Phase Acquisition Statistics for Phase-Locked Loops

Meyr, H.; Popken, L.

doi:10.1109/tcom.1980.1094794

Cited by 24 publications

(5 citation statements)

References 2 publications

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“…As expected, for small K the loop bandwidth is approximately inversely proportional to the time constant. This characteristic matches well the time constant derived for the analog loop [17].…”

Section: Acquisition Performancesupporting

confidence: 86%

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A performance analysis of a digital PLL based MPSK demodulator

Fitz

Cramer

1995

IEEE Trans. Commun.

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This paper presents a generalized nonlinear (Markov) analysis technique that is used to evaluate the statistical performance of uniforn~ly sampled digital phase-locked loop (DPLL) demodulators. Although the rigorous analysis of the statistical performance of the analog PLL for digitally modulated signals (i.e., Costas loops) remains an open problem, the discrete time analysis for MPSK modulation is tractable. This paper characterizes the first-order, decisiondirected DPLL based demodulator as a Markov chain. Traditional analytical techniques are used to evaluate the steady-state statistical performance. Numerical results for the steady-state density function are derived for BPSK, QPSK, and 8PSK. The resulting steady-state bit error probabilities for these modulations are also calculated. Traditional Markov analytical techniques (absorbing boundaries) permit a numerical evaluation of the transient characteristics of the DPLL. The numerical work focuses on loops for both unmodulated and BPSK, QPSK, andl 8PSK modulated input signals. The transient characteristics are shown to be a function of the loop bandwidth but converge to those predicted by a diffusion analysis as the loop bandwidth decreases. The susceptibility of small bandwidth loops to hangup is shown to be the largest reason for the acquisition performance difference. The cycle slipping characterization for 'MPSK modulated signals is also a function of the loop bandwidth and each increase (doubling) of the modulation alphabet size reduces the slipping performance by approximately 6dB.

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Section: Acquisition Performancesupporting

confidence: 86%

“…A steady-state pmf is obtained by iterating the CK equation (17) until the resulting pmf ceases to change by more than a prescribed amount. This iteration method is also useful for examining the transient characteristics of the DPLL.…”

mentioning

confidence: 99%

A performance analysis of a digital PLL based MPSK demodulator

Fitz

Cramer

1995

IEEE Trans. Commun.

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“…However, if the related analog model is assumed with the NCO replaced by a simple integrator and the loop noise n(t) as a zero-mean white Gaussian process, the trajectory (t) follows a Fokker-Planck equation, which can be solved by numerical means [7][8][9]. Unfortunately, the analytical results of the analog loop could not be verified by simulation of the digital tracker shown in Figure 1, mainly due to the fact that the noise characteristic of the latter is neither white (the samples are correlated) nor Gaussian (because of self-noise).…”

Section: Acquisition With Non-adaptive Loop Filtersmentioning

confidence: 99%

“…For analog first-order loops, the acquisition of the carrier phase may be derived in closed form [7][8][9]. It is verified in this letter that the model can be successfully applied to NDA recovery of the symbol timing with GA detectors.…”

Section: Introductionmentioning

confidence: 99%

Acquisition performance for NDA symbol‐timing recovery with simple adaptive first‐order loops

Gappmair

Flohberger

Koudelka

2006

Trans Emerging Tel Tech

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SUMMARYPowerful feedforward estimators for symbol-timing recovery are more or less mandatory for efficient acquisition in time-division multiple access (TDMA) modems. However, in many cases, feedback solutions are much less complex from the computational point of view. The latter can be an attractive alternative for continuous transmission of data like DVB, where rapid acquisition is not so important as with TDMA. In order to describe analytically the acquisition performance of first-order loops with Gardner detectors, it is shown that the related analog model can be successfully applied. In the sequel, this approach is used to demonstrate that the acquisition process may be accelerated significantly via simple adaptive loop filters.

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“…Meyr and Popken [2] investigated the statistics of hangup, using a diffusion analysis and a sinusoidal phase detector model. They confirm the importance of the reverse-slope null, but found no evidence of equivocation in their analysis.…”

Section: Introductionmentioning

confidence: 99%