Blind, MIMO system estimation based on PARAFAC decomposition of higher order output tensors

IEEE Transactions on Signal Processing, 54(11): pp. 4156-4168.We present a novel framework for the identification of a multiple-input multiple-output (MIMO) system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on parallel factorization (PARAFAC) of three- or four-way tensors constructed based on, respectively, third- or fourth-order cross spectra of the system outputs. The main difficulties in frequency-domain methods are frequency- dependent permutation and filtering ambiguities.We show that the information available in the higher order spectra allows for the ambiguities to be resolved up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approach are that it does not require channel length information, needs no phase unwrapping, and unlike the majority of existing methods, needs no prewhitening of the system outputs

Blind identification of possibly under-determined convolutive MIMO systems

Blind identi¯cation of a Linear Time Invariant (LTI) Multiple-Input Multiple-Output (MIMO) system is of great importance in many applications, such as speech processing, multi-access communication, multi-sensor sonar/radar systems, and biomedical applications. The objective of blind identi¯cation for a MIMO system is to identify an unknown system, driven by Ni unobservable inputs, based on the No system outputs. We ¯rst present a novel blind approach for the identi¯cation of a over-determined (No ¸ Ni) MIMO system driven by white, mutually independent unobservable inputs. Samples of the system frequency response are obtained based on Parallel Factorization (PARAFAC) of three- or four-way tensors constructed respectively based on third- or fourth-order cross-spectra of the system outputs. We show that the information available in the higher-order spectra allows for the system response to be identi¯ed up to a constant scaling and permutation ambiguities and a linear phase ambiguity. Important features of the proposed approaches are that they do not require channel length information, need no phase unwrapping, and unlike the majority of existing methods, need no pre-whitening of the system outputs.While several methods have been proposed to blindly identify over-determined convolutive MIMO systems, very scarce results exist for under-determined (No < Ni) case, all of which refer to systems that either have some special structure, or special No, Ni values. We propose a novel approach for blind identi¯cation of under-determined convolutive MIMO systems of general dimensions. As long as min(No;Ni) ¸ 2, we can always ¯nd the appropriate order of statistics that guarantees identi¯ability of the system response within trivial ambiguities. We provide the description of the class of identi¯able MIMO systems for a certain order of statistics K, and an algorithm to reach the solution.Finally we propose a novel approach for blind identi¯cation and symbol recovery of a distributed antenna system with multiple carrier-frequency o®sets (CFO), arising due to mismatch between the oscillators of transmitters and receivers. The received base-band signal is over-sampled, and its polyphase components are used to formulate a virtual MIMO problem. By applying blind MIMO system estimation techniques, the system response is estimated and used to subsequently decouple the users and transform the multiple CFOs estimation problem into a set of independent single CFO estimation problems.Ph.D., Electrical Engineering -- Drexel University, 200

Validating and improving the correction of ocular artifacts in electro-encephalography

For modern applications of electro-encephalography, including brain computer interfaces and single-trial Event Related Potential detection, it is becoming increasingly important that artifacts are accurately removed from a recorded electro-encephalogram (EEG) without affecting the part of the EEG that reflects cerebral activity. Ocular artifacts are caused by movement of the eyes and the eyelids. They occur frequently in the raw EEG and are often the most prominent artifacts in EEG recordings. Their accurate removal is therefore an important procedure in nearly all electro-encephalographic research. As a result of this, a considerable number of ocular artifact correction methods have been introduced over the past decades. A selection of these methods, which contains some of the most frequently used correction methods, is given in Section 1.5. When two different correction methods are applied to the same raw EEG, this usually results in two different corrected EEGs. A measure for the accuracy of correction should indicate how well each of these corrected EEGs recovers the part of the raw EEG that truly reflects cerebral activity. The fact that this accuracy cannot be determined directly from a raw EEG is intrinsic to the need for artifact removal. If, based on a raw EEG, it would be possible to derive an exact reference on what the corrected EEG should be, then there would not be any need for adequate artifact correction methods. Estimating the accuracy of correction methods is mostly done either by using models to simulate EEGs and artifacts, or by manipulating the experimental data in such a way that the effects of artifacts to the raw EEG can be isolated. In this thesis, modeling of EEG and artifact is used to validate correction methods based on simulated data. A new correction method is introduced which, unlike all existing methods, uses a camera to monitor eye(lid) movements as a basis for ocular artifact correction. The simulated data is used to estimate the accuracy of this new correction method and to compare it against the estimated accuracy of existing correction methods. The results of this comparison suggest that the new method significantly increases correction accuracy compared to the other methods. Next, an experiment is performed, based on which the accuracy of correction can be estimated on raw EEGs. Results on this experimental data comply very well with the results on the simulated data. It is therefore concluded that using a camera during EEG recordings provides valuable extra information that can be used in the process of ocular artifact correction. In Chapter 2, a model is introduced that assists in estimating the accuracy of eye movement artifacts for simulated EEG recordings. This model simulates EEG and eye movement artifacts simultaneously. For this, the model uses a realistic representation of the head, multiple dipoles to model cerebral and ocular electrical activity, and the boundary element method to calculate changes in electrical potential at different positions on the scalp. With the model, it is possible to simulate different data sets as if they are recorded using different electrode configurations. Signal to noise ratios are used to assess the accuracy of these six correction methods for various electrode configurations before and after applying six different correction methods. Results show that out of the six methods, second order blind identification, SOBI, and multiple linear regression, MLR, correct most accurately overall as they achieve the highest rise in signal to noise ratio. The occurrence of ocular artifacts is linked to changes in eyeball orientation. In Chapter 2 an eye tracker is used to record pupil position, which is closely linked to eyeball orientation. The pupil position information is used in the model to simulate eye movements. Recognizing the potential benefit of using an eye tracker not only for simulations, but also for correction, Chapter 3 introduces an eye movement artifact correction method that exploits the pupil position information that is provided by an eye tracker. Other correction methods use the electrooculogram (EOG) and/or the EEG to estimate ocular artifacts. Because both the EEG and the EOG recordings are susceptive to cerebral activity as well as to ocular activity, these other methods are at risk of overcorrecting the raw EEG. Pupil position information provides a reference that is linked to the ocular artifact in the EEG but that cannot be affected by cerebral activity, and as a result the new correction method avoids having to solve traditionally problematic issues like forward/backward propagation and evaluating the accuracy of component extraction. By using both simulated and experimental data, it is determined how pupil position influences the raw EEG and it is found that this relation is linear or quadratic. A Kalman filter is used for tuning of the parameters that specify the relation. On simulated data, the new method performs very well, resulting in an SNR after correction of over 10 dB for various patterns of eye movements. When compared to the three methods that performed best in the evaluation of Chapter 2, only the SOBI method which performed best in that evaluation shows similar results for some of the eye movement patterns. However, a serious limitation of the correction method is its inability to correct blink artifacts. In order to increase the variety of applications for which the new method can be used, the new correction should be improved in a way that enables it to correct the raw EEG for blinking artifacts. Chapter 4 deals with implementing such improvements based on the idea that a more advanced eye-tracker should be able to detect both the pupil position and the eyelid position. The improved eye tracker-based ocular artifact correction method is named EYE. Driven by some practical limitations regarding the eye tracking device currently available to us, an alternative way to estimate eyelid position is suggested, based on an EOG recorded above one eye. The EYE method can be used with both the eye tracker information or with the EOG substitute. On simulated data, accuracy of the EYE method is estimated using the EOGbased eyelid reference. This accuracy is again compared against the six other correction methods. Two different SNR-based measures of accuracy are proposed. One of these quantifies the correction of the entire simulated data set and the other focuses on those segments containing simulated blinking artifacts. After applying EYE, an average SNR of at least 9 dB for both these measures is achieved. This implies that the power of the corrected signal is at least eight times the power of the remaining noise. The simulated data sets contain a wide range of eye movements and blink frequencies. For almost all of these data sets, 16 out of 20, the correction results for EYE are better than for any of the other evaluated correction method. On experimental data, the EYE method appears to adequately correct for ocular artifacts as well. As the detection of eyelid position from the EOG is in principle inferior to the detection of eyelid position with the use of an eye tracker, these results should also be considered as an indicator of even higher accuracies that could be obtained with a more advanced eye tracker. Considering the simplicity of the MLR method, this method also performs remarkably well, which may explain why EOG-based regression is still often used for correction. In Chapter 5, the simulation model of Chapter 2 is put aside and, alternatively, experimentally recorded data is manipulated in a way that correction inaccuracies can be highlighted. Correction accuracies of eight correction methods, including EYE, are estimated based on data that are recorded during stop-signal tasks. In the analysis of these tasks it is essential that ocular artifacts are adequately removed because the task-related ERPs, are located mostly at frontal electrode positions and are low-amplitude. These data are corrected and subsequently evaluated. For the eight methods, the overall ranking of estimated accuracy in Figure 5.3, corresponds very well with the correction accuracy of these methods on simulated data as was found in Chapter 4. In a single-trial correction comparison, results suggest that the EYE corrected EEG, is not susceptible to overcorrection, whereas the other corrected EEGs are

Channel estimation for SISO and MIMO OFDM communications systems.

Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2010.Telecommunications in the current information age is increasingly relying on the wireless link. This is because wireless communication has made possible a variety of services ranging from voice to data and now to multimedia. Consequently, demand for new wireless capacity is growing rapidly at a very alarming rate. In a bid to cope with challenges of increasing demand for higher data rate, better quality of service, and higher network capacity, there is a migration from Single Input Single Output (SISO) antenna technology to a more promising Multiple Input Multiple Output (MIMO) antenna technology. On the other hand, Orthogonal Frequency Division Multiplexing (OFDM) technique has emerged as a very popular multi-carrier modulation technique to combat the problems associated with physical properties of the wireless channels such as multipath fading, dispersion, and interference. The combination of MIMO technology with OFDM techniques, known as MIMO-OFDM Systems, is considered as a promising solution to enhance the data rate of future broadband wireless communication Systems. This thesis addresses a major area of challenge to both SISO-OFDM and MIMO-OFDM Systems; estimation of accurate channel state information (CSI) in order to make possible coherent detection of the transmitted signal at the receiver end of the system. Hence, the first novel contribution of this thesis is the development of a low complexity adaptive algorithm that is robust against both slow and fast fading channel scenarios, in comparison with other algorithms employed in literature, to implement soft iterative channel estimator for turbo equalizer-based receiver for single antenna communication Systems. Subsequently, a Fast Data Projection Method (FDPM) subspace tracking algorithm is adapted to derive Channel Impulse Response Estimator for implementation of Decision Directed Channel Estimation (DDCE) for Single Input Single Output - Orthogonal Frequency Division Multiplexing (SISO-OFDM) Systems. This is implemented in the context of a more realistic Fractionally Spaced-Channel Impulse Response (FS-CIR) channel model, as against the channel characterized by a Sample Spaced-Channel Impulse Response (SS)-CIR widely assumed by other authors. In addition, a fast convergence Variable Step Size Normalized Least Mean Square (VSSNLMS)-based predictor, with low computational complexity in comparison with others in literatures, is derived for the implementation of the CIR predictor module of the DDCE scheme. A novel iterative receiver structure for the FDPM-based Decision Directed Channel Estimation scheme is also designed for SISO-OFDM Systems. The iterative idea is based on Turbo iterative principle. It is shown that improvement in the performance can be achieved with the iterative DDCE scheme for OFDM system in comparison with the non iterative scheme. Lastly, an iterative receiver structure for FDPM-based DDCE scheme earlier designed for SISO OFDM is extended to MIMO-OFDM Systems. In addition, Variable Step Size Normalized Least Mean Square (VSSNLMS)-based channel transfer function estimator is derived in the context of MIMO Channel for the implementation of the CTF estimator module of the iterative Decision Directed Channel Estimation scheme for MIMO-OFDM Systems in place of linear minimum mean square error (MMSE) criterion. The VSSNLMS-based channel transfer function estimator is found to show improved MSE performance of about -4 MSE (dB) at SNR of 5dB in comparison with linear MMSE-based channel transfer function estimator