A Theoretical Framework for Soft-Information-Based Synchronization in Iterative (Turbo) Receivers

Abstract

<p>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 &#8220;turbo-estimation&#8221; 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.</p

LDPC codes over channels with memory

“…The third algorithm is the "ultra fast" algorithm with overlapped windows described in [23], with the value of N optimized by computer simulation. Finally, the fourth one is based on the EM algorithm [24]- [27], [22]. In order to adapt this algorithm to a time-varying channel phase, different phase estimates are computed for each code symbol, taking into account the contribution of the adjacent symbols belonging to a window whose dimension is optimized by computer simulation.…”

“…A non-Bayesian approach is adopted in [22], [23]. In [22] the channel phase is estimated by using the expectationmaximization (EM) algorithm, as originally proposed in [24]- [27] for turbo codes, and the estimation algorithm is embedded into the LDPC iterative decoding process. On the contrary, in [23] a class of problems is identified for which the optimal (in the sense of the generalized-likelihood ratio test) computation of the symbol a posteriori probabilities can be performed with polynomial complexity and the application to LDPC codes and the noncoherent channel is discussed.…”

Pilotless carrier phase-synchronization via LDPC code feedback

“…As described by Noels et al [2], two somewhat distinct groups of joint decoding and synchronization algorithms have evolved. The first of these groups, approaches the problem by modifying iterative detection/decoding algorithms and/or graphs to include parameter estimation.…”

Carrier and Timing Synchronization of BPSK via LDPC Code Feedback

“…As clearly explained by Noels et al [5] two somewhat distinct groups of joint decoding and synchronization algorithms have evolved. The first group approaches the parameter estimation problem by…”

“…The resulting architectures are often said to employ turbo synchronization. Noels et al [5] have done a careful study of the mathematical interpretation of turbo synchronization algorithms by means of the expectationmaximization (EM) algorithm. Algorithms of this type can can be found in [10]- [13].…”