Abstract
The standard APA has three parameters: the step-size parameter, the projection order, and the regularization factor, which are all assumed to be invariable in the preceding chapters. However, by adjusting those parameters adaptively, it is possible to improve the performance of the APA. This chapter gives an overview of such variable parameter APAs. First, two variable step-size APAs are reviewed. The second topic is the proportionate APA, in which each component of the coefficient vector of the adaptive filter is given a step-size that is approximately proportional to its own magnitude. The proportionate technique is effective for echo cancellation, where the impulse response of the unknown system is sparse and long. The third topic is the evolving order APA. The projection order gives a definite influence on the behavior of the APA, i.e., a larger projection order results in faster convergence with a larger misadjustment. In the evolving order APA, the projection order is so adjusted that it takes a large value in the initial convergence phase, and a small value in the steady-state phase. The last topic is the variable regularized APA. Two methods are described, one based on minimization of the a posteriori error, and the other using a variable regularization matrix. In the latter method, the eigenvalues of the matrix to be regularized are given different regularization parameters individually.
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Notes
- 1.
This is different from the a posteriori error vector \(e_{p,k}\) defined in Chap. 5. The a posteriori error vectors \(\epsilon _{k}\) and \(e_{p,k}\) are related by \(\epsilon _{k}= e_{p,k} + v_{k}\).
References
Shin, H.-C., Sayed, A.H., Song, W.-J.: Variable step-size NLMS and affine projection algorithms. IEEE Signal Process. Lett. 11(2), 132–135 (2004)
Paleologu, C., Benesty, J., Ciochină, S.: A variable step-size affine projection algorithm designed for acoustic echo cancellation. IEEE Trans. Audio Speech Lang. Process 16(8), 1466–1478 (2008)
Duttweiler, D.L.: Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Trans. Speech Audio Process. 8(5), 508–518 (2000)
Benesty, J., Gansler, T., Morgan, D.R., Sondhi, M.M., Gay, S.L.: Advances in Network and Acoustic Echo Cancellation. Springer, Berlin (2001)
Benesty, J., Gay, S.L.: An improved PNLMS algorithm. In: Proceedings of the ICASSP 2002, vol. 2, pp. 1881–1884. Orlando, 13–17 May (2002)
Paleologu, C., Ciochină, S., Benesty, J.: An efficient proportionate affine projection algorithm for echo cancellation. IEEE Signal Process. Lett. 17(2), 165–168 (2010)
Paleologu, C., Benesty, J., Albu, F., Ciochină, S.: An efficient variable step-size proportionate affine projection algorithm. In: Proceedings of the ICASSP, pp. 77–80. Prague, 22–27 May (2011)
Albu, F., Paleologu, C., Benesty, J., Ciochina, S.: A low complexity proportionate affine projection algorithm for echo cancellation. In: Proceedings of the EUSIPCO, pp. 6–10. Aalborg, 23–27 Aug 2010
Albu, F.: Simplified proportionate affine projection algorithms. In: Proceedings of the IWSSIP, pp. 382–385. Vienna, 11–13 April (2012)
Kim, S.-E., Kong, S.-J., Song, W.-J.: An affine projection algorithm with evolving order. IEEE Signal Process. Lett. 16(11), 937–940 (2009)
Ji, C.-P., Ji, H.-H., Guo, W.-P., Wang, J.: APA with evolving order and variable regularization for echo cancellation. J. Netw. 9(1), 210–215 (2014)
Yoo, J.W., Shin, J.W., Choi, H.-T., Park, P.G.: An affine projection algorithm with evolving order using variable step-size. Int. J. Comput. Electr. Eng. 5(1), 5–8 (2013)
Yin, W., Mehr, A.S.: A variable regularization method for affine projection algorithm. IEEE Trans. Circuits Syst. II 57(6), 476–480 (2010)
Paleologu, C., Benesty, J., Albu, F., Ciochină, S.: Practical regularization of the affine projection algorithm. In: Proceedings of the EUSIPCO, pp. 704–708. Barcelona, 29 Aug.–2 Sept. 2011
Paleologu, C., Benesty, J., Albu, F., Ciochină, S.: Regularization of the affine projection algorithm. IEEE Trans. Circuits Syst. II 58(6), 366–370 (2011)
Paleologu, C., Benesty, J., Albu, F.: Regularization of the improved proportionate affine projection algorithm. In: Proceedings of the ICASSP, pp. 169–172. Kyoto, 25–30 March 2012
Choi, Y.-S., Shin, H.-C., Song, W.-J.: Adaptive regularization matrix for affine projection algorithm. IEEE Trans. Circuits Syst. II 54(12), 1087–1091 (2007)
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Ozeki, K. (2016). Variable Parameter APAs. In: Theory of Affine Projection Algorithms for Adaptive Filtering. Mathematics for Industry, vol 22. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55738-8_8
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DOI: https://doi.org/10.1007/978-4-431-55738-8_8
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