This paper proposes a stochastic approximation adaptive algorithm aiming at a fast convergence speed, where the step size. is normalized by the instantaneous power \\x(k)\\(2) of the input signal and a constant time s...
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This paper proposes a stochastic approximation adaptive algorithm aiming at a fast convergence speed, where the step size. is normalized by the instantaneous power \\x(k)\\(2) of the input signal and a constant time shift beta is included at the weight update, as alpha/(k + beta)\\x(k)\\(2). If is shown first that the proposed algorithm gives a convergence to the Wiener solution. Then the transient response of the mean error is analyzed. It is shown as a result that beta greater than or equal to alpha/2 is the condition for the time-shift parameter to guarantee the uniform convergence of the algorithm. It is shown also that the speed of convergence is improved greatly compared to the conventional algorithm when a is set large enough so that the product of alpha and the minimum eigenvalue of the autocorrelation matrix exceeds 100 and the time-shift parameter is set as beta similar to alpha/2. The performance is evaluated by a computer simulation. The above result of analysis is verified, and it is shown that the proposed algorithm can realize the same convergence speed as that of the recursive least-squares (RLS) algorithm.
The hybrid least mean square (HLMS) adaptive filter is a filter with an adaptation algorithm that is a combination of the conventional LMS algorithm and the normalized LMS (NLMS) algorithm. In this paper, the performa...
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The hybrid least mean square (HLMS) adaptive filter is a filter with an adaptation algorithm that is a combination of the conventional LMS algorithm and the normalized LMS (NLMS) algorithm. In this paper, the performance of the HLMS adaptive filtering algorithm is investigated. To do so, an analytical expression, in terms of the transient mean square error (MSE), is derived with application to the adaptive line enhancer (ALE). Based on this expression, we are able to examine the convergence properties of the FILMS. Simulation data using the ALE as an application verifies the accuracy of the analytical results. The performance of the FILMS algorithm is also compared with the conventional LMS algorithm as well as the NLMS algorithm. From the simulation results, we observed that, in general, the FILMS algorithm performs more robustly than the conventional LMS and the NLMS algorithms. Since the FILMS algorithm is a combination of the LMS algorithm and the NLMS algorithm, the selection of the optimum switching point of the FILMS algorithm is also addressed using a numerical approach. Many interesting characteristics of the switching point are obtained which show the relationship with the relevant parameters of the FILMS adaptive filter. The sensitivity of the selection of switching point is also examined.
Due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. The Non-Negative Least-...
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Due to the inherent physical characteristics of systems under investigation, non-negativity is one of the most interesting constraints that can usually be imposed on the parameters to estimate. The Non-Negative Least-Mean-Square algorithm (NNLMS) was proposed to adaptively find solutions of a typical Wiener filtering problem but with the side constraint that the resulting weights need to be non-negative. It has been shown to have good convergence properties. Nevertheless, certain practical applications may benefit from the use of modified versions of this algorithm. In this paper, we derive three variants of NNLMS. Each variant aims at improving the NNLMS performance regarding one of the following aspects: sensitivity of input power, unbalance of convergence rates for different weights and computational cost. We study the stochastic behavior of the adaptive weights for these three new algorithms for non-stationary environments. This study leads to analytical models to predict the first and second order moment behaviors of the weights for Gaussian inputs. Simulation results are presented to illustrate the performance of the new algorithms and the accuracy of the derived models.
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