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Accurate channel estimation plays a pivotal role in realizing the passive beamforming gain of reconfigurable intelligent surfaces (RIS). Multi-user RIS-assisted channels exhibit a common sparse structure in the angular domain, which offers the potential to enhance channel estimation performance. Nonetheless, most existing methods simply partition the multi-user channel estimation problem into multiple sub-problems, which regrettably neglect the exploitation of the shared property across different users. In this paper, we formulate a unified multi-user channel estimation problem and propose a computationally efficient message passing approach to jointly extract the common sparsity. We first introduce a new sparse Bayesian learning (SBL) framework for joint multi-user RIS-assisted channel estimation, where some auxiliary variables and Dirac delta distributions are introduced to handle the intricate interplay of numerous unknown variables within the joint sparse channel representation. Subsequently, we devise a reassembled message passing algorithm for the associated joint Bayesian inference, incorporating a three-stage expected propagation approximation (EPA) procedure along with a novel reassembling technology to facilitate variable decoupling and ensure reliable sparse signal recovery. Simulation results demonstrate the superiority of the proposed algorithm over the state-of-the-art counterparts.

Compound bearing fault diagnosis is an essentially challenging task due to the mutual interference among multiple fault components. The state-of-the-art methods usually take the potential fault characteristic frequencies as the prior knowledge and then try to recover every fault component by exploiting the impulse signal sparsity. However, they inevitably suffer from algorithmic degradation caused by energy leakage, $l_{1}$-norm approximation, and/or improper parameter selection. To handle these shortcomings, in this article, we propose a novel sparse Bayesian learning (SBL)-based method for the compound bearing fault diagnosis. We first present a new categorical probabilistic model to efficiently capture the truly-occurred fault components with a truncated feasible domain, which can greatly reduce the energy leakage effect. Then, we devise a more general SBL framework to recover the compound sparse impulse signal under the new categorical probabilistic model. The newly proposed method successfully avoids the $l_{1}$-norm approximation and manual parameter selection; thus, it can yield much higher accuracy and robustness. Both simulations and experiments demonstrate the superiority of the developed method.

In the presence of non-Gaussian noise, traditional spectrum sensing techniques optimized for Gaussian noise may experience significant performance degradation. To address this challenge, this paper employs Kendall's tau (KT) as a detector to detect the primary signal in additive Laplace noise. Unlike techniques relying on fundamental information from raw observation data, this detector utilizes ranks to reduce the impact of impulsive component, thus being robust against large valued outliers. The analytic expressions concerning the expectation and variance of KT under Laplace noise are firstly established. Performance analyses are further conducted in terms of false alarm probability and detection probability. Monte Carlo simulations not only verified the correctness of the established theoretical results, but also demonstrated the superiority of KT over other commonly used methods in terms of detection probability under Laplace noise.

In this letter, we propose an improved weighted covariance based detector (IWCD) for spatially correlated time-varying Rayleigh fading channel. The proposed method uses adaptive weights that are tailored to the dynamic nature of the channels. These weights can be chosen manually to meet practical requirements or derived theoretically by optimizing some performance index, such that the IWCD outperforms traditional weighted covariance-based detectors (WCDs), which rely heavily on data-aided weights determined by the sample covariance matrix (SCM). Performance merits in terms of the probabilities of false alarm and detection are analyzed in the low signal-to-noise-ratio (SNR) regime. Besides, the optimal weights are derived via maximizing the modified deflection coefficient (MDC). A reasonable estimator of the optimal weights is also constructed armed with the available samples at hand. Theoretical analyses and experimental results demonstrate the superiority of our proposed method over existing works in various scenarios.