A BPSK/QPSK Timing-Error Detector for Sampled Receivers
TL;DR: A simple algorithm for detection of timing error of a synchronous, band-limited, BPSK or QPSK data stream is proposed and derivation of the s curve reveals a sinusoidal shape.
Abstract: A simple algorithm for detection of timing error of a synchronous, band-limited, BPSK or QPSK data stream is proposed. The algorithm requires only two samples per symbol for its operation. One of the two samples is also used for the symbol decision. Derivation of the s curve reveals a sinusoidal shape.
Citations
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TL;DR: In this article, a theoretical analysis of the dual-polarization constant modulus algorithm is presented, where the control surfaces several different equalizer algorithms are derived, including the decision-directed, trained, and the radially directed equalizer for both polarization division multiplexed quadriphase shift keyed (PDM-QPSK) and 16 level quadrature amplitude modulation (PDm-16-QAM).
Abstract: Digital coherent receivers have caused a revolution in the design of optical transmission systems, due to the subsystems and algorithms embedded within such a receiver. After giving a high-level overview of the subsystems, the optical front end, the analog-to-digital converter (ADC) and the digital signal processing (DSP) algorithms, which relax the tolerances on these subsystems are discussed. Attention is then turned to the compensation of transmission impairments, both static and dynamic. The discussion of dynamic-channel equalization, which forms a significant part of the paper, includes a theoretical analysis of the dual-polarization constant modulus algorithm, where the control surfaces several different equalizer algorithms are derived, including the constant modulus, decision-directed, trained, and the radially directed equalizer for both polarization division multiplexed quadriphase shift keyed (PDM-QPSK) and 16 level quadrature amplitude modulation (PDM-16-QAM). Synchronization algorithms employed to recover the timing and carrier phase information are then examined, after which the data may be recovered. The paper concludes with a discussion of the challenges for future coherent optical transmission systems.
772 citations
Cites methods from "A BPSK/QPSK Timing-Error Detector f..."
...Digital timing recovery has been a topic of extensive research [13] with both non-data-aided [71] and data-aided [72] algorithms being employed....
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TL;DR: The author describes the fundamental equation for interpolation, proposes a method for control, and outlines the signal-processing characteristics appropriate to an interpolator.
Abstract: Timing adjustment in a digital modem must be performed by interpolation if sampling is not synchronized to the data symbols. The author describes the fundamental equation for interpolation, proposes a method for control, and outlines the signal-processing characteristics appropriate to an interpolator. A review of previous results and a tutorial exposition of the subject are given, along with new results. >
706 citations
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TL;DR: The NCO-based control method presented in Part I is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation, demonstrating that simple interpolators give excellent performance.
Abstract: For pt.I, see ibid., vol.41, no.3, p.502-208 (1993). Properties of a specific class of interpolators that are based upon polynomials are discussed. Several implementations are described, one of which is particularly convenient in practical hardware. Simulations demonstrate that simple interpolators give excellent performance. In many cases, two-point, linear interpolation is adequate. If better performance is needed, classical four-point, third-order polynomials could be used. Better yet, a novel four-point interpolating filter with piecewise-parabolic impulse response can have performance superior to that of the standard cubic interpolator and still be implemented much more simply. The NCO-based control method presented in Part I is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation. >
640 citations
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TL;DR: A digital algorithm is proposed that can be implemented very efficiently even at high data rates and allows free-running sampling oscillators and a novel planar filtering method that prevents synchronization hangups.
Abstract: The digital realization of timing recovery circuits for digital data transmission is considered. A digital algorithm is proposed that can be implemented very efficiently even at high data rates. The resulting timing jitter has been computed and verified by simulations. In contrast to other known algorithms, the one presented here allows free-running sampling oscillators and a novel planar filtering method that prevents synchronization hangups. >
604 citations
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TL;DR: The modified Cramer-Rao bound (CRB) is introduced which, like the true CRB, is a lower bound to the error variance of any parameter estimator.
Abstract: We introduce the modified Cramer-Rao bound (CRB) which, like the true CRB, is a lower bound to the error variance of any parameter estimator. The modified CRB proves useful when, in addition to the parameter to be estimated, the observed data also depend on other unwanted parameters. The relationship between the modified and true CRB is established and applications are discussed regarding the estimation of carrier-frequency offset, carrier phase, and timing epoch in linearly modulated signals. Modified CRBs for phase and timing estimation have been already discussed in previous works where it is shown that several practical carrier-phase and clock recovery circuits do attain such bounds. Frequency discrimination, instead, is not so well-represented in the literature and a significant contribution of this paper is the calculation of the modified CRB for frequency estimation. This bound is compared with the performance of some frequency detectors and it is concluded that further work is needed in search of more efficient frequency discrimination methods. >
540 citations
References
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TL;DR: A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated, and a general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion.
Abstract: A new class of fast-converging timing recovery methods for synchronous digital data receivers is investigated. Starting with a worst-case timing offset, convergence with random binary data will typically occur within 10-20 symbols. The input signal is sampled at the baud rate; these samples are then processed to derive a suitable control signal to adjust the timing phase. A general method is outlined to obtain near-minimum-variance estimates of the timing offset with respect to a given steady-state sampling criterion. Although we make certain independence assumptions between successive samples and postulate ideal decisions to obtain convenient analytical results, our simulations with a decision-directed reference and baud-to-baud adjustments yield very similar results. Convergence is exponential, and for small loop gains the residual jitter is proportional and convergence time is inversely proportional to the loop gain. The proposed algorithms are simple and economic to implement. They apply to binary or multilevel PAM signals as well as to partial response signals.
747 citations
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01 Jan 1973TL;DR: This classic graduate- and research-level texty by two leading experts in the field of telecommunications is essential reading for anyone workign today in space and satellite digital communicatiions and those seeking a wider background in statistical communication theory and its applications.
Abstract: From the Publisher:
This classic graduate- and research-level texty by two leading experts in the field of telecommunications is essential reading for anyone workign today in space and satellite digital communicatiions and those seeking a wider background in statistical communication theory and its applications. Ideal for practicing engineers as well as graduate students in communication systems courses, the book clearly presents and develops theory that can be used in the design and planning of telecommunication systems operating with either small or large performance margins. The book includes in its coverage a theory for use in the design of one-way and two-way phase-coherent and communication systems; and analysis and comparison of carrier and suppressed carrier synchronization techniques; treatment of the band-pass limiter theory; unification of phase-coherent detection with perfect and noisy synchronization reference signals. Convolutional codes, symbol synchronization, and noncoherent detection of M-ary signals are among the otehr subjects addressed in this comprehensive study. Dr. Lindsey, who is with the Communication Sciences Institute at the University of Southern California, and Dr. Simon, who is with the Jet Propulsion Laboratory at the California Institute of Technology, include at the end of each chapter a comprehensive set of problems that demonstrate the application of the theory developed. Unabridged Dover (1991) republication of the edition published by Prentice-Hall, Inc., Englewood Cliffs, N.J., 1973.265 line illustrations. 3 photographs. References at chapter ends. Problems. Index. xviii + 574pp. 5 3/8 x 8 1/2. Paperbound.
387 citations
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TL;DR: This paper examines the problems of carrier phase estimation and symbol timing estimation for carrier-type synchronous digital data signals, with tutorial objectives foremost.
Abstract: This paper examines the problems of carrier phase estimation and symbol timing estimation for carrier-type synchronous digital data signals, with tutorial objectives foremost. Carrier phase recovery for suppressed-carrier versions of double sideband (DSB), vestigial sideband (VSB), and quadrature amplitude modulation (QAM) signal formats is considered first. Then the problem of symbol timing recovery for a baseband pulse-amplitude modulation (PAM) signal is examined. Timing recovery circuits based on elementary statistical properties are discussed as well as timing recovery based on maximum-likelihood estimation theory. A relatively simple approach to evaluation of timing recovery circuit performance in terms of rms jitter of the timing parameters is presented.
317 citations
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TL;DR: A new technique is presented for evaluating the performance of a popular type of timing recovery circuit for baseband synchronous pulse amplitude modulation (PAM) data signals and expressions for rms phase fluctuation in the timing wave are presented.
Abstract: A new technique is presented for evaluating the performance of a popular type of timing recovery circuit for baseband synchronous pulse amplitude modulation (PAM) data signals. The timing circuit consists of a square-law device followed by a narrowband filter tuned to the pulse repetition frequency along with provision for reshaping the pulses entering the timing path (prefiltering). The output of the timing circuit is a nearly sinusoidal timing wave whose zero crossings indicate the appropriate sampling instants for demodulation of the PAM signal. For a random data sequence, the timing wave exhibits phase fluctuations which are strongly dependent on the pulse shapes entering the timing path and the passband shape of the narrow-band filter. Expressions for rms phase fluctuation in the timing wave as a function of the prefiltering and postfiltering characteristics of the filters preceding and following the square-law device are presented. These expressions have a form which is especially suitable for studying the case where the baseband PAM signal is band-limited to frequencies less than the pulse repetition frequency. A condition on prefiltering and postfiltering which gives error-free timing recovery is presented. Results obtained from some specific examples serve to illustrate several aspects of the timing recovery problem.
168 citations
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TL;DR: Emphasis is on those techniques that lend themselves to implementation in MOSLSI technology, where the objective requirement is that timing recovery be implemented on a sampled-data signal (with the minimum possible sampling rate where EC is used).
Abstract: Tradeoffs in the design of the timing recovery functions in a subscriber loop receiver are analyzed. The techniques considered are applicable to both the echo cancellation (EC) and time compression multiplexing (TCM) methods of full duplex transmission. Emphasis is on those techniques that lend themselves to implementation in MOSLSI technology, where the objective requirement is that timing recovery be implemented on a sampled-data signal (with the minimum possible sampling rate where EC is used). The wave difference method (WDM) for timing recovery appears to be the best candidate. A detailed study of its performance is carried out analytically and by computer simulation for the case of binary and alternate mark-inversion (AMI) line coding. A closed form expression describing the binary jitter performance of the WDM and its continuous time counterpart, the spectral line technique, is used to compare the two techniques. Analytical and simulation results for recovered phase and jitter are presented for various cable pulse responses carefully chosen to represent worst-case or nearly worst-case conditions. Two methods for including frequency detection in the WDM, the quadricorrelator and the rotational detector, are also simulated.
65 citations