EM-based Algorithms Research Articles

Comparison of EM-Based Algorithms for MIMO Channel Estimation

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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. </para>

Code-aided frame synchronization and phase ambiguity resolution

This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful error-correcting codes and operate at low signal-to-noise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a re-encoding (REEN) technique, an algorithm we previously derived from the expectation-maximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudo-ML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum-product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EM-based and the PML algorithms have excellent performance. The MS, PML, REEN, and EM-based algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance

LDPC-based space-time coded OFDM systems: Turbo-EM receiver design with channel state information guessing algorithms

In this paper we study some turbo receiver architectures employing low-density parity check (Ldpc) codes together with orthogonal frequency division multiplexing (Ofdm) for high data rate wireless transmissions. Different demodulation schemes based on expectation-maximization (Em) algorithm are studied along with the channel impulse response (Em) algorithms. We studied differentCir guessing algorithms including the EM-based algorithms such as a space-alternating generalized expectation-maximization algorithm (Sage). It is shown that the proposed turbo-Em receiver employing a soft maximum a posteriori (Map)Em demodulator and a belief propagationLdpc decoder can perform within 1 dB from the ergodic capacity of the studiedMimo ofdm channels. Besides, we find that a suboptimum structure based on a soft interference cancellationMmse filtering demodulator exhibits negligible loss in non-correlated fadingMimo channels but suffer extra performance loss in highly correlatedMimo channels.

Application of expectation maximization algorithms for image resolution improvement in a small animal PET system

Modern positron emission tomography (PET) systems, offering high counting rate capabilities, high sensitivity, and near-submillimeter coordinate resolution, require fast image reconstruction software that can operate on list-mode data and take into account most of finite resolution effects such as photon scattering, positron range in tissue, and detector features. It has already been demonstrated that the expectation maximization (EM) method with extended system matrix modeling looks very attractive for image resolution recovery in PET imaging studies. In this paper, the performance of EM-based algorithms (in particular, their ability to improve the image resolution) is evaluated for a small animal PET imager with several phantoms. The achievement of a substantial decrease in processing time using an EM deblurring procedure is shown, as is an approach to successfully treat what are essentially nonspace-invariant resolution effects within a shift-invariant model.

EM-Based Channel Estimation Algorithms for OFDM

Estimating a channel that is subject to frequency-selective Rayleigh fading is a challenging problem in an orthogonal frequency division multiplexing (OFDM) system. We propose three EM-based algorithms to effciently estimate the channel impulse response (CIR) or channel frequency response of such a system operating on a channel with multipath fading and additive white Gaussian noise (AWGN). These algorithms are capable of improving the channel estimate by making use of a modest number of pilot tones or using the channel estimate of the previous frame to obtain the initial estimate for the iterative procedure. Simulation results show that the bit error rate (BER) as well as the mean square error (MSE) of the channel can be significantly reduced by these algorithms. We present simulation results to compare these algorithms on the basis of their performance and rate of convergence. We also derive Cramer-Rao-like lower bounds for the unbiased channel estimate, which can be achieved via these EM-based algorithms. It is shown that the convergence rate of two of the algorithms is independent of the length of the multipath spread. One of them also converges most rapidly and has the smallest overall computational burden.

Finite dimensional smoothers for MAP state estimation of bilinear systems

In this paper, we present two finite-dimensional iterative algorithms for maximum a posteriori (MAP) state sequence estimation of bilinear systems. Bilinear models are appealing in their ability to represent or approximate a broad class of nonlinear systems. Our iterative algorithms for state estimation are based on the expectation-maximization (EM) algorithm and outperform the widely used extended Kalman smoother (EKS). Unlike the EKS, these EM algorithms are optimal (in the MAP sense) finite-dimensional solutions to the state sequence estimation problem for bilinear models. We also present recursive (on-line) versions of the two algorithms and show that they outperform the extended Kalman filter (EKF). Our main conclusion is that the EM-based algorithms presented in this paper are novel nonlinear filtering methods that perform better than traditional methods such as the EKF.

Region of interest evaluation of SPECT image reconstruction methods using a realistic brain phantom

A realistic numerical brain phantom, developed by Zubal et al. (1994), was used for a region-of-interest evaluation of the accuracy and noise variance of the following SPECT reconstruction methods: (1) maximum-likelihood reconstruction using the expectation-maximization (ML-EM) algorithm; (2) an EM algorithm using ordered-subsets (OS-EM); (3) a re-scaled block iterative EM algorithm (RBI-EM); and (4) a filtered backprojection algorithm that uses a combination of the Bellini method for attenuation compensation and an iterative spatial blurring correction method using the frequency-distance principle (FDP). The Zubal phantom was made from segmented MRI slices of the brain, so that neuro-anatomical structures are well defined and indexed. Small regions-of-interest (ROIs) from the white matter, grey matter in the center of the brain and grey matter from the peripheral area of the brain were selected for the evaluation. Photon attenuation and distance-dependent collimator blurring were modeled. Multiple independent noise realizations were generated for two different count levels. The simulation study showed that the ROI bias measured for the EM-based algorithms decreased as the iteration number increased, and that the OS-EM and RBI-EM algorithms (16 and 64 subsets were used) achieved the equivalent accuracy of the ML-EM algorithm at about the same noise variance, with much fewer number of iterations. The Bellini-FDP restoration algorithm converged fast and required less computation per iteration. The ML-EM algorithm had a slightly better ROI bias vs. variance trade-off than the other algorithms.

Iterative multiuser receivers for CDMA channels: an EM-based approach

Maximum-likelihood detection for the multiuser code-division multiple-access (CDMA) channel is prohibitively complex. This paper considers new iterative multiuser receivers based on the expectation-maximization (EM) algorithm and related, more powerful "space-alternating" algorithms. The latter algorithms include the SAGE algorithm and a new "missing parameter" space-alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data. Application of these EM-based algorithms to the problem of discrete parameter estimation (i.e., data detection) in the Gaussian multiple-access channel leads to a variety of convergent receiver structures that incorporate soft-decision feedback for interference cancellation and/or sequential updating of iterative bit estimates. Convergence and performance analyses are based on well-known properties of the EM algorithm and on numerical simulation.