Detection and parameter estimation of a transient signal usingorder statistics

Detection and parameter estimation of a transient signal in noise is a problem of many applications. It is characterized by the fact that some of the measurements consist of noise only. Modern statistical signal processing techniques are applied on a discrete version of the received data and are implemented by digital signal processing (DSP). In this correspondence, we show how order statistics (OS)-based signal processing, which is of a discrete nature, can be used for simultaneous detection and estimation of parameters (such as time of arrival and signal duration) of a sampled transient signal in white noise. We show that the resulting processors are more robust than the conventional processors, whereas their performance is about the same, at the cost of increased computational complexity     

Noise radar using random phase and frequency modulation

Pulse compression radar is used in a great number of applications. Excellent range resolution and high electronic counter-countermeasures performance is achieved by wideband long pulses, which spread out the transmitted energy in frequency and time. By using a random noise waveform, the range ambiguity is suppressed as well. In most applications, the random signal is transmitted directly from a noise-generating microwave source. A sine wave, which is phase or frequency modulated by random noise, is an alternative, and in this paper, the ambiguity function and the statistical characteristics of the correlation output for the latter configuration are further analyzed. Range resolution is then improved because the noise bandwidth of the modulated carrier is wider than that of the modulating signal, and the range sidelobes are also further suppressed. Random biphase modulation gives a 4-dB (/spl pi//sup 2//4) improvement, but much higher sidelobe suppression could be achieved using continuous phase/frequency modulation. Due to the randomness of the waveform, the output correlation integral is accompanied by a noise floor, which limits the possible sidelobe suppression as determined by the time-bandwidth product. In synthetic aperture radar (SAR) applications with distributed targets, this product should be large compared with the number of resolution elements inside the antenna main beam. The advantages of low range sidelobes and enhanced range resolution make frequency/phase-modulated noise radar attractive for many applications, including SAR mapping, surveillance, altimetry, and scatterometry. Computer algorithms for reference signal delay and compression are discussed as replacements for the classical delay line implementation.     

双稳系统中非周期随机共振的数值仿真

本文采用互相关方法研究了噪声和随机二进制信号同时激励双稳系统(施密特触发器和双势阱系统)时的输出响应，观察到非周期随机共振：利用双稳系统中的非周期随机共振效应，可以减小随机信号传输中的噪声水平，改善输出信号质量，这在数字通信领域具有十分重要的意义。     

The linear random process

A survey of the theory and applications of the class of random processes is presented. Topics discussed include the law of large numbers, covariance estimation, and the relationship of linear to normal processes. Various applications of the linear process to problems of communication theory are considered. These include prediction, signal extraction, and detection, using the linear process as a model for the signal or noise. Several exmples illustrating certain aspects of linear processes are given.     

Frequency or phase modulation with a noise carrier

The behavior of an ideal angle-modulation system in which the usual sinusoidal carrier has been replaced by a narrow-band Gaussian random noise or by an amplitude-limited narrow-band Gaussian random noise is studied. The use of a noise carrier results in an additive output noise (in addition to the usual output noise due to the noise in the channel, which is neglected here). It is assumed that the system is to be used to transmit a single-sideband multiplex signal consisting of many adjacent, narrow-band channels, and that the same output signal-to-noise ratio is desired in each of these channels. Subject to these assumptions, it turns out that the phase modulator need have a peak phase index of only about 1 radian. Further, this phase modulator should be driven by a band-pass modulating signal with an appropriately shaped spectrum, rather than by a base-band signal. Based on results of S. O. Rice, curves are presented relating the output signal-to-noise ratio, the required channel bandwidth, the bandwidth of the intelligence transmitted over the system, the required frequency translation of a baseband multiplex signal before modulation, and the peak phase index required of the modulator; all three bandwidths are normalized to the half-bandwidth of the noise carrier.     

Processing gain of surface-acoustic-wave convolver with noise-corrupted reference waveform

An analysis is given for the output signal/noise ratio of a convolver when both input waveforms are accompanied by noise. It is shown that a close approximation to the ideal matched-filter performance can be obtained if the signal/noise ratio at the reference input is only 10 dB. Experimental measurements support the analysis.     

Quantum-mechanical linear filtering of random signal sequences

The problem of estimating a member of a scalar random signal sequence with quantum-mechanical measurements is considered. The minimum variance linear estimator based on an optimal present quantum measurement and optimal linear processing of past measurements is found. When the average optimal measurement without postprocessing, for a fixed signal, is linear in the random signal and the signal sequence is pairwise Gaussian, the optimal processing separates: the optimal measurement is the same as the optimal measurement without regard to past data, and the past and present data are processed classically. The results are illustrated by considering the estimator of the real amplitude of a laser signal received in a single-mode cavity along with thermal noise; when the random signal sequence satisfies a linear recursion, the estimate can be computed recursively. For a one-step memory signal sequence it is shown that the optimal observable generally differs from the optimal observable disregarding the past; the optimal measurement can be computed recursively.     

噪声密度不敏感的随机采样椒盐噪声滤波算法

中值滤波系列算法在处理被不同密度椒盐噪声污染的细节图像和平坦图像时,降噪性能不一致。本文借鉴开关中值滤波和压缩感知的思想,提出了随机采样滤波算法去除椒盐噪声。算法以噪声检测为基础,将被椒盐噪声污染的图像分为疑似噪声像素和信号像素,随机采样仅对信号像素采样。然后,利用正交匹配追踪算法重构出被污染前的图像,替代了中值滤波对噪声像素的估计。由于随机采样滤波基于压缩感知理论,对稀疏信号的重构具有最少测量次数的条件,因此随机采样点的数量具有一定的浮动空间,表现为对噪声密度不敏感。以被不同噪声密度污染图像的纹理、平坦局部区域进行验证,实验表明,当噪声密度在一定范围内变化时,算法可以实现对噪声密度不敏感。在高密度噪声污染的情况下,相较于中值滤波系列算法,随机采样滤波算法具有更好的细节保留能力和滤波能力。对标准测试图像进行了全局滤波,不同噪声密度具有一致的滤波效果,与自适应滤波算法相比,随机采样滤波算法在处理包含密集边缘特征的区域时更具备优势。      

Single channel nonstationary stochastic signal separation using linear time-varying filters

Separability of signal mixtures given only one mixture observation is defined as the identification of the accuracy to which the signals can be separated. The paper shows that when signals are separated using the generalized Wiener filter, the degree of separability can be deduced from the signal structure. To identify this structure, the processes are represented on an general spectral domain, and a sufficient solution to the Wiener filter is obtained. The filter is composed of a term independent of the signal values, corresponding to regions in the spectral domain where the desired signal components are not distorted by interfering noise components, and a term dependent on the signal correlations, corresponding to the region where components overlap. An example of determining perfect separability of modulated random signals is given with application in radar and speech processing.     

Estimation for discrete Markov random fields observed in Gaussiannoise

A finite state Markov random field is observed in Gaussian noise. Changes of measures are defined under which all random variables of the signal are independent and uniformly distributed over the finite state space and all random variables of the observation are independent and N(0,1). The problem of estimating the most likely signal given the observations is treated in a related form by introducing probabilities over the possible signals     

Analysis of Random Step Frequency Radar and Comparison With Experiments

Linear stepped frequency radar is used in wide-band radar applications, such as airborne synthetic aperture radar (SAR), turntable inverse SAR, and ground penetration radar. The frequency is stepped linearly with a constant frequency change, and range cells are formed by fast Fourier transform processing. The covered bandwidth defines the range resolution, and the length of the frequency step restricts the nonambiguous range interval. A random choice of the transmitted frequencies suppresses the range ambiguity, improves covert detection, and reduces the signal interference between adjacent sensors. As a result of the random modulation, however, a noise component is added to the range/Doppler sidelobes. In this paper, relationships of random step frequency radar are compared with frequency-modulated continuous wave noise radar and the statistical characteristics of the ambiguity function and the sidelobe noise floor are analyzed. Algorithms are investigated, which reduce the sidelobes and the noise-floor contribution from strong dominating reflectors in the scene. Theoretical predictions are compared with Monte Carlo simulations and experimental data     

Array signal Processing in the known waveform and steering vector case

The amplitude estimation of a signal that is known only up to an unknown scaling factor, with interference and noise present, is of interest in several applications, including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications, a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. Two approaches, viz., the Capon and the maximum likelihood (ML) methods, are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise. We derive closed-form expressions for the expected values and mean-squared errors (MSEs) of the two estimators. A comparative study shows that the ML estimate is unbiased, whereas the Capon estimate is biased downwards for finite data sample lengths. We show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal-to-noise ratio (SNR) is high. Furthermore, we consider a more general scenario where the interference and noise are both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. An alternating least squares (ALS) method for parameter estimation is presented. We show that in most cases, the ALS method is superior to the model-mismatched ML (M/sup 3/L) method, which ignores the temporal correlation of the interference and noise.     

Electrical noise and RTS fluctuations in advanced CMOS devices

A brief overview of recent issues concerning the low frequency (LF) noise in modern CMOS devices is given. The approaches such as the carrier number and the Hooge mobility fluctuations used for the analysis of the noise sources are presented and illustrated through experimental results obtained on advanced CMOS generations. The use of the LF noise measurements as a characterization tool of large area MOS devices is also discussed. The main physical features of random telegraph signals (RTSs) observed in small area MOS transistors are reviewed. The impact of scaling on the LF noise and RTS fluctuations in CMOS silicon devices is also addressed. Experimental results obtained on 0.18 μm CMOS technologies are used to predicting the trends for the noise figure of foregoing CMOS technologies e.g. 0.1 μm and beyond. The formulation of the thermal noise underlying the LF fluctuations in MOSFETs is recalled for completeness.     

Minimax estimation of unknown deterministic signals in colorednoise

The estimation of a deterministic signal corrupted by random noise is considered. The strategy is to find a linear noncausal estimator which minimizes the maximum mean square error over an a priori set of signals. This signal set is specified in terms of frequency/energy constraints via the discrete Fourier transform. Exact filter expressions are given for the case of additive white noise. For the case of additive colored noise possessing a continuous power spectral density, a suboptimal filter is derived whose asymptotic performance is optimal. Asymptotic expressions for the minimax estimator error are developed for both cases. The minimax filter is applied to random data and is shown to solve asymptotically a certain worst-case Wiener filter problem     

Noise in amplifiers

In practically every type of research program in the physical sciences as well as in sophisticated engineering analyses, very small electrical signals must be measured and, in general, the limit of attainable precision and detectability is set by noise. This is true for the physicist and chemist performing nuclear magnetic resonance or spectroscopy experiments, for medical and biological researchers interested in evoked potentials, for geologists measuring small remanent magnetic fields in rock samples, for the metallurgist making Fermi surface measurements, and for the engineer performing vibration analysis and sensitive bridge measurements. These are only a few examples of applications in which noise plays a critical role in limiting measurement precision and signal detectability. This article discusses some of the inherent problems and describes techniques for improving signal-to-noise ratio.     

Fluctuations in noise level

Consideration is given to the equations for the r.m.s. fluctuations of noise power, when the noise is random, is stationary and follows a Gaussian amplitude distribution. The results are briefly compared with published measurements, most of which show much larger fluctuations, both for white noise and 1/f noise.     

Detection of non-Gaussian signals using integrated polyspectrum

We consider the problem of detecting an unknown, random, stationary, non-Gaussian signal in Gaussian noise of unknown correlation structure. The same framework applies if one desires to determine whether the given random signal is non-Gaussian. The most commonly used method for detection of random signals is the so-called energy detector, which cannot distinguish between Gaussian and non-Gaussian signals and requires the knowledge of the noise power. Recently, the use of bispectrum and/or trispectrum of the signal has been suggested for detection of non-Gaussian signals. The higher order spectra-based detectors do not require the knowledge of the noise statistics if the noise is Gaussian. In this paper, we suggest the use of an integrated polyspectrum (bispectrum of trispectrum) to improve computational efficiency of the detectors based on polyspectrum and to possibly further enhance their detection performance. We investigate conditions under which use of the integrated polyspectrum is appropriate. The detector structure is derived, acid its performance is evaluated via simulations and comparisons with several other existing approaches     

Subband coding systems incorporating quantizer models

A new method for dealing with the effects of quantization in a subband system is proposed. It uses the "gain plus additive noise" linear model for the Lloyd-Max quantizer. Based on this, it is demonstrated how, by an appropriate choice of synthesis filters, one can cancel all signal-dependent errors at the output of the system. The only remaining error is random in nature and not correlated with the input signal. We therefore have a tradeoff between the error being only random or having signal-dependent components as well (since the error variances in both cases are comparable). As a result of having only a random error, it is possible to reduce this error using, for example, a noise removal technique. The result is then extended to the case where the input is a multidimensional signal, and arbitrary sampling lattices are used, as well as to the QMF (alias cancellation) case. To demonstrate the validity of the proposed approach, two types of experiments on images are carried out: In a toy example, it is shown that using noise removal could be beneficial. For a more realistic coding scheme, however, it is demonstrated that even in the case when the model is no longer valid (when some of the subbands are discarded), the output error is still much less correlated with the input signal as opposed to the commonly used subband system, while visually, the reconstructed images look very similar.     

基于随机误差项的小波阈值去噪算法研究

针对振动环境下陀螺仪输出信号噪声干扰严重的问题,提出了一种用随机误差项改进小波阈值的去噪算法。通过对陀螺仪输出信号进行小波分解,根据频率成分将信号分解为多层;然后,对分解在各层的信号进行随机误差项辨识,进而利用随机误差项系数获取各层的噪声阈值;最后,利用获取的阈值进行小波去噪。改进阈值的提出,旨在解决Donoho全局阈值中因阈值选取过大或过小而产生的噪声误判或噪声残留问题,使噪声去除更彻底。通过实验分析,证明了本算法既能有效去除信号噪声,解决噪声残留的问题;又能保留输出的有效信号,解决噪声误判的问题。