Fractionally-spaced equalization: An improved digital transversal equalizer
TL;DR: The performance improvement of voice-grade modems which use a Fractionally-Spaced Equalizer (FSE) instead of a conventional synchronous equalizer is described and demonstrated, via analysis and simulation.
Abstract: Here we describe and demonstrate, via analysis and simulation, the performance improvement of voice-grade modems which use a Fractionally-Spaced Equalizer (FSE) instead of a conventional synchronous equalizer. The reason for this superior performance is that the fse adoptively realizes the optimum linear receiver; consequently it can effectively compensate for more severe delay distortion than the conventional adaptive equalizer, which suffers from aliasing effects. An additional advantage of the FSE is that data transmission can begin with an arbitrary sampling phase, since the equalizer synthesizes the correct delay during adaptation. We show that an FSE combined with a decision feedback section, which can mitigate the effect of severe amplitude distortion, can compensate for a wide range of linear distortion. At 9.6 kbit/s, the FSE provides a 2 to 3 dB gain in output signal-to-noise ratio, relative to the synchronous equalizer, over worst-case private-line channels. This translates to a theoretical improvement of approximately two orders of magnitude in bit error rate.
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
01 Sep 1987
TL;DR: A preliminary SDF software system for automatically generating assembly language code for DSP microcomputers is described, and two new efficiency techniques are introduced, static buffering and an extension to SDF to efficiently implement conditionals.
Abstract: Data flow is a natural paradigm for describing DSP applications for concurrent implementation on parallel hardware. Data flow programs for signal processing are directed graphs where each node represents a function and each arc represents a signal path. Synchronous data flow (SDF) is a special case of data flow (either atomic or large grain) in which the number of data samples produced or consumed by each node on each invocation is specified a priori. Nodes can be scheduled statically (at compile time) onto single or parallel programmable processors so the run-time overhead usually associated with data flow evaporates. Multiple sample rates within the same system are easily and naturally handled. Conditions for correctness of SDF graph are explained and scheduling algorithms are described for homogeneous parallel processors sharing memory. A preliminary SDF software system for automatically generating assembly language code for DSP microcomputers is described. Two new efficiency techniques are introduced, static buffering and an extension to SDF to efficiently implement conditionals.
1,985Â citations
01 Sep 1985
TL;DR: This tutorial paper gives an overview of the current state of the art in adaptive equalization and discusses the convergence and steady-state properties of least mean-square (LMS) adaptation algorithms, including digital precision considerations, and three classes of rapidly converging adaptive equalizer algorithms.
Abstract: 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.
1,186Â citations
TL;DR: A concise survey of the literature on cyclostationarity is presented and includes an extensive bibliography and applications of cyclostatedarity in communications, signal processing, and many other research areas are considered.
935Â citations
01 Oct 1998
TL;DR: The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.
Abstract: This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical decisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.
907Â citations
Cites methods from "Fractionally-spaced equalization: A..."
...In Section III we construct a categorization of literature focusing on the application of the CM criterion to blind equalization....
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References
More filters
TL;DR: An easily implemented system for automatic equalization is described which makes use of a steepest-descent technique of minimization, and the effect of a transversal filter equalizer in terms of the system frequency-domain characteristics is considered.
Abstract: Distortion in transmission channels causes intersymbol interference in digital communication systems. This distortion may be partially corrected at the receiver through the use of a tapped delay line having adjustable tap gain settings (transversal filter), The problem of minimizing distortion with a finite-length transversal filter is examined. In the region of small initial channel distortion where most existing systems operate, the best tap gain settings satisfy a set of simultaneous linear equations. For larger initial distortion, iterative techniques are required to find best gain settings. The distortion is shown to be a convex function of the tap gains, so mathematical programming techniques may be employed for optimization. The practical problem is that of evolving a logical strategy whereby the tap gains of the transversal filter may be set to optimum values. An easily implemented system for automatic equalization is described which makes use of a steepest-descent technique of minimization. The equalizer is automatically set prior to data transmission in a training period during which a series of test pulses is transmitted. Only polarity information is required, so digital logic may be used in the equalizer. For application to high-speed data transmission, great accuracies are required for the tap gain settings. Thus the problem of noise in the channel during equalization is quite important. The final error due to noise and channel distortion and the equalizer settling time are discussed and evaluated. Finally, the effect of a transversal filter equalizer in terms of the system frequency-domain characteristics is considered.
512Â citations
TL;DR: It is shown that, in all cases of practical interest, signaling faster than the Nyquist rate, while keeping fixed the information rate, increases the mean-square error.
Abstract: In this work we report new results relating to decision feedback equalization. The equalizer and the transmitting filter are optimized in a PAM data communication system operating over a linear noisy channel. We use a mean-square error criterion and impose an average power constraint at the transmitter. Assuming correct past decisions, an explicit formula for the minimum attainable mean-square error is given. The possible advantages of signaling faster than the Nyquist rate while decreasing the number of levels to maintain the same information rate are investigated. It is shown that, in all cases of practical interest, signaling faster than the Nyquist rate, while keeping fixed the information rate, increases the mean-square error. Finally, to illustrate the use of the results, application is made to a cable channel where the loss in dB varies as the square root of frequency. Various asymptotic formulas and curves are provided to exhibit the relationships between the quantities of interest.
360Â citations
"Fractionally-spaced equalization: A..." refers methods in this paper
...(14) In writing (14) we have used the notation gi(t) and g2(t) rather than g(t) andg(t) to emphasize that the receiving filter does not correspond to an analytic pulse....
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IBM1
TL;DR: It is shown that making the tap spacing of the equalizer somewhat smaller than T (fractional tap spacing) leads to satisfactory performance of theequalizer for a broad continuous range of clock phases, without penalizing the speed of convergence.
Abstract: Adaptive equalizers are usually realized in the form of a transversal filter with variable tap gains and tap spacing equal to the symbol spacing T . The performance of these equalizers depends critically on the symbol-clock phase derived in the receiver, due to the clock-phase dependent aliasing of the spectral roll-off components, upon which the conventional equalizer has no influence. In this paper we study the possibility of overcoming this difficulty by making the tap spacing of the equalizer somewhat smaller than T (fractional tap spacing). It is shown that this leads to satisfactory performance of the equalizer for a broad continuous range of clock phases, without penalizing the speed of convergence. Furthermore, it allows the application of a simple clock recovery scheme which derives a phase control signal from the equalizer tap-gain values.
309Â citations
TL;DR: A novel receiver structure for two-dimensional-modulated, suppressed-carrier data signals that consists of a passband equalizer followed by a demodulator which compensates for frequency offset and phase jitter is described.
Abstract: In this paper, we describe a novel receiver structure for two-dimensional-modulated, suppressed-carrier data signals. The receiver consists of a passband equalizer followed by a demodulator which compensates for frequency offset and phase jitter; the demodulator's phase angle is provided by a data-directed, carrier recovery loop, which is shown by analysis and simulation to be capable of tracking relatively high frequency phase jitter. A derivation of the receiver parameters is presented, based on a gradient algorithm for jointly optimizing the equalizer tap coefficients and the carrier phase estimate, to minimize the output mean-squared error. System performance is related to carrier phase-tracking parameters by analysis. Computer simulations confirm the feasibility of the receiver structure.
156Â citations
"Fractionally-spaced equalization: A..." refers background in this paper
...(2) m The noiseless output of this nonrecursive digital filter, with tap weights { c / } , is the sample sequence u(nT+T) = Zamh(nT-mT+T), (3) m...
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TL;DR: In this article, the tradeoff between the equalizer mean-squared error, the number of taps, the channel characteristics, and digital resolution is analyzed for typical basic-conditioned voiceband channels.
Abstract: An analysis is made of the degree of precision required in a digitally implemented adaptive equalizer to achieve a satisfactory level of performance. Considering both the conventional synchronously spaced equalizer and the newer fractionally spaced equalizer, insight is provided into the relationship between the tap-weight precision and the steady-state, mean-squared error. It is demonstrated why the number of adaptive tap weights should be kept to a minimum (consistent with acceptable steady-state performance), both from convergence and precision requirements. A simple formula is given that displays the tradeoff among the equalizer mean-squared error, the number of taps, the channel characteristics, and digital resolution. For typical basic-conditioned voiceband channels operating at 9.6 kb/s, and neglecting the effects that limited resolution might have on timing and carrier phase tracking, analysis and simulation both indicate that the required top-weight resolution is of the order of 11 or 12 bits. Moreover, the minimum precision is only weakly dependent on the quality of the channel.
85Â citations