are presented in some depth in the next part. It is shown that a fractionally spaced equalizer can serve as the optimum receive filter for any receiver. Decision-feedback equalization, decision-aided ISI cancellation, and adaptive filtering for maximum-likelihood sequence estimation are presented in a common framework. The next two parts of the paper are devoted to a discussion of the convergence and steady-state properties of least mean-square (LMS) adaptation algorithms, including digital precision considerations, and three classes of rapidly converging adaptive equalization algorithms: namely, orthogonalized LMS, periodic or cyclic, and recursive least squares algorithms. An attempt is made throughout the paper to describe important principles and results in a heuristic manner, without formal proofs, using simple mathematical notation where possible.

https://ieeexplore.ieee.org/iel5/35/23767/01090994.pdf

Adaptive equalization

A reduced-state sequence estimator for linear intersymbol interference channels is described. The estimator uses a conventional Viterbi algorithm with decision feedback to search a reduced-state subset trellis that is constructed using set-partitioning principles. The complexity of maximum-likelihood sequence estimation (MLSE) due to the length of the channel memory and the size of the signal set is systematically reduced. An error probability analysis shows that a good performance/complexity tradeoff can be obtained. In particular, the results indicate that the required complexity to achieve the performance of MLSE is independent of the size of the signal set for large enough signal sets. Simulation results are provided for two partial-response systems. A simple technique for quadrature partial-response signaling (QPRS) is described that eliminates the quasicatastrophic nature of the ML trellis. >

Reduced-state sequence estimation with set partitioning and decision feedback

From the Publisher:
Multi-carrier modulation, in particular orthogonal frequency division multiplexing (OFDM), has been successfully applied to a wide variety of digital communications applications for several years. Although OFDM has been chosen as the physical layer standard for a diversity of important systems, the theory, algorithms, and implementation techniques remain subjects of current interest. 

This book is intended to be a concise summary of the present state of the art of the theory and practice of OFDM technology. This book offers a unified presentation of OFDM theory and high speed and wireless applications. In particular, ADSL, wireless LAN, and digital broadcasting technologies are explained. 

It is hoped that this book will prove valuable both to developers of such systems, and to researchers and graduate students involved in analysis of digital communications, and will remain a valuable summary of the technology, providing an understanding of new advances as well as the present core technology.

/pdf/multi-carrier-digital-communications-theory-and-applications-15x93hdfw3.pdf

Multi-Carrier Digital Communications: Theory and Applications of OFDM

Maximum likelihood data sequence estimation, implemented by a dynamic programming algorithm known as the Viterbi algorithm (VA), is of considerable interest for data transmission in the presence of severe intersymbol interference and additive Gaussian noise. Unfortunately, the required number of receiver operations per data symbol is an exponential function of the duration of the channel impulse response, resulting in unacceptably large receiver complexity for high-speed PAM data transmission on many channels. We propose a linear prefilter to force the overall impulse response of the channel/prefilter combination to approximate a desired truncated impulse response (DIR) of acceptably short duration. Given the duration of the DIR, the prefilter parameters and the DIR itself can be optimized adaptively to minimize the mean-square error between the output of the prefilter and the desired prefilter output, while constraining the energy in the DIR to be fixed. In this work we show that the minimum mean-square error can be expressed as the minimum eigenvalue of a certain channel-dependent matrix, and that the corresponding eigenvector represents the optimum DIR. An adaptive algorithm is developed and successfully tested. The simulations also show that the prefiltering scheme, used together with the VA for two different channel models, compares favorably in performance with another recently proposed prefiltering scheme. Limiting results for the case where the prefilter is considered to be of infinite length are obtained; it is shown that the optimum DIR of length two must be one of two possible impulse responses related to the duobinary impulse response. Finally we obtain limiting results for the case where the transmitting filter is optimized.

F. R. Magee

Papers

Adaptive channel memory truncation for maximum likelihood sequence estimation