Mapping The Impulse Noise Spectral Features From Waveform Domain Onto Symbol Domain Ronaldo de Freitas Zampolo, Jaume Rius I Riu, Elmar Trojer and Boris Dortschy Abstract— In this paper the spectral features of impulse noise in DSL systems are mapped from the waveform domain onto the symbol domain, considering a QAM receiver. This work can be viewed as part of a full symbol domain model for impulse noise, which should include the amplitude and spectral aspects. Since the available models of impulse noise in DSL are generally waveform-based, this kind of mapping is justified when symbol-based simulations are intended, in order to avoid computational overhead due to demodulating noise samples generated on waveform domain. The analytical development of such mapping is provided as well as some simulation results. Index Terms— DSL, impulse noise, spectral modeling, QAM I. I NTRODUCTION This work addresses the mapping of the spectral features of an impulse noise model for digital subscriber line (DSL) systems from waveform domain onto symbol domain. The waveform model on which our development is based was presented in [1]. Impulse noise is one of the major impairments in DSL systems due to its non-stationary behavior and consequent dif- ficulty for shielding transmitted information from it. Modeling impulse noise is rather important for simulating realistic DSL scenarios as well as evaluating the impact of new schemes concerning noise robustness. There is no doubt that models of such an impairment should be part of any DSL simulation tool, but research community opinions are divided between developing statistical models or simply using recorded samples of actual noise impulses. Even though the controversy remains, impulse noise models have been proposed time to time as an attempt to obtain a generalized but simple and adequate description for such a nonstationary interference. The very most widely used impulse noise model for DSL was proposed by Cook. Although based on a plenty of measurements (about 89,000 noise impulses analyzed) per- formed on Brithish Telecom (BT) network, the Cook pulse is considered too simple to represent actual noise impulses [2]. The state-of-art model (waveform) on which this work is based was developed in a series of papers written [1], [3]– [5] by Henkel, Kessler, and their colleagues. This model is derived from experimentation performed on BT’s and Deustch Telekom’s (DT) networks. The modeled statistics include: Ronaldo F. Zampolo is with the Signal Processing Laboratory - LaPS at Federal University of Par´ a, C.P. 479, CEP: 66075-110, Bel´ em-PA, Brazil. Jaume Rius i Riu, Elmar Trojer and Boris Dortschy are with EAB, ASP Lab, ¨ Alvsj¨ o, Sweden. Emails: zampolo@ufpa.br, {jaume.rius.i.riu, Elmar.Trojer, boris.dortschy}@ericsson.com. This work has been funded by Ericsson AB. noise amplitude, inter-arrival time between noise impulses, impulse length, and noise spectral features. However, if one intends to simulate DSL scenarios at symbol level, the referred model should be mapped from the waveform domain onto symbol domain in order to avoid the overhead caused by explicitly demodulating the artificially generated noise impulses. In [6], [7], the authors just focused on mapping amplitude statistics, proposing a model obtained from simulated data. In turn, this work presents an analytical mapping of the spectral features of model in [1], which is tested by simulation. The remaining part of this text is outlined as follows. Section II addresses the spectral model porposed in [6], [7] from which our symbol domain model is developed. In Section III, our model derivation is discussed in some detail. Section IV shows some simulation data. In Section V conclusions and suggestions for future works are presented, followed by aknowledgments and references. II. MODEL FOR THE SPECTRAL FEATURES OF IMPULSE NOISE IN DSL SYSTEMS IN WAVEFORM DOMAIN This section briefly discusses the model proposed in [1], [5] for the spectral features of impulse noise in waveform domain. According to the measurements performed in BT and DT networks, it is considered that expression (refeq:acf01) provides and adequate representation of the autocorrelation function (ACF) of noise impulses in DSL systems. ˆ R(τ )= m  i=1 cos(2πα i τ ) exp(-β i |τ |), (1) where ˆ R(·) denotes the estimated and normalized ACF of a single noise impulse; α i and β i are stochastic parameters that must be defined for each impulse noise; and τ represents the time lag. The probability density function (PDF) of α i can be, in turn, approximated by a mixture of Gaussians as given in (2). f (α)= 3  i=1 p i √ 2πσ i exp [-(α - m i ) 2 /2πσ 2 i ], (2) where p i , denotes the mixing proportions of each Gaussian term; m i and σ i are Gaussian’s means and standard deviations, respectively. The default values for α PDF parameters (p i , m i and σ i ) are shown in Table I. The parameter β in (1) is drawn from a Gaussian process, whose PDF parameters depends on the impulse length, accord- ing to the Table II. 85-89748-04-9/06/$25.00 © 2006 IEEE ITS2006 193