Lower Bounds to the Performance of Bit Synchronization for Bandwidth Efficient Pulse-Shaping

Bandwidth efficient signaling requires using pulse-shaping that inherently has intersymbol interference (ISI) except when the timing is perfect. Several lower bounds to the mean-square-error (MSE) of non-data-aided bit-synchronizers are derived for this case. The optimal lower bound is derived using...

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Bibliographic Details
Published in:IEEE transactions on communications Vol. 58; no. 10; pp. 2789 - 2794
Main Authors: Emad, A, Beaulieu, N C
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.10.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Bandwidth
Benchmarking
Bit synchronizer
Cramer-Rao bound
Cramer-Rao bounds
detection theory bound
Equations
Exact sciences and technology
Gaussian
Heuristic
intersymbol interference
Lower bounds
Mathematical model
non-data-aided synchronization
Optimization
Pulse amplitude
Random variables
Signal to noise ratio
Studies
Switching and signalling
Synchronization
Synchronizers
Systems, networks and services of telecommunications
Telecommunications
Telecommunications and information theory
Time measurements
Transmission and modulation (techniques and equipments)
zero-crossing synchronizer
Ziv-Zakai bound
Performance evaluation
non-data-aided synchronization
Pulse shaping
Ziv-Zakai bound
Zero crossing
Mean square error
Gaussian noise
Binary modulation
Detection limit
Pulse amplitude modulation
Cramer Rao inequality
Pulse sequence
Lower bound
Cramer-Rao bound
zero-crossing synchronizer
Signalling
Synchronization
Clock recovery
Symbol manipulation
Intersymbol interference
Bit synchronizer
detection theory bound
Maximum likelihood
Timing
Signal to noise ratio
ISSN:0090-6778, 1558-0857
Online Access:Get full text
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Summary:Bandwidth efficient signaling requires using pulse-shaping that inherently has intersymbol interference (ISI) except when the timing is perfect. Several lower bounds to the mean-square-error (MSE) of non-data-aided bit-synchronizers are derived for this case. The optimal lower bound is derived using the maximum likelihood (ML) criterion for a sequence of binary pulse amplitude modulated pulses in the presence of ISI and Gaussian noise. This lower bound is used as a benchmark to evaluate the performance of other synchronizers in a practical scenario. It is shown that a previous lower bound based on the ISI-free ML synchronizer cannot be used to lower bound the MSE of bit-synchronizers. A detection theory bound (DTB) (also called Ziv-Zakai bound) is applied to the symbol timing recovery problem in the presence of ISI and it is shown that this bound is a tight lower bound on the MSE of the ML synchronizer. A simple lower bound on this DTB is derived and it is shown that the simple bound is almost as tight as the well known modified Cramer-Rao bound (MCRB) at moderate values of SNR, while it does not suffer from the shortcomings of the MCRB at small values of SNR.
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ISSN:0090-6778
1558-0857
DOI:10.1109/TCOMM.2010.083110.090070