Wafer-level performance prediction techniques have been increasingly gaining attention in production LSI testing due to their ability to reduce measurement costs without compromising test quality. Despite the availability of several efficient methods, the site-to-site variation commonly observed in multi-site testing for radio frequency circuits remains inadequately addressed. In this manuscript, we propose a wafer-level performance prediction approach for multi-site testing that takes into account the site-to-site variation. Our proposed method is built on the Gaussian process, a widely utilized wafer-level spatial correlation modeling technique, and enhances prediction accuracy by extending hierarchical modeling to leverage the test site information test engineers provide. Additionally, we propose a test-site sampling method that maximizes cost reduction while maintaining sufficient estimation accuracy. Our experimental results, which employ industrial production test data, demonstrate that our proposed method can decrease the estimation error to 1/19 of that a conventional method achieves. Furthermore, our sampling method can reduce the required measurements by 97% while ensuring satisfactory estimation accuracy.

Representation learning is a crucial and complex task for multivariate time series data analysis, with a wide range of applications including trend analysis, time series data search, and forecasting. In practice, unsupervised learning is strongly preferred owing to sparse labeling. However, most existing studies focus on the representation of individual subseries without considering relationships between different subseries. In certain scenarios, this may lead to downstream task failures. Here, an unsupervised representation learning model is proposed for multivariate time series that considers the semantic relationship among subseries of time series. Specifically, the covariance calculated by the Gaussian process (GP) is introduced to the self-attention mechanism, capturing relationship features of the subseries. Additionally, a novel unsupervised method is designed to learn the representation of multivariate time series. To address the challenges of variable lengths of input subseries, a temporal pyramid pooling (TPP) method is applied to construct input vectors with equal length. The experimental results show that our model has substantial advantages compared with other representation learning models. We conducted experiments on the proposed algorithm and baseline algorithms in two downstream tasks: classification and retrieval. In classification task, the proposed model demonstrated the best performance on seven of ten datasets, achieving an average accuracy of 76%. In retrieval task, the proposed algorithm achieved the best performance under different datasets and hidden sizes. The result of ablation study also demonstrates significance of semantic relationship in multivariate time series representation learning.

Statistical wafer-level characteristic variation modeling offers an attractive method for reducing the measurement cost in large-scale integrated (LSI) circuit testing while maintaining test quality. In this method, the performance of unmeasured LSI circuits fabricated on a wafer is statistically predicted based on a few measured LSI circuits. Conventional statistical methods model spatially smooth variations in the wafers. However, actual wafers can exhibit discontinuous variations that are systematically caused by the manufacturing environment, such as shot dependence. In this paper, we propose a modeling method that considers discontinuous variations in wafer characteristics by applying the knowledge of manufacturing engineers to a model estimated using Gaussian process regression. In the proposed method, the process variation is decomposed into systematic discontinuous and global components to improve estimation accuracy. An evaluation performed using an industrial production test dataset indicates that the proposed method effectively reduces the estimation error for an entire wafer by over 36% compared with conventional methods.

Seen from the Internet Service Provider (ISP) side, network traffic monitoring is an indispensable part during network service provisioning, which facilitates maintaining the security and reliability of the communication networks. Among the numerous traffic conditions, we should pay extra attention to traffic anomaly, which significantly affects the network performance. With the advancement of Machine Learning (ML), data-driven traffic anomaly detection algorithms have established high reputation due to the high accuracy and generality. However, they are faced with challenges on inefficient traffic feature extraction and high computational complexity, especially when taking the evolving property of traffic process into consideration. In this paper, we proposed an online learning framework for traffic anomaly detection by embracing Gaussian Process (GP) and Sparse Representation (SR) in two steps: 1). To extract traffic features from past records, and better understand these features, we adopt GP with a special kernel, i.e., mixture of Gaussian in the spectral domain, which makes it possible to more accurately model the network traffic for improving the performance of traffic anomaly detection. 2). To combat noise and modeling error, observing the inherent self-similarity and periodicity properties of network traffic, we manually design a feature vector, based on which SR is adopted to perform robust binary classification. Finally, we demonstrate the superiority of the proposed framework in terms of detection accuracy through simulation.

This paper presents a deep network based on unrolling the diffusion process with the morphological Laplacian. The diffusion process is an iterative algorithm that can solve the diffusion equation and represents time evolution with Laplacian. The diffusion process is applied to smoothing of images and has been extended with non-linear operators for various image processing tasks. In this study, we introduce the morphological Laplacian to the basic diffusion process and unwrap to deep networks. The morphological filters are non-linear operators with parameters that are referred to as structuring elements. The discrete Laplacian can be approximated with the morphological filters without multiplications. Owing to the non-linearity of the morphological filter with trainable structuring elements, the training uses error back propagation and the network of the morphology can be adapted to specific image processing applications. We introduce two extensions of the morphological Laplacian for deep networks. Since the morphological filters are realized with addition, max, and min, the error caused by the limited bit-length is not amplified. Consequently, the morphological parts of the network are implemented in unsigned 8-bit integer with single instruction multiple data set (SIMD) to achieve fast computation on small devices. We applied the proposed network to image completion and Gaussian denoising. The results and computational time are compared with other denoising algorithm and deep networks.

Bandpass filters (BPFs) are very important to extract target signals and eliminate noise from the received signals. A BPF of which frequency characteristics is a sum of Gaussian functions is called the Gaussian mixture BPF (GMBPF). In this research, we propose to implement the GMBPF approximately by the sum of several frequency components of the sliding Fourier transform (SFT) or the attenuated SFT (ASFT). Because a component of the SFT/ASFT can be approximately realized using the finite impulse response (FIR) recursive filters, its calculation complexity does not depend on the length of the impulse response. The property makes GMBPF ideal for narrow bandpass filtering applications. We conducted experiments to demonstrate the advantages of the proposed GMBPF over FIR filters designed by a MATLAB function with regard to the computational complexity.

With the emergence of a large quantity of data in science and industry, it is urgent to improve the prediction accuracy and reduce the high complexity of Gaussian process regression (GPR). However, the traditional global approximation and local approximation have corresponding shortcomings, such as global approximation tends to ignore local features, and local approximation has the problem of over-fitting. In order to solve these problems, a large-scale Gaussian process regression algorithm (RFFLT) combining random Fourier features (RFF) and local approximation is proposed. 1) In order to speed up the training time, we use the random Fourier feature map input data mapped to the random low-dimensional feature space for processing. The main innovation of the algorithm is to design features by using existing fast linear processing methods, so that the inner product of the transformed data is approximately equal to the inner product in the feature space of the shift invariant kernel specified by the user. 2) The generalized robust Bayesian committee machine (GRBCM) based on Tsallis mutual information method is used in local approximation, which enhances the flexibility of the model and generates a sparse representation of the expert weight distribution compared with previous work. The algorithm RFFLT was tested on six real data sets, which greatly shortened the time of regression prediction and improved the prediction accuracy.

In a free-space method using a pair of horn antennas with dielectric lenses, we demonstrated that the permittivity of a sample can be estimated with good accuracy by equalizing a measured transmission coefficient of a sample to a transmission coefficient for a Gaussian beam, which is approximately equal to the transmission coefficient for a plane wave multiplied by a term that changes the phase. In this permittivity estimation method, because the spot size at the beam waist in a Gaussian beam needs to be determined, we proposed an estimation method of the spot size by employing the measurement of the Line in Thru-Reflect-Line calibration; thus, no additional measurement is required. The permittivity estimation method was investigated for the E-band (60-90 GHz), and it was demonstrated that the relative permittivity of air with a thickness of 2mm and a sample with the relative permittivity of 2.05 and a thickness of 1mm is estimated with errors less than ±0.5% and ±0.2%, respectively. Moreover, in measuring a sample without displacing the receiving horn antenna to avoid the error in measurement, we derived an expression of the permittivity estimation for S parameters measured using a vector network analyzer, and demonstrated that the measurement of a sample without antenna displacement is valid.

We propose a biometric identification system where the chosen- and generated-secret keys are used simultaneously, and investigate its fundamental limits from information theoretic perspectives. The system consists of two phases: enrollment and identification phases. In the enrollment phase, for each user, the encoder uses a secret key, which is chosen independently, and the biometric identifier to generate another secret key and a helper data. In the identification phase, observing the biometric sequence of the identified user, the decoder estimates index, chosen- and generated-secret keys of the identified user based on the helper data stored in the system database. In this study, the capacity region of such system is characterized. In the problem settings, we allow chosen- and generated-secret keys to be correlated. As a result, by permitting the correlation of the two secret keys, the sum rate of the identification, chosen- and generated-secret key rates can achieve a larger value compared to the case where the keys do not correlate. Moreover, the minimum amount of the storage rate changes in accordance with both the identification and chosen-secret key rates, but that of the privacy-leakage rate depends only on the identification rate.

In this letter, we discuss the ambiguity function of interleaved sequences. Furthermore, using the Guassian sum and choosing binary m-sequences as column sequences, we investigate the property of a binary sequence set given by Zhou, Tang, Gong (IEEE Trans. Inf. Theory, 54(9), 2008), which has low ambiguity property in a large region. Those sequences could be used in radar systems.

This paper presents a deep network based on morphological filters for Gaussian denoising. The morphological filters can be applied with only addition, max, and min functions and require few computational resources. Therefore, the proposed network is suitable for implementation using a small microprocessor. Each layer of the proposed network consists of a top-hat transform, which extracts small peaks and valleys of noise components from the input image. Noise components are iteratively reduced in each layer by subtracting the noise components from the input image. In this paper, the extensions of opening and closing are introduced as linear combinations of the morphological filters for the top-hat transform of this deep network. Multiplications are only required for the linear combination of the morphological filters in the proposed network. Because almost all parameters of the network are structuring elements of the morphological filters, the feature maps and parameters can be represented in short bit-length integer form, which is suitable for implementation with single instructions, multiple data (SIMD) instructions. Denoising examples show that the proposed network obtains denoising results comparable to those of BM3D [1] without linear convolutions and with approximately one tenth the number of parameters of a full-scale deep convolutional neural network [2]. Moreover, the computational time of the proposed method using SIMD instructions of a microprocessor is also presented.

In this study, Bayesian image denoising, in which the prior distribution is assumed to be a Gaussian Markov random field (GMRF), is considered. Recently, an effective algorithm for Bayesian image denoising with a standard GMRF prior has been proposed, which can help implement the overall procedure and optimize its parameters in O(n)-time, where n is the size of the image. A new GMRF-type prior, referred to as a hierarchical GMRF (HGMRF) prior, is proposed, which is obtained by applying a hierarchical Bayesian approach to the standard GMRF prior; in addition, an effective denoising algorithm based on the HGMRF prior is proposed. The proposed HGMRF method can help implement the overall procedure and optimize its parameters in O(n)-time, as well as the previous GMRF method. The restoration quality of the proposed method is found to be significantly higher than that of the previous GMRF method as well as that of a non-local means filter in several cases. Furthermore, numerical evidence implies that the proposed HGMRF prior is more suitable for the image prior than the standard GMRF prior.

The efficient implementation strategy for speeding up high-quality clustering algorithms is developed on the basis of general purpose graphic processing units (GPGPUs) in this work. Among various clustering algorithms, a sophisticated Gaussian mixture model (GMM) by estimating parameters through variational Bayesian (VB) mechanism is conducted due to its superior performances. Since the VB-GMM methodology is computation-hungry, the GPGPU is employed to carry out massive matrix-computations. To efficiently migrate the conventional CPU-oriented schemes of VB-GMM onto GPGPU platforms, an entire migration-flow with thirteen stages is presented in detail. The CPU-GPGPU co-operation scheme, execution re-order, and memory access optimization are proposed for optimizing the GPGPU utilization and maximizing the clustering speed. Five types of real-world applications along with relevant data-sets are introduced for the cross-validation. From the experimental results, the feasibility of implementing VB-GMM algorithm by GPGPU is verified with practical benefits. The proposed GPGPU migration achieves 192x speedup in maximum. Furthermore, it succeeded in identifying the proper number of clusters, which is hardly conducted by the EM-algotihm.

Convolutional approximate message-passing (CAMP) is an efficient algorithm to solve linear inverse problems. CAMP aims to realize advantages of both approximate message-passing (AMP) and orthogonal/vector AMP. CAMP uses the same low-complexity matched-filter as AMP. To realize the asymptotic Gaussianity of estimation errors for all right-orthogonally invariant matrices, as guaranteed in orthogonal/vector AMP, the Onsager correction in AMP is replaced with a convolution of all preceding messages. CAMP was proved to be asymptotically Bayes-optimal if a state-evolution (SE) recursion converges to a fixed-point (FP) and if the FP is unique. However, no proofs for the convergence were provided. This paper presents a theoretical analysis for the convergence of the SE recursion. Gaussian signaling is assumed to linearize the SE recursion. A condition for the convergence is derived via a necessary and sufficient condition for which the linearized SE recursion has a unique stationary solution. The SE recursion is numerically verified to converge toward the Bayes-optimal solution if and only if the condition is satisfied. CAMP is compared to conjugate gradient (CG) for Gaussian signaling in terms of the convergence properties. CAMP is inferior to CG for matrices with a large condition number while they are comparable to each other for a small condition number. These results imply that CAMP has room for improvement in terms of the convergence properties.

Time of arrival (TOA) is a widely used wireless cellular network ranging technology. How to perform accurate TOA estimation in multi-path and non-line-of-sight (NLOS) environments and then accurately calculating mobile terminal locations are two critical issues in positioning research. NLOS identification can be performed in the TOA measurement part and the position calculation part. In this paper, for the above two steps, two schemes for mitigating NLOS errors are proposed. First, a TOA ranging method based on clustering theory is proposed to solve the problem of line-of-sight (LOS) path estimation in multi-path channels. We model the TOA range as a Gaussian mixture model and illustrate how LOS and NLOS can be measured and identified based on non-parametric Bayesian methods when the wireless transmission environment is unknown. Moreover, for NLOS propagation channels, this paper proposes a user location estimator based on the maximum a posteriori criterion. Combined with the TOA estimation and user location computation scheme proposed in this paper, the terminal's positioning accuracy is improved. Experiments showed that the TOA measurement and localization algorithms presented in this paper have good robustness in complex wireless environments.

Recently the data-driven learning of dynamic systems has become a promising approach because no physical knowledge is needed. Pure machine learning approaches such as Gaussian process regression (GPR) learns a dynamic model from data, with all physical knowledge about the system discarded. This goes from one extreme, namely methods based on optimizing parametric physical models derived from physical laws, to the other. GPR has high flexibility and is able to model any dynamics as long as they are locally smooth, but can not generalize well to unexplored areas with little or no training data. The analytic physical model derived under assumptions is an abstract approximation of the true system, but has global generalization ability. Hence the optimal learning strategy is to combine GPR with the analytic physical model. This paper proposes a method to learn dynamic systems using GPR with analytic ordinary differential equations (ODEs) as prior information. The one-time-step integration of analytic ODEs is used as the mean function of the Gaussian process prior. The total parameters to be trained include physical parameters of analytic ODEs and parameters of GPR. A novel method is proposed to simultaneously learn all parameters, which is realized by the fully Bayesian GPR and more promising to learn an optimal model. The standard Gaussian process regression, the ODE method and the existing method in the literature are chosen as baselines to verify the benefit of the proposed method. The predictive performance is evaluated by both one-time-step prediction and long-term prediction. By simulation of the cart-pole system, it is demonstrated that the proposed method has better predictive performances.

To meet the increasing demand for high-speed communication in VLSI (very large-scale integration) systems, next-generation high-speed data transmission standards (e.g., IEEE 802.3bs and PCIe 6.0) will adopt four-level pulse amplitude modulation (PAM-4) for data coding. Although PAM-4 is spectrally efficient to mitigate inter-symbol interference caused by bandwidth-limited wired channels, it is more sensitive than conventional non-return-to-zero line coding. To evaluate the received signal quality when using adaptive coefficient settings for a PAM-4 equalizer during data transmission, we propose an eye-opening monitor technique based on machine learning. The proposed technique uses a Gaussian mixture model to classify the received PAM-4 symbols. Simulation and experimental results demonstrate the feasibility of adaptive equalization for PAM-4 coding.

This paper proposes statistical analysis of phase-only correlation (POC) functions under the phase fluctuation of signals due to additive Gaussian noise. We derive probability density function of phase-spectrum differences between original signal and its noise-corrupted signal with additive Gaussian noise. Furthermore, we evaluate the expectation and variance of the POC functions between these two signals. As the variance of Gaussian noise increases, the expectation of the peak of the POC function monotonically decreases and variance of the POC function monotonically increases. These results mathematically guarantee the validity of the POC functions used for similarity measure in matching techniques.

We studied an acoustic anomaly detection system for equipments, where the outlier detection method based on recorded sounds is used. In a real environment, the SNR of the target sound against background noise is low, and there is the problem that it is necessary to catch slight changes in sound buried in noise. In this paper, we propose a system in which a sound source extraction process is provided at the preliminary stage of the outlier detection process. In the proposed system, nonnegative matrix factorization based on generalized Gaussian distribution (GGD-NMF) is used as a sound source extraction process. We evaluated the improvement of the anomaly detection performance in a low-SNR environment. In this experiment, SNR capable of detecting an anomaly was greatly improved by providing GGD-NMF for preprocessing.

In high range resolution radar systems, the detection of range-spread target under correlated non-Gaussian clutter faces many problems. In this paper, a novel detector employing an autoregressive (AR) model is proposed to improve the detection performance. The algorithm is elaborately designed and analyzed considering the clutter characteristics. Numerical simulations and measurement data verify the effectiveness and advantages of the proposed detector for the range-spread target in spatially correlated non-Gaussian clutter.