Zero-memory Nonlinearity Research Articles

Study of the Windowing and Overlap-Add Operation for a Super-Gaussian Random Vibration Test

Random vibration environmental testing employs the specified statistical properties of the real world vibration to reproduce the desired excitations on the shaker table for fatigue test purposes. Smooth and safe operation is the essential requirement for a long-duration test. Traditionally, the windowing and overlap-add (WOA) method is applied to the acceleration signals of the shaker table, and previous studies have indicated that this operation reduces the kurtoses of the processed signals. To protect the test equipment from abrupt changes in the input voltage, the WOA method is proposed to operate on the input voltage signals in a frame-by-frame form for super-Gaussian environmental testing. To figure out the impacts of the proposed operation on the response kurtoses of a shaker table, we express the system transfer function in the time domain, and the WOA method is analysed considering the transfer function of a dynamic system. Based on the analysis, a further study is made to explain the mechanism of the kurtosis decrease due to the WOA method. Through the study, we find that the kurtosis reduction conclusion is not applicable to all types of super-Gaussian signals, and the kurtoses can be invariable and even increased by allocating the positions of the high-excursion peaks of super-Gaussian signals when the WOA method is applied. A window function is recommended for zero-memory nonlinear (ZMNL) transformation to move the positions of the high-excursion peaks of a super-Gaussian signal, providing a novel way of adjusting kurtosis when WOA method is applied. The proposed WOA method and window function are first verified in a single-input-single-output (SISO) numerical simulation to test their effectiveness under different reference kurtoses. Then, they are evaluated in a two-input-two-output shaker table test. The test results demonstrate that the proposed window function can prevent the kurtosis decrease with the application of the WOA method.

Generation of non-Gaussian stationary random excitations with specified cross-power spectral densities using zero memory non-linear transformation for fatigue test purposes

Zero-memory non-linear (ZMNL) methods have long been a type of very useful tools in creating super-Gaussian random excitations for fatigue test. The major drawback of this method is that the magnitude distortion can be seen in both auto-power spectral density (ASD) and cross power-spectral density (CSD) of the excitation if the dynamic range of the target power spectral density (PSD) is large. To study the problem, we introduced Fourier series of a Gaussian signal into a cubic system, which is a common mathematical model shared by most of the ZMNL functions. We found that the cubic system produces a component leading to the distortion of both ASD and CSD. Meanwhile, if the shape of the reference ASD is flat in a frequency band, the distortion will not happen in the band. Based on this findings, a novel method is proposed in this article. It employs a pseudo reference PSD with flat ASDs to generate non-Gaussian signals in order to avoid the PSD distortions. Designed FIR filters are then applied to rescale the ASDs of the generated signals. After, iterative processes are introduced to recover the kurtoses of these filtered signals. The method is applied on a two-input and two-output numerical model, the feasibility and the availability of the method is verified. Finally, two control schemes based on the proposed pseudo reference PSD method are provided for a shaker table test. Test results show that both control schemes can eliminate the mismatch between the target PSD and the measured PSD of a shaker table.

A generalized collaborative functional link adaptive filter for nonlinear active noise control

This paper derives a collaborative control algorithm called generalized collaborative functional link adaptive filter (GCFLAF) for nonlinear active noise control (NANC). The algorithm adopts the collaborative scheme by handling the noise cancellation problem divisionally and parallelly, and working coordinately. It takes the characteristics of different nonlinear components into consideration and handles them separately. And a hierarchical adaption law is adopted in which linear filter is always prior to nonlinear filters no matter whether nonlinear distortions arise from the primary path as required by the filtering scenario. Thus the proposed scheme can tailor to different nonlinear characters arising from the primary path and can hierarchically adapt to the influences of the distinct nonlinearities. Particularly, since the zero-memory nonlinearity and memory nonlinearity are often unavoidable in NANC, it employs two shrinkage parameters to regulate the contribution of the different degrees of memory and zero-memory nonlinearity as required by the filtering scenario, aiming to achieve a better convergence performance and robustness to nonlinear distortions. Some numerical simulation results in the context of random noises as well as the real noise signals verify the improved convergence behavior of the presented architecture in NANC scenarios.

A Novel Gamma Distributed Random Variable (RV) Generation Method for Clutter Simulation with Non-Integral Shape Parameters.

Sea clutter simulation is a well-known research endeavour in radar detector analysis and design, and many approaches to it have been proposed in recent years, among which zero memory non-linear (ZMNL) and spherically invariant random process (SIRP) are the most two widely used methods for compound Gaussian distribution. However, the shape parameter of the compound Gaussian clutter model cannot be a non-integer nor non-semi-integer in the ZMNL method, and the computational complexity of the SIRP method is very high because of the complex non-linear operation. Although some improved methods have been proposed to solve the problem, the fitting degree of these methods is not high because of the introduction of Beta distribution. To overcome these disadvantages, a novel Gamma distributed random variable (RV) generation method for clutter simulation is proposed in this paper. In our method, Gamma RV with non-integral or non-semi-integral shape parameters is generated directly by multiplying an integral-shape-parameter Gamma RV with a Beta RV whose parameters are larger than 0.5, thus avoiding the deviation of simulation of Beta RV. A large number of simulation experimental results show that the proposed method not only can be used in the clutter simulation with a non-integer or non-semi-integer shape parameter value, but also has higher fitting degree than the existing methods.

Blind Fractionally Spaced Channel Equalization for Shallow Water PPM Digital Communications Links.

Underwater acoustic digital communications suffer from inter-symbol interference deriving from signal distortions caused by the channel propagation. Facing such kind of impairment becomes particularly challenging when dealing with shallow water scenarios characterized by short channel coherence time and large delay spread caused by time-varying multipath effects. Channel equalization operated on the received signal represents a crucial issue in order to mitigate the effect of inter-symbol interference and improve the link reliability. In this direction, this contribution presents a preliminary performance analysis of acoustic digital links adopting pulse position modulation in severe multipath scenarios. First, we show how the spectral redundancy offered by pulse position modulated signals can be fruitfully exploited when using fractional sampling at the receiver side, which is an interesting approach rarely addressed by the current literature. In this context, a novel blind equalization scheme is devised. Specifically, the equalizer is blindly designed according to a suitably modified Bussgang scheme in which the zero-memory nonlinearity is replaced by a M-memory nonlinearity, M being the pulse position modulation order. Numerical results not only confirm the feasibility of the technique described here, but also assess the quality of its performance. An extension to a very interesting complex case is also provided.

Robust transform domain signal processing for GNSS

Robust signal processing techniques are effective mitigation approaches that can enable Global Navigation Satellite System (GNSS) receiver operations even in the presence of strong interference. We extend robust GNSS signal processing to the case where interference admits a sparse representation in a transform domain (TD). More specifically, an orthonormal transformation is used to project the received GNSS samples into an appropriate TD. Robust signal processing strategies are then applied. The robust transform domain (RTD) cross-ambiguity function (CAF) is obtained by applying a zero-memory nonlinearity (ZMNL) to the TD samples, which, in turn, are used for the evaluation of the CAF. Different nonlinearities are analyzed and different implementations for the evaluation of the RTD CAF are proposed. The RTD approach is characterized from a theoretical point of view, with the usage of Monte Carlo simulations and through the processing of GNSS signals generated with a hardware simulator.

Optimal and efficient designs of Gaussian‐tailed non‐linearity in symmetric α ‐stable noise

This Letter proposes two methods for the Gaussian-tailed zero-memory non-linearity (GZMNL) design in symmetric α -stable noise. The optimal GZMNL is designed by maximising the efficacy via a derivative-free method. The efficient GZMNL is designed by polynomial fitting with the derived coefficients. Simulated results demonstrate that the GZMNL designs are nearly as optimal as the locally optimal detector, with an advantage of closed-form formulas.

In brief

PAGE 353 Two methods for Gaussian-tailed zero-memory nonlinearity design in symmetric noise have been advanced by researchers from China. Their Letter describes the use of a derivative-free method to maximise the efficacy and identify an optimal design. Simulations show the design performs almost as well as the locally optimal detector but with the added advantage of good practicability for applications. PAGE 300 Researchers from Queens University Belfast show how two cascaded Rotman lenses feeding a circular array do not require phase shifters to beam steer/shape and perform retrodirective action. The additional flexibility of beamwidth control was demonstrated by switching the interconnections between the cascaded lenses with experimental validation at 9.3 GHz. The efficacy of the objective function. PAGE 350 A team of researchers from China has proposed a reverse blocking insulated-gate bipolar transistor (IGBT) with a partially narrow mesa structure and trench-collectors. An introduced n-cs layer between two trench gates shields a forward blocking state from high electric fields. Numerical simulation results show that the proposed IGBT can use a 38% thinner n-drift region than the conventional counterpart. Circular patch array. PAGE 334 Smart devices, such as TVs and phones, benefit greatly from the integration of LEDs and embedded cameras, with these additions providing the opportunity to establish optical camera communication systems for Internet-of-Things applications. An experimental demonstration of such a system is detailed in a collaborative Letter by researchers from Spain and the Czech Republic. Proposed IGBT cross section. PAGE 333 A pair of researchers from Japan have realised the first E-band thulium-doped fiber amplifier (TDFA). This novel design includes a three-stage configuration fluoride-based TDF and two filters suppressing amplified spontaneous emission in the S-band. The TDFA exhibits a high signal gain achieved at the shortest wavelength in the gain band when compared with TDFA gains without filters. Bit error rate distance dependence. Stimulated emission spectra.

A Semi-Empirical Model Of Sea Clutter Based On Zero Memory Nonlinearity

Based on the computer simulation technology of zero memory nonlinearity (ZMNL), this paper combines with the backscattering features of sea clutter and conducts simulation for four typical backscattering coefficient empirical models of sea clutter, namely, Technology Service Corporation, Georgia Institutes of Technology, Hybrid Sea Clutter Model, and Naval Research Laboratory. According to the results, the signals of sea clutter simulated by zero memory nonlinearity are able to well satisfy the requirements of spectrum characteristics and amplitude distribution according to experiments on the fitting characteristics of simulated signals. After that, the above-mentioned sea clutter scattering coefficient fitting characteristics are applied to the finite difference time domain (FDTD) electromagnetic scattering equation of the numerical method, and the optimal recursive solution to the backward scattering area fitted by the above four semi-empirical models is proposed for the first time. Then, the method of discretizing the power spectrum equation of the differential form is combined with the FDTD discrete form. The numerical results of discrete simulation take the form of the random phase $\omega $ between 0 and $2\pi $ and then are converted into a basic iteration of one-dimensional rough length, thus realizing time domain power spectrum inversion. Finally, combined with the above conclusions, this paper proposes a new statistical model based on sea surface backscatter coefficient to invert the two-dimensional sea surface, that is, the three-parameter statistical model. At the same time, this paper further deduces the backscattering function of sea clutter based on random distribution and points out that the incident frequency and the rubbing angle are the main factors affecting the sea clutter scattering model. Based on this conclusion, this paper combines the sea clutter estimation model and the directional function model to simulate a two-dimensional random rough sea surface satisfying the physical laws of the ocean.

Complex signum non‐linearity for robust GNSS interference mitigation

The performance of a global navigation satellite system (GNSS) receiver can be significantly degraded in the presence of pulsed interference and jamming. In this study, the authors leverage on tools from robust statistics to enhance the receiver performance, with jamming signals treated as outliers to the nominal, interference-free model. Particularly, the signal samples are pre-processed with a zero-memory non-linearity (ZMNL), which limits the impact of pulsed inference in a principled way. A possible approach for the design of such ZMNL is provided by the M-estimator framework when the noise at the receiver input is modelled with a heavy-tailed distribution. This approach is adopted in this study and the complex signum non-linearity is analysed. This ZMNL is obtained by considering a complex Laplacian noise. This choice is discussed and analysed in the context of GNSS receivers under jamming. The impact of the complex signum non-linearity is theoretically analysed under nominal conditions, that is, in the absence of interference. Theoretical results are supported by Monte Carlo simulations. Real GNSS signals, collected in the presence of jamming, are used to demonstrate the advantages brought by the complex signum non-linearity. Theoretical and experimental results demonstrate the benefits of the proposed approach.

Locally optimal detector design in impulsive noise with unknown distribution

This paper designs the locally optimal detector (LOD) in additive white impulsive noise with unknown distribution. Unlike traditional LODs derived from a known or approximated noise probability density function (PDF), the LOD proposed in this paper is achieved by designing the zero-memory non-linearity (ZMNL) function based on real data. After the PDF estimation in a nonparametric way by a kernel method, the ZMNL function is designed as a piecewise differentiable function consisting of a polynomial function and inverse proportional functions. Then, we analyze the detection performance and develop the constant false alarm ratio technique. Simulation results show that the LOD design is near-optimal in α-stable noise and the optimal in real atmospheric data, compared with the maximum likelihood detector of α-stable distribution.

Generation of coherent lognormal clutter with specified power spectrum using ZMNL transform

The paper is concerned with the modeling and simulation of coherent lognormal clutter with specified power spectrum. A generation model is first developed by Zero Memory Nonlinearity (ZMNL) transform with white complex Gaussian clutter as input. Then based on the nonlinear relationship of coherent Gaussian random variable and coherent lognormal random variable in the model, the nonlinear relationship between the complex lognormal covariance sequence and Gaussian covariance sequence is derived. The proposed model and method have been verified with three examples, and the simulation results indicate that the scheme works very well. The constraints of the method are also discussed.

Myriad non‐linearity for GNSS robust signal processing

The robustness of standard correlation-based Global Navigation Satellite System (GNSS) signal processing can be significantly improved by pre-processing the input samples with a zero-memory non-linearity (ZMNL). A paradigm for the design of ZMNLs is provided by the M-estimator framework where heavy-tailed probability density functions (pdfs) are used to model the impairments affecting the input samples. The myriad non-linearity, obtained considering a Cauchy pdf, is analysed for the acquisition and tracking of GNSS signals in the presence of pulsed interference. The impact of the myriad non-linearity is theoretically characterised and Monte Carlo simulations are used to support theoretical findings. Finally, real GNSS signals collected in the presence of jamming are processed: the myriad non-linearity provides a significant performance improvement with respect to standard GNSS signal processing which is unable to acquire and track the samples affected by interference.

Near‐optimal detection with constant false alarm ratio in varying impulsive interference

As an important class of non-Gaussian statistic model, α -stable distribution has received much attention because of its generality to represent impulsive interference. Unfortunately, it does not have a closed-form probability density function (PDF) except for a few cases. For this reason, suboptimal zero-memory non-linearity (ZMNL) function has to be used as an approximation in designing locally optimal detector, such as classical Cauchy and Gaussian-tailed ZMNL (GZMNL). To enhance the performance of detectors, the authors first investigate the approximate PDFs for the symmetric α -stable. In particular, a simplified version of Cauchy–Gaussian mixture (CGM) model, called bi-parameter CGM (BCGM) model is detailed. This BCGM model has a concise closed-form, and hence is more tractable than the classical Gaussian mixture model and CGM model. Then based on the preset false alarm ratio (FAR), the test threshold is adaptively evaluated by using BCGM to maintain a constant FAR. The authors further devise an algebraic-tailed ZMNL (AZMNL) with a simplified form. Simulation results show that the detector with AZMNL outperforms the ones with classical Cauchy and GZMNL, and achieves near-optimal performance in varying impulsive interference.

Spatial Sign Cyclic-Feature Detection

This paper studies the impact of the spatial sign function on the cyclic features of communication signals and thereby on the performance of cyclic-feature detectors. It extends the existing results obtained for Gaussian signals and provides new insights into the interactions between the cyclic features of a cyclostationary signal sent through a spatial sign filter, which lead to the modified cyclic features at the output. We apply these results to analytically derive the performance of the spatial sign cyclic correlation (SSCC) detector, which filters a received signal by the spatial sign function prior to its processing using a cyclic-feature detector. These results are extended to variations of the spatial sign function and we further motivate their application to general zero-memory non-linear (ZMNL) functions.

Normalisation‐based receiver using BCGM approximation for α ‐stable noise channels

Aiming at signal detection in α-stable (SαS) noise, a receiver with a new zero-memory nonlinearity limiter (ZMNL) is designed. The proposed ZMNL serves to transform the SαS noise into a standard Gaussian one by using the bi-parameter Cauchy-Gaussian mixture (BCGM) model to approximate the SαS density. Simulation results indicate that the proposed receiver outperforms the conventional sub-optimal receivers for α > 1.5.

Natural versus Synthetic Stimuli for Estimating Receptive Field Models: A Comparison of Predictive Robustness

An ultimate goal of visual neuroscience is to understand the neural encoding of complex, everyday scenes. Yet most of our knowledge of neuronal receptive fields has come from studies using simple artificial stimuli (e.g., bars, gratings) that may fail to reveal the full nature of a neuron's actual response properties. Our goal was to compare the utility of artificial and natural stimuli for estimating receptive field (RF) models. Using extracellular recordings from simple type cells in cat A18, we acquired responses to three types of broadband stimulus ensembles: two widely used artificial patterns (white noise and short bars), and natural images. We used a primary dataset to estimate the spatiotemporal receptive field (STRF) with two hold-back datasets for regularization and validation. STRFs were estimated using an iterative regression algorithm with regularization and subsequently fit with a zero-memory nonlinearity. Each RF model (STRF and zero-memory nonlinearity) was then used in simulations to predict responses to the same stimulus type used to estimate it, as well as to other broadband stimuli and sinewave gratings. White noise stimuli often elicited poor responses leading to noisy RF estimates, while short bars and natural image stimuli were more successful in driving A18 neurons and producing clear RF estimates with strong predictive ability. Natural image-derived RF models were the most robust at predicting responses to other broadband stimulus ensembles that were not used in their estimation and also provided good predictions of tuning curves for sinewave gratings.

계산 복잡도가 줄어든 새로운 Bussgang 자력 등화 알고리듬

눈 모형이 열린 경우 간결하고 좋은 수렴 특성을 갖는 결정-지향 자력 등화 알고리듬이 자주 사용된다. 그러나 눈 모형이 닫힌 채널에서 결정-지향 알고리듬의 수렴은 보장되지 않는다. 이러한 문제를 해결하기 위하여 무기억 비선형 함수로 hyperbolic tangent 함수를 사용하는 수정된 Bussgang 알고리듬의 적용이 Filho 등에 의하여 제안되었다. 그러나 이 알고리듬의 적용은 hyperbolic tangent 함수 그리고 이의 미분에 대한 계산 및 채널의 변화에 따른 룩업 테이블을 위한 많은 메모리를 필요로 한다. 따라서 본 논문에서는 Filho 등이 제안한 알고리듬의 계산량 또는 하드웨어 복잡도를 줄이기 위하여 결정-지향 알고리듬을 위한 개선된 기법을 제안한다. 무기억 비선형 함수를 signum 함수로 설정하고, 이의 미분인 디락 델타 함수(Dirac delta function)를 협소한 사각 펄스로 근사화하여 결정-지향 알고리듬에 적용하면 Filho가 제안한 알고리듬의 수렴 및 정상 상태 성능은 유지하면서 계산 복잡도를 크게 줄일 수 있다. The decision-directed blind equalization algorithm is often used due to its simplicity and good convergence property when the eye pattern is open. However, in a channel where the eye pattern is closed, the decision-directed algorithm is not guaranteed to converge. Hence, a modified Bussgang-type algorithm using a hyperbolic tangent function for zero-memory nonlinear(ZNL) function has been proposed and applied to avoid this problem by Filho et al. But application of this algorithm includes the calculation of hyperbolic tangent function and its derivative or a look-up table which may need a large amount of memory due to channel variations. To reduce the computational and/or hardware complexity of Filho's algorithm, in this paper, an improved method for the decision-directed algorithm is proposed. In the proposed scheme, the ZNL function and its derivative are respectively set to be the original signum function and a narrow rectangular pulse which is an approximation of Dirac delta function. It is shown that the proposed scheme, when it is combined with decision-directed algorithm, reduces the computational complexity drastically while it retains the convergence and steady-state performance of the Filho's algorithm.

Self-critical detection of signals: narrowband and stochastic signal representations

The concept of self-critical locally optimum receivers (SCLORs) developed for lowpass signals are extended to the detection of known and stochastic signals in lowpass and narrowband noise. It is shown that the self-critical locally optimum detectors for stochastic signals implement a statistic which depends on an adaptive weighting factor and on the conventional zero-memory non-linearities for both known and stochastic signal detectors. The weighting factor, which depends on the probability density function of the prevailing noise, is responsible for the self-criticism of the detector. It is shown that self-critical detectors are most appropriate for impulsive noise environments.

Nonlinear Evolution of Gaussian ASE Noise in ZMNL Fiber

This paper investigates the evolution of kurtosis of the input Gaussian amplified spontaneous emission (ASE) noise in a nonlinear fiber with negligible dispersion. The nonlinear Schrodinger equation (NLSE) describing propagation in optical fibers is simplified such that the fiber represents a zero memory nonlinear (ZMNL) system, and this approximation allows the development of analytical formulas for the statistical moments of the output noise. It is possible to calculate moments of all integer orders and the explicit expressions for the first four moments are given. The investigations show that the ASE noise does not preserve its Gaussian character when Kerr nonlinearity is significant. This observation proves that the common assumption of the Gaussian output ASE is not necessarily valid. Numerical simulations are provided to support the derivation. Kurtosis deviating significantly from the value typical for Gaussian noise is also an indicator that BER calculation in the coherent systems based on the assumption that ASE is Gaussian is likely to be inaccurate.