A Theoretical Framework for Soft-Information-Based Synchronization in Iterative (Turbo) Receivers
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A Theoretical Framework for Soft-Information-Based Synchronization in Iterative (Turbo) Receivers Nele Noels,1 Vincenzo Lottici,2 Antoine Dejonghe,3 Heidi Steendam,1 Marc Moeneclaey,1 Marco Luise,2 Luc Vandendorpe3 1 Department
of Telecommunications and Information Processing, Ghent University, 9000 Gent, Belgium Emails: [email protected], [email protected], [email protected]
2 Department
of Information Engineering, University of Pisa, 56122 Pisa, Italy Emails: [email protected], [email protected]
3 Communications
and Remote Sensing Laboratory, Universit´e Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium Email: [email protected], [email protected]
Received 13 May 2004; Revised 29 September 2004 This contribution considers turbo synchronization, that is to say, the use of soft data information to estimate parameters like carrier phase, frequency, or timing offsets of a modulated signal within an iterative data demodulator. In turbo synchronization, the receiver exploits the soft decisions computed at each turbo decoding iteration to provide a reliable estimate of some signal parameters. The aim of our paper is to show that such “turbo-estimation” approach can be regarded as a special case of the expectation-maximization (EM) algorithm. This leads to a general theoretical framework for turbo synchronization that allows to derive parameter estimation procedures for carrier phase and frequency offset, as well as for timing offset and signal amplitude. The proposed mathematical framework is illustrated by simulation results reported for the particular case of carrier phase and frequency offsets estimation of a turbo-coded 16-QAM signal. Keywords and phrases: turbo synchronization, iterative detection, turbo codes, parameter estimation.
1.
INTRODUCTION
The impressive performance of turbo codes [1] has triggered in the last decade a lot of research addressing the application of this powerful coding technique to digital communications [2]. More recently, the associated idea of iterative decoding has been extended to other receiver functions. This led to the so-called turbo principle which enables to perform (sub)optimal joint detection and decoding through the iterative exchange of soft information between soft-input/softoutput (SISO) stages. See [3, 4] for a review of some existing turbo receivers. In addition to detection/decoding a receiver has also to perform signal synchronization, that is, to estimate a number of parameters like carrier phase offset, frequency offset, timing offset, and so forth. Synchronization for turbo-encoded systems is a challenging task since the receiver usually 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.
operates at low SNR values (which can be defined as the ratio between the mean bit energy and the noise spectral density). In the technical literature a great effort is thus being devoted to the develop
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