MLSE for an unknown channel .I. Optimality considerations
TL;DR: It is shown that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model.
Abstract: The problem of performing joint maximum-likelihood (ML) estimation of a digital sequence and unknown dispersive channel impulse response is considered starting from a continuous-time (CT) model. Previous investigations of this problem have not considered the front-end (FE) processing in detail; rather, a discrete-time signal model has been assumed. We show that a fractionally-spaced whitened matched filter, matched to the known data pulse, provides a set of sufficient statistics when a tapped delay line channel model is assumed, and that the problem is ill-posed when the channel impulse response is generalized to a CT, finite-length model. Practical approximations are considered that circumvent this ill-posed condition. Recursive computation of the joint-ML metric is developed. Together, the FE processing and metric recursion provide a receiver structure which may be interpreted as the theoretical foundation for the previously introduced technique of per-survivor processing, and they lead directly to generalizations. Several FE processors representative of those suggested in the literature are developed and related to the practically optimal FE.
Citations
More filters
TL;DR: This paper describes the statistical models of fading channels which are frequently used in the analysis and design of communication systems, and focuses on the information theory of fading channel, by emphasizing capacity as the most important performance measure.
Abstract: In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.
2,017Â citations
Book•
01 Jan 2003TL;DR: Space-time block coding for wireless communications as mentioned in this paper is a technique that promises greatly improved performance in wireless networks by using multiple antennas at the transmitter and receiver, which can be classified into two categories: flat and frequency-selective fading.
Abstract: Space-time coding is a technique that promises greatly improved performance in wireless networks by using multiple antennas at the transmitter and receiver. Space-Time Block Coding for Wireless Communications is an introduction to the theory of this technology. The authors develop the topic using a unified framework and cover a variety of topics ranging from information theory to performance analysis and state-of-the-art space-time coding methods for both flat and frequency-selective fading multiple-antenna channels. The authors concentrate on key principles rather than specific practical applications, and present the material in a concise and accessible manner. Their treatment reviews the fundamental aspects of multiple-input, multiple output communication theory, and guides the reader through a number of topics at the forefront of current research and development. The book includes homework exercises and is aimed at graduate students and researchers working on wireless communications, as well as practitioners in the wireless industry.
803Â citations
Book•
30 Nov 2004
TL;DR: Thank you very much for downloading quadrature amplitude modulation from basics to adaptive trellis coded turbo equalised and space time coded ofdm cdma and mc cdma systems.
Abstract: Thank you very much for downloading quadrature amplitude modulation from basics to adaptive trellis coded turbo equalised and space time coded ofdm cdma and mc cdma systems. Maybe you have knowledge that, people have look hundreds times for their favorite books like this quadrature amplitude modulation from basics to adaptive trellis coded turbo equalised and space time coded ofdm cdma and mc cdma systems, but end up in malicious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they cope with some harmful virus inside their desktop computer.
281Â citations
TL;DR: Simulations show that the EKF channel estimator performance is improved when the QRD-M algorithm is used instead of the MMSE detector or decorrelator for data decisions, and the computational complexity can be significantly reduced as the number of users increases.
Abstract: We consider a quasi-synchronous code-division multiple access (QS-CDMA) cellular system, where the code delay uncertainty at the base station is limited to a small number of chips. For such QS-CDMA systems, the need for code acquisition is eliminated, however, the residual code tracking and channel estimation problems still have to be solved. An extended Kalman filter (EKF) is employed to track the user delays and channel coefficients. By separating data detection, based on the QR decomposition combined with the M-algorithm (QRD-M) from the delay/channel estimation process, the computational complexity can be significantly reduced as the number of users increases. Simulations show that the EKF channel estimator performance is improved when the QRD-M algorithm is used instead of the MMSE detector or decorrelator for data decisions.
147Â citations
Cites background from "MLSE for an unknown channel .I. Opt..."
...Note that , a vector of Nyquist samples, becomes an approximate sufficient statistic as the observation window becomes larger than the duration of [18]....
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TL;DR: The exact expressions for the soft metrics in the presence of parametric uncertainty modeled as a Gauss-Markov process are derived in a novel way that enables the decoupling of complexity and observation length.
Abstract: The soft-input soft-output (SISO) module is the basic building block for established iterative detection (ID) algorithms for a system consisting of a network of finite state machines. The problem of performing ID for systems having parametric uncertainty has received relatively little attention in the open literature. Previously proposed adaptive SISO (A-SISO) algorithms are either based on an oversimplified channel model, or have a complexity that grows exponentially with the observation length N (or the smoothing lag D). In this paper, the exact expressions for the soft metrics in the presence of parametric uncertainty modeled as a Gauss-Markov process are derived in a novel way that enables the decoupling of complexity and observation length. Starting from these expressions, a family of suboptimal (practical) algorithms is motivated, based on forward/backward adaptive processing with linear complexity in N. Previously proposed A-SISO algorithms, as well as existing adaptive hard decision algorithms are interpreted as special cases within this framework. Using a representative application-joint iterative equalization-decoding for trellis-based codes over frequency-selective channels-several design options are compared and the impact of parametric uncertainty on previously established results for ID with perfect channel state information is assessed.
112Â citations
References
More filters
Book•
01 Jan 1986
TL;DR: In this paper, the authors propose a recursive least square adaptive filter (RLF) based on the Kalman filter, which is used as the unifying base for RLS Filters.
Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.
16,062Â citations
Book•
01 Jan 1968
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Abstract: From the Publisher:
Engineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book.
5,667Â citations
TL;DR: In this paper, a maximum likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, which comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm.
Abstract: A maximum-likelihood sequence estimator for a digital pulse-amplitude-modulated sequence in the presence of finite intersymbol interference and white Gaussian noise is developed, The structure comprises a sampled linear filter, called a whitened matched filter, and a recursive nonlinear processor, called the Viterbi algorithm. The outputs of the whitened matched filter, sampled once for each input symbol, are shown to form a set of sufficient statistics for estimation of the input sequence, a fact that makes obvious some earlier results on optimum linear processors. The Viterbi algorithm is easier to implement than earlier optimum nonlinear processors and its performance can be straightforwardly and accurately estimated. It is shown that performance (by whatever criterion) is effectively as good as could be attained by any receiver structure and in many cases is as good as if intersymbol interference were absent. Finally, a simplified but effectively optimum algorithm suitable for the most popular partial-response schemes is described.
2,667Â citations
TL;DR: Several new canonical channel models are derived in this paper, some of which are dual to those of Kailath, and a model called the Quasi-WSSUS channel is presented to model the behavior of such channels.
Abstract: This paper is concerned with various aspects of the characterization of randomly time-variant linear channels. At the outset it is demonstrated that time-varying linear channels (or filters) may be characterized in an interesting symmetrical manner in time and frequency variables by arranging system functions in (timefrequency) dual pairs. Following this a statistical characterization of randomly time-variant linear channels is carried out in terms of correlation functions for the various system functions. These results are specialized by considering three classes of practically interesting channels. These are the wide-sense stationary (WSS) channel, the uncorrelated scattering (US) channel, and the wide-sense stationary uncorrelated scattering (WSSUS) channel. The WSS and US channels are shown to be (time-frequency) duals. Previous discussions of channel correlation functions and their relationships have dealt exclusively with the WSSUS channel. The point of view presented here of dealing with the dually related system functions and starting with the unrestricted linear channels is considerably more general and places in proper perspective previous results on the WSSUS channel. Some attention is given to the problem of characterizing radio channels. A model called the Quasi-WSSUS channel is presented to model the behavior of such channels. All real-life channels and signals have an essentially finite number of degrees of freedom due to restrictions on time duration and bandwidth. This fact may be used to derive useful canonical channel models with the aid of sampling theorems and power series expansions. Several new canonical channel models are derived in this paper, some of which are dual to those of Kailath.
2,431Â citations
IBM1
TL;DR: A uniform receiver structure for linear carrier-modulated data-transmission systems is derived which for decision making uses a modified version of the Viterbi algorithm, which operates directly on the output signal of a complex matched filter and requires no squaring operations.
Abstract: A new look is taken at maximum-likelihood sequence estimation in the presence of intersymbol interference. A uniform receiver structure for linear carrier-modulated data-transmission systems is derived which for decision making uses a modified version of the Viterbi algorithm. The algorithm operates directly on the output signal of a complex matched filter and, in contrast to the original algorithm, requires no squaring operations; only multiplications by discrete pulse-amplitude values are needed. Decoding of redundantly coded sequences is included in the consideration. The reason and limits for the superior error performance of the receiver over a conventional receiver employing zero-forcing equalization and symbol-by-symbol decision making are explained. An adjustment algorithm for jointly approximating the matched filter by a transversal filter, estimating intersymbol interference present at the transversal filter output, and controlling the demodulating carrier phase and the sample timing, is presented.
821Â citations