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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| Vydané v: | IEEE transactions on communications Ročník 58; číslo 10; s. 2789 - 2794 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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New York, NY
IEEE
01.10.2010
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 0090-6778, 1558-0857 |
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| Abstract | 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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| AbstractList | 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. |
| Author | Emad, A Beaulieu, N C |
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| Keywords | 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 |
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| Snippet | Bandwidth efficient signaling requires using pulse-shaping that inherently has intersymbol interference (ISI) except when the timing is perfect. Several lower... |
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| SubjectTerms | 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 |
| Title | Lower Bounds to the Performance of Bit Synchronization for Bandwidth Efficient Pulse-Shaping |
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