This paper addresses the challenge of composite binary hypothesis testing in the presence of outliers. Within this framework, we introduce a new robust score-type detector. The proposed detector, called K-score test (K-ST), relies on an empirical version of the K-divergence that utilizes Parzen’s non-parametric "K"ernel density estimator. The use of Parzen’s density estimator provides a model-free weighting mechanism to mitigate the impact of low-density contaminations, attributed to outliers. The performance advantage of the K-ST over other robust scoretype tests, that employ model-based weighting, is demonstrated through a simulation study focusing on subspace detection.

Deep learning is envisioned to facilitate the operation of wireless receivers, with emerging architectures integrating deep neural networks (DNNs) with traditional modular receiver processing. While deep receivers were shown to operate reliably in complex settings for which they were trained, the dynamic nature of wireless communications gives rise to the need to repeatedly adapt deep receivers to channel variations. However, frequent re-training is costly and ineffective, while in practice, not every channel variation necessitates adaptation of the entire DNN. In this paper, we study concept drift detection for identifying when does a deep receiver no longer match the channel, enabling asynchronous adaptation, i.e., re-training only when necessary. We identify existing drift detection schemes from the machine learning literature that can be adapted for deep receivers in dynamic channels, and propose a novel soft-output detection mechanism tailored to the communication domain. Moreover, for deep receivers that preserve conventional modular receiver processing, we design modular drift detection mechanisms, that simultaneously identify when and which sub-module to re-train. The provided numerical studies show that even in a rapidly time-varying scenarios, asynchronous adaptation via modular drift detection dramatically reduces the number of trained parameters and re-training times, with little compromise on performance.

This paper presents a new framework for robust regression analysis. Under this framework, the input-output relation of a system is inferred by minimizing a new robust loss which relates the outputs to a presumed parametric function of the inputs. The considered loss arises from a modified version of the recently developed $\mathcal{K}$-divergence (tailored here for regression analysis), whose empirical estimate employs Parzen’s non-parametric kernel density estimator to mitigate the effect of low-density contaminations, attributed to outliers. The use of Parzen’s non-parametric density estimator provides a model-free weighting mechanism to mitigate the effect of outlying measurements in both input and output data sets. The performance advantage of the considered approach, over other robust regression methods, is illustrated in a simulation study focusing on robust training of a shallow GELU neural network.

In this paper, we develop an expectation-maximization (EM)-like scheme, called ${\mathcal{K}}$-BM, for iterative numerical computation of the minimum ${\mathcal{K}}$-divergence estimator (M${\mathcal{K}}$DE). This estimator utilizes Parzen’s non-parameteric ${\mathcal{K}}$ernel density estimate to down weight low density areas attributed to outliers. Similarly to the standard EM algorithm, the ${\mathcal{K}}$-BM involves successive Maximizations of lower Bounds on the objective function of the M${\mathcal{K}}$DE. Differently from EM, these bounds do not rely on conditional expectations only. The proposed ${\mathcal{K}}$-BM algorithm is applied to robust parameter estimation of a finite-order multivariate Gaussian mixture model (GMM). Simulation studies illustrate the performance advantage of the ${\mathcal{K}}$-BM as compared to other state-of-the-art robust GMM estimators.

In this paper, we consider the problem of blind source separation (BSS) under non-Gaussian impulsive noise . We consider the case of overdetermined instantaneous-linear-mixtures of piecewise-stationary signals. These are corrupted by additive stationary noise. Under this framework, we propose a two-stage separation method, called measure-transformed BSS (MT-BSS), that applies a transform to the probability distribution associated with each data segment. The generating function of the transform at hand is a non-negative function, called MT-function, that weights the data points. We show that proper choice of the involved MT-functions can lead to enhanced separation performance. The performance advantage of MT-BSS over alternative BSS techniques is illustrated in simulation examples. In these studies, we consider synthetic data and real audio signals .

This letter deals with robust estimation of the output layer weights in a radial basis function network (RBFN) with predetermined hidden layer parameters. Specifically, we presume a RBFN regression model interfered by non-Gaussian impulsive noise. Under this framework, a new robust extension of the least-squares-estimator (LSE) is introduced. This estimator, called measure-transformed LSE (MT-LSE), operates by applying a transform to the joint probability measure associated with reshaped versions of the input-target training data pairs. The considered transform is generated by a non-negative function, called MT-function, that weights the data points. We show that proper selection of the MT-function substantially improves the estimation accuracy in the presence of impulsive noise, while maintaining the implementation simplicity of the standard LSE. The performance advantage of the MT-LSE, comparing to the LSE and other robust alternatives, is illustrated in a simulation study focusing on time-series prediction.

In this paper we present a new divergence, called $\mathcal{K}$-divergence, that involves a weighted version of the hypothesized log-likelihood function. To down-weight low density areas, attributed to outliers, the corresponding weight function is a convolved version of the underlying density with a strictly positive smoothing "$\mathcal{K}$"ernel function parameterized by a bandwidth parameter. The resulting minimum $\mathcal{K}$-divergence estimator $({\text{M}}\mathcal{K}{\text{DE}})$ operates by minimizing the empirical $\mathcal{K}$-divergence w.r.t. the vector parameter of interest. The ${\text{M}}\mathcal{K}{\text{DE}}$ utilizes Parzen's non-parametric kernel density estimator, arising from the nature of the weight function, to suppress outliers. By proper selection of the kernel's bandwidth parameter we show that the ${\text{M}}\mathcal{K}{\text{DE}}$ can gain enhanced estimation performance along with implementation simplicity as compared to other robust estimators.

In this paper, we develop a new robust spectrum sensing method for MIMO cognitive radios in the presence of heavy-tailed noise. The proposed sensing technique, called measure-transformed covariance test (MTCT), operates by applying a transform to the probability measure of the data. The considered probability measure transform is structured by a non-negative function, called MT-function, that weights the data points. We show that proper selection of the MT-function, under the class of zero-centered spherical Gaussian functions, can lead to significant mitigation of heavy-tailed noise effects. Simulation studies illustrate the advantages of the proposed MTCT comparing to state-of-the-art spectrum sensing techniques.

This letter deals with the problem of robust beamforming in the presence of non-Gaussian impulsive noise. Under this framework, a new robust extension of the empirical MVDR beamformer is developed. The proposed extension is a plug-in estimate of a measure-transformed MVDR (MT-MVDR) beamformer, that operates by applying a transform to the probability distribution of the data. The considered transform is generated by a non-negative data-weighting function, called MT-function. We show that proper selection of the MT-function can result in significantly enhanced beamforming performance in the presence of impulsive noise, while maintaining the implementation simplicity of the empirical MVDR. The proposed beamformer is evaluated in simulation studies that illustrate its advantages as compared to the empirical MVDR and other robust alternatives.

The measure-transformed (MT) MUltiple SIgnal Classification (MUSIC) algorithm is a robust MUSIC generalization that operates by applying a transform to the probability measure (distribution) of the data. In this paper, we first provide an asymptotic mean-squared-error (MSE) performance analysis of the MT-MUSIC algorithm. Under some mild assumptions, we show that the MT-MUSIC estimator is asymptotically normal and unbiased, and obtain an analytic expression for the asymptotic MSE matrix. We then proceed to develop a strongly consistent estimator for the asymptotic MSE matrix that is constructed from the same data samples being used for implementation of the MT-MUSIC. This paves the way for development of a data-driven procedure for optimal selection of the measure transformation parameters that minimizes an empirical estimate of the asymptotic average root MSE (RMSE). Simulation examples illustrate the performance advantage of the proposed MSE based optimization of the MT-MUSIC.

Recently, we developed a robust generalization of the Gaussian quasi-likelihood ratio test (GQLRT). This generalization, called measure-transformed GQLRT (MT-GQLRT), operates by selecting a Gaussian model that best empirically fits a transformed probability measure of the data. In this letter, a plug-in version of the MT-GQLRT is developed for robust detection of a random signal in nonspherical noise. The proposed detector is derived by plugging an empirical measure-transformed noise covariance, obtained from noise-only secondary data, into the MT-GQLRT. The plug-in MT-GQLRT is illustrated in simulation examples that show its advantages as compared to other detectors.

Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary. Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS, is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed.

In this paper, a generalization of the Gaussian quasi likelihood ratio test (GQLRT) for simple hypotheses is developed. The proposed generalization, called measure-transformed GQLRT (MT-GQLRT), selects a Gaussian probability model that best empirically fits a transformed probability measure of the data. By judicious choice of the transform we show that, unlike the GQLRT, the proposed test can gain sensitivity to higher-order statistical moments and resilience to outliers leading to significant mitigation of the model mismatch effect on the decision performance. Under some mild regularity conditions we show that the proposed test statistic is asymptotically normal. A data driven procedure for optimal selection of the measure transformation parameters is developed that maximizes an empirical estimate of the asymptotic power given a fixed empirical asymptotic size. The MT-GQLRT is applied to signal classification in a simulation example that illustrates its sensitivity to higher-order statistical moments and resilience to outliers.

In this paper, we consider the problem of estimating a deterministic vector parameter when the likelihood function is unknown or not expressible. We develop an estimator, called measure-transformed quasi maximum likelihood estimator (MT-QMLE), that minimizes the empirical Kullback-Leibler divergence between the transformed probability measure of the data and a hypothesized Gaussian probability distribution. By judicious choice of the transform we show that the proposed estimator can gain sensitivity to higher-order statistical information and resilience to outliers. Under some regularity conditions we show that the MT-QMLE is consistent, asymptotically normal and unbiased. Furthermore, we derive a necessary and sufficient condition for its asymptotic efficiency. The MT-QMLE is applied to source localization in a simulation example that illustrates its sensitivity to higher-order information and resilience to outliers.

In this paper, we introduce a new framework for robust multiple signal classification (MUSIC). The proposed framework, called robust measure-transformed (MT) MUSIC, is based on applying a transform to the probability distribution of the received signals, i.e., transformation of the probability measure defined on their observation space. In robust MT-MUSIC, the sample covariance is replaced by the empirical MT-covariance. By judicious choice of the transform we show that: (1) the resulting empirical MT-covariance is B-robust, with bounded influence function that takes negligible values for large norm outliers, and (2) under the assumption of spherical compound Gaussian noise, the noise subspace can be determined from the eigendecomposition of the MT-covariance. The proposed approach is illustrated for direction-of-arrival (DOA) estimation in a simulation example that shows its advantages as compared to other robust MUSIC generalizations.

In this paper, a new structured approach for obtaining uniformly best non-Bayesian biased estimators, which attain minimum-mean-square-error performance at any point in the parameter space, is established. We show that if a uniformly best biased (UBB) estimator exists, then it is unique, and it can be directly obtained from any locally best biased (LBB) estimator. A necessary and sufficient condition for the existence of a UBB estimator is derived. It is shown that if there exists an optimal bias, such that this condition is satisfied, then it is unique, and its closed-form expression is obtained. The proposed approach is exemplified in two nonlinear estimation problems, where uniformly minimum-variance-unbiased estimators do not exist. In the considered examples, we show that the UBB estimators outperform the corresponding maximum-likelihood estimators in the MSE sense.

Recently, some general classes of non-Bayesian, Bayesian and Hybrid lower bounds on the mean square error (MSE) of estimators have been developed via projection of each entry of the vector of estimation error on some Hilbert subspaces of L2. In this paper, we utilize this framework for derivation of order relations between lower bounds on the MSE of unbiased estimators. We show that some existing and new order relations can be simply obtained by comparing the corresponding Hilbert subspaces on which each entry of the vector of estimation error is projected.

In this paper, a new class of lower bounds on the mean square error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by projecting each entry of the vector of estimation error on a Hilbert subspace of L2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform of the likelihood-ratio function. The integral transform generalizes the traditional derivative and sampling operators, which are applied on the likelihood-ratio function for computation of performance lower bounds, such as Cramér-Rao, Bhattacharyya, and McAulay-Seidman bounds. It is shown that some well-known lower bounds on the MSE of unbiased estimators can be derived from this class by modifying the kernel of the integral transform. A new lower bound is derived from the proposed class using the kernel of the Fourier transform. In comparison with other existing bounds, the proposed bound is computationally manageable and provides better prediction of the threshold region of the maximum-likelihood estimator, in the problem of single tone estimation.

In this paper, a new class of Bayesian lower bounds is proposed. Derivation of the proposed class is performed via projection of each entry of the vector-function to be estimated on a Hilbert subspace ofL2. This Hilbert subspace contains linear transformations of elements in the domain of an integral transform, applied on functions used for computation of bounds in the Weiss-Weinstein class. The integral transform generalizes the traditional derivative and sampling operators, used for computation of existing performance lower bounds, such as the Bayesian Cramér-Rao, Bayesian Bhattacharyya, and Weiss-Weinstein bounds. It is shown that some well-known Bayesian lower bounds can be derived from the proposed class by specific choice of the integral transform kernel. A new lower bound is derived from the proposed class using the Fourier transform kernel. The proposed bound is compared with other existing bounds in terms of signal-to-noise ratio (SNR) threshold region prediction in the problem of frequency estimation. The bound is shown to be computationally manageable and provides better prediction of the SNR threshold region, exhibited by the maximum a posteriori probability (MAP) and minimum-mean-square-error (MMSE) estimators.

In this paper, a new class of lower bounds on the mean-square-error (MSE) of unbiased estimators of deterministic parameters is proposed. Derivation of the proposed class is performed by approximating each entry of the vector of estimation error in a closed Hilbert subspace of L2- This Hilbert subspace is spanned by a set of linear combinations of elements in the domain of an integral transform of the likelihood-ratio function. It is shown that some well known lower bounds on the MSE of unbiased estimators, can be derived from this class by inferring the integral transform. A new lower bound is derived from this class by choosing the Fourier transform. The bound is computationally manageable and provides better prediction of the signal-to-noise ratio (SNR) threshold region, exhibited by the maximum-likelihood estimator. The proposed bound is compared with other existing bounds in term of threshold SNR prediction in the problem of single tone estimation.

In this paper, a new efficient iterative algorithm for approximate joint diagonalization of positive-definite Hermitian matrices is presented. The proposed algorithm, named as SVDJD, estimates the diagonalization matrix by iterative optimization of a maximum likelihood based objective function. The columns of the diagonalization matrix is not assumed to be orthogonal, and they are estimated separately by using iterative singular value decompositions of a weighted sum of the matrices to be diagonalized. The performance of the proposed SVDJD algorithm is evaluated and compared to other existing state-of-the-art algorithms for approximate joint diagonalization. The results imply that the SVDJD algorithm is computationally efficient with performance similar to state-of-the-art algorithms for approximate joint diagonalization.