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Parameter λ controls the level of sparsity of the resulting model.
Since the practical multipath channels often show some level of sparsity, where very limited channel paths carry significant energy.
Kurtosis is a measure of peakedness of a distribution and higher values of kurtosis implies higher level of sparsity.
This was an improvement over OMP algorithm, which usually requires the level of sparsity as a priori information to estimate the original signal.
The HNN MLSE equalizer thus exploits sparsity in communication channels by reducing the BER as the level of sparsity increases, given that the nonzero CIR taps remains constant.
It is clear that the weighted-l2 and also l1-norm criteria achieve higher level of sparsity compared to the classic l2-norm criterion.
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Figure 3 shows the contour set for two levels of sparsity ( and ) as a function of the number of projections and of the quantization distortion of the measurements.
From this figure, it can be clearly observed that the multichannel reference spectra exhibit even higher levels of sparsity when analyzed across multiple dimensions, with Gini indices on average above 0.85.
Our estimation and tracking algorithm is designed for robustness with respect to the ill-conditioned nature of the data matrix, can smoothly handle different levels of sparsity, and is modeled to include delays due to multi-path and the Doppler spread induced by the channel.
The resulting sequence of and associated optimal allow us to model the data at varying levels of sparsity.
We study the performance of our algorithm on two specific classes of "biologically inspired" models, although we believe our results are generic for any nonlinear models with similar levels of sparsity, nonlinear variance, etc.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com