Symmetric Noise Research Articles

A Noisy Sample Selection Framework Based on a Mixup Loss and Recalibration Strategy

Deep neural networks (DNNs) have achieved breakthrough progress in various fields, largely owing to the support of large-scale datasets with manually annotated labels. However, obtaining such datasets is costly and time-consuming, making high-quality annotation a challenging task. In this work, we propose an improved noisy sample selection method, termed “sample selection framework,” based on a mixup loss and recalibration strategy (SMR). This framework enhances the robustness and generalization abilities of models. First, we introduce a robust mixup loss function to pre-train two models with identical structures separately. This approach avoids additional hyperparameter adjustments and reduces the need for prior knowledge of noise types. Additionally, we use a Gaussian Mixture Model (GMM) to divide the entire training set into labeled and unlabeled subsets, followed by robust training using semi-supervised learning (SSL) techniques. Furthermore, we propose a recalibration strategy based on cross-entropy (CE) loss to prevent the models from converging to local optima during the SSL process, thus further improving performance. Ablation experiments on CIFAR-10 with 50% symmetric noise and 40% asymmetric noise demonstrate that the two modules introduced in this paper improve the accuracy of the baseline (i.e., DivideMix) by 1.5% and 0.5%, respectively. Moreover, the experimental results on multiple benchmark datasets demonstrate that our proposed method effectively mitigates the impact of noisy labels and significantly enhances the performance of DNNs on noisy datasets. For instance, on the WebVision dataset, our method improves the top-1 accuracy by 0.7% and 2.4% compared to the baseline method.

Enhancement noise margin and delay time performance of novel punch-through nMOS for single-carrier CMOS

In this paper, we propose the use of punch-through nMOS (PTnMOS) as an alternative to pMOS in complementary metal oxide semiconductor (CMOS) circuits. According to the TCAD simulation results, PTnMOS exhibit sub-threshold characteristics similar to those of pMOS and can be formed by simply changing the doping concentration of the source and drain. Without the need for sizing, which solves the area occupation problem caused by the need to increase the width of pMOS due to insufficient hole mobility. In addition, we compose a PTnMOS and nMOS without sizing to form a single-carrier CMOS in which only electrons are transmitted, and We extract its performance for comparison with conventional CMOS (Wp/Wn = 1). The results indicate that single-carrier CMOS has symmetric noise margin and 29% faster delay time compared to conventional CMOS (Wp/Wn = 1). If III–V or II–VI group materials could be applied to single-carrier CMOS, not only could costs be reduced and wafer area occupancy minimized, but also significant improvements in the performance and bandwidth application of microwave circuits could be achieved.

Performance analysis of hybrid combining schemes under Middleton class‐A and SαS${\rm S}\alpha{\rm S}$ impulsive noise model

AbstractImpulsive noise poses a significant challenge to single input multiple output wireless communication systems. This paper assesses the effectiveness of hybrid combining techniques, namely selection combining‐equal gain combining and selection combining‐maximal ratio combining, in mitigating impulsive noise impact caused by both man‐made and natural phenomena. The evaluation considers three different noise models: Additive white Gaussian noise, Middleton class‐A impulsive noise, and symmetric alpha stable impulsive noise, across Rayleigh and Rician fading channels. Bit error rate is employed to gauge channel performance. Our research contribution lies in the comprehensive assessment of hybrid combining techniques under diverse noise models, addressing a critical research gap in wireless communication. Findings indicate that impulsive noise has a more pronounced impact on channel performance than additive white Gaussian noise, and hybrid combining techniques prove more effective in mitigating these effects. The results hold significant implications for single input multiple output wireless communication systems, guiding the development of more robust and reliable communication systems in impulsive noise scenarios.

Existence and uniqueness of solutions for forward and backward nonlocal Fokker-Planck equations with time-dependent coefficients

Based on the Feynman-Kac formula, we develop a new approach to show the global existence and uniqueness of the solutions for the forward and backward time-dependent multidimensional nonlocal Fokker-Planck equations, which are associated with a class of time-dependent stochastic differential equations driven by symmetric (or asymmetric) non-Gaussian Lévy process. First, after deriving the forward time-dependent multidimensional nonlocal Fokker-Planck equation, the Feynman-Kac formula for the forward nonlocal Fokker-Planck equation is established by using Itô's formula and techniques for the backward nonlocal Fokker-Planck equation corresponding to the backward stochastic differential equation driven by Lévy process. Then, from the Feynman-Kac formula, we prove the global existence and uniqueness of the solutions for the forward and backward time-dependent multidimensional nonlocal Fokker-Planck equations by using techniques from stochastic analysis. Finally, the dynamic evolution of the probability density function corresponding to the stochastic model for the MeKS network (reflecting the interactions among the MecA complex, comK, comS) is investigated over an extended period by Feynman-Kac formula and Monte Carlo simulations. In particular, we reveal the influence of symmetric and asymmetric stable noises as well as tempered stable noise on the probability density function corresponding to the stochastic MeKS network model.

Performance of Relaying System with NOMA over Symmetric a-Stable Noise Channels

Objectives: This paper investigates the performance of a candidate 5G transmission system technique that is Non-Orthogonal Multiple Access (NOMA) over α-stable channels. This type of channel gets more attention in the research community because of its ability to model new IoT scenarios. However, there is a research gap in applying this type of channel to different wireless communications scenarios. In this work, we envision a scenario where users employ NOMA communications in the presence of an obstacle. As our mathematical analysis and simulation results show, there is a significant difference in performance when considering α-stable channels. Methods: To characterize the performance of the proposed noise channel, performance metrics such as outage probability and achievable rate are discussed. More particularly, we derive expressions for both outage probability and achievable rate for three NOMA users, considering the near user as a relay. In this paper, we consider additive symmetric α-stable noise channels with alpha α ∈ (1, 2). We present expressions for achievable rate and outage probability for each user (near, middle, and far) and investigate its behavior for different values of alpha (α). Findings: Based on the simulation results, it is shown that the high achievable rate observed for low alpha values while reduced as alpha is increased. Also, due to the influence of alpha, the outage probability is highly affected by α for small rate thresholds (Ro). In an envisioned scenario of three users with only one user forwarding the transmission to the other two, our results show that the near and middle users’ outage probability decreases as alpha α increases. Novelty: Despite this extensive study of the NOMA on individual channels, transmission under α-stable channel is not considered to the best of the authors’ knowledge. Keywords: NOMA, relaying, Cooperative Non-Orthogonal Multiple Access, Symmetric α-Stable Noise Channels, Achievable rate

Underdetermined blind source separation based on third‐order cumulant and tensor compression

AbstractA method for Underdetermined Blind Source Separation is proposed using third‐order cumulants and tensor compression. To effectively suppress symmetrical distributed noise, the third‐order cumulant is considered. Additionally, the complexity of high‐dimensional tensors can be reduced through high order singular value decomposition (HOSVD) for compression purposes. The method begins by calculating the third‐order cumulant tensor for whitening signals at different time delays, and then stacks several cumulants into a fourth‐order tensor. The HOSVD decomposition is applied to the fourth‐order tensor, compressing the high‐dimensional tensor into a low‐dimensional core tensor. Next, the core tensor is further decomposed using the canonical polyadic decomposition, and the resulting factor matrices are fused to obtain an estimation of the mixed matrix. Finally, leveraging the signal independence, a matrix diagonalisation method is employed to recover the source signals. Theoretical analysis and simulation results demonstrate that the proposed method effectively suppresses the influence of Gaussian noise, reduces computational complexity, and saves computational time. Moreover, compared with five representative approaches, the proposed method achieves superior separation results. Specifically, for the 3 × 4 mixed model with a signal‐to‐noise ratio of 20 dB, the average relative error of speech signal and radio signal are −11.02 and −6.8 dB respectively.

SigCo: Eliminate the inter-class competition via sigmoid for learning with noisy labels

Accurate predictions from deep neural networks are crucial for distinguishing clean data and correcting noisy labels in current label noise learning methods. However, the conventional Softmax classifier used in most relevant works is highly sensitive to label noise due to its inherent competition-prompting mechanism, i.e., similar categories are encouraged to compete for limited confidence scores during class activation, especially between the noisy classes and the ground-truth, which can inevitably lead to suboptimal predictions and eventually hamper model performance. To address this inter-class competition problem, we propose a novel Sigmoid-based Sample Selection and Correction method named SigCo for learning with noisy labels. Different from previous works, we develop a Sigmoid-based network in which each Sigmoid classifier independently predicts its respective class, improving the reliability of the selection and correction process through more accurate predictions. Besides, in order to mitigate the negative impact of noisy labels, we design a noise-adaptive learning strategy by imposing stringent class masking constraints on clean samples to enhance the learning of discriminative features, while adopting a loose masking strategy for noisy data to improve the robustness to label noise. Additionally, we introduce a co-training strategy between our Sigmoid-based network and the conventional Softmax-based network to implicitly boost the generalization capability of the model. Extensive experiments on synthetic and real-world benchmarks show that SigCo consistently outperforms state-of-the-art methods. Especially on CIFAR-100N with 80% and 90% symmetric noise ratios, it improves test accuracy by 5.10% and 18.44%, respectively.

On the Efficiency of the newly Proposed Convex Olanrewaju-Olanrewaju Lo-oλγ(|θ|) Penalized Regression-Type Estimator via GLMs Technique.

In this article, we proposed a novel convex penalized regression-type estimator, termed Olanrewaju-Olanrewaju penalized regression-type estimator, denoted by Lo-oλγ(|θ|) for ultra and high-dimensional data consideration whenever the number of covariates (p) is strictly greater than the sample size(n⁡). The newly proposed penalized estimator was formulated via the unique combination of arctangent and hyperbolic functions. It was noted that the newly proposed estimator could efficiently work under the constraint p<n formulated for, and as well as for the conventional regression methods of n>p. The proposed convex penalized regression-type estimator was formulated via three symmetric distributional noises of Gaussian, Laplace, and Normal Inverse Gaussian (NIG), considered being the three certified symmetric distributions that belong to the exponential family of distributions. The regularity axioms and oracle properties of the newly proposed penalized estimator were worked-out, as well as the parameter estimation for the penalized regression-type estimator for the three symmetric noises via canonical expressible form of Generalized Linear Models (GLMs) and first-order Karush-Kuhn-Tucker (KKT) condition. The Lo-oλγ(|θ|) regression-type estimator was subjected to simulation studies of well-generated symmetric observations. The US Longley macroeconomic dataset with the constraint p<n was fitted to Lo-oλγ(|θ|) regression-type estimator under the umbrella of three symmetric distributional noises. In conclusion, Gaussian noise for Lo-oλγ(|θ|) penalized regression-type estimator under the umbrella of p<n for the simulation and real life analyzes was considered effectively efficient because of its most reduced Mean Square Error (mse) measured error-type in comparison to Gaussian, Laplace, and NIG noises for LASSO and Atan penalties; and as well for Laplace, and NIG noises for Lo-oλγ(|θ|).

A Tremor Suppression and Noise Removal Algorithm for Microscopic Robot-Assisted Cataract Surgery

Ophthalmic surgery consists of a series of precise manipulations performed using a surgical microscope. A surgical robot with a master–slave paradigm is commonly adopted to improve the precision and guidance intelligence for ophthalmic surgery; however, the surgeon's hand tremor, misoperation, inherent characteristics of the robot, and environmental interference may cause tremors of the end-effector of the surgical manipulator, thus increasing the risk of soft tissue damage and poor prognosis for the patient. A symmetrical threshold noise reduction combiner (STIC) is proposed to suppress hand tremors and reduce environmental noise interference. Additionally, the inverse kinematic model of the eight-degrees-of-freedom surgical robot for cataract surgery is developed, with the constraints of continuous circular capsulorhexis manipulation. Simulation results show that the signal-to-noise ratio of the STIC is increased from 35.3907 to 57.0158 dB, whereas the maximum, average, standard deviation, and root mean square of the output of the STIC are decreased by 64.79%, 77.24%, 74.50%, and 75.86%, respectively. Three sets of in vitro experimental results show that these four indicators of the STIC performance are reduced by 59.73%, 76.57%, 57.23%, and 65.02%, respectively. These results validate the feasibility and effectiveness of the proposed method on hand tremor suppression and inherent high-frequency disturbance elimination, thereby enhancing the accuracy of the microsurgical operation.

Smoothing Codes and Lattices: Systematic Study and New Bounds

In this article we revisit smoothing bounds in parallel between lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> codes. Initially introduced by Micciancio and Regev, these bounds were instantiated with Gaussian distributions and were crucial for arguing the security of many lattice-based cryptosystems. Unencumbered by direct application concerns, we provide a systematic study of how these bounds are obtained for both lattices <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">and</i> codes, transferring techniques between both areas. We also consider multiple choices of spherically symmetric noise distributions. We found that the best strategy for a worst-case bound combines Parseval’s Identity, the Cauchy-Schwarz inequality, and the second linear programming bound, and this holds for both codes and lattices and all noise distributions at hand. For an average-case analysis, the linear programming bound can be replaced by an expected value computation. This alone gives optimal results for spherically uniform noise over random codes and random lattices. This also improves prior Gaussian smoothing bounds for worst-case lattices, but surprisingly this provides even better results with uniform ball noise than for Gaussian (or Bernoulli noise for codes). This counterintuitive situation can be resolved by adequate decomposition and truncation of Gaussian and Bernoulli distributions into a superposition of uniform noise, giving further improvement for those cases, and putting them on par with the uniform cases.

Trade efficiency under FTA for Thailand’s agricultural exports: copula-based gravity stochastic frontier model

This study investigated the trade efficiency and trade effects under Free Trade Agreements for Thailand’s agricultural exports. There are five main trading partners comprising China, Japan, Australia, New Zealand, and India. The important agricultural commodities of rubber, cassava, fruits, vegetables, and herbs were assessed from 1998 to 2019. In a traditional stochastic frontier model the two error components of symmetric noise ({nu }_{j}) and a non-negative inefficiency ({u}_{j}) are assumed to be independent. This may result in invalid inferences due to misspecification. To address this obstacle, copula-based Gravity Stochastic Frontier Models (GSFM) using panel criteria were constructed to estimate trade efficiency. Empirically, the Student-t copula-based SFM minimizes both AIC and BIC. According to their mean TE, China (0.48) and Japan (0.48) had the highest export efficiencies followed by India (0.41), New Zealand (0.39), and Australia (0.33) in rank order. Hence, Thailand should pursue more FTA negotiations with the trading partners. Moreover, they should promote miscellaneous behind-the-border barriers to stimulate flows of goods to enhance the country’s trade efficiency substantially.

Robust Point Cloud Segmentation with Noisy Annotations.

Point cloud segmentation is a fundamental task in 3D. Despite recent progress on point cloud segmentation with the power of deep networks, current learning methods based on the clean label assumptions may fail with noisy labels. Yet, class labels are often mislabeled at both instance-level and boundary-level in real-world datasets. In this work, we take the lead in solving the instance-level label noise by proposing a Point Noise-Adaptive Learning (PNAL) framework. Compared to noise-robust methods on image tasks, our framework is noise-rate blind, to cope with the spatially variant noise rate specific to point clouds. Specifically, we propose a point-wise confidence selection to obtain reliable labels from the historical predictions of each point. A cluster-wise label correction is proposed with a voting strategy to generate the best possible label by considering the neighbor correlations. To handle boundary-level label noise, we also propose a variant "PNAL-boundary" with a progressive boundary label cleaning strategy. Extensive experiments demonstrate its effectiveness on both synthetic and real-world noisy datasets. Even with 60% symmetric noise and high-level boundary noise, our framework significantly outperforms its baselines, and is comparable to the upper bound trained on completely clean data. Moreover, we cleaned the popular real-world dataset ScanNetV2 for rigorous experiment. Our code and data is available at https://github.com/pleaseconnectwifi/PNAL.

Variable Step Size Methods of the Hybrid Affine Projection Adaptive Filtering Algorithm under Symmetrical Non-Gaussian Noise

The idea of variable step-size was introduced into the Hybrid Affine Projection Algorithm (H-APA) and we propose two variable step size algorithms based on H-APA, which are called the Variable Step-Size Hybrid Affine Projection Algorithm (VSS-H-APA) and the Modified Variable Step-Size Hybrid Affine Projection Algorithm (MVSS-H-APA). These are two variable-step algorithms aim to further improve the robust performance and convergence speed of H-APA under non-Gaussian noise. This allows for faster convergence while maintaining stability. The MVSS-H-APA goes further than VSS-H-APA to estimate the noise in order to achieve better convergence performance. The proposed algorithm performs better than the existing algorithms in system identification under symmetric non-Gaussian noise.

An Improved Heteroscedastic Modeling Method for Chest X-ray Image Classification with Noisy Labels

Chest X-ray image classification suffers from the high inter-similarity in appearance that is vulnerable to noisy labels. The data-dependent and heteroscedastic characteristic label noise make chest X-ray image classification more challenging. To address this problem, in this paper, we first revisit the heteroscedastic modeling (HM) for image classification with noise labels. Rather than modeling all images in one fell swoop as in HM, we instead propose a novel framework that considers the noisy and clean samples separately for chest X-ray image classification. The proposed framework consists of a Gaussian Mixture Model-based noise detector and a Heteroscedastic Modeling-based noise-aware classification network, named GMM-HM. The noise detector is constructed to judge whether one sample is clean or noisy. The noise-aware classification network models the noisy and clean samples with heteroscedastic and homoscedastic hypotheses, respectively. Through building the correlations between the corrupted noisy samples, the GMM-HM is much more robust than HM, which uses only the homoscedastic hypothesis. Compared with HM, we show consistent improvements on the ChestX-ray2017 dataset with different levels of symmetric and asymmetric noise. Furthermore, we also conduct experiments on a real asymmetric noisy dataset, ChestX-ray14. The experimental results on ChestX-ray14 show the superiority of the proposed method.

Structural damping renders the hawkmoth exoskeleton mechanically insensitive to non-sinusoidal deformations.

Muscles act through elastic and dissipative elements to mediate movement, which can introduce dissipation and filtering which are important for energetics and control. The high power requirements of flapping flight can be reduced by an insect's exoskeleton, which acts as a spring with frequency-independent material properties under purely sinusoidal deformation. However, this purely sinusoidal dynamic regime does not encompass the asymmetric wing strokes of many insects or non-periodic deformations induced by external perturbations. As such, it remains unknown whether a frequency-independent model applies broadly and what implications it has for control. We used a vibration testing system to measure the mechanical properties of isolated Manduca sexta thoraces under symmetric, asymmetric and band-limited white noise deformations. The asymmetric and white noise conditions represent two types of generalized, multi-frequency deformations that may be encountered during steady-state and perturbed flight. Power savings and dissipation were indistinguishable between symmetric and asymmetric conditions, demonstrating that no additional energy is required to deform the thorax non-sinusoidally. Under white noise conditions, stiffness and damping were invariant with frequency, suggesting that the thorax has no frequency-dependent filtering properties. A simple flat frequency response function fits our measured frequency response. This work demonstrates the potential of materials with frequency-independent damping to simplify motor control by eliminating any velocity-dependent filtering that viscoelastic elements usually impose between muscle and wing.

TCC-net: A two-stage training method with contradictory loss and co-teaching based on meta-learning for learning with noisy labels

With the rapid development of deep neural networks, the demand for large-scale accurately labeled datasets is growing rapidly. However, human-labeled datasets often produce misleading information due to mistakes in manual labeling. Most previous works fail to control well the overfitting of the trained model to noisy labels. In this paper, we propose a novel two-stage learning framework for learning with noisy labels, called the Two-stage training method with Contradictory loss and Co-teaching based on meta-learning (TCC-net). First, a novel robust loss function called contradictory loss is designed for pre-training, which is proved to be sufficiently robust both in the experimental results and theoretical foundation. During the training stage, we co-teach two pretrained networks based on meta-learning without any auxiliary clean subset as meta-data. Unlike other co-teaching methods, we introduce two multilayer perceptron to assist in weighting the selected samples, meaning each network updates itself with weighted-selected samples by its peer network and self-perceptron. Experimental results on corrupted datasets, such as Cifar10, Cifar100, Animal10N, and Clothing1M, demonstrate that TCC-net is superior to other state-of-the-art methods on shallower layers. Specifically, we achieve 12.59% improvement on synthetic Cifar10 with 80% symmetric noise and 0.27% on the real-world Animal10N dataset. Code is released at https://github.com/QiangqiangXia/TCC-net.

Robust sparse Bayesian learning based on the Bernoulli-Gaussian model of impulsive noise

Traditional sparse reconstruction methods suffer from performance degradation in the presence of impulsive noise. In this paper, we adopt the Bernoulli-Gaussian distribution to model the impulsive noise and introduce the hidden state variables to indicate the state of the noise. Based on the new hierarchical Bayesian model, a robust sparse reconstruction algorithm called Bernoulli-Gaussian robust sparse Bayesian learning (BG-RSBL) is developed through the variational Bayesian inference framework. Different from existing robust reconstruction methods, BG-RSBL does not make sparse assumptions about the impulses and outliers. The employment of the Bernoulli-Gaussian model enables BG-RSBL to adapt to environments with a wider range of impulse densities. Comparative analysis shows that the reconstruction performance can be improved by including the outliers in posterior inference with appropriate weightings. Simulations performed under both Bernoulli-Gaussian and symmetric α-stable distributed impulsive noise demonstrate the robust and outstanding reconstruction performance of the proposed algorithm.

Two-tier stochastic frontier analysis using Stata

In this article, we introduce the sftt command, which fits two-tier stochastic frontier (2TSF) models with cross-sectional data. Like most frontier models, a 2TSF model consists of a linear frontier model and a composite error term. The error term is assumed to be a mixture of three components: two onesided inefficiency terms—strictly nonnegative and nonpositive, respectively—and a symmetric noise term. When providing appropriate distributional assumptions, sftt can fit models with exponential and half-normal specifications. sftt also fits 2TSF models with the scaling property to mitigate concerns over distributional specifications. In addition, we provide two subcommands, sftt sigs and sftt eff, to assist in postestimation efficiency analysis. We provide an overview of the 2TSF literature, a description of the sftt command and its options, and examples using simulated and actual data.

Instantaneous Frequency Estimation of FM Signals under Gaussian and Symmetric α-Stable Noise: Deep Learning versus Time–Frequency Analysis

Deep learning (DL) and machine learning (ML) are widely used in many fields but rarely used in the frequency estimation (FE) and slope estimation (SE) of signals. Frequency and slope estimation for frequency-modulated (FM) and single-tone sinusoidal signals are essential in various applications, such as wireless communications, sound navigation and ranging (SONAR), and radio detection and ranging (RADAR) measurements. This work proposed a novel frequency estimation technique for instantaneous linear FM (LFM) sinusoidal wave using deep learning. Deep neural networks (DNN) and convolutional neural networks (CNN) are classes of artificial neural networks (ANNs) used for the frequency and slope estimation for LFM signals under additive white Gaussian noise (AWGN) and additive symmetric alpha stable noise (SαSN). DNN is composed of input, output, and two hidden layers, where several nodes in the first and second hidden layers are 25 and 8, respectively. CNN is the content input layer; many hidden layers include convolution, batch normalization, ReLU, max pooling, fully connected, and dropout. The output layer consists of a fully connected softmax and classification layers. SαS distributions are impulsive noise disturbances found in many communication environments such as marine systems, their distribution lacks a closed-form probability density function (PDF), except for specific cases, and infinite second-order statistics, hence geometric SNR (GSNR) is used in this work to determine the effect of noise in a mixture of Gaussian and SαS noise processes. DNN is a machine learning classifier with few layers for reducing FE and SE complexity. CNN is a deep learning classifier, designed with many layers, and proved to be more accurate than DNN when dealing with big data and finding optimal features. Simulation results show that SαS noise can be much more harmful to the FE and SE of FM signals than Gaussian noise. DL and ML can significantly reduce FE complexity, memory cost, and power consumption as compared to the classical FE based on time–frequency analysis, which are important requirements for many systems, such as some Internet of Things (IoT) sensor applications. After training CNN for frequency and slope estimation of LFM signals, the performance of CNN (in terms of accuracy) can give good results at very low signal-to-noise ratios where time–frequency distribution (TFD) fails, giving more than 20 dB difference in the GSNR working range as compared to the classical spectrogram-based estimation, and over 15 dB difference with Viterbi-based estimate.

Tunnel magnetoresistance sensors with symmetric resistance-field response and noise properties under AC magnetic field modulation

Magnetoresistance (MR) devices with symmetric (even-function) resistance change to an external magnetic field is useful for various magnetic sensor applications, such as encoders for position and rotation detection and ultra-sensitive magnetic field sensors, when combined with a frequency modulation method. In this study, we developed tunnel magnetoresistance (TMR) sensors with even-function resistance–field (R–H) responses and investigated their noise properties. The developed TMR sensors achieved a higher MR ratio (∼120%) than those of conventional giant magnetoresistive multilayers exhibiting even-function R–H responses. The TMR sensors were realized by stabilizing the magnetization of the magnetic free layer (FL) in an anti-parallel configuration with respect to that of the reference layer. Orange-peel ferromagnetic coupling between the FL and a pinned layer through an AgSn spacer layer was used to control the strength of the unidirectional magnetic anisotropy of the FL, by which even-function R–H responses with negligible hysteresis were obtained. The sensors enabled us to study the intrinsic noise properties of TMR devices, particularly under an external AC modulation magnetic field. We found that the magnetic 1/f noise originating from thermal magnetization fluctuation was the dominant noise of the TMR sensors at low frequencies. We observed that the application of an AC modulation field to the TMR sensors increased the noise owing to the magnetic domain fluctuation and the transfer of magnetic 1/f noise to the modulation frequency.