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Research Letters in Communications
Volume 2008 (2008), Article ID 235761, 4 pages
Research Letter

Wiener's Loop Filter for PLL-Based Carrier Recovery of OQPSK and MSK-Type Modulations

Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy

Received 7 April 2008; Accepted 28 May 2008

Academic Editor: J. S. Mandeep

Copyright © 2008 Arnaldo Spalvieri and Maurizio Magarini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This letter considers carrier recovery for offset quadrature phase shift keying (OQPSK) and minimum shift keying-type (MSK-type) modulations based on phase-lock loop (PLL). The concern of the letter is the optimization of the loop filter of the PLL. The optimization is worked out in the light of Wiener's theory taking into account the phase noise affecting the incoming carrier, the additive white Gaussian noise that is present on the channel, and the self-noise produced by the phase detector. Delay in the loop, which may affect the numerical implementation of the PLL, is also considered. Closed-form expressions for the loop filter and for the mean-square error are given for the case where the phase noise is characterized as a first-order process.