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The topic of nonparametric estimation of nonlinear characteristics in the Wiener system is examined. In this regard, the traditional kernel algorithm faces difficulties stemming from the dimensionality associated with the memory length of the dynamic block. A particular class of input sequences has been proposed, which aids in reducing dimensionality and consequently improves the convergence rate of the estimator to the true characteristics. A theoretical analysis of the suggested method is presented.

Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it is applied to discrete-time (DT) processes obtained by sampling the CT processes. When sampling is applied to a CT WSCS process, the statistics of the resulting DT process depends on the relationship between the sampling interval and the period of the statistics of the CT process: When these two parameters have a common integer factor, then the DT process is WSCS. This situation is referred to as synchronous sampling. When this is not the case, which is referred to as asynchronous sampling, the resulting DT process is wide-sense almost cyclostationary (WSACS). The sampled CT processes are commonly encoded using a source code to facilitate storage or transmission over wireless networks, e.g., using compress-and-forward relaying. In this work, we study the fundamental tradeoff between rate and distortion for source codes applied to sampled CT WSCS processes, characterized via the rate-distortion function (RDF). We note that while RDF characterization for the case of synchronous sampling directly follows from classic information-theoretic tools utilizing ergodicity and the law of large numbers, when sampling is asynchronous, the resulting process is not information stable. In such cases, the commonly used information-theoretic tools are inapplicable to RDF analysis, which poses a major challenge. Using the information-spectrum framework, we show that the RDF for asynchronous sampling in the low distortion regime can be expressed as the limit superior of a sequence of RDFs in which each element corresponds to the RDF of a synchronously sampled WSCS process (yet their limit is not guaranteed to exist). The resulting characterization allows us to introduce novel insights on the relationship between sampling synchronization and the RDF. For example, we demonstrate that, differently from stationary processes, small differences in the sampling rate and the sampling time offset can notably affect the RDF of sampled CT WSCS processes.

Propeller noise is the main source of ship-radiated noise. Extracting and analyzing the modulation characteristics from the propeller noise plays a crucial role in classifying and identifying vessel targets. Existing demodulation methods such as Detection of Envelope Modulation On Noise (DEMON), narrowband demodulation, and cyclostationary analysis can be used to extract modulation features. However, capturing the modulation features on the envelope spectrum may be hard under low signal-to-noise ratio scenarios, since the envelope spectrum is contaminated by interference noise. To address this challenge, selecting an optimal frequency band rich in modulation information can significantly enhance demodulation performance. This paper proposes an Adaptive Hoyer-L-moment Envelope Spectrum (AHLES) method. The method first introduces an optimal frequency band selection method based on the golden section search strategy. A Hoyer-L-moment metric is then designed to quantify the modulation intensity within narrow frequency bands. Based on this metric, the optimal spectral coherence integration band is adaptively selected according to the signal's inherent modulation characteristics, thereby enhancing demodulation performance. The effectiveness of the proposed method is validated through experiments on both simulated signals and merchant ship data.

Cognitive radio technology was introduced as a possible solution for spectrum scarcity by exploiting dynamic spectrum access. In the last two decades, most researchers focused on enabling cognitive radios for managing the spectrum. However, due to their intelligent nature, cognitive radios can scan the radio frequency environment and change their transmission parameters accordingly on-the-fly. Such capabilities make it suitable for the design of both advanced jamming and anti-jamming systems. In this context, our work presents a novel, robust algorithm for spectrum characterisation in wideband radios. The proposed algorithm considers that a wideband spectrum is sensed by a cognitive radio terminal. The wideband is constituted of different narrowband signals that could either be licit signals or signals jammed by stealthy jammers. Cyclostationary feature detection is adopted to measure the spectral correlation density function of each narrowband signal. Then, cyclic and angular frequency profiles are obtained from the spectral correlation density function, concatenated, and used as the feature sets for the artificial neural network, which characterise each narrowband signal as a licit signal with a particular modulation scheme or a signal jammed by a specific stealthy jammer. The algorithm is tested under both multi-tone and modulated stealthy jamming attacks. Results show that the classification accuracy of our novel algorithm is superior when compared with recently proposed signal classifications and jamming detection algorithms. The applications of the algorithm can be found in both commercial and military communication systems.

Simple processes (SPs) are a class of spectrally correlated (SC) processes that their Loeve bi-frequency spectrum is supported by a countable collection of special curves. While spectral coherence is a well-established tool for analyzing relationships between stationary processes, its extension to SC processes like discrete time harmonizable simple processes (DTHSPs) remains underexplored. This gap limits the ability to study the coherencies among many real-world signals. In this work, the spectral coherence for two DTHSPs is defined and robust estimator of the introduced spectral coherence for both known and unknown spectral structures is proposed. For known SP’s structures, we employ the periodogram covariances to establish the estimator and characterize its asymptotic properties. For unknown SP’s structures, a spectral ciphering-based approach is employed to estimate the coherence. Then, multiple testing procedures are developed to determine whether two DTHSPs are coherent or incoherent. Theoretical results are validated through simulations under two scenarios: (1) a time-lagged linear relationship between two DTHSPs and (2) independent DTHSPs. According to the numerical simulations, the proposed approach demonstrates superior performance compared to existing approaches in terms of key metrics such as precision, recall, F1-score and specificity. Finally, the proposed framework is applied to a real-world dataset, showcasing its practical utility in identifying spectral dependencies.

This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals. The theoretical framework behind the SCF estimation is briefly reviewed so that an important difference between the width of the resolution cell in bifrequency plane and the step between the centers of neighboring cells is highlighted. The outline of the proposed double-number fast Fourier transform algorithm (2N-FFT) is described in the paper as a sequence of steps directly leading to a digital signal processing technique. The 2N-FFT algorithm is derived from the time-smoothing approach to cyclic periodogram estimation where the spectral interpolation based on doubling the FFT base is employed. This guarantees that no cyclic frequency is left out of the coverage grid so that at least one resolution element intersects it. A numerical simulation involving two processes, a harmonic amplitude modulated by stationary noise and a binary-pulse amplitude-modulated train, demonstrated that their cyclic frequencies are estimated with a high accuracy, reaching the size of step between resolution cells. In addition, the SCF components estimated by the proposed algorithm are shown to be similar to the curves provided by the theoretical models of the observed processes. The comparison between the proposed algorithm and the well-known FFT accumulation method in terms of computational complexity and required memory size reveals the cases where the 2N-FFT algorithm offers a reasonable trade-off.

Rolling element bearings are widely used in various industrial machines. Fault diagnosis of rolling element bearings is a necessary tool to prevent any unexpected accidents and improve industrial efficiency. Although proved to be a powerful method in detecting the resonance band excited by faults, the spectral kurtosis (SK) exposes an obvious weakness in the case of impulsive background noise. To well process the bearing fault signal in the presence of impulsive noise, this paper proposes a fault diagnosis method based on the cyclic correntropy (CCE) function and its spectrum. Furthermore, an important parameter of CCE function, namely kernel size, is analyzed to emphasize its critical influence on the fault diagnosis performance. Finally, comparisons with the SK-based Fast Kurtogram are conducted to highlight the superiority of the proposed method. The experimental results show that the proposed method not only largely suppresses the impulsive noise, but also has a robust self-adaptation ability. The application of the proposed method is validated on a simulated signal and real data, including rolling element bearing data of a train axle.

Due to the non-contact nature, using Doppler radar sensors to detect vital signs such as heart and respiration rates of a human subject is getting more and more attention. However, the related detection-method research meets lots of challenges due to electromagnetic interferences, clutter and random motion interferences. In this paper, a novel third-order cyclic cummulant (TOCC) detection method, which is insensitive to Gaussian interference and non-cyclic signals, is proposed to investigate the heart and respiration rate based on continuous wave Doppler radars. The k-th order cyclostationary properties of the radar signal with hidden periodicities and random motions are analyzed. The third-order cyclostationary detection theory of the heart and respiration rate is studied. Experimental results show that the third-order cyclostationary approach has better estimation accuracy for detecting the vital signs from the received radar signal under low SNR, strong clutter noise and random motion interferences.

Since published in 1988, the FFT Accumulation Method (FAM) has been used extensively to compute the Spectral Correlation Function (SCF) and the Spectral Coherence Function (SCoF) to obtain or detect cyclic features of cyclostationary signals. When the input is a Gaussian random variable (r.v.), the SCF (or SCoF) estimates are also random variables with some probability density function (pdf). Although the FAM is considered the most computationally efficient method, there has been no in-depth statistical analysis of the algorithm. This paper analyzes the statistics of spectral estimates of the SCF using the FAM algorithm by obtaining the pdf for the points covering the frequency and cycle frequency f ; α plane, and application examples with simulation results are provided. The method proposed in the paper can be extended to other algorithms, provided they can be given by a quadratic form.

Two distinct modes of snow cover variability over Eurasia are investigated using cyclostationary empirical orthogonal function (CSEOF) analysis. The first mode of Eurasian snow cover extent (SCE) represents a seasonally asymmetric trend between spring and fall. The spring SCE shows a decreasing trend, while the fall SCE particularly in October exhibits a clear increasing trend. This seasonally asymmetric trend of SCE is closely linked to Arctic sea ice decline accompanied by warming in the northern Eurasia. The decreased SCE during spring is primarily attributed to the warm air temperature anomalies, while the increased SCE in October results from the loss of sea ice and the ensuing moisture transport to the atmosphere, which is realized as increased snow in October. The second mode of Eurasian SCE, on the other hand, is closely related to Arctic Oscillation (AO), which is a dominant mode of Northern Hemisphere atmospheric variability. The snow cover variability over Europe during winter is largely affected by AO variability, rather than the warming signal represented by the first CSEOF mode. Detailed descriptions of the two distinct modes of Eurasian SCE and their interactions with oceanic and atmospheric variables are presented along with possible implications for future climate.