Generalized Expectation Maximization Research Articles

Cross-ambiguity function domain multipath channel parameter estimation

A new array signal processing technique is proposed to estimate the direction-of-arrivals (DOAs), time delays, Doppler shifts and amplitudes of a known waveform impinging on an array of antennas from several distinct paths. The proposed technique detects the presence of multipath components by integrating cross-ambiguity functions (CAF) of array outputs, hence, it is called as the cross-ambiguity function direction finding (CAF-DF). The performance of the CAF-DF technique is compared with the space-alternating generalized expectation–maximization (SAGE) and the multiple signal classification (MUSIC) techniques as well as the Cramér–Rao lower bound. The CAF-DF technique is found to be superior in terms of root-mean-squared-error (rMSE) to the SAGE and MUSIC techniques.

Space-alternating generalised expectation–maximisation-based H-infinity channel estimator for multiple-input multiple-output-orthogonal frequency division multiplexing systems

This study presents a low-complexity and robust H-infinity channel estimator for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The H-infinity estimator, which has never been devoted to MIMO-OFDM systems, could be implemented by applying a multiple-order auto-regression (AR) model. However, it may increase the design complexity of receivers and lead to poor real-time property when this model is used for MIMO-OFDM systems, which makes the authors abandon AR model. In order to reduce the number of matrices manipulations because of the each received OFDM symbols from different transmit antennas, the iterative space-alternating generalised expectation–maximisation (SAGE) algorithm is adopted. Furthermore, to deal with the effect of non-Gaussian noise (NGN) channels, because of various natural or man-made impulsive sources, an equivalent signal model (ESM) is introduced to alleviate the effect of this issue and enhance the robust of SAGE-based H-infinity estimator. Simulation results show that H-infinity estimator has almost the same bit error rate performance as optimal maximum a posteriori estimator. The performance gain afforded by using ESM can be substantial when compared with using the traditional signal model, which dramatically enhance the robustness of SAGE-based H-infinity estimator against NGN channels.

Multipath channel identification by using global optimization in ambiguity function domain

A new transform domain array signal processing technique is proposed for identification of multipath communication channels. The received array element outputs are transformed to delay–Doppler domain by using the cross-ambiguity function (CAF) for efficient exploitation of the delay–Doppler diversity of the multipath components. Clusters of multipath components can be identified by using a simple amplitude thresholding in the delay–Doppler domain. Particle swarm optimization (PSO) can be used to identify parameters of the multipath components in each cluster. The performance of the proposed PSO-CAF technique is compared with the space alternating generalized expectation maximization (SAGE) technique and with a recently proposed PSO based technique at various SNR levels. Simulation results clearly quantify the superior performance of the PSO-CAF technique over the alternative techniques at all practically significant SNR levels.

Improved ICI Mitigation Scheme over Time-varying Channels for High-Mobility OFDM Systems

Based on the space alternating generalized expectation maximization (SAGE) technique, and the ordered serial interference cancellation (OSIC) algorithm, an improved low-complexity inter-carrier interference (ICI) mitigation scheme, named SAGE-OSIC, is proposed for high mobile orthogonal frequency division multiplexing (OFDM) systems, where the subcarriers are updated in series, according to the order of the decreasing signal to interference plus noise ratio (SINR) or signal to noise ratio (SNR). The computational complexity is investigated, and simulation studies are concluded over multipath fading and rapidly time-varying channels. It is indicated that the proposed SAGE-OSIC scheme significantly outperforms the existing low-complexity ICI mitigation methods based on SAGE, without any increase in the computational complexity, especially for the large Doppler shifts in highly mobile environments. Furthermore, it can also be concluded that the performance of the proposed SAGE-OSIC approaches that of the vertical Bell laboratory layered space-time (VBLAST) scheme, which demands very high computation.

Radio interferometric calibration using the SAGE algorithm

The aim of the new generation of radio synthesis arrays such as LOFAR and SKA is to achieve much higher sensitivity, resolution and frequency coverage than what is available now, especially at low frequencies. To accomplish this goal, the accuracy of the calibration techniques used is of considerable importance. Moreover, since these telescopes produce huge amounts of data, speed of convergence of calibration is a major bottleneck. The errors in calibration are due to system noise (sky and instrumental) as well as the estimation errors introduced by the calibration technique itself, which we call solver noise. We define solver noise as the distance between the optimal solution (the true value of the unknowns, uncorrupted by the system noise) and the solution obtained by calibration. We present the Space Alternating Generalized Expectation Maximization (SAGE) calibration technique, which is a modification of the Expectation Maximization algorithm, and compare its performance with the traditional Least Squares calibration based on the level of solver noise introduced by each technique. For this purpose, we develop statistical methods that use the calibrated solutions to estimate the level of solver noise. The SAGE calibration algorithm yields very promising results both in terms of accuracy and speed of convergence. The comparison approaches we adopt introduce a new framework for assessing the performance of different calibration schemes.

Reliability Assessment of Numerical Control Machine Tools Using Weibull Mixture Models

Weibull distribution is one of the most widely used model in reliability analysis of NC machine tools. In order to assess the reliability of NC machine tool, Generalized Expectation Maximization (GEM) algorithm is used to estimate parameters of mixture Weibull models. Akaike information criterion (AIC) and Bayesian information criterion (BIC) are used as comprehensive criteria to select the number of subpopulations of mixture models. The results show that mixture models are more suitable to assess reliability of NC machine tools than that of single model. Root mean square errors (RMSE) of mixture models reduce by 87.5% than that of single model. Reliability evaluation results of machine tool, such as MTBF etc., are given.

Estimation of Radar Cross Section of a Target under Track

In allocating radar beam for tracking a target, it is attempted to maintain the signal-to-noise ratio (SNR) of signal returning from the illuminated target close to an optimum value for efficient track updates. An estimate of the average radar cross section (RCS) of the target is required in order to adjust transmitted power based on the estimate such that a desired SNR can be realized. In this paper, a maximum-likelihood (ML) approach is presented for estimating the average RCS, and a numerical solution to the approach is proposed based on a generalized expectation maximization (GEM) algorithm. Estimation accuracy of the approach is compared to that of a previously reported procedure.

Joint Channel Estimation, Equalization, and Data Detection for OFDM Systems in the Presence of Very High Mobility

This paper is concerned with the challenging and timely problem of joint channel estimation, equalization, and data detection for uplink orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The resulting algorithm is based on the space alternating generalized expectation maximization (SAGE) technique which is particularly well suited to multicarrier signal formats leading to a receiver structure that also incorporates interchannel interference (ICI) cancelation. In order to reduce the computational complexity of the algorithm, band-limited, discrete cosine orthogonal basis functions are employed to represent the rapidly time-varying fading channel by the discrete cosine serial expansion coefficients. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal. In this way, the resulting reduced dimensional channel coefficients are estimated and the data symbols detected iteratively with tractable complexity. The proposed SAGE joint detection algorithm updates the data sequences serially and the channel parameters are updated in parallel, leading to a receiver structure that also incorporates ICI cancelation. Computer simulations show that the cosine transformation represents the time-varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm, resulting in substantial reduction of the computational complexity.

Generalized EM estimation for semi-parametric mixture distributions with discretized non-parametric component

We consider independent sampling from a two-component mixture distribution, where one component (called the parametric component) is from a known distributional family and the other component (called the non-parametric component) is unknown. This is a semi-parametric mixture distribution. We discretize the non-parametric component and estimate the parameters of this mixture model, namely the mixing proportion, the unknown parameters of the parametric component and the discretized non-parametric component. We define the maximum penalized likelihood (MPL) estimates of the mixture model parameters and then develop a generalized EM (GEM) iterative scheme to compute the MPL estimates. A simulation study and an example from biology are presented.

Axonal Transport Proteomics Reveals Mobilization of Translation Machinery to the Lesion Site in Injured Sciatic Nerve

Investigations of the molecular mechanisms underlying responses to nerve injury have highlighted the importance of axonal transport systems. To obtain a comprehensive view of the protein ensembles associated with axonal transport in injured axons, we analyzed the protein compositions of axoplasm concentrated at ligatures following crush injury of rat sciatic nerve. LC-MS/MS analyses of iTRAQ-labeled peptides from axoplasm distal and proximal to the ligation sites revealed protein ensembles transported in both anterograde and retrograde directions. Variability of replicates did not allow straightforward assignment of proteins to functional transport categories; hence, we performed principal component analysis and factor analysis with subsequent clustering to determine the most prominent injury-related transported proteins. This strategy circumvented experimental variability and allowed the extraction of biologically meaningful information from the quantitative neuroproteomics experiments. 299 proteins were highlighted by principal component analysis and factor analysis, 145 of which correlate with retrograde and 154 of which correlate with anterograde transport after injury. The analyses reveal extensive changes in both anterograde and retrograde transport proteomes in injured peripheral axons and emphasize the importance of RNA binding and translational machineries in the axonal response to injury.

Three-dimensional FLASH laser radar range estimation via blind deconvolution

Three-dimensional (3D) FLASH Laser Radar (LADAR) sensors are unique due to the ability to rapidly acquire a series of two dimensional remote scene data (i.e. range images). Principal causes of 3D FLASH LADAR range estimation error include spatial blur, detector blurring, noise, timing jitter, and inter-sample targets. Unlike previous research, this paper accounts for pixel coupling by defining the range image mathematical model as a 2D convolution between the system spatial impulse response and the object (target or remote scene) at a particular point in time. Using this model, improved range estimation is possible by object restoration from the data observations. Object estimation is performed by deriving a blind deconvolution Generalized Expectation Maximization (GEM) algorithm with the range determined from the estimated object by a normalized correlation method. Theoretical derivations and simulation results are verified with experimental data of a bar target taken from a 3D FLASH LADAR system in a laboratory environment. Simulation examples show that the GEM improves range estimation over the unprocessed data and a Wiener filter method by 75% and 26% respectively. In the laboratory experiment, the GEM improves range estimation by 34% and 18%over the unprocessed data and Wiener filter method respectively.

Use of reference distributions when dealing with unknown regression errors

A problem of estimating regression coefficients is considered when the distribution of error terms is unknown but symmetric. We propose the use of reference distributions having various kurtosis values. It is assumed that the true error distribution is one of the reference distributions, but the indicator variable for the true distribution is missing. The generalized expectation–maximization algorithm combined with a line search is developed for estimating regression coefficients. Simulation experiments are carried out to compare the performance of the proposed approach with some existing robust regression methods including least absolute deviation, Lp, Huber M regression and an approximation using normal mixtures under various error distributions. As the error distribution is far from a normal distribution, the proposed method is observed to show better performance than other methods.

Identification and Estimation of Level-K Auctions

I develop a structural econometric framework for first-price auctions by generalizing the assumption of Bayesian Nash Equilibrium within the context of a level-k behavioral model, which nests equilibrium by allowing bidders to hold heterogeneous beliefs about opponents' bidding strategies. While behavioral heterogeneity causes identification to fail under benchmark equilibrium conditions, independence and exclusion restrictions recover identification of the joint distribution over valuations and bidder-types in heterogeneous populations. Establishing consistent maximum likelihood sieve estimation with an upper semicontinuous population log-likelihood function leads to a natural semi-nonparametric maximum likelihood estimator based on Legendre polynomials. The level-k model introduces a mixture structure to the estimation problem, requiring a generalized expectation maximization algorithm. Presenting evidence from a pilot study of vintage computer auctions, I find a high level of bidder sophistication in the field. To further apply the econometric framework, I characterize expected revenues in first price auctions with level-k bidders, establishing a partial identification result for expected revenues in unidentified models. An empirical analysis of USFS timber auctions finds that a misspecified equilibrium optimal reserve price could reduce expected revenues up to 30% relative to an unbinding reserve price.

MIMO-AR System Identification and Blind Source Separation for GMM-Distributed Sources

The problem of blind source separation (BSS) and system identification for multiple-input multiple-output (MIMO) auto-regressive (AR) mixtures is addressed in this paper. Two new time-domain algorithms for system identification and BSS are proposed based on the Gaussian mixture model (GMM) for sources distribution. Both algorithms are based on the generalized expectation-maximization (GEM) method for joint estimation of the MIMO-AR model parameters and the GMM parameters of the sources. The first algorithm is derived under the assumption of unstructured input signal statistics, while the second algorithm incorporates the prior knowledge about the structure of the input signal statistics due to the statistically independent source assumption. These methods are tested via simulations using synthetic and audio signals. The system identification performances are tested by comparison between the state transition matrix estimation using the proposed algorithms and the well-known multidimensional Yule-Walker solution followed by an instantaneous BSS method. The results show that the proposed algorithms outperform the Yule-Walker based approach. The BSS performances were compared to other convolutive BSS methods. The results show that the proposed algorithms achieve higher signal-to-interference ratio (SIR) compared to the other tested methods.

Consistency Clustering: A Robust Algorithm for Group-wise Registration, Segmentation and Automatic Atlas Construction in Diffusion MRI

We propose an integrated registration and clustering algorithm, called "consistency clustering", that automatically constructs a probabilistic white-matter atlas from a set of multi-subject diffusion weighted MR images. We formulate the atlas creation as a maximum likelihood problem which the proposed method solves using a generalized Expectation Maximization (EM) framework. Additionally, the algorithm employs an outlier rejection and denoising strategy to produce sharp probabilistic maps of certain bundles of interest. We test this algorithm on synthetic and real data, and evaluate its stability against initialization. We demonstrate labeling a novel subject using the resulting spatial atlas and evaluate the accuracy of this labeling. Consistency clustering is a viable tool for completely automatic white-matter atlas construction for sub-populations and the resulting atlas is potentially useful for making diffusion measurements in a common coordinate system to identify pathology related changes or developmental trends.

Robust brain registration using adaptive probabilistic atlas.

Elastic image registration is widely used to adapt brain images to a common template space, and, in complementary fashion, to adapt an anatomical template to a subject's anatomy. Although HAMMER is a very accurate image-registration algorithm, it requires a 3-class segmentation step prior to registration, and its performance is affected by segmentation quality. We here propose a new framework to improve this algorithm's robustness to poor initial segmentation. Our new framework is based on Adaptive Generalized Expectation Maximization (AGEM) for unified segmentation and registration, in which we use an adaptive strategy to incorporate spatial information from a probabilistic atlas to improve segmentation and registration simultaneously. Our experiments using real MR brain images indicate that our integrated approach improves registration accuracy; we have also found that our iterative approach renders HAMMER robust to low tissue contrast, which hinders 3-class segmentation.

An EM-Based Iterative Receiver for MIMO-OFDM Under Interference-Limited Environments

In this paper, we derive an iterative receiver for multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. As MIMO-OFDM is considered for future cellular systems, the iterative receiver is investigated when the co-channel interference (CCI) exists. It is assumed that the CCI's are also OFDM signals. Since a joint detection of the desired signal and CCI is difficult, we only detect the desired signal, while the CCI is assumed to be a (colored) noise. This approach can avoid the channel estimation and detection of the CCI and keep the complexity of the receiver low. The proposed iterative receiver estimates the channel impulse response of the desired signal and the covariance matrix of the CCI for the detection based on a generalized expectation- maximization (GEM) algorithm. Through GEM iterations, we can observe the performance is improved.

SAGE-based estimation of doubly selective channel with an orthogonal polynomial model

A space alternating generalized expectation–maximization (SAGE)-based estimation algorithm for doubly selective channel is proposed, which has very similar performance to the rectangular-windowed least squares methods introduced by Borah and Hart while providing large savings in computational complexity. Theoretical analysis shows that the proposed algorithm is always globally convergent. The convergence rate is also investigated through simulations.

Maximum likelihood delay estimation in a navigation receiver for aeronautical applications

The potential of the SAGE (Space Alternating Generalized Expectation Maximization) algorithm for navigation systems in order to distinguish the line-of-sight signal (LOSS) is to be considered. The SAGE algorithm is a low-complexity generalization of the EM (Expectation-Maximization) algorithm, which iteratively approximates the maximum likelihood estimator (MLE) and has been successfully applied for parameter estimation (relative delay, incident azimuth, incident elevation, Doppler frequency, and complex amplitude of impinging waves) in mobile radio environments. This study discusses receivers using a single antenna or an antenna array. Whereas we estimate the complex amplitudes, relative delays, and Doppler frequencies of the impinging waves, in the latter additionally the spatial signature of the impinging waves (incident azimuth and elevation) is estimated. The results of the performed computer simulations and discussion indicate that the SAGE algorithm has the potential to be a very powerful high resolution method to successfully estimate parameters of impinging waves for navigation systems. SAGE has proven to be a promising method to combat multipath for aircraft navigation applications due to its good performance, fast convergence, and low complexity.

Impact of channel sounder phase noise on directional channel estimation by space-alternating generalised expectation maximisation

Multi-input multi-output (MIMO) radio channel sounders commonly employ time-division multiplexing (TDM) technique to switch between transmit and receive antennas. The TDM method offers single-input single-output sounders the MIMO capability in a cost-effective manner. However, the TDM approach leads to errors in MIMO channel measurements because of phase noise in local oscillators. Phase noise varies in the short term during the switching sequence for a MIMO channel sample. The high-resolution space-alternating generalised expectation maximisation (SAGE) algorithm has been efficiently applied for the estimation of the channel parameters. The impact of phase noise on the directional channel parameters, which are estimated by the SAGE algorithm, has been studied. Although the previous studies have investigated long-term random walk noise, we concentrate on the short-term noise which affects consecutive MIMO channel matrix measurements. It has been shown that errors in direction of arrival and direction of departure estimation because of the short-term phase noise can be effectively decreased by time domain filtering of the impulse responses prior to the SAGE processing.