On Toeplitz and Kronecker structured covariance matrix estimation

Wirfält, Petter; Jansson, Magnus

doi:10.1109/sam.2010.5606733

Cited by 9 publications

(12 citation statements)

References 7 publications

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“…From [15,18], we know that the multivariate WSS time series has a block-Toeplitz covariance matrix. We remark here that Toeplitz structured matrices belong to a subclass of the persymmetric matrices [19,21,29]. Furthermore, considering structured antenna array configurations (i.e., uniform linear arrays) at the SU, the spatio-temporal covariance matrix can be modelled as persymmetricblock-Toeplitz, as shown in [30].…”

Section: Persymmetric Structurementioning

confidence: 99%

“…We show that it is possible to account for the persymmetric structure by a simple modification of the Flip-Flop algorithm. Hence, as we did in Section 4.1, the persymmetric structures are exploited by imposing the constraints [21]:…”

Section: Pk-glrtmentioning

confidence: 99%

“…Moving one step forward, we also approximate the block-Toeplitz structure of the spatio-temporal correlated multi-antenna measurements with a Kronecker product structure [20,21]. Recently, exploitation of the Kronecker structure in covariance matrices has received a lot of interest in statistics [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…In order to do so, we adopt and extend our earlier work [25] by using the Kronecker product to efficiently exploit the space-time correlation in a multi-antenna spectrum sensing scheme. In addition to the Kronecker productbased factorization, we also exploit the fact that the factored matrices could have additional persymmetric structure [21]. Therefore, by exploiting the Kronecker product structure jointly with the persymmetric structure, the performance of the proposed detection scheme can further be improved in terms of the required number of sample to estimate the covariance matrix (i.e.…”

Section: Introductionmentioning

confidence: 99%

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Multi-antenna spectrum sensing by exploiting spatio-temporal correlation

Ali

Ramírez

Jansson

et al. 2014

EURASIP J. Adv. Signal Process.

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In this paper, we propose a novel mechanism for spectrum sensing that leads us to exploit the spatio-temporal correlation present in the received signal at a multi-antenna receiver. For the proposed mechanism, we formulate the spectrum sensing scheme by adopting the generalized likelihood ratio test (GLRT). However, the GLRT degenerates in the case of limited sample support. To circumvent this problem, several extensions are proposed that bring robustness to the GLRT in the case of high dimensionality and small sample size. In order to achieve these sample-efficient detection schemes, we modify the GLRT-based detector by exploiting the covariance structure and factoring the large spatio-temporal covariance matrix into spatial and temporal covariance matrices. The performance of the proposed detectors is evaluated by means of numerical simulations, showing important advantages over existing detectors.

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Section: Persymmetric Structurementioning

confidence: 99%

Section: Pk-glrtmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-antenna spectrum sensing by exploiting spatio-temporal correlation

Ali

Ramírez

Jansson

et al. 2014

EURASIP J. Adv. Signal Process.

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“…To satisfy the first condition, however, the arrangement of the recorded trials was verified to be Toeplitz matrix and thus implying ergodicity (Wirfalt and Jansson, 2010).…”

Section: Introductionmentioning

confidence: 99%

A Novel Signal Processing Method for Intraoperative Neurophysiological Monitoring in Spinal Surgeries

Vedala¹

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My mentor Dr. Malek Adjouadi has taught me a great deal in professional, personal and intellectual development. He has always had my best interest at heart and has provided me with every opportunity to grow. I am grateful for all the kindness and patience that he has shown me over the years. I would like to thank my gurus, Dr.Armando Barreto, Dr. Jean Andrian and Dr. Naphtalie Rishe, naming a few, whose trials to obtain an SSEP signal, which is excessive and introduces a significant delay to prevent potential neurological risks during surgery. The main objective of this dissertation is to develop a means to obtain the SSEP signal using a much reduced number of trials (20 trials or less) while still optimizing the effectiveness of the monitoring system. The preliminary research steps were to determine those characteristics that distinguish the SSEP with the ongoing brain activity. We first established that the brain activity is indeed quasi-stationary whereas an SSEP is expected to be identical every time a trial is recorded.A novel algorithm is subsequently developed using Chebyshev time windowing for preconditioning of SSEP trials to retain the morphological characteristics of somatosensory evoked potentials (SSEP). This preconditioning was followed by the application of a principal component analysis (PCA)-based algorithm utilizing quasistationarity of EEG on 12 preconditioned trials. A unique Walsh transform operation was then used to identify the position of the SSEP event. An alarm is raised vii when there is a 10% time in latency deviation and/or 50% peak-to-peak amplitude deviation, as per the clinical requirements. The algorithm shows consistency in the results in monitoring SSEP in up to 6-hour surgical procedures even under this significantly reduced number of trials.In this study, the analysis was performed on the data recorded in 29 patients who underwent surgery during which the posterior tibial nerve was stimulated and SSEP response was recorded from scalp EEG. This method is shown empirically to be more clinically viable than present day approaches. In all 29 cases, the algorithm took on an average 4sec to extract an SSEP signal, as compared to conventional methods, which take up to several minutes.The monitoring process using the algorithm was successful and proved conclusive under the clinical constraints throughout the different surgical procedures with an accuracy of 91.5%. Higher accuracy and faster execution time, observed in the present study, in determining the SSEP signals provided for a much improved and effective neurophysiological monitoring process.

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Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure

Roś

Bijma

Munck

et al. 2016

Journal of Multivariate Analysis

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This paper deals with multivariate Gaussian models for which the covariance matrix is a Kronecker product of two matrices. We consider maximum likelihood estimation of the model parameters, in particular of the covariance matrix. There is no explicit expression for the maximum likelihood estimator of a Kronecker product covariance matrix. The main question in this paper is whether the maximum likelihood estimator of the covariance matrix exists and if it is unique. The answers are different for different models that we consider.

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On Toeplitz and Kronecker structured covariance matrix estimation

Cited by 9 publications

References 7 publications

Multi-antenna spectrum sensing by exploiting spatio-temporal correlation

Multi-antenna spectrum sensing by exploiting spatio-temporal correlation

A Novel Signal Processing Method for Intraoperative Neurophysiological Monitoring in Spinal Surgeries

Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure

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