Cédric Herzet

Turbo synchronization: an EM algorithm interpretation

This paper is devoted to turbo synchronization, that is to say the use of soft information to estimate parameters like carrier phase, frequency offset or timing within a turbo receiver. It is shown how maximum-likelihood estimation of those synchronization parameters can be implemented by means of the iterative expectation-maximization (EM) algorithm [A.P. Dempster, et al., 1977]. Then we show that the EM algorithm iterations can be combined with those of a turbo receiver. This leads to a general theoretical framework for turbo synchronization. The soft decision-directed ad-hoc algorithm proposed in V. Lottici and M. Luise, [2002] for carrier phase recovery turns out to be a particular instance of this implementation. The proposed mathematical framework is illustrated by simulations reported for the particular case of carrier phase estimation combined with iterative demodulation and decoding [S. ten Brink, et al., 1998].

Code-Aided Turbo Synchronization

The introduction of turbo and low-density parity-check (LDPC) codes with iterative decoding that almost attain Shannon capacity challenges the synchronization subsystems of a data modem. Fast and accurate signal synchronization has to be performed at a much lower value of signal-to-noise ratio (SNR) than in previous less efficiently coded systems. The solution to this issue is developing specific synchronization techniques that take advantage of the presence of the channel code and of the iterative nature of decoding: the so-called turbo-synchronization algorithms. The aim of this paper within this special issue devoted to the turbo principle is twofold: on the one hand, it shows how the many turbo-synchronization algorithms that have already appeared in the literature can be cast into a simple and rigorous theoretical framework. On the other hand, it shows the application of such techniques in a few simple cases, and evaluates improvement that can be obtained from them, especially in the low-SNR regime.

Comparison of EM-Based Algorithms for MIMO Channel Estimation

Iterative channel estimation can improve the channel-state information (CSI) with respect to noniterative estimation. New iterative channel estimators based on the expectation-maximization (EM) algorithm are proposed in this paper. A first estimator, called the unbiased EM (UEM), is designed to unbias the EM estimates. A second estimator is then put forward, which is based on the expectation-conditional-maximization (ECM) algorithm, and its complexity is lower than that of the EM. An unbiased ECM (UECM) estimator is also proposed. Although the unbiasedness of the UEM and UECM estimators is not rigorously proved, the use of these names is explained in the paper. The new estimators are compared with well-known ones, such as the EM, the decision-directed (DD), and the data-aided (DA) estimators. Simulations are reported for a turbo receiver operating over frequency-selective multiple-input multiple-output channels. It is shown that the UEM channel estimator outperforms the EM, and that the ECM-based estimators are very close to the EM-based ones

EM algorithm-based timing synchronization in turbo receivers

The paper addresses the issue of estimating the sampling instant in turbo receivers. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the turbo system. Performance of the proposed synchronizer is illustrated by simulation results. In particular, the mean and the variance of the estimator as well as the bit error rate reached by the synchronized system are reported.

A Theoretical Framework for Iterative Synchronization Based on the Sum–Product and the Expectation-Maximization Algorithms

This paper deals with maximum-likelihood (ML) estimation of synchronization parameters for coded transmission systems. In particular, we present a unified framework based on both the sum-product (SP) algorithm and the expectation-maximization (EM) algorithm for the design of iterative synchronizers. The proposed approach is shown to encompass some known iterative synchronizers. In particular, we revisit a previously proposed framework based on the EM algorithm only by means of our SP-EM approach. The performance of the proposed synchronization method is assessed in terms of mean-square error and bit-error rate by simulation results. In particular, we consider the joint synchronization of the timing epoch and the carrier phase offset in the case of convolutionally coded and turbo-coded transmissions

On Maximum-Likelihood Timing Synchronization

In this paper, we address the issue of symbol timing recovery for a coded burst transmission system. As direct maximum-likelihood (ML) estimation is intractable, we resort to the expectation-maximization (EM) algorithm in order to derive a receiver that iterates between data detection and synchronization. Conventional data-aided (DA) and decision-directed (DD) synchronizers can be interpreted as special cases of the proposed algorithm. The EM-based technique takes into account code properties and is especially well suited to scenarios where conventional schemes fail to provide the detector with a reliable timing estimate. The performance of the proposed algorithm is compared with conventional techniques through computer simulations, both in terms of mean-square estimation error (MSEE) and bit error rate (BER).

A Semi-Analytical Method for Predicting the Performance and Convergence Behavior of a Multiuser Turbo-Equalizer/Demapper

This paper proposes a simple semi-analytical method with reduced simulation time for predicting at any iteration the performance of a turbo-equalization/demapping scheme using the Wang and Poor soft-in/soft-out (SISO) minimum mean-square error (MMSE)/interference cancellation (IC) equalizer and a SISO decoder. The proposed method may be applied to multilevel/phase data modulations as well as multiuser context. This paper shows that the equalizer behavior may be very reliably predicted totally by calculations (no simulations are needed) whereas that of the decoder still requires simulations. A comparison between the proposed prediction method and plain simulations of the overall turbo equalization scheme demonstrates that our method accurately determines the system performance at any iteration. Static channels, long frames, and perfect channel knowledge are assumed throughout the paper

Turbo synchronization: a combined sum-product and expectation-maximization algorithm approach

This paper places turbo synchronization into the sum-product (SP) and the expectation-maximization (EM) algorithm framework. In particular, we show that the combination of these algorithms enables to design low-complexity and very powerful synchronisers. The proposed synchronizer is compared to a previously-proposed EM framework. As the derivation suggests, our new iterative scheme clearly outperforms the classical use of the EM algorithm.

EM algorithm-based multiuser synchronization in turbo receivers

The current paper addresses the issue of estimating the user propagation delays, received carrier phase offsets and received amplitudes in an asynchronous DS-CDMA environment with frequency non-selective propagation channels. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the receiver which is of the turbo type. The performance of the proposed synchronizer is illustrated by simulation results. In particular, the mean and the mean squared error of the estimator, as well as the bit error rate reached by the synchronized system, are reported.

EM algorithm-based estimation of amplitude, carrier phase and noise variance in multiuser turbo receivers

The current paper addresses the issue of estimating the users received carrier phase offsets and received amplitudes as well as the noise variance in an asynchronous DS-CDMA environment with frequency nonselective propagation channels. The user propagation delays are assumed to be known or estimated beforehand. The proposed synchronizer is based on the expectation-maximization (EM) algorithm and takes benefit from the soft information delivered by the receiver which is of turbo type. Besides, this paper explains which training symbols should be preferably chosen to initialize this synchronizer. It also compares two methods for combining the training-based estimate and the EM estimate. Performance of the resulting synchronizer is illustrated by simulation results.