Convergence bounds of an SMI/Gram-Schmidt canceler in colored noise

The performance of the sampled matrix inversion (SMI) adaptive algorithm in colored noise is investigated using the Gram-Schmidt (GS) canceler as an analysis tool. Lower and upper bounds of average convergence are derived, indicating that average convergence slows as the input time samples become correlated. When the input samples are uncorrelated, the fastest SMI algorithm convergence occurs. When the input samples are correlated then the convergence bounds depend on the number of channels N, the number of samples per channels K , and the eigenvalues associated with K×K correlation matrix of the samples in a given channel. This matrix is assumed identical for all channels     

Properties of Low Precision Analog-to-Digital Converters

The problem of quantization and saturation noise introduced by the process of analog-to-digital conversion is addressed. Analog-to-digital converters (ADC) with even versus odd numbers of output states are compared. Expressions are derived and evaluated which yield the signal-to-noise ratio and the gain versus signal level input when the input signal has an assumed Gaussian probability density. The results presented should have application in all fields in which digital signal processing is performed.     

Postfiltering in Digital Beamformers

Assuming a sinusoidal signal superimposed on a narrow-band Gaussian noise as the input to a receiving array, the output power and signal-to-noise ratio of a digital beamformer with postfiltering were formulated so that subsequent calculations could be made without an analysis in the frequency domain. The formulation utilized the quantizer functions previously given by the author and certain spectral power distribution factors originally attributed to Davenport but more rigorously derived and discussed in the present work. A numerical study based on this formulation for a DIMUS array in a correlated noise field reveals that except for certain rare circumstances, postfiltering generally improves the output SNR or array gain. It is demonstrated that the amount of postfiltering gain not only varies with array input SNR but also depends strongly upon the spacing-to-wavelength ratio, and its meaningful interpretation can only be made in conjunction with both the clipping and noise correlation losses. In particular, balancing postfiltering gain against the two losses suggests that receiving arrays with element spacings smaller than one-half of the operating wavelength may be used to the advantage of system design under certain conditions.     

Detection Probabilities for Log-Normally Distributed Signals

The amplitude and power of a large family of radio signals are observed to have log-normal probability density functions. Among these are signals propagated through random inhomogeneous media, a notable example being low frequency atmospheric radio noise. Of greater importance are certain radar targets that have been observed to have essentially log-normal density functions. Both ships and space vehicles may fall into this category. Curves of probability of detection vs. signal-to-noise ratio for the case of log-normal signals in Gaussian noise have been computed and are presented in this paper. The curves apply for square-law detection with varying degrees of postdetection linear integration. Both fully correlated and completely uncorrelated fluctuating signals are considered. It is shown that for log-normal signal distributions having large variances, the probability of detection differs significantly from that obtained using curves based on an assumed Rayleigh signal distribution.     

Background noise suppression for signal enhancement by noveltyfiltering

The enhancement of weak signals in the presence of background and channel noise is necessary to design a robust automatic signal detection and recognition system. The autoassociative property of neural networks can be used to map the identifying characteristics of input source waveforms or their spectra. This paper is directed at the exploitation of such neural network properties for novelty filtering that improves the detection probability of weak signals by learning and subsequent subtraction of noise background from the input waveform. A neural-network-based preprocessor that learns to selectively filter out the background noise without significantly affecting the signal will be highly useful in solving practical signal enhancement problems. An analytical basis is established for the operation of neural-network-based novelty filters that enhance the signal detectability in the presence of noise background and channel noise     

Robust detection of small stochastic signals

We consider the problem of detecting a stochastic signal in white not-necessarily-Gaussian noise, using vector valued observations. The locally optimal detector is presented and its performance evaluated. The least-favorable signal spectrum and noise density (over specified classes) are found, and it is shown that the detector using these least-favorable assumptions is minimax robust. The class of spectra is that of any stochastic signal of specified power whose spectrum can be bounded from above and from below by two given positive functions. The class of densities is the ε-contamination model. We present examples of the performance achievable with the robust detector in one of these the spectral uncertainty class corresponds to the unknown Doppler shift of a radar return signal. It is demonstrated that the standard matched-filter's performance degradation with increasing Doppler shift can be avoided almost entirely through use of the robust processor     

The Output Pdf of a Polarity Coincidence Correlation Detector

A general expression is derived for the probability density function of the output of a cross correlator, the inputs of which are assumed to consist of clipped sine waves of similar frequency plus uncorrelated, stationary Gaussian noise. The correlator output is shown to be a piecewise linear function of the random phase difference between the two input processes; hence, the density function for the correlator output is obtained by a relatively simple transformationfrom the probability density function of the random phase difference.     

Testing the Independence of Nonhomogeneous Rayleigh Clutter

Two attractive real-time implementation tests are presented that discriminate between correlated and uncorrelated clutter. A clutter model is assumed in which the envelope distribution within a cell is Rayleigh, but the mean clutter level fluctuates from cell to cell. Both the tests utilize observations made in pairs on two clutter envelopes corresponding to two consecutive azimuth sweeps. The results are applicable to real-time testing of the effectiveness of various decorrelation techniques employed by radar systems.     

Angle-of-Arrival Estimation Using an Adaptive Antenna Array

A direction-finding technique is presented that is capable of simultaneously estimating the arrival angles of multiple signals. Pulsed as well as continuous signals can be handled with the signal form only approximately specified. An adaptive antenna array is used as a processing device in the estimation technique. The effect of input signal and feedback loop parameters upon estimate bias is discussed.     

Spectral Moment Estimates from Correlated Pulse Pairs

Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.     

Estimation of Phase Difference in Multiple Sensor Arrays

The likelihood functional for estimating parameter differences in coherent multiple-sensor receivers is developed assuming Gaussian statistics on both signal and noise. The development relies on a matrix formulation and a subsequent factorization of a parameter constraint matrix from the signal matrix. A two-antenna phase-difference radar example is presented for cases of uncorrelated and antenna-correlated noise.     

Generation of Non-Gaussian Random Vibration Excitation Signal for Reliability Enhancement Test

During environment testing, the time histories of some dynamic environments follow non-Gaussian distribution. It is always assumed that the random vibration simulated follows Gaussian distribution, because the traditional digital random vibration control system can only supply the random vibration excitation signal of Gaussian. Yo simulate the real environment of product, a method is developed in this paper that can generate non-Gaussian random signal with specified power spectrum density （PSD）, skewness and kurtosis by shot noise. In this way, non-Gaussian random vibration can be produced on traditional electrodynamic shaker. It solves the problems of spectral valley and energy shortage in low frequency on omni-axis shaker. At last, the wavelet is used to analyze the non-Gaussian signal     

Detectors for Multiomial Input

The binary detection problem is considered. Under an arbitrary noise environment, the input sample space can be transformed into a multinomial vector. Based on observations of this vector, the Neyman-Pearson optimal detector is developed for a known signal. When the signal strength is unknown, the likelihood ratio principle is followed to obtain consistent tests which use the Pearson's chisquare statistic. The resulting detectors are compared to others in terms of asymptotic relative efficiency under some actual noise distributions.     

基于方差的相关输入变量重要性测度分析新方法

为了清晰地掌握相关输入变量情况下响应量方差的来源,非常有必要将基于方差的重要性测度( VBIM)分离为相关部分和独立部分.为此,在二阶非线性回归的基础上,提出了一种适用于非线性响应量的相关变量重要性分析的新方法.一个输入变量对响应量方差的相关贡献由该变量与每一个剩余变量两两相关的贡献分量组成,所以又进一步提出了一种概念...     

Signal Interference and Improvement of Signal-to-Noise Ratios in a Half-Wave Linear Detector

Signal interference in the half-wave linear detector has been studied only for amplitude modulation. In this paper, we treat signal interference for both an amplitude-and an angle-modulation communication system. The input to the half-wave linear detector is assumed to be composed of an amplitude-modulated wave, an angle-modulated wave, and narrow-band Gaussian noise. In particular, when strongweak relations exist in the input processes, a detailed analysis for the output component is presented to clarify some useful output properties.     

Detection of Known Signals in Nonstationary Noise

The basic design of a nonlinear, time-invariant filter is postulated for detecting signal pulses of known shape imbedded in nonstationary noise. The noise is a sample function of a Gaussian random process whose statistics are approximately constant during the length of a signal pulse. The parameters of the filter are optimized to maximize the output signal-to-noise ratio (SNR). The resulting nonlinear filter has the interesting property of approximating the performance of an adaptive filter in that it weights each frequency band of each input pulse by a factor that depends on the instantaneous noise power spectrum present at that time. The SNR at the output of the nonlinear filter is compared to that at the output of a matched filter. The relative performance of the nonlinear system is good when the signal pulses have large time-bandwidth products and the instantaneous noise power spectrum is colored in the signal pass band.     

Prediction of noise radiation from basic configurations of landing gears by means of computational aeroacoustics

Noise radiation from aircraft during the takeoff and landing has become a major issue for inhabitants living in the vicinity of airports and thus for regulation authorities and aircraft developers. However the numerical simulation of aeroacoustic noise, especially for complex geometries like a landing gear, remains one of the most difficult challenges in aeroacoustics. The present study, aiming at predicting noise radiation from basic geometries as well as the noise radiation of a simplified landing gear, employs a hybrid approach that combines a CFD simulation with the decoupled computational aeroacoustics (CAA) simulation. Flow-induced noise is assumed to originate from turbulence. Reynolds-averaged Navier–Stokes equations with different closure approaches can be employed to gain the required turbulent quantities. Subsequently, quantities as the mean flow velocities, pressure, density, turbulent kinetic energy and dissipation rate of the CFD simulation are the starting point for the generation of the transient acoustic sources by the stochastic noise generation and radiation (SNGR) method. It is assumed that the acoustic phenomena do not provide feedback to the mean flow field and turbulence and thus a recalculation of the flow field is not required. Since the propagation of sound is insignificantly influenced by turbulent and viscous effects, it can be described by the Euler equations in the near field. The CAA simulation is extended with a Ffowcs Williams Hawkings (FWH) module that calculates the noise levels in the far field upon integrating the surface source terms on a porous FWH surface within the CAA domain. The results of the simulations are compared with experimental data, obtained by measurements in an acoustic wind tunnel.     

Phase Analysis in Multiple-Sensor Receivers with High Signal-to-Noise Ratio

The ideal phase detector characteristic is analyzed for estimating the phase difference between two stochastic input signals. This can essentially be described as a correlation process formed by multiplying the two input signals and extracting the phase. High signal-to-noise ratio conditions are assumed to linearize the system with respect to the noise. The effects of the nonlinearity on the signal are handled in terms of a series expansion and by using low-pass filtering on the receiver output. The mean square error of the system is calculated for some typical parameters.     

Analysis of a Class of Nonlinear Sampled-Data Systems with a Gaussian Input Signal

The problem treated here is the analysis of a class of nonlinear sampled-data systems with a Gaussian input signal. The nonlinear element is a symmetrical limiter (memoryless device) that feeds the linear element. Preceding the limiter is a sampler and zero-order hold unit for data reconstruction. The analysis is predicated on finding an equivalent gain for the nonlinear element such that the mean-square error is a minimum. The nonlinearity is thus replaced by a linear component and the system is then analyzed by conventional techniques. It is also shown that for appropriate sampling rates the sampled-data system is equivalent to a continuous system due to the action of the sampler-hold combination. All calculations pertaining to the limiter input signal require the use of a transfer function that is interior to the feedback loop. However, in developing this transfer function, the overall system is considered so that the system output may be evaluated after the value of equivalent gain has been found.     

Data quantization effects in CFAR signal detection

In this paper, we investigate data quantization effects in constant false alarm rate (CFAR) signal detection. Exponential distribution for the input data and uniform quantization are assumed for the CFAR detector analysis. Such assumptions are valid in the case of radar for a Swerling I target in Gaussian clutter plus noise and a receiver with analog square-law detection followed by analog-to-digital (A/D) conversion. False alarm and detection probabilities of the cell averaging (CA) and order statistic (OS) CFAR detectors operating on quantized observations are analytically determined. In homogeneous backgrounds with 15 dB clutter power fluctuations, we show analytically that a 12-bit uniform quantizer is sufficient to achieve false alarm rate invariance. Detector performance characteristics in nonhomogeneous backgrounds, due to regions of clutter power transitions and multiple interfering targets, are also presented and detailed comparisons are given