Showing papers on "White noise published in 1990"

Near-far resistance of multiuser detectors in asynchronous channels

Abstract: We consider an asynchronous code-division multiple-access environment in which the receiver has knowledge of the signature waveforms of all the users. Under the assumption of white Gaussian background noise, we compare detectors by their worst case bit error rate in a low background noise near-far environment where the received energies of the users are unknown to the receiver and are not necessarily similar.

A family of suboptimum detectors for coherent multiuser communications

Abstract: Consideration is given to a class of suboptimum detectors for data transmitted asynchronously by K users employing direct-sequence spread-spectrum multiple access (DS/SSMA) on the additive white Gaussian noise (AWGN) channel. The general structure of these detectors consists of a bank of matched filters, a linear transformation that operates on the matched-filter outputs, and a set of threshold devices. The linear transformations are chosen to minimize either a mean-squared-error or a weighted-squared-error performance criterion. Each detector can be implemented using a tapped delay line. The number of computations performed per detected bit is linear in K in each case, and the resulting detectors are thus much simpler than the optimum detector. Under typical operating conditions, these detectors will perform much better than the conventional receiver and often nearly as well as the optimum detector. >

On the detection and classification of quadrature digital modulations in broad-band noise

Abstract: Optimal and suboptimal decision rules for the detection of constant-envelope quadrature digital modulations in broadband noise are derived and analyzed. The effect of various stochastic models for the carrier phase is examined in detail, while no epoch or frequency uncertainty is assumed. The delay-and-multiply type of detector is considered. A new binary/quadrature phase shift keying (BPSK/QPSK) classifier is compared to the more traditional ad hoc techniques of a square-law classifier and a phase-based classifier (weighting on the phase histogram). The new classifier is derived by approximating the likelihood-ratio functionals of phase-modulated digital signals in white Gaussian noise, hence is named the quasi-log-likelihood ratio (qLLR) rule. It is shown analytically that its performance is significantly better than that of intuitively designed phase-based rules or the conventional square-law classifier. >

A New Example of'Independence' and ' White Noise'

Abstract: We examine the notion of ‘free independence’ according to Voiculescu. This form of independence is used for defining ‘free white noise’ or ‘process with stationary and freely independent increments’. We prove a general limit theorem giving the combinatorics of infinitely freely divisible states and thus of free white noises with the help of ‘admissible’ partitions. We realize the free analogues of the Wiener process and of the Poisson process as processes on the full Fock space ofL2 (—).

The Generalized Cell Mapping Method in Nonlinear Random Vibration Based Upon Short-Time Gaussian Approximation

Abstract: This scheme provides a very efficient and accurate way of computing the one-step transition probability matrix of the previously developed generalized cell mapping (GCM) method in nonlinear random vibration

Estimation of instantaneous frequency using the discrete Wigner distribution

Abstract: Analytical expressions for the performance of the discrete Wigner distribution (DWD) in estimating the instantaneous frequency of linear frequency modulated signals in additive white noise are derived and verified using simulation. It is shown that the DWD peak provides an optimal estimate at high input signal-to-noise ratios. The applicability of these results to the general case of nonlinear FM signals is discussed.

Multiuser signal detection using sequential decoding

Abstract: The application of sequential decoding to the detection of data transmitted over the additive white Gaussian noise channel by K asynchronous transmitters using direct-sequence spread-spectrum multiple access (DS/SSMA) is considered. A modification of R.M. Fano's (1963) sequential-decoding metric, allowing the messages from a given user to be safely decoded if its E/sub b//N/sub 0/ exceeds -1.6 dB, is presented. Computer simulation is used to evaluate the performance of a sequential decoder that uses this metric in conjunction with the stack algorithm. In many circumstances, the sequential decoder achieves results comparable to those obtained using the much more complicated optimal receiver. >

Harmonic noise: Effect on bistable systems

Abstract: The coordinate of a white noise driven harmonic oscillator is used as a stochastic source term in bistable dynamics. This new kind of Gaussian colored noise gives rise to resonance phenomena due to a peak in the spectrum. We investigate its effect on linear and bistable systems. We derive a Markovian approximation for driven bistable oscillators and overdamped systems. In the resonance region computer simulations were carried out using an extension of Fox' algorithm procedure for colored noise. We find an increase of the transition rates in bistable systems as compared with the case of bistable systems driven by white and exponentially correlated noise.

On the capacity of a twisted-wire pair: Gaussian model

Abstract: The performance of a twisted-pair channel is assumed to be dominated by near-end crosstalk (NEXT) from other pairs in the same cable. Both intrabuilding local and central office loop channels can be modeled as NEXT-dominated channels. The capacity of this type of channel is found, using a Gaussian model. It is shown that the capacity is independent of the transmitted power spectral density. The results also indicate that present systems operate far below theoretical capacity. The capacity of a twisted-pair channel with both NEXT and white Gaussian noise present is also addressed. >

Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm

Abstract: A novel direction-of-arrival estimation algorithm is proposed that applies to wideband emitter signals. A sensor array with a translation invariance structure is assumed, and an extension of the ESPRIT algorithm for narrowband emitter signals is obtained. The emitter signals are modeled as the stationary output of a finite-dimensional linear system driven by white noise. The array response to a unit impulse from a given direction is represented as the impulse response of a linear system. The measured data from the sensor array can then be seen as the output of a multidimensional linear system driven by white noise sources and corrupted by additive noise. The emitter signals and the array output are characterized by the modes of the linear system. The ESPRIT algorithm is applied at the poles of the system, the power of the signals sharing the pole is captured, and the effect of noise is reduced. The algorithm requires no knowledge, storage, or search of the array manifold, as opposed to wideband extensions of the MUSIC algorithm. This results in a computationally efficient algorithm that is insensitive to array perturbations. Simulations are presented comparing the wideband and ESPRIT algorithm to the modal signal subspace method and the coherent signal subspace method. >

The performance of trellis-coded MDPSK with multiple symbol detection

Abstract: The idea of using a multiple (more than two) symbol observation interval to improve error probability performance is applied to differential detection of trellis-coded multiple phase-shift keying (MPSK) over an additive white Gaussian noise (AWGN) channels. An equivalent Euclidean distance measure per trellis branch is determined for this detection scheme. This is used to define an augmented (larger multiplicity) trellis code whose distance measure is the conventional squared Euclidean distance typical of conventional trellis-coded modulation on the AWGN. Such an augmented multiple trellis code is a convenient mathematical tool for simplifying the analysis. Results are obtained by a combination of analysis and computer simulation. It is shown that only a slight increase (e.g. one symbol) in the length of the observation interval will provide a significant improvement in bit error probability performance. >

Effect of spatial smoothing on the performance of MUSIC and the minimum-norm method

Abstract: The effect of using a spatially smoothed forward-backward covariance matrix on the performance of MUSIC and the minimum-norm method for estimating the direction of arrival of plane waves in white noise using a uniformly spaced linear array (ULA) is analysed. In particular, asymptotic results for the mean squared error in the estimates of the signal zeros and the direction of arrival are derived. It is shown that in general for subspace methods a forward-backward smoothing approach is preferable to a forward smoothing approach. An important outcome of this analysis is that for MUSIC, the error in the signal zeros is shown to exhibit a different trend compared to the error in the DOA estimates and this leads to difficulty in interpreting the spatial spectrum. For instance, when smoothing is used, the peaks in the spatial spectrum become sharper, giving the impression of higher resolution, whereas in reality the estimates of the DOA may in fact have deteriorated compared with the ones obtained using minimal or no smoothing. With regard to the minimum-norm method, the errors in the signal zeros exhibit the same trend as the DOA estimates so that no such problem is created. As to the relative comparison of the methods, it is shown that proper spatial smoothing enables the performance of the minimum-norm method to be made comparable to MUSIC.

Digital noise generator

Abstract: A digital noise generator is provided for producing white noise during a period when a digital telephone speech signal is absent. The digital noise generator comprises a pseudo-random bit sequence generator (43), an amplitude control circuit (51) and a PCM code-word-generating shift register (52), wherein a pseudo-random bit sequence is generated by the pseudo-random bit sequence generator (43), an amplitude code-word is generated by the amplitude control circuit (51), and a pseudo-random noise signal is generated and outputted by the PCM code-word-generating shift register (52) having regard to the pseudo-random bit sequence and the amplitude code-word.

Detection of non-Gaussian signals in non-Gaussian noise using the bispectrum

Abstract: The problem of detecting a non-Gaussian time series in the presence of additive Gaussian or non-Gaussian noise is cast into a classical hypothesis testing framework, using the sample bispectrum as the test statistic The power of the test is demonstrated as a function of signal-to-noise ratio, the degree of skewness of the signal, and processing parameters The results are compared to the power of a classical energy detection test It is concluded that the bispectrum can be used effectively to detect non-Gaussian signals in the presence of interfering noise and that it may perform better, depending on the degree of non-Gaussianity, than energy detection >

Adaptive deconvolution and identification of nonminimum phase FIR systems based on cumulants

Abstract: A novel adaptive deconvolution and system identification scheme is introduced for a linear, non-minimum-phase finite-impulse-response (FIR) system driven by non-Gaussian white noise. The adaptive scheme is based on approximating the FIR system by noncausal autoregressive (AR) models and using higher order cumulants of the system output. As such, it is a blind equalization (deconvolution) scheme. The set of updated AR parameters is obtained by using a gradient-type algorithm and by using higher order cumulants instead of time samples of the output signal. It is demonstrated by means of extensive simulations that the adaptive scheme works well for both stationary and nonstationary cases. As expected, it outperforms the autocorrelation-based gradient method for nonminimum-phase system identification and deconvolution. Performance comparisons to existing methods are given, using as figures of merit the probability of errors in the restored input sequence, computational complexity, and convergence rate. >

Response statistics of non-linear systems to combined deterministic and random excitations

Abstract: A second-order closure method is presented for determining the response of non-linear systems to random excitations. The excitation is taken to be the sum of a deterministic harmonic component and a random component. The latter may be white noise or harmonic with separable non-stationary random amplitude and phase. The method of multiple scales is used to determine the equations describing the modulation of the amplitude and phase. Neglecting the third-order central moments, we use these equations to determine the stationary mean and mean-square response. The effect of the system parameters on the response statistics is investigated. The presence of the nonlinearity causes multi-valued regions where more than one mean-square value of the response is possible. The local stability of the stationary mean and mean-square responses is analysed. Alternatively, assuming the random component of the response to be small compared with the mean response, we determine steady-state periodic responses to the deterministic part of the excitation. The effect of the random part of the excitation on the stable periodic responses is analysed as a perturbation and a closed-form expression for the mean-square response is obtained. Away from the transition zone separating stable and unstable periodic responses, the results of these two approaches are in good agreement. Comparisons of the results of these methods with that obtained by the method of equivalent linearization are presented.

Stochastic inversion for scaling geology

Abstract: SUMMARY We have examined acoustic, density resistivity, gamma-ray and neutron logs from a number of boreholes in both sedimentary and igneous sequences. We show that the power spectra of these geophysical variables obey a scaling law, that is, the power spectra are proportional to some power of the frequency. In general, the power spectra are approximately inversely proportional to the frequency. This suggests that frequency-dependent noise models are more appropriate for modelling the spatial variation of geophysical parameters than the widely assumed white noise (frequency-independent) model and should be incorporated into the inversion for these variables, through a priori parameter covariances. the covariance of a scaling variable is simply obtained from the power spectrum. It is independent of the absolute value of the lag, that is, there is no preferred length scale, but is dependent upon the sample length. We demonstrate the advantage of scaling noise covariances with the inversion of DC resistivity sounding data both with the exact covariance and with the approximate case of inverse proportionality. Adoption of a frequency-dependent noise model leads to a reduction in the a posteriori parameter variances and to solutions exhibiting a degree of smoothness commensurate with measured spatial variations of these parameters.

On the error probability of linearly modulated signals on Rayleigh frequency-flat fading channels

Abstract: Consideration is given to optimal detection of linearly modulated signals subject to multiplicative Rayleigh-distributed distortion and additive white Gaussian noise. For coherent detection, regenerated amplitude and phase references are employed at the receiver to compensate for amplitude and phase deviations from the correct values. A system model is formulated under the assumption of perfect symbol timing and in the absence of intersymbol interference, producing a final additive noise term, applied just before the detection, which contains the effects of the original additive and multiplicative distortions and of the errors in the phase and amplitude references. By determining the probability density function of this final noise term for arbitrary types of linear modulation, it is possible to perform exact calculations of error probabilities. >

Real‐Time System Identification of Degrading Structures

Abstract: On-line identification becomes an important issue when structures undergo nonlinear and time-dependent degrading behavior under large loads. In this paper, a real-time, time-domain system-identification technique is developed to identify time-varying system parameters for a multidegree-of-freedom degrading structure subjected to general dynamic loads, such as earthquakes. A system of second-order, linear, ordinary differential equations with time-varying system parameters is solved to generate the system response using the Newmark time-integration method. Gaussian white noise is added to the response and the results are used to simulate the measurements. Then, a least-square’s method is employed to estimate the system parameters in real time based on input data and corresponding response measurements with or without noise. Two numerical examples, a single-degree-of-freedom and a three-degree-of-freedom structure subjected to a simulated El Centro earthquake, are considered. The changes in structural stiffnesses for the example problems are identified. Encouraging results are obtained for both cases.

The split symbol moments SNR estimator in narrow-band channels

Abstract: The split symbol moments estimator (SSME) is an algorithm that is designed to estimate symbol signal-to-noise ratio (SNR) in the presence of additive white Gaussian noise (AWGN). The performance of the SSME algorithm in bandlimited channels is examined, and the effects of the resulting intersymbol interference (ISI) are quantified. All results obtained are in closed form and can be easily evaluated numerically for performance-prediction purposes. The results are also validated through digital simulations. >

Two-stage sigma-delta modulation

Abstract: An exact analysis of the nonlinear difference equation describing a discrete time two-stage sigma-delta quantizer with DC and sinusoidal inputs is presented. It is shown that for DC inputs, the binary quantizer error of the second quantizer, which appears at the output of the modulator as a second-order difference, is asymptotically white, uniformly distributed, and uncorrelated with the input. For sinusoidal inputs, this result holds with one exception: the autocorrelation, which is a sum of weighted Bessel functions, does not correspond to that of a white noise process. At large oversampling ratios, the autocorrelation is approximately white and hence the white additive noise model is a good approximation for evaluating the first- and second-order moments. It is found that for both a sinc/sup 3/ decoder filter and an ideal low-pass filter decoder, the average quantization noise power is inversely proportional to the fifth power of the oversampling ratio R for both types of inputs. This represents an improvement over the single-loop sigma-delta quantizer by a factor of R/sup 2/. Simulation results that agree with the theoretical analysis are presented. >

Motion compensated enhancement of noisy image sequences

Abstract: A motion compensated image sequence enhancement algorithm is presented. A combined segmentation and motion estimation algorithm is employed. A temporal or a spatiotemporal low-pass filter is then applied. Mean and median filters are presented as low-pass filters. The temporal filtering is performed over the motion path of each pixel, which is provided by the motion-estimation algorithm. The spatial filtering does not blur the boundaries of the moving objects because the boundary locations are provided by the segmentation algorithm. The performance of the combined algorithm is examined using computer-generated and real image sequences corrupted by additive white Gaussian noise. The algorithm performs very well in a very noisy environment. Mean filtering is more effective in the case of white Gaussian noise, and median filtering is more effective in the case of salt-and-pepper noise and burst noise. >

Analysis and Simulation of Nonlinear Stochastic Systems

Abstract: The paper discusses the transition from deterministic to stochastic dynamic systems under external or internal excitations. For this purpose, we apply harmonic excitation models with frequency fluctuations by white noise and derive invariant measures as stationary solutions of associated Fokker-Planck equations. In case of periodic system solutions, the measures degenerate to singular distributions. They become regular for increasing frequency fluctuations. In particular, they determine Lyapunov exponents of systems with generalized parameter fluctuations.

Spectro-temporal integration in signal detection.

Abstract: This paper is concerned with aspects of temporal integration and across‐frequency integration in signal detection. Previous experiments on the detection of brief broadband signals (clicks) in continuous broadband noise revealed efficient spectral integration. The extent to which this effect is restricted to a critical time window was investigated by manipulating the temporal relations among the signal components in different frequency regions. In a typical experiment, the signal consists of nine brief Gaussian‐shaped tone pulses, equally distributed at 1/3‐oct intervals, each with a spectral width of about 1/3 oct, and each equally detectable in white noise. In the synchronized condition (i.e., coinciding peaks of the nine Gaussian envelopes), the detection threshold is reached when the levels of the nine individual tone pulses are about 8 dB below their individual threshold levels (efficient spectral integration). When the signal is progressively desynchronized (i.e., noncoinciding peaks of the Gaussian envelopes), detection threshold is found to increase. This suggests that efficient spectral integration in signal detection is confined to a narrow time window, with a typical value of 30 ms. Similar experiments were performed with respect to the efficiency of temporal integration. For constant‐duration signals (100 ms), the detection threshold is found to increase when progressively widening signal bandwidth. The data indicate that the efficient temporal integration in signal detection is confined to a narrow frequency window, which, not surprisingly, corresponds to the critical bandwidth.

Changes in voice level caused by several forms of altered feedback in fluent speakers and stutterers.

Abstract: Speakers change the level of their voice when they listen to noise or hear their own speech amplified: When noise level is increased the voice becomes louder, whilst the response to speech amplification is a reduction of voice level. The question posed here is whether, when the level of various sounds concurrent with vocalisation is raised, the direction of the vocal level response is like that to the speaker's speech or like that to noise. Voice level was measured in response to speech, white noise, delayed auditory feedback, frequency-shifted speech, and noise created by an "Edinburgh masker". Selection of these sounds was governed by the role they have played in the explanation and treatment of stuttering. Fluent speakers and stutterers increased voice level when played delayed auditory feedback, the Edinburgh masker, or white noise; they reduced the level slightly in the remaining conditions. These results are used to assess auditory feedback monitoring accounts of the speech behavior of fluent speakers and stutterers, and some implications for the treatment of stuttering are pointed out.

Noise-Induced Global Asymptotic Stability

Abstract: We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the It6 or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching between a single, globally stable steady state and multiple, locally stable steady states. With additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter. However, parametric noise causes a noise-amplitude-dependent shift (postponement) in the parameter value at which the switching occurs. It is shown analytically that the density converges to a Dirac delta function when the solution of the Fokker-Planck equation is no longer normalizable.

A State-Space Approach to the Synthesis of Random Vertical and Crosslevel Rail Irregularities

Abstract: The work described in this paper provides a convenient method to generate random vertical and crosslevel irregularities when their time histories are required as inputs to a numerical simulation. The solution begins with mathematical models of vertical and crosslevel power spectral densities (PSDs) representing PSDs of track classes 4, 5, and 6. The method implements state-space models of shape filters whose frequency response magnitude squared matches the desired PSDs. The shape filters give time histories possessing the proper spectral content when driven by white noise inputs. The state equations are solved directly under the assumption that the white noise inputs are constant between time steps. Thus, the state transition matrix and the forcing matrix are obtained in closed form