Internet of Things (IoT) has emerged as a key application domain in modern wireless communication systems, where its effectiveness heavily relies on the accuracy of channel state information (CSI). The deployment of large-scale reconfigurable intelligent surfaces (RIS) makes near-field effects non-negligible, bringing great challenges to channel estimation in RIS-assisted IoT scenarios. Existing near-field estimation methods often suffer from modeling errors due to Fresnel approximation or excessive computational complexity arising from dense polar-domain sparse representation. In this paper, we propose a novel RIS-aided near-field channel estimation framework tailored for IoT environments. We first present an accurate sparse channel model that captures the true spherical wavefront propagation and thus eliminates the modeling inaccuracies introduced by Fresnel approximation. Leveraging this model, we further incorporate IoT environmental context to derive a novel dimensionality-reduced sparse representation. Subsequently, we devise a fast sparse Bayesian learning (SBL)-based sparsity recovery scheme with coarse off-grid refinement, and embed generalized approximate message passing (GAMP) to significantly reduce computational complexity. Simulation results demonstrate that the proposed method achieves high estimation accuracy with reduced complexity, owing to the dimensionality-reduced sparse representation and the fast GAMP-embedded SBL framework. These advantages make it highly suitable for RIS-assisted IoT systems.

Joint channel estimation and data detection can enhance the performance of both tasks, improve communication efficiency, and reduce pilot overhead. However, this has been rarely explored in the context of reconfigurable intelligent surface (RIS)-assisted OFDM systems due to the complexity of handling multiple coupling effects between various data sequences and reflection coefficients. The recently proposed solution is tailored for purely phase modulations, whereas modern 5G/6G systems predominantly use quadrature amplitude modulation (QAM). To overcome this limitation, the paper proposes an auxiliary Bayesian learning approach for joint channel estimation and data detection with RIS-assisted OFDM systems, which integrates advanced techniques to offer robustness, improved performance, and reduced computational complexity. The novelties of the proposed method are threefold: i) present an auxiliary Bayesian learning framework to probabilistically link pilot and data information, effectively formulating the common sparsity pattern while avoiding potential modeling errors introduced by modulation schemes; ii) derive a hybrid approximate message passing (AMP) approach for efficient execution of Bayesian inference, with various approximation strategies seamlessly integrated to balance computational complexity and approximation accuracy; and iii) embed a novel rearrangement strategy to streamline multilayer message extraction, facilitating efficient message passing among sub-modules and subsequent parameter learning. Simulation results demonstrate its superiority.

Massive machine-type communication (mMTC) is characterized by sporadic device activities and angular-sparse channels, creating an opportunity for efficient joint device active detection (AD) and channel estimation (CE). However, it is computationally intractable to solve the related 2D-sparse recovery problem. Existing methods often resort to transforming this problem into a 1D-sparse recovery issue, which can result in performance degradation due to energy leakage from the off-grid effect. Moreover, these methods overlook the potential benefits of common sparsity across different frequency bands. To address these limitations, a novel sparse Bayesian learning (SBL) framework for the joint AD and CE is proposed in the paper, and two advanced sparsity structures under the frequency multiplex (corresponding to frequency sparsity and partial common sparsity) are additionally exploited to elevate the sparse recovery performance substantially. The key to the success of the proposed method lies in two crucial factors: (i) the employment of an innovative independent variational Bayesian inference (VBI) factorization technique, effectively decoupling the challenging 2D-sparse recovery problem and mitigating the off-grid mismatch; and (ii) the introduction of a hybrid sparsity prior into the SBL framework, seamlessly integrating additional frequency sparsity and common sparsity across different active frequency bands. Simulation results verify the superiority of the proposed method and indicate that the proposed method can achieve almost 50% NMSE performance enhancement compared with the state-of-the-art methods, attributed to its flexible employment of the sophisticated sparsity structure.

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.

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.

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.

Intelligent reflecting surface (IRS) is deemed as a potential technology for future communications due to its adaptive enhancement for the propagation environment. To achieve the passive beamforming gain of IRS, accurate channel state information (CSI) is essential but practically challenging since its massive passive reflecting elements have no transmitting/receiving capability. This paper presents a new channel estimation problem formulation for IRS-assisted orthogonal frequency division multiplexing (OFDM) systems, where the channel sparsity is exploited in the time-domain. Considering the surfaces are physically close to each other, we further utilize the common sparsity among the different sub-surfaces and automatically cluster them into several groups by introducing a Dirichlet process (DP)-based clustering model. Then, a DP-based variational Bayesian inference (VBI) framework is proposed to jointly estimate the channel and cluster the sub-surfaces, which is expected to significantly improve the channel estimation performance. Moreover, a novel decoupling trick is combined into the VBI framework to efficiently handle the coupling effect brought by the reflection coefficients, as well as facilitate the Bayesian inference. Simulation results verify the effectiveness of the proposed channel estimation scheme and show its significant performance improvement over various benchmark schemes.

Direction-of-arrival (DOA) estimation can be represented as a sparse signal recovery problem and effectively solved by sparse Bayesian learning (SBL). For the DOA estimation in active sensing, the SBL-based estimation error is related to the transmitted probing waveform. Therefore, it is expected to improve the estimation by waveform optimization. In this paper, we propose a recurrent scheme of waveform design by sequentially leveraging on the previous-round SBL estimates. Within this scheme, we formulate the waveform design problem as a minimization of the SBL estimation variance, which is non-convex and then solved by a majorization-minimization based algorithm. The simulations demonstrate the efficacy of the proposed design scheme in terms of avoiding incorrect detection and accelerating the DOA estimation convergence. Further, the results indicate that the waveform design is essentially a beampattern shaping methodology.

In this work, a separating function estimation test (SFET) based detector is proposed for the problem of impropriety test of complex signals. With the establishment of closed-form expressions concerning the first two raw moments of the proposed test statistic, we can obtain the analytic form for the probability of false alarm (PFA) based on moment-matching method. Moreover, the threshold can be further obtained for a given user-specified PFA. Numerical examples are provided to verify our theoretical results and demonstrate the performance gain of our proposed detector.

Fault impulse extraction under strong background noise and/or multiple interferences is a challenging task for bearing fault diagnosis. Sparse representation has been widely applied to extract fault impulses and can achieve state-of-the-art performance. However, most of the current methods rely on carefully tuning several hyperparameters and suffer from possible algorithmic degradation due to the approximate regularization and/or heuristic sparsity model. To overcome these drawbacks, in this article, we present a sparse Bayesian learning (SBL) framework for bearing fault diagnosis, and then propose two group-sparsity learning algorithms to extract fault impulses, where the first one exploits the group-sparsity of fault impulses only, whereas the second one utilizes additional periodicity behavior of fault impulses. Due to the inherent learning capability of the SBL framework, the proposed algorithms can tune hyperparameters automatically and do not require any prior knowledge. Another advantage is that our solutions are maximuma$posteriori$estimators in the sense of Bayesian optimality, which can yield higher accuracy. Results on both simulated and real datasets demonstrate the superiority of the developed algorithms.

The performance of sparse signal recovery (SSR) can be enhanced by exploiting rich temporal correlation in the multiple snapshots of signal of interest. However, existing methods need to transform the temporally correlated multiple measurements SSR problem into its vectorization form, imposing huge computational cost for algorithmic realization. To overcome this drawback, we propose a novel formulation to model the temporal correlation so that variational Bayesian inference (VBI) can be applied to simplify the inference and a novel uncoupling trick is also proposed to reduce the computation. Theoretical and simulation results indicate that our method can bring a considerable computational complexity reduction and achieve a performance improvement for the temporally correlated SSR problem compared to the state of arts time-varying sparse Bayesian learning (TSBL) method.

Testing the impropriety of complex signals is of great importance in complex signal processing. Such test is often accomplished by the generalized likelihood ratio test (GLRT) in the literature. However, when the sample size is small, the associated decision threshold obtained via the existing methods is not accurate enough, which might produce incorrect decisions in practice. Moreover, few methods are available to deal with scenarios where the system dimensionality may be either low or high. To overcome these drawbacks, this letter develops two new methods to compute the threshold for a given nominal false alarm probability (FAP), without any assumptions on the sample size and system dimensionality. Specifically, the exact result of FAP in terms of MeijerG function is established, which enables us to accurately determine the threshold through numerical solution. We also develop an approximate method with low computational load and high precision, by means of box approximation as well as the properties of chi-square distribution. The effectiveness of our proposed methods is demonstrated via simulation results.

This paper addresses the problem of massive multiple-input multiple-output (MIMO) channel estimation in the presence of impulsive noise. In the literature, a sparse Bayesian learning (SBL) approach for outlier-resistant direction-of-arrival (DOA) estimation can be tailored to handle this problem. However, it suffers from two major shortcomings: first, it takes the impulsive noise as a part of the unknown signal-of-interest, which brings a high computational complexity due to the larger size of the problem; and second, the assumption that both the signal-of-interest and the impulsive noise have a common sparsity level is not always valid, which could cause a performance loss. To deal with these shortcomings, we resort to the variational Bayesian inference (VBI) methodology to separate effects from the signal-of-interest and the impulsive noise. Then, we introduce an improved two-stage hierarchical prior to enforce sparsity while guarantee a denser impulsive noise over the signal-of-interest simultaneously. Due to adopting the VBI separation and the new sparsity prior, our method can bring a considerable computational complexity reduction and achieve better channel estimation accuracy. Simulation results reveal substantial performance improvement over the existing methods.

Receiver operating characteristic (ROC) analysis has become an indispensable tool in medical care, with a major application to characterizing the performance of binary diagnostic tests in clinical practice. In many circumstances, however, the diagnostic test has three outcomes, that is, the abnormalities are two sided. To deal with this scenario, this letter develops a recursive algorithm for computing the exact null distribution of the volume under the ordered three-class ROC surface (VUS) for samples following continuous distributions. Based on the asymptotic normality, an approximately normal distribution with exact mean and variance is also proposed, which is hoped to be useful for large-sample scenarios. Moreover, an efficient rank-based formula, in linearithmic time, is established for nonparametric estimation of VUS. Monte Carlo simulations verify the usefulness of the theoretical and algorithmic findings in this letter.

The performance of the existing sparse Bayesian learning (SBL) methods for off-grid direction-of-arrival (DOA) estimation is dependent on the tradeoff between the accuracy and the computational workload. To speed up the off-grid SBL method while remain a reasonable accuracy, this letter describes a computationally efficient root SBL method for off-grid DOA estimation, which adopts a coarse grid and considers the sampled locations in the coarse grid as the adjustable parameters. We utilize an expectation-maximization algorithm to iteratively refine this coarse grid and illustrate that each updated grid point can be simply achieved by the root of a certain polynomial. Simulation results demonstrate that the computational complexity is significantly reduced, and the modeling error can be almost eliminated.

Underdetermined direction-of-arrival (DOA) estimation for wideband signals by sparse arrays is discussed in the framework of sparse Bayesian learning (SBL). The problem is transformed to recovering multiple nonnegative sparse vectors, which share the same sparse support but correspond to distinct overcomplete basis matrices, from their noise contaminated linear combination vectors. A two-layer Bayesian model is established, and a hyperparameter vector, which reveals the true DOAs, is set to control this common sparsity in the model. The expectation-maximization algorithm is employed to realize this joint nonnegative SBL procedure, which can give the DOA estimation in a few iterations. The proposed method manifests mild computational complexity, and numerical simulation results show that compared with the existing underdetermined DOA estimation methods, it yields superior estimation accuracy, without the prior knowledge of number of sources.

This paper proposes a novel approach to handle the singularity problem in the Homotopy algorithm. Following a state‐of‐art ridge‐adding‐based method, the authors introduce a random ridge term to each element of the measure matrix to avoid the occurrence of singularities. Then, the authors give the sufficient condition of avoiding singularities, and prove that adding random ridge is greatly useful to deal with the singularity problem, even the random ridge tends to zero. Although the main procedures in the method coincide with the state‐of‐art method, all the derivations and theoretical analyses are different because of distinct forms of optimisation problems. Thus, this work is by no means a trivial task. Moreover, the authors note that the most computationally expensive step in the proposed method is the inversion of active matrices, whose time complexity relative to that of other required operations is proportional to the active set's cardinality. This motivates us to develop an efficient QR update algorithm based on the new ridge‐adding‐based method, which is incorporated in Givens QR factorisation and Gaussian elimination. It turns out that, with such new QR update algorithm, the previous ratio of time complexities can be reduced to a constant order. As a consequence, the new method can eliminate the bottleneck of matrix inversion in the improved Homotopy algorithm.

This paper proposes a novel ridge-adding-based approach for handling singularities that are frequently encountered in the powerful SVMpath algorithm. Unlike the existing method that performs linear programming as an additional step to track the optimality condition path in a multidimensional feasible space, our new approach provides a simpler and computationally more efficient implementation, which needs no extra time-consuming procedures other than introducing a random ridge term to each data point. Contrary to the existing ridge-adding method, which fails to avoid singularities as the ridge terms tend to zero, our novel approach, for any small random ridge terms, guarantees the existence of the inverse matrix by ensuring that only one index is added into or removed from the active set. The performance of the proposed algorithm, in terms of both computational complexity and the ability of singularity avoidance, is manifested by rigorous mathematical analyses as well as experimental results.

This paper considers linear precoder optimization problems for multiple-input multiple-output (MIMO) systems. In addition to the conventionally used sum-power constraint, maximum eigenvalue constraint on the precoding matrix is also considered so as to account for power limitations imposed on each antenna by the linearity of its own power amplifier in practical implementations. A framework employing directional derivative is developed to obtain optimal precoder designs for different criteria including maximizing the information rate and minimizing the sum of mean-square error (MSE). It turns out that power allocations in such situations are piecewise linear in sum-power space. The piecewise linear property allows us to generate the entire path of solution through finding out a finite number of breakpoints. A Homotopy-type algorithm is then proposed to obtain the solution for an arbitrary sum-power constraint. The number of breakpoints to be determined in our exact piecewise linear solution is in fact only about two times of the number of transmit antennas, so that our method is super fast and outperforms existing approximate solutions in the literature in both effectiveness and efficiency. Simulated experiments are performed to verify our theoretical analysis.

Optimal designs for minimising the combination of symbol estimation errors subject to lp-norm constraint are investigated. Instead of considering each constraint in a separate way, the authors develop a unifying framework to obtain the optimal solution by employing a directional derivative method. The sum or peak power constraint turns out to be the case of p=1 or p→∞. Simulation results demonstrate the effectiveness of the proposed algorithm. Moreover, based on directional derivative, the authors show that the minimisation of the determinant of the minimum mean-square error (MMSE) matrix and the maximisation of mutual information are equivalent criteria.

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M-1), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.