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Semi-blind Data-Selective and Multiple Threshold Volterra Adaptive Filtering

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Abstract

This work proposes the use of data-selective semi-blind schemes in order to decrease the amount of data used to train the adaptive filters that employ Volterra series, while reducing its computational complexity. It is also proposed a data-selective technique that exploits the structure of Volterra series, employing a different filter for each of its kernels. The parameter vector of these filters grows as the order of the kernel increases. Therefore, by assigning larger error thresholds to higher-order filters, it is possible to decrease their update rates, thus reducing the overall computational complexity. Results in an equalization setup indicate that both proposals are capable of achieving promising results in terms of mean square error and bit error rate at low computational complexity, and in the case of semi-blind algorithms, using much less training data.

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Notes

  1. The elements of the kernels are related to the order of the product of the terms of the Volterra series. As described in (3), the entries of the Nth-order kernel are related to N products. For example, the first-order kernel elements are related to the linear terms, while the second-order elements are related to the quadratic ones, and so on.

  2. Despite the sum of number of elements of \(\mathbf {w}_1[k]\) and \(\mathbf {w}_2[k]\) is 2L, due to the partial-update technique, only L elements are actually updated in this case.

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Acknowledgements

The authors would like to thank CNPq, CAPES (Grant No. 23038.009440/2012-42), and FAPERJ, Brazilian research councils, for funding this work.

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Authors and Affiliations

  1. School of Engineering, Macquarie University, Sydney, NSW, 2113, Australia

    Felipe B. da Silva

  2. Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg, 1855, Luxembourg City, Luxembourg

    Wallace A. Martins

  3. COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, RJ, 21941-450, Brazil

    Felipe B. da Silva & Wallace A. Martins

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  1. Felipe B. da Silva
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  2. Wallace A. Martins
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Correspondence to Felipe B. da Silva.

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da Silva, F.B., Martins, W.A. Semi-blind Data-Selective and Multiple Threshold Volterra Adaptive Filtering. Circuits Syst Signal Process 39, 1509–1532 (2020). https://doi.org/10.1007/s00034-019-01219-6

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