Recent breakthroughs in natural language processing show that attention mechanism in Transformer networks, trained via masked-token prediction, enables models to capture the semantic context of the tokens and internalize the grammar of language. While the application of Transformers to communication systems is a burgeoning field, the notion of context within physical waveforms remains under-explored. This paper addresses that gap by re-examining inter-symbol contribution (ISC) caused by pulse-shaping overlap. Rather than treating ISC as a nuisance, we view it as a deterministic source of contextual information embedded in oversampled complex baseband signals. We propose Masked Symbol Modeling (MSM), a framework for the physical (PHY) layer inspired by Bidirectional Encoder Representations from Transformers methodology. In MSM, a subset of symbol aligned samples is randomly masked, and a Transformer predicts the missing symbol identifiers using the surrounding "in-between" samples. Through this objective, the model learns the latent syntax of complex baseband waveforms. We illustrate MSM's potential by applying it to the task of demodulating signals corrupted by impulsive noise, where the model infers corrupted segments by leveraging the learned context. Our results suggest a path toward receivers that interpret, rather than merely detect communication signals, opening new avenues for context-aware PHY layer design.

Abstract--In this work, we propose a robust adaptive filtering approach for active noise control applications in the prese nce of impulsive noise. In particular, we develop the filtered-x hyperbolic tangent exponential generalized Kernel M-esti mate function (FXHEKM) robust adaptive algorithm. A statistica l analysis of the proposed FXHEKM algorithm is carried out alo ng with a study of its computational cost. In order to evaluate t he proposed FXHEKM algorithm, the mean-square error (MSE) and the average noise reduction (ANR) performance metrics have been adopted. Numerical results show the efficiency of the proposed FXHEKM algorithm to cancel the presence of the additive spurious signals, such as α-stable noises against competing algorithms. Signal processing applications suffer from the effects of undesired acoustic signals, known as noise, which come from different sources and heavily degrade the general operatio n of digital signal processing systems.

Standard Direction of Arrival (DOA) estimation methods are typically derived based on the Gaussian noise assumption, making them highly sensitive to outliers. Therefore, in the presence of impulsive noise, the performance of these methods may significantly deteriorate. In this paper, we model impulsive noise as Gaussian noise mixed with sparse outliers. By exploiting their statistical differences, we propose a novel DOA estimation method based on sparse signal recovery (SSR). Furthermore, to address the issue of grid mismatch, we utilize an alternating optimization approach that relies on the estimated outlier matrix and the on-grid DOA estimates to obtain the off-grid DOA estimates. Simulation results demonstrate that the proposed method exhibits robustness against large outliers.

Recently, new types of interference in electric vehicles (EVs), such as converters switching and/or battery chargers, have been found to degrade the performance of wireless digital transmission systems. Measurements show that such an interference is characterized by impulsive behavior and is widely varying in time. This paper uses recorded data from our EV testbed to analyze the impulsive interference in the digital audio broadcasting band. Moreover, we use our analysis to obtain a corresponding interference model. In particular, we studied the temporal characteristics of the interference and confirmed that its amplitude indeed exhibits an impulsive behavior. Our results show that impulsive events span successive received signal samples and thus indicate a bursty nature. To this end, we performed a data-driven modification of a well-established model for bursty impulsive interference, the Markov-Middleton model, to produce synthetic noise realization. We investigate the optimal symbol detector design based on the proposed model and show significant performance gains compared to the conventional detector based on the additive white Gaussian noise assumption.

In the presence of impulsive noise, and missing observations, accurate online prediction of time-varying graph signals poses a crucial challenge in numerous application domains. We propose the Adaptive Least Mean $p^{th}$ Power Graph Neural Networks (LMP-GNN), a universal framework combining adaptive filter and graph neural network for online graph signal estimation. LMP-GNN retains the advantage of adaptive filtering in handling noise and missing observations as well as the online update capability. The incorporated graph neural network within the LMP-GNN can train and update filter parameters online instead of predefined filter parameters in previous methods, outputting more accurate prediction results. The adaptive update scheme of the LMP-GNN follows the solution of a $l_p$-norm optimization, rooting to the minimum dispersion criterion, and yields robust estimation results for time-varying graph signals under impulsive noise. A special case of LMP-GNN named the Sign-GNN is also provided and analyzed, Experiment results on two real-world datasets of temperature graph and traffic graph under four different noise distributions prove the effectiveness and robustness of our proposed LMP-GNN.

With the increasing use of deep learning on data collected by non-perfect sensors and in non-perfect environments, the robustness of deep learning systems has become an important issue. A common approach for obtaining robustness to noise has been to train deep learning systems with data augmented with Gaussian noise. In this work, we challenge the common choice of Gaussian noise and explore the possibility of stronger robustness for non-Gaussian impulsive noise, specifically alpha-stable noise. Justified by the Generalized Central Limit Theorem and evidenced by observations in various application areas, alpha-stable noise is widely present in nature. By comparing the testing accuracy of models trained with Gaussian noise and alpha-stable noise on data corrupted by different noise, we find that training with alpha-stable noise is more effective than Gaussian noise, especially when the dataset is corrupted by impulsive noise, thus improving the robustness of the model. The generality of this conclusion is validated through experiments conducted on various deep learning models with image and time series datasets, and other benchmark corrupted datasets. Consequently, we propose a novel data augmentation method that replaces Gaussian noise, which is typically added to the training data, with alpha-stable noise.

Random noise arising from physical processes is an inherent characteristic of measurements and a limiting factor for most signal processing and data analysis tasks. Given the recent interest in generative adversarial networks (GANs) for data-driven modeling, it is important to determine to what extent GANs can faithfully reproduce noise in target data sets. In this paper, we present an empirical investigation that aims to shed light on this issue for time series. Namely, we assess two general-purpose GANs for time series that are based on the popular deep convolutional GAN (DCGAN) architecture, a direct time-series model and an image-based model that uses a short-time Fourier transform (STFT) data representation. The GAN models are trained and quantitatively evaluated using distributions of simulated noise time series with known ground-truth parameters. Target time series distributions include a broad range of noise types commonly encountered in physical measurements, electronics, and communication systems: band-limited thermal noise, power law noise, shot noise, and impulsive noise. We find that GANs are capable of learning many noise types, although they predictably struggle when the GAN architecture is not well suited to some aspects of the noise, e.g., impulsive time-series with extreme outliers. Our findings provide insights into the capabilities and potential limitations of current approaches to time-series GANs and highlight areas for further research. In addition, our battery of tests provides a useful benchmark to aid the development of deep generative models for time series.

In this paper, we propose a general robust subband adaptive filtering (GR-SAF) scheme against impulsive noise by minimizing the mean square deviation under the random-walk model with individual weight uncertainty. Specifically, by choosing different scaling factors such as from the M-estimate and maximum correntropy robust criteria in the GR-SAF scheme, we can easily obtain different GR-SAF algorithms. Importantly, the proposed GR-SAF algorithm can be reduced to a variable regularization robust normalized SAF algorithm, thus having fast convergence rate and low steady-state error. Simulations in the contexts of system identification with impulsive noise and echo cancellation with double-talk have verified that the proposed GR-SAF algorithms outperforms its counterparts.

In this paper, we introduce an adaptive graph normalized least mean pth power (GNLMP) algorithm for graph signal processing (GSP) that utilizes GSP techniques, including bandlimited filtering and node sampling, to estimate sampled graph signals under impulsive noise. Different from least-squares-based algorithms, such as the adaptive GSP Least Mean Squares (GLMS) algorithm and the normalized GLMS (GNLMS) algorithm, the GNLMP algorithm has the ability to reconstruct a graph signal that is corrupted by non-Gaussian noise with heavy-tailed characteristics. Compared to the recently introduced adaptive GSP least mean pth power (GLMP) algorithm, the GNLMP algorithm reduces the number of iterations to converge to a steady graph signal. The convergence condition of the GNLMP algorithm is derived, and the ability of the GNLMP algorithm to process multidimensional time-varying graph signals with multiple features is demonstrated as well. Simulations show the performance of the GNLMP algorithm in estimating steady-state and time-varying graph signals is faster than GLMP and more robust in comparison to GLMS and GNLMS.

The dichotomous coordinate descent (DCD) algorithm has been successfully used for significant reduction in the complexity of recursive least squares (RLS) algorithms. In this work, we generalize the application of the DCD algorithm to RLS adaptive filtering in impulsive noise scenarios and derive a unified update formula. By employing different robust strategies against impulsive noise, we develop novel computationally efficient DCD-based robust recursive algorithms. Furthermore, to equip the proposed algorithms with the ability to track abrupt changes in unknown systems, a simple variable forgetting factor mechanism is also developed. Simulation results for channel identification scenarios in impulsive noise demonstrate the effectiveness of the proposed algorithms.