Impulsive Noise Model Research Articles

Analysis and modeling of impulsive noise in broad-band powerline communications

Contrary to many other communication channels, the powerline channel does not represent an additive white Gaussian noise environment. In the frequency range from several hundred kilohertz up to 20 MHz, it is mostly dominated by narrow-band interference and impulsive noise. In particular, the impulsive noise introduces significant time variance into the powerline channel. Spectral analysis and time-domain analysis of impulsive noise give some figures of the power spectral density as well as distributions of amplitude, impulse width, and "interarrival" times in typical powerline scenarios. Furthermore, the impulse rate and the disturbance ratio of the scenarios are examined. Finally, a statistical model of the time behavior of random impulsive noise based on a partitioned Markov chain is developed, which is suitable for implementation in computer-based communication system simulations.

Two-dimensional impulse noise model for digitalsubscriber loopenvironment

The wideband impulse noise modelling over the subscriber loop recently conducted over the German telephone network is extended to the narrowband scenario. The narrowband impulse noise is resolved into in-phase and quadrature components and each component modelled as a generalised error distribution. Simulation is used to verify the theory.

Error performance evaluation of the MDPSK-DMT systems in DSL with AWGN and impulse noise

A new digital multitone (DMT)-digital subscriber loop (DSL) system with MDPSK modulation for each subcarrier is proposed in this paper. The error performance of the system in the presence of additive white Gaussian noise (AWGN) and impulse noise (IN) is investigated. The bandlimitation effect of the DSL on the DMT signal is studied based on a discrete model of channel impulse response. A previously proposed impulse noise model, in which IN is viewed as the product of a Bernoulli process and a Gaussian process is adopted. Impairments after Fourier transform at the receiver end are analysed. A closed-form expression for the symbol error rate (SER) of the MDPSK-DMT system is derived. Based on the impulse noise generator proposed in this paper, system simulations are also conducted to verify the performance analysis.

Modelling and analysis of error probability performance for DMT-based DSL system with impulse noise and crosstalk

The transmission of high-speed data over Digital Subscriber Loop (DSL) can be accomplished through the use of Discrete Multitone (DMT). Due to the frequency dependent channel distortion and crosstalk, there is a need to determine the performance of DMT-based DSL for system optimization purpose. This paper presents an error probability analysis for the DMT-based DSL in presence of additive white Gaussian noise (AWGN), impulse noise (IN) and crosstalk. The bandlimitation effect of the DSL on the DMT signal is studied based on the discrete impulse response of the channel. Impairments after Fourier transformation at the receiver end are analysed. A recently proposed impulse noise model, in which IN is viewed as the product of a Bernoulli process and a Gaussian process is adopted. Crosstalk noise is assumed to be Gaussian distributed with its variance determined from the frequency response of the DSL and empirically obtained coupling constants. A closed-form expression for the error probability performance of the DMT system with Quadrature Amplitude Modulation (QAM) modulation is derived.

Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution

There has been great interest in symmetric /spl alpha/-stable distributions which have proved to be very good models for impulsive noise. However, most of the classical non-Gaussian receiver design techniques cannot be extended to the symmetric /spl alpha/-stable noise case since these techniques require an explicit compact analytical form for the probability density function (PDF) of the noise distribution which /spl alpha/-stable distributions do not possess. A new analytical representation has been suggested for the symmetric /spl alpha/-stable PDF which is based on scale mixtures of Gaussians. Based on this new analytical representation, this paper introduces a novel near-optimal receiver for the detection of signals in symmetric /spl alpha/-stable noise. The performance of the new receiver is very close to the locally optimum receiver and is significantly better than the performance of previously suggested sub-optimum receivers. The new technique has important potential in radar, sonar, and other applications.

Effect of interference of impulse noise induced by clipping on BER of M‐QAM signal in analog/digital hybrid optical transmission systems

The bit error rate (BER) of the M-QAM signal in analog/digital hybrid optical transmission (hybrid transmission) shows a floor-like feature due to impulse noise induced by clipping the subcarrier multiplexed signal at the laser threshold. This paper proposes a new BER analysis model, which is modified from our previous one based on Middleton's class A impulse noise model, and compares analytical results with experimental data. The analytical results agree particularly well with the experimental data for small optical modulation indexes (OMI) of the M-QAM signal; consequently, these results can be applied to estimating the bit error rate of the digital channel in hybrid transmission. There is also a tendency for the analysis results to diverge more greatly from the experimental data as the OMIs of the M-QAM signal increase. We also discuss the reasons for this divergence. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(8): 1–8, 1998

Least Lp-norm impulsive noise cancellation with polynomial filters

It is a common experience in signal processing that impulsive noise observed in various natural environments cannot be described with the Gaussian distribution. Recently, a heavy tailed distribution namely the α- stable distribution has become a popular model for impulsive noise since it agrees very well with empirical data and is also theoretically justified with the generalised central limit theorem. Although, it is a generalisation of the Gaussian distribution and shares important properties with it, the non-Gaussian α-stable distribution differs from the Gaussian distribution in many ways, the most notable of which is the lack of finite second-order statistics. Therefore, the classical techniques based on linear least-squares estimation perform very poorly in impulsive noise elimination. In this paper, motivated by some properties of the α-stable distribution, new techniques based on linear and nonlinear least l p -norm estimation are introduced and several simulation results are presented which show that least l p -norm estimation with a Volterra-type prediction filter performs significantly better than the conventional linear techniques such as linear least-squares estimation and than nonlinear least-squares estimation. A new measure for signal distortion in impulsive noise, namely fractional order signal-to-noise ratio (FSNR) is also introduced to quantify the performance of various impulsive noise cancellation algorithms.

Symbol-to-symbol performance evaluation of densely populated asynchronous DS-CDMA in Gaussian and impulsive noise environments: a Fourier-Bessel series approach

This letter considers the well-established Poisson impulse noise model with a random amplitude area distributed according to the /spl epsiv/-mixture Gaussian probability density function. This model is used to develop fast converging truncated Fourier-Bessel (FB) series expressions, required to evaluate accurately the performance of a binary phase-shift keying (BPSK) modulation scheme as part of a densely populated asynchronous direct-sequence code-division multiple-access (A/DS-CDMA) configuration. The average error probability of the correlation receiver is easily and quickly obtained here, even for the case of a large number of users (K=100), unlike earlier attempts in this area in which the use of other analysis approaches (e.g., closed-form approach or Taylor series expansion approach) could not exceed the limit of K=2 and K=24 in an /spl epsiv/-mixture impulsive and/or Gaussian noise environment, respectively.

A new efficient approach for the removal of impulse noise from highly corrupted images

A new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. As part of this framework, several algorithms are examined, each of which is applicable to fixed and random-valued impulse noise models. First, a simple two-state approach is described in which the algorithm switches between the output of an identity filter and a rank-ordered mean (ROM) filter. The technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter. For a small additional cost in memory, this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and ROM filter in which the weighting coefficients can be optimized using image training data. Extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40% impulse noise corruption. Moreover, the method can effectively restore images corrupted with Gaussian noise and mixed Gaussian and impulse noise. Finally, the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise.

Analysis of the effect of impulse noise on multicarrier and single carrier QAM systems

The paper first shows the equivalence of the Bernoulli-Gaussian impulse noise model in the discrete time domain to the continuous-time model of Poisson arriving delta functions with random area distributed according to the power Rayleigh probability density function. This equivalence is then used to develop a closed form expression for the probability of error for single carrier QAM that is easily evaluated. Furthermore, the performance of multicarrier modulation (MCM) is also analyzed using the same impulse noise model and it is shown that in most cases MCM performs better than single carrier systems, specifically when the probability of an impulse is not too high and the impulse power is moderate.

Performance of optimum and suboptimum receivers in the presence of impulsive noise modeled as an alpha-stable process

Impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration. An empirical justification for this procedure is that it generally causes the signal-to-noise ratio to increase. Recently, very accurate models of impulsive noise were presented, based on the theory of symmetric /spl alpha/-stable probability density functions. We examine the performance of optimum receivers, designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric /spl alpha/-stable process, and compare it against the performance of several suboptimum receivers. As a measure of receiver performance, we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive Monte-Carlo simulation. >

Impact of noise and nonlinear distortion due to clipping on the BER performance of a 64-QAM signal in hybrid AM-VSB/QAM optical fiber transmission system

Experimental BER measurements of a 64-QAM signal in a hybrid AM-VSB/QAM optical fiber transmission system are shown to be in good agreement with a corrected and reinterpreted theory of impulsive and Gaussian noise based on Middleton's class B impulsive noise model. Fiber dispersion induced distortion of the chirped laser output is also shown to adversely affect the QAM signal.

Weak-Signal DPSK Detection in Narrow-Band Impulsive Noise

The weak-signal receiver for binary differential phase-shift keying (DPSK) in additive noise is derived, and its performance in terms of the error probability in the most general narrow-band impulsive (nonGaussian) noise model, Middleton's class A noise, is analyzed.

The Detection of Signals in Impulsive Noise Modeled as a Mixture Process

A first-order mixture noise density is considered as a model for impulsive noise channels. It consists of a mixture of a small variance, probably Gaussian, background noise pdf and a large variance impulsive pdf. Optimal nonlinear detector structures for known discretetime signals in such noise are derived. Their large-sample performance compared to that of a linear detector is studied using asymptotic relative efficiency.

Analysis and Digital Realization of a Pseudorandom Gaussian and Impulsive Noise Source

This paper presents results on the analysis and digital hardware realization of a non-Gaussian impulse noise source which can be used to model the impulsive noise present in wide-band communications systems. The impulse noise appearing in practical systems is characterized by bursts of much higher amplitudes than would be predicted by a normal- or Gaussian-distribution law. A need exists for a better characterization of this non-Gaussian impulsive noise as well as actual noise generators which can be used for evaluation of present and future communications equipment under realistic system-operating conditions. The impulse noise model and the realization of the noise generator described in this paper are capable of producing Gaussian background noise, lognormal impulsive noise, and burst timing to set prescribed starting and ending times of the bursts and impulse density within each of the burst periods. The techniques used in this paper are based on first generating a basic pseudorandom binary sequence (PRBS) and then from this deriving the Gaussian background noise by adding samples from the PRBS generator. The lognormal noise is then derived from the same sequence by using an incremental exponential generator. The burst timing signals which realize an approximate Poisson distribution are obtained by observing the occurrences of specific subsequences from the PRBS generator.

Ignition Noise Measurements in the VHF/UHF Bands

In the operational use of mobile communication terminals, it may often be unavoidable to park them in a location where they would be subject to ignition noise due to local traffic. This type of noise causes errors in digital systems. Since it is impossible to define a general model for impulsive noise, one must measure the necessary statistical paramaters to be used for calculating its effect on a communication link. Although these parameters vary for different types of links, peak amplitude distribution, time distribution, and duration of impulses at various amplitude levels should be known. In this paper noise amplitude distribution (NAD) measurements carried out on the VHF/UHF bands for ignition noise are explained. The information derived from the NAD is the peak amplitude distribution of the impulses; in addition, the average repetition frequency of the impulses is also obtained. An analytical expression is found for the probability density function of the idealized NAD.

Correction to "A Model of HF Impulsive Atmospheric Noise"

Correction to "A Model of HF Impulsive Atmospheric Noise"

A Study on Impulse Noise and Its Models

This article gives an overview of impulse noise and its models, and points out some important and interesting facts about the study of impulse noise which are sometimes overlooked or not well understood. We discuss the different impulse noise models in the literature, focusing on their similarities and differences when applied in communications systems. The impulse noise models discussed are memoryless (Middleton Class A, Bernoulli-Gaussian and Symmetric alpha-stable), and with memory (Markov-Middleton and Markov-Gaussian). We then go further to give performance comparisons in terms of bit error rates for some of the variants of impulse noise models. We also compare the bit error rate performance of single-carrier (SC) and multi-carrier (MC) communications systems operating under impulse noise. It can be seen that MC is not always better than SC under impulse noise. Lastly, the known impulse noise mitigation schemes (clipping/nulling using thresholds, iterative based and error control coding methods) are discussed.

Amplitude Distributions of Telephone Channel Noise and a Model for Impulse Noise

The noise waveforms found on voice bandwidth telephone channels are generally recognized to be non-gaussian in their amplitude distribution. This paper presents data which suggests that a simple exponential is a good function to describe amplitude densities in the extreme tails. A comprehenisve model of impulse noise as viewed on trunk groups is then presented. The model relates the distributions of impulse noise levels and impulse noise counts.

Error Probabilities Due to Additive Combinations of Gaussian and Impulsive Noise

In this paper a Poisson impulse noise model is utilized to calculate error probability characteristics of a matched filter receiver operating in an additive combination of impulsive and Gaussian noise. Comparisons of the theoretical predictions are made with experimental data obtained from a simulated communication system. The results indicate that only a small amount of Gaussian noise power has a considerable effect on the probability of error for small signal-to-noise ratios (SNRs). Also, it is found that each noise component may be looked upon as acting separately, the Gaussian noise component dominating the error probability for low SNRs and the impulsive component dominating for high SNRs. Thus, approximate error probability curves may be calculated by using a result applicable for Gaussian interference at low SNRs, and an asymptotic formula corresponding to impulsive background noise at high SNRs.