6 research outputs found
A CLT on the SNR of Diagonally Loaded MVDR Filters
This paper studies the fluctuations of the signal-to-noise ratio (SNR) of
minimum variance distorsionless response (MVDR) filters implementing diagonal
loading in the estimation of the covariance matrix. Previous results in the
signal processing literature are generalized and extended by considering both
spatially as well as temporarily correlated samples. Specifically, a central
limit theorem (CLT) is established for the fluctuations of the SNR of the
diagonally loaded MVDR filter, under both supervised and unsupervised training
settings in adaptive filtering applications. Our second-order analysis is based
on the Nash-Poincar\'e inequality and the integration by parts formula for
Gaussian functionals, as well as classical tools from statistical asymptotic
theory. Numerical evaluations validating the accuracy of the CLT confirm the
asymptotic Gaussianity of the fluctuations of the SNR of the MVDR filter.Comment: This is a corrected version of the paper that will appear at IEEE
Transactions on Signal Processing September 201
Widely-Linear MMSE Estimation of Complex-Valued Graph Signals
In this paper, we consider the problem of recovering random graph signals
with complex values. For general Bayesian estimation of complex-valued vectors,
it is known that the widely-linear minimum mean-squared-error (WLMMSE)
estimator can achieve a lower mean-squared-error (MSE) than that of the linear
minimum MSE (LMMSE) estimator. Inspired by the WLMMSE estimator, in this paper
we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes
the MSE among estimators that are represented as a two-channel output of a
graph filter, i.e. widely-linear GSP estimators. We discuss the properties of
the proposed GSP-WLMMSE estimator. In particular, we show that the MSE of the
GSP-WLMMSE estimator is always equal to or lower than the MSE of the GSP-LMMSE
estimator. The GSP-WLMMSE estimator is based on diagonal covariance matrices in
the graph frequency domain, and thus has reduced complexity compared with the
WLMMSE estimator. This property is especially important when using the
sample-mean versions of these estimators that are based on a training dataset.
We then state conditions under which the low-complexity GSP-WLMMSE estimator
coincides with the WLMMSE estimator. In the simulations, we investigate two
synthetic estimation problems (with linear and nonlinear models) and the
problem of state estimation in power systems. For these problems, it is shown
that the GSP-WLMMSE estimator outperforms the GSP-LMMSE estimator and achieves
similar performance to that of the WLMMSE estimator.Comment: This work has been submitted to the IEEE for possible publication.
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Modelling, Simulation and Data Analysis in Acoustical Problems
Modelling and simulation in acoustics is currently gaining importance. In fact, with the development and improvement of innovative computational techniques and with the growing need for predictive models, an impressive boost has been observed in several research and application areas, such as noise control, indoor acoustics, and industrial applications. This led us to the proposal of a special issue about “Modelling, Simulation and Data Analysis in Acoustical Problems”, as we believe in the importance of these topics in modern acoustics’ studies. In total, 81 papers were submitted and 33 of them were published, with an acceptance rate of 37.5%. According to the number of papers submitted, it can be affirmed that this is a trending topic in the scientific and academic community and this special issue will try to provide a future reference for the research that will be developed in coming years
Blind source separation for interference cancellation in CDMA systems
Communication is the science of "reliable" transfer of information between two parties, in the sense that the information reaches the intended party with as few errors as possible. Modern wireless systems have many interfering sources that hinder reliable communication. The performance of receivers severely deteriorates in the presence of unknown or unaccounted interference. The goal of a receiver is then to combat these sources of interference in a robust manner while trying to optimize the trade-off between gain and computational complexity.
Conventional methods mitigate these sources of interference by taking into account all available information and at times seeking additional information e.g., channel characteristics, direction of arrival, etc. This usually costs bandwidth. This thesis examines the issue of developing mitigating algorithms that utilize as little as possible or no prior information about the nature of the interference. These methods are either semi-blind, in the former case, or blind in the latter case.
Blind source separation (BSS) involves solving a source separation problem with very little prior information. A popular framework for solving the BSS problem is independent component analysis (ICA). This thesis combines techniques of ICA with conventional signal detection to cancel out unaccounted sources of interference. Combining an ICA element to standard techniques enables a robust and computationally efficient structure. This thesis proposes switching techniques based on BSS/ICA effectively to combat interference. Additionally, a structure based on a generalized framework termed as denoising source separation (DSS) is presented. In cases where more information is known about the nature of interference, it is natural to incorporate this knowledge in the separation process, so finally this thesis looks at the issue of using some prior knowledge in these techniques. In the simple case, the advantage of using priors should at least lead to faster algorithms.reviewe
Asymptotically optimal linear shrinkage of sample LMMSE and MVDR filters
Conventional implementations of the linearminimum mean-square (LMMSE) and minimum variance distortionless response (MVDR) estimators rely on the sample matrix inversion (SMI) technique, i.e., on the sample covariance matrix (SCM). This approach is optimal in the large sample size regime. Nonetheless, in small sample size situations, those sample estimators suffer a large performance degradation. Thus, the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations. To this aim, a twofold approach is proposed. First, shrinkage estimators are considered, as they are known to be robust to the small sample size regime. Namely, the proposed methods are based on shrinking the sample LMMSE or sample MVDR filters towards a variously called matched filter or conventional (Bartlett) beamformer in array processing. Second, random matrix theory is used to obtain the optimal shrinkage factors for large filters. The simulation results highlight that the proposed methods outperform the sample LMMSE and MVDR. Also, provided that the sample size is higher than the observation dimension, they improve classical diagonal loading (DL) and Ledoit-Wolf (LW) techniques, which counteract the small sample size degradation by regularizing the SCM. Finally, compared to state-of-the-art DL, the proposed methods reduce the computational cost and the proposed shrinkage of the LMMSE obtains performance gains.Peer ReviewedPostprint (published version
Asymptotically optimal linear shrinkage of sample LMMSE and MVDR filters
Conventional implementations of the linearminimum mean-square (LMMSE) and minimum variance distortionless response (MVDR) estimators rely on the sample matrix inversion (SMI) technique, i.e., on the sample covariance matrix (SCM). This approach is optimal in the large sample size regime. Nonetheless, in small sample size situations, those sample estimators suffer a large performance degradation. Thus, the aim of this paper is to propose corrections of these sample methods that counteract their performance degradation in the small sample size regime and keep their optimality in large sample size situations. To this aim, a twofold approach is proposed. First, shrinkage estimators are considered, as they are known to be robust to the small sample size regime. Namely, the proposed methods are based on shrinking the sample LMMSE or sample MVDR filters towards a variously called matched filter or conventional (Bartlett) beamformer in array processing. Second, random matrix theory is used to obtain the optimal shrinkage factors for large filters. The simulation results highlight that the proposed methods outperform the sample LMMSE and MVDR. Also, provided that the sample size is higher than the observation dimension, they improve classical diagonal loading (DL) and Ledoit-Wolf (LW) techniques, which counteract the small sample size degradation by regularizing the SCM. Finally, compared to state-of-the-art DL, the proposed methods reduce the computational cost and the proposed shrinkage of the LMMSE obtains performance gains.Peer Reviewe