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Exact tracking analysis of the NLMS algorithm for correlated Gaussian inputs | IEEE Conference Publication | IEEE Xplore

Exact tracking analysis of the NLMS algorithm for correlated Gaussian inputs


Abstract:

This work presents an exact tracking analysis of the Normalized Least Mean Square (NLMS) algorithm for circular complex correlated Gaussian inputs. Unlike the existing wo...Show More

Abstract:

This work presents an exact tracking analysis of the Normalized Least Mean Square (NLMS) algorithm for circular complex correlated Gaussian inputs. Unlike the existing works, the analysis presented neither uses separation principle nor small step-size assumption. The approach is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form (∥u∥D12)(∥u∥D22)-1 where u is a white Gaussian vector and D1 and D2 are diagonal matrices and using that to derive the first and second moments of such variables. These moments are then used to evaluate the tracking behavior of the NLMS algorithm in closed form. Thus, both the steady-state mean-square-error (MSE) and mean-square-deviation (MSD )tracking behaviors of the NLMS algorithm are evaluated. The analysis is also used to derive the optimum step-size that minimizes the excess MSE (EMSE). Simulations presented for the steady-state tracking behavior support the theoretical findings for a wide range of step-size and input correlation.
Date of Conference: 09-13 September 2013
Date Added to IEEE Xplore: 08 May 2014
Electronic ISBN:978-0-9928626-0-2

ISSN Information:

Conference Location: Marrakech, Morocco

References

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