Zero-Order Statistics: A Mathematical Framework for the Processing and Characterization of Very Impulsive Signals

Robust compressive sensing of sparse signals: a review

“…However, it defines a robust metric that does not heavily penalize large deviations, with the robustness depending on the scale parameter γ , thus making it an appropriate metric for impulsive environments (optimal in ML sense under the Cauchy model) [16,72,76,77]. Further justification for the use of the Lorentzian norm is the existence of logarithmic moments for algebraic-tailed distributions, as second moments are infinite or not defined for such distributions and therefore not an appropriate measure of the process strength [13,16].…”

“…However, it is well known that least squaresbased estimators are highly sensitive to outliers present in the measurement vector, leading to a poor performance *Correspondence: rafael.carrillo@epfl.ch 1 Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland Full list of author information is available at the end of the article when the noise does not follow the Gaussian assumption and is, instead, better characterized by heavier-thanGaussian-tailed distributions [11][12][13][14]. A broad spectrum of applications exists in which such processes emerge, including wireless and power line communications, teletraffic, hydrology, geology, atmospheric noise compensation, economics, and image and video processing (see [14][15][16] and references therein).…”

Applications of Wireless Communications: Performance Analysis of Diversity Combining over Rayleigh Fading Channels with Impulsive Noise

“…Hence, the variance of SαS distributed noises, is undefined. As a result, the geometric SNR (GSNR) [19] is used in this paper, i.e.,…”

Clipping Demapper for LDPC Decoding in Impulsive Channel

“…Moreover, comparison of the scale parameters between two systems is meaningful only when they share the same index α. Several papers deal with this aspect and propose other "power" measurements [8]. To make things simple we will only consider γ as a measurement of the strength of the noise.…”

“…These values were chosen because the results obtained are representative of the behaviors under weak and strong impulsiveness respectively. Note however, that the comparison of the results for different values of alpha is not straightforward as the notion of SNR is not well-defined [8].…”