• The Journal of Natural Sciences
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• v.8 no.2
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• pp.63-67
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• 1996

Adaptive algorithms based on the higher order error criterion such as the LVCMS and the LMF show performance degradation if input signal contains additive noise with a heavier-tailed density. Conventional analysis often neglects higher order terms in the recursion and my not suit for prediction exact behavior of these higher order algorithms. This paper presents a new convergence analysis which contains all the higher order term in the recursion. The analysis shows that the higher order terms, which are often neglected, dose not affect the upper bound on the step size but the misadjustment. However, the effect decreases sharply proportional to the square of the step size.

• The Journal of the Acoustical Society of Korea
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• v.15 no.3E
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• pp.19-26
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• 1996

In this paper, convergence properties of the LMS, LMF, and LVCMS algorithms are investigated under the assumption of the uncorrelated Gaussian input data. By treating these algorithms as special cases of more general algorithm family, unified results on these algorithms are obtained. First the upper bound on the step size parameter is obtained. Second, an expression for misadjustment is obtained. These theoretical results confirm earlier LMS works. Further, the results explain why the LMS and LVCMS algorithms are experiencing difficulties with plant noise having heavier tailed densities. Simulation results agree with theoretical expectation closely for various plant noise statistics.