Abstract
A novel algorithm, called the signed regressor least mean fourth (SRLMF) adaptive algorithm, that reduces the computational cost and complexity while maintaining good performance is presented. Expressions are derived for the steady-state excess-mean-square error (EMSE) of the SRLMF algorithm in a stationary environment. A sufficient condition for the convergence in the mean of the SRLMF algorithm is derived. Also, expressions are obtained for the tracking EMSE of the SRLMF algorithm in a nonstationary environment, and consequently an optimum value of the step-size is obtained. Moreover, the weighted variance relation has been extended in order to derive expressions for the mean-square error (MSE) and the mean-square deviation (MSD) of the proposed algorithm during the transient phase. Computer simulations are carried out to corroborate the theoretical findings. It is shown that there is a good match between the theoretical and simulated results. It is also shown that the SRLMF algorithm has no performance degradation when compared with the least mean fourth (LMF) algorithm. The results in this study emphasize the usefulness of this algorithm in applications requiring reduced implementation costs for which the LMF algorithm is too complex.
Highlights
Reduction in complexity of the least mean square (LMS) algorithm has always received attention in the area of adaptive filtering [1,2,3]
An extension of the weighted variance relation is provided in order to derive expressions for the mean-square error (MSE) and the mean-square deviation (MSD) of the proposed algorithm during the transient phase
Since σe2 is usually large at the beginning of adaptation processes, we can see that the convergence of the signed regressor least mean fourth (SRLMF) algorithm strongly depends on the choice of initial conditions
Summary
Reduction in complexity of the least mean square (LMS) algorithm has always received attention in the area of adaptive filtering [1,2,3]. The performance of the SRA algorithm is superior to that of the SA algorithm for Gaussian input data It is shown in [10] that the SRA algorithm is much faster than the SA algorithm in achieving the desired steady-state mean-square error for white Gaussian data. EURASIP Journal on Advances in Signal Processing by a factor of 2/π for the same steady-state mean-square error It is shown in [17] that the SRA algorithm exhibits significantly higher robustness against the impulse noise than the LMS algorithm. From the simulation results it is shown that both the SRLMF algorithm and the least mean fourth (LMF) algorithm [19] have a similar performance for the same steady-state EMSE.
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