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Mixed third- and fourth-order cumulants-based algorithm for nonlinear kernels identification in cubic systems

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Abstract

Ignoring nonlinear effects in many practical situations degrades the performance. This paper considers nonlinear system characterization using higher-order cumulants and polyspectra. A novel method to blindly identify the kernels of cubic systems using mixed third- and fourth-order cumulants is developed. We study the link between the Fourier transform of third-order and fourth-order cumulants in nonlinear cubic systems. Then, we use the inverse Fourier transform to build a new formula which combines third- and fourth-order cumulants. Then, we generalize it to the nth-order cumulants and the kernels of nonlinear cubic systems driven by a non-Gaussian random signal, independent, identically distributed (i.i.d.) in Gaussian noise environment. Our performances results indicate that the proposed approach is able to identify blindly the kernels in cubic systems.

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Acknowledgements

This work was supported by Fundação para a Ciencia e Tecnologia and Instituto de Telecomunicações under projects UIDB/50008/2020 and MASSIVE5G (SAICT-45-2017-02).

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Correspondence to Mohammed Zidane.

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Zidane, M., Dinis, R. Mixed third- and fourth-order cumulants-based algorithm for nonlinear kernels identification in cubic systems. SIViP 16, 651–659 (2022). https://doi.org/10.1007/s11760-021-02004-2

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  • DOI: https://doi.org/10.1007/s11760-021-02004-2

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