Signal Space Research Articles

Optimal multi-kernel local fisher discriminant analysis for feature dimensionality reduction and fault diagnosis

To achieve a more desirable fault diagnosis accuracy by applying multi-domain features of vibration signals, it is significative and challenging to refine the most representative and intrinsic feature components from the original high dimensional feature space. A novel dimensionality reduction method for fault diagnosis is proposed based on local Fisher discriminant analysis (LFDA) which takes both label information and local geometric structure of the high dimensional features into consideration. Multi-kernel trick is introduced into the LFDA to improve its performance in dealing with the nonlinearity of mapping high dimensional feature space into a lower one. To obtain an optimal diagnosis accuracy by the reduced features of low dimensionality, binary particle swarm optimization (BPSO) algorithm is utilized to search for the most appropriate parameters of kernels and K-nearest neighbor (kNN) recognition model. Samples with labels are used to train the optimal multi-kernel LFDA and kNN (OMKLFDA-kNN) fault diagnosis model to obtain the optimal transformation matrix. Consequently, the trained fault diagnosis model implements the recognition of machinery health condition with the most representative feature space of vibration signals. A bearing fault diagnosis experiment is conducted to verify the effectiveness of proposed diagnostic approach. Performance comparison with some other methods are investigated, and the improvement for fault diagnosis of the proposed method are confirmed in different aspects.

Signal Space Diversity for Improving the Reliability Performance of OFDM with Subcarrier Power Modulation

As the demand for higher data rates continues to increase exponentially, there is a shift towards exploring contemporary techniques that are likely to offer higher spectral efficiency. A new modulation technique termed as orthogonal frequency division multiplexing with sub‐carrier power modulation (OFDM‐SPM) has recently been introduced. It is an original technique that is still largely under-explored and aims at transmitting more bits per sub‐carrier by manipulating the power of the sub‐carriers in an OFDM block, in addition to those bits that are usually transmitted by conventional modulation schemes such as M-PSK. During the investigation and theoretical testing stages, it was found that the additional data stream conveyed by subcarriers' power has higher bit error rate (BER) performance compared to the data stream conveyed by conventional modulation schemes. To overcome this shortfall, signal space diversity (SSD) along with coordinate interleaving is proposed in this work to be integrated with OFDM‐SPM to help improve the overall BER performance. By doing so, it is shown that a BER performance of 10-3 can be obtained at SNR of 15 dB, which means achieving an improvement of more than 5 dB compared to the case of using OFDM‐SPM without SSD. Furthermore, the performance results of OFDM‐SPM‐SSD is compared with those of OFDM‐SPM with maximal ratio combining (MRC) and the obtained results show that OFDM‐SPM‐SSD offers superior performance. Additionally, a study of the effect of the constellation rotation on OFDM‐SPM is provided and an in‐depth analysis is also carried out for different power polices of sub‐carrier power modulation with regards to two main performance metrics; namely BER and the throughput. Simulation results show that SSD provides a considerable improvement in the BER over both plain OFDM‐SPM and OFDM‐SPM‐MRC. The analysis also reveal that when considering the different power policies of SPM, the BER results are optimum in the case of using power‐reassignment policy.

The Importance of Phase in Complex Compressive Sensing

We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this phase-only compressive sensing (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the complexity level of the signal space. Our approach proceeds by recasting the (non-linear) PO-CS scheme as a linear compressive sensing model built from a signal normalization constraint, and a phase-consistency constraint imposing any signal estimate to match the observed phases in the measurement domain. Practically, stable and robust estimation of the signal direction is achieved from any instance optimal algorithm of the compressive sensing literature (such as basis pursuit denoising). This is ensured by proving that the matrix associated with this equivalent linear model satisfies with high probability the restricted isometry property under the above condition on the number of measurements. We finally observe experimentally that robust signal direction recovery is reached at about twice the number of measurements needed for signal recovery in compressive sensing.

Toward Deep Generalization of Peripheral EMG-Based Human-Robot Interfacing: A Hybrid Explainable Solution for NeuroRobotic Systems

This letter investigates the feasibility of a generalizable solution for human-robot interfaces through peripheral multichannel Electromyography (EMG) recording. We propose a tangential approach in comparison to the literature to minimize the need for (re)calibration of the system for new users. The proposed algorithm decodes the signal space and detects the common underlying global neurophysiological components, which can be detected robustly across various users, minimizing the need for retraining and (re)calibration. The research question is how to go beyond techniques that detect a high number of gestures for a given individual (which requires extensive calibration) and achieve an algorithm that can detect a lower number of classes but without the need for (re)calibration. The outcomes of this letter address a challenge affecting the usability and acceptance of advanced myoelectric prostheses. For this, the paper proposes an explainable generalizable hybrid deep learning architecture that incorporates CNN and LSTM. We also utilize the GradCAM analysis to explain and optimize the structure of the generalized model, securing higher computational performance whiles proposing a shallower design.

Continuous LTI Input\u2013Output Stable Systems on {L^{p}(mathbb {R})} and {mathscr {D'}_{L^{p}}(mathbb {R})} Associated with Differential Equations: Existence, Invertibility Conditions and Inversion

A usual problem in analog signal processing is to ascertain the existence of a continuous single-input single-output linear time-invariant input–output stable system associated with a linear differential equation, i.e., of a continuous system such that, for every input signal in a given space of signals, yields an output, in the same space, which verifies the equation with known term the input, and to ascertain the existence of its inverse system. In this paper, we consider, as space of signals, the usual Banach space of {L^{p}} functions, or the space of distributions spanned by {L^{p}} functions and by their distributional derivatives, of any order (input spaces which include signals with not necessarily left-bounded support), we give a systematic theoretical analysis of the existence, uniqueness and invertibility of continuous linear time-invariant input–output stable systems (both causal and non-causal ones) associated with the differential equation and, in case of invertibility, we characterize the continuous inverse system. We also give necessary and sufficient conditions for causality. As an application, we consider the problem of finding a suitable almost inverse of a causal continuous linear time-invariant input–output stable non-invertible system, defined on the space of finite-energy functions, associated with a simple differential equation.

Efficient Approach of Automatic Speech Emotion Recognition (ASR) Using Mutual Information

Speech is a significant quality for distinguishing a person in daily human to human interaction/ communication. Like other biometric measures, such as face, iris and fingerprints, voice can therefore be used as a biometric measure for perceiving or identifying the person. Speaker recognition is almost the same as a kind of voice recognition in which the speaker is identified from the expression instead of the message. Automatic Speaker Recognition (ASR) is the way to identify people who rely on highlights that are omitted from speech expressions. Speech signals are awesome correspondence media that constantly pass on rich and useful knowledge, such as a speaker's feeling, sexual orientation, complement, and other interesting attributes. In any speaker identification, the essential task is to delete helpful highlights and allow for significant examples of speaker models.
 Hypothetical description, organization of the full state of feeling and the modalities of articulation of feeling are added. A SER framework is developed to conduct this investigation, in view of different classifiers and different techniques for extracting highlights. In this work various machine learning algorithms are investigated to identify decision boundary in feature space of audio signals. Moreover novelty of this art lies in improving the performance of classical machine learning algorithms using information theory based feature selection methods. The higher accuracy retrieved is 96 percent using Random forest algorithm incorporated with Joint Mutual information feature selection method.

An Automatic Identification Method for the Blink Artifacts in the Magnetoencephalography with Machine Learning

Magnetoencephalography (MEG) detects very weak magnetic fields originating from the neurons so as to study human brain functions. The original detected MEG data always include interference generated by blinks, which can be called blink artifacts. Blink artifacts could cover the MEG signal we are interested in, and therefore need to be removed. Commonly used artifact cleaning algorithms are signal space projection (SSP) and independent component analysis (ICA). These algorithms need to locate the blink artifacts, which is typically done with the identification of the blink signals in the electrooculogram (EOG). The EOG needs to be measured by electrodes placed near the eye. In this work, a new algorithm is proposed for automatic and on-the-fly identification of the blink artifacts from the original detected MEG data based on machine learning; specifically, the artificial neural network (ANN). Seven hundred and one blink artifacts contained in eight MEG signal data sets are harnessed to verify the effect of the proposed blink artifacts identification algorithm. The results show that the method can recognize the blink artifacts from the original detected MEG data, providing a feasible MEG data-processing approach that can potentially be implemented automatically and simultaneously with MEG data measurement.

Galileo L10 Satellites: Orbit, Clock and Signal-in-Space Performance Analysis.

The tenth launch (L10) of the European Global Navigation Satellite System Galileo filled in all orbital slots in the constellation. The launch carried four Galileo satellites and took place in July 2018. The satellites were declared operational in February 2019. In this study, we report on the performance of the Galileo L10 satellites in terms of orbital inclination and repeat period parameters, broadcast satellite clocks and signal in space (SiS) performance indicators. We used all available broadcast navigation data from the IGS consolidated navigation files. These satellites have not been reported in the previous studies. First, the orbital inclination (°) and repeat period ( s) for all four satellites are within the nominal values. The data analysis reveals also 13.5-, 27-, 177- and 354-days periodic signals. Second, the broadcast satellite clocks show different correction magnitude due to different trends in the bias component. One clock switch and several other minor correction jumps have occurred since the satellites were declared operational. Short-term discontinuities are within ±1 ps/s, whereas clock accuracy values are constantly below 0.20 m (root-mean-square—rms). Finally, the SiS performance has been very high in terms of availability and accuracy. Monthly SiS availability has been constantly above the target value of 87% and much higher in 2020 as compared to 2019. Monthly SiS accuracy has been below 0.20 m (95th percentile) and below 0.40 m (99th percentile). The performance figures depend on the content and quality of the consolidated navigation files as well as the precise reference products. Nevertheless, these levels of accuracy are well below the 7 m threshold (95th percentile) specified in the Galileo service definition document.

2-designs and redundant syndrome extraction for quantum error correction

Imperfect measurement can degrade a quantum error correction scheme. A solution that restores fault tolerance is to add redundancy to the process of syndrome extraction. In this work, we show how to optimize this process for an arbitrary ratio of data qubit error probability to measurement error probability. The key is to design the measurements so that syndromes that correspond to different errors are separated by the maximum distance in the signal space, in close analogy to classical error correction codes. We find that the mathematical theory of 2-designs, appropriately modified, is the right tool for this. Analytical and simulation results for the bit-flip code, the 5-qubit code, and the Steane code are presented. The results show that design-based redundancy protocols show improvement in both cost and performance relative to conventional fault-tolerant error-correction schemes in situations, quite important in practice, where measurement errors are common. In the near term, the construction of a fault-tolerant logical qubit with a small number of noisy physical qubits will benefit from targeted redundancy in syndrome extraction.

Energy Detector Based Spectrum Sensing Performance Analysis over Fading Environment

Cognitive radio is a new concept of wireless communication that offers increased usage of the limited spectral resource and is considered to be a revolutionary technology that will influence how radio spectrum is accessed, accessed and controlled in the future. Spectrum sensing is needed to allow optimal use of spectral resource. Secondary user performs spectrum sensing to recognize the transmission possibilities. Secondary users have lower priority when using spectrum, so a basic principle is that secondary users should avoid / minimize interference with primary users. We seek to identify the transmission from primary users for the spectrum sensing. Detection of the primary transmitter assists in the recognition of the spectrum it uses. Utilizing spectrum sensing approach, secondary user starts communication if it detects a weak signal or white space. Because of multipath propagation and shadowing effects, primary transmitter's detection is severely influenced. There are numerous spectrum sensing mechanisms and one of them is energy detection approach. In this paper, we have examined the impact of SNR on probability of detection in order to assess the performance of spectrum sensing using energy detector. Also the receiver operating characteristic curve was plotted for performance analysis of spectrum sensing employing energy detector. In addition, we also examined the impact of threshold value on the probability of the false alarm.

Analytical Modeling of Nonlinear Fiber Propagation for Four Dimensional Symmetric Constellations

Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such 4D spaces, taking the interpolarization dependency into account. This is in contrast to previous models such as the GN and EGN models, which are valid for polarization multiplexed (PM) formats, where the two polarizations are seen as independent channels on which data is multiplexed. The proposed model agrees with the EGN model in the special case of independent two-dimensional modulation in each polarization. The model accounts for the predominant nonlinear terms in a WDM system, namely self-phase modulation and and cross-phase modulation. Numerical results show that the EGN model may inaccurately estimate the nonlinear interference of 4D formats. This nonlinear interference discrepancy between the results of the proposed model and the EGN model could be up to 2.8 dB for a system with 80 WDM channels. The derived model is validated by split-step Fourier simulations, and it is shown to follow simulations very closely.

Mutual interference alignment for co-existing radar and communication systems

In this paper, we propose a mutual interference alignment (IA) method for interference elimination in co-existing multiple-input multiple-output (MIMO) radar and multi-user MIMO communication systems, namely, radar-communication systems. Traditional IA methods proposed for communication systems cannot be directly adopted in the radar-communications due to failure to fulfill the requirements of radar target detection. In contrast, our proposed mutual IA method can efficiently improve the signal-to-noise ratio (SNR) needed by radar functionalities without reducing the degrees-of-freedom (DoFs) of communication system, which implies no degradation for the communication performance. The algorithm idea is first to align all interferences at every receiver to one signal space, then the interferences can be easily canceled by receive filter. It is examined by the Neyman-Pearson (NP) test for radar functionality, while the communication performance is evaluated by DoFs and bit error rate (BER) analysis. Both theory analysis and numerical results are provided to validate the effectiveness of the proposed mutual IA method for co-existing radar and communication systems.

Optimal Transport of Information

We study the general problem of Bayesian persuasion (optimal information design) with continuous actions and continuous state space in arbitrary dimensions. First, we show that with a finite signal space, the optimal information design is always given by a partition. Second, we take the limit of an infinite signal space and characterize the solution in terms of a Monge-Kantorovich optimal transport problem with an endogenous information transport cost. We use our novel approach to: 1. Derive necessary and sufficient conditions for optimality based on Bregman divergences for non-convex functions. 2. Compute exact bounds for the Hausdorff dimension of the support of an optimal policy. 3. Derive a non-linear, second-order partial differential equation whose solutions correspond to regular optimal policies. We illustrate the power of our approach by providing explicit solutions to several non-linear, multidimensional Bayesian persuasion problems.

Encoding Multiple Virtual Signals in DNA Barcodes with Single-Molecule FRET.

DNA barcoding provides a way to label a myriad of different biological molecules using the extreme programmability in DNA sequence synthesis. Fluorescence imaging is presumably the most easy-to-access method for DNA barcoding, yet large spectral overlaps between fluorescence dyes severely limit the numbers of barcodes that can be detected simultaneously. We here demonstrate the use of single-molecule fluorescence resonance energy transfer (FRET) to encode virtual signals in DNA barcodes using conventional two-color fluorescence microscopy. By optimizing imaging and biochemistry conditions for weak DNA hybridization events, we markedly enhanced accuracy in our determination of the single-molecule FRET efficiency exhibited by each binding event between DNA barcode sequences. This allowed us to unambiguously differentiate six DNA barcodes encoding different FRET values without involving any probe sequence exchanges. Our method can be directly incorporated with previous DNA barcode techniques, and may thus be widely adopted to expand the signal space of DNA barcoding.

Low-Complexity Blind PAPR Reduction for OFDM Systems With Rotated Constellations

The high Peak-to-Average Power Ratio (PAPR) of Orthogonal Frequency Division Multiplexing (OFDM) signals leads to a serious system performance degradation. To work around this issue, several algorithms have been proposed in the literature to reduce the PAPR, but, they often suffer from multiple limitations; in particular, the main issue with interleaving techniques is the spectral efficiency loss, as the transmission of a Side Information (SI) is generally required. In contrast to previous works, this article proposes a blind interleaving technique for OFDM systems with signal space diversity. Indeed, with Rotated and Cyclically Q-Delayed (RCQD) constellations, the In-phase (I) and Quadrature (Q) components of constellations symbols are correlated, which allows the receiver to estimate the interleaver index without any SI. Moreover, to lower down the complexity burden at the receiver side, we first design a blind decoder based on the Minimum Mean Square Error (MMSE) criterion and we then propose a low complexity decoder for the Uniformly Projected RCQD (UP-RCQD) QAM, as this constellation has several interesting structural properties and achieves near optimum BER performance. Simulation results show that our proposal leads to a large PAPR reduction and to a near optimum BER performance that outperforms, over various channels, the solution currently used in DVB-T2. They also underline the good performance of the blind decoding performed with up to 98% of complexity reduction compared to the max-log Maximum Likelihood (ML) estimation.

BDS signal-in-space anomaly probability analysis over the last 6 years

Knowledge of the signal-in-space (SIS) anomaly probability is important for the integrity monitoring of satellite navigation. An efficient SIS anomaly detection method is indispensable for characterizing the probability of SIS anomalies with sufficient confidence. The traditional GPS anomaly detection method based on the zero-mean Gaussian distribution assumption of the instantaneous signal-in-space user range error (IURE) is not suitable for the emerging BeiDou navigation satellite system (BDS) because of the nonzero-mean, asymmetric distribution of the BDS IURE. By deliberately extracting the time series trend terms of the satellite orbit and clock errors, an SIS anomaly detection method with the worst user location protection principle is proposed based on 6 years of BDS data from March 2013 to March 2019. The detection results have shown that the probability of single-satellite SIS anomalies is at the 10−3 level and the probability of multiple-satellite SIS concurrent anomalies is at the 10−4 level. Meanwhile, the operational service performance provided by the BDS gradually improves over time.

One‐to‐one non‐linear transformation for RSS‐based localization with unknown transmit power

For most of the positioning algorithms, based on the received signal strength, the objective function of the estimator is linearized so that the conventional least square algorithm can be executed. This would necessitate using a data model containing many noisy elements which implicitly violates the least squares assumptions. To avoid this violation, an optimized data modelling would have to be set up as shown in this paper. The authors then trivially provide the solution of this new least square problem which is still a primary coarse position estimation because of ignoring the non-linear relationships existing among parameters of the estimation. To extract quantitative information from these non-linear relationships, the authors also propose two new signal space points for using Taylor-series expansion as effectively as possible in accordance of the new data model. The proposed algorithms work without any knowledge about the transmit power. The performance evaluation of the proposed idea indicates that the new suggested estimators perform significantly better than the other existing linear position estimators for a large range of noise variance and path-loss exponent values.

Characterizing BDS signal‐in‐space performance from integrity perspective

The full deployment of China’s BeiDou navigation satellite system (BDS) was finalized in June 2020. To support safety-critical applications, the system must provide assured signal-in-space (SIS) performance. As one of the key steps forward for BDS, this paper characterizes the SIS range errors (SISREs) for both the regional (BDS-2) and the global (BDS-3) systems from the integrity perspective. Following the safety standards in aviation, a data-driven SISRE evaluation scheme is presented in this work. This scheme evaluates the overbounding user range accuracy (URA) and the prior fault probability to respectively capture the nominal and anomalous SIS behaviors. By processing the 4.5-year ephemerides starting from 2016 for BDS-2 and the recent 1.5-year data from2019 for BDS-3, we preliminarily provide an overall picture of the BDS SIS characteristics and reveal the significant performance variation among different satellites.

Transcranial Evoked Potentials Can Be Reliably Recorded with Active Electrodes.

Electroencephalographic (EEG) signals evoked by transcranial magnetic stimulation (TMS) are usually recorded with passive electrodes (PE). Active electrode (AE) systems have recently become widely available; compared to PE, they allow for easier electrode preparation and a higher-quality signal, due to the preamplification at the electrode stage, which reduces electrical line noise. The performance between the AE and PE can differ, especially with fast EEG voltage changes, which can easily occur with TMS-EEG; however, a systematic comparison in the TMS-EEG setting has not been made. Therefore, we recorded TMS-evoked EEG potentials (TEPs) in a group of healthy subjects in two sessions, one using PE and the other using AE. We stimulated the left primary motor cortex and right medial prefrontal cortex and used two different approaches to remove early TMS artefacts, Independent Component Analysis and Signal Space Projection—Source Informed Recovery. We assessed statistical differences in amplitude and topography of TEPs, and their similarity, by means of the concordance correlation coefficient (CCC). We also tested the capability of each system to approximate the final TEP waveform with a reduced number of trials. The results showed that TEPs recorded with AE and PE do not differ in amplitude and topography, and only few electrodes showed a lower-than-expected CCC between the two methods of amplification. We conclude that AE are a viable solution for TMS-EEG recording.

On Estimating Nonlinear Frequency Modulated Radar Signals in Low SNR Environments

Estimating the signal transmitted by a noncooperating radar is of great use in radar countermeasures. In this article, we propose to improve the noise resilience of the radar signal estimation by constraining the estimate to be in a low-dimensional signal space. In particular, we focus on estimating nonlinear frequency modulated radar signals that have good target resolution characteristics. A flexible 3-D odd polynomial frequency signal model is introduced as the low-dimensional signal space to compute accurate estimates at low signal-to-noise ratios (SNRs) with small number of intercepted signals. The quality of the low-dimensional signal estimates is compared with that of the estimate from the unconstrained high-dimensional space computed using principal component analysis estimator, which is the method in predominant use in the multisensor scenario. It is shown that signal estimation through low-dimensional signal spaces yields more accurate estimates at low SNRs with a smaller number of sensors compared to searching in the unconstrained high-dimensional signal space.