Abstract
The leaky LMS algorithm has been extensively studied because of its control of parameter drift. This unexpected parameter drift is linked to the inadequacy of excitation in the input sequence. And generally leaky LMS algorithms use fixed step size to force the performance of compromise between the fast convergence rate and small steady-state misalignment. In this paper, variable step-size (VSS) leaky LMS algorithm is proposed. And the variable step-size method combines the time average estimation of the error and the time average estimation of the normalized quantity. Variable step-size method proposed incorporating with leaky LMS algorithm can effectively eliminate noise interference and make the early convergence, and final small misalignments are obtained together. Simulation results demonstrate that the proposed algorithm has better performance than the existing variable step-size algorithms in the unexcited environment. Furthermore, the proposed algorithm is comparable in performance to other variable step-size algorithms under the adequacy of excitation.
Highlights
The least-mean-square (LMS) algorithm is widely used in many fields, such as system identification [1, 2], echo cancellation [3], adaptive channel equalization [4], adaptive antenna array [5], and adaptive spectral line enhancement [6], due to its good robustness, low computational complexity, and simple structure
The L-LMS algorithm that is same as the conventional LMS algorithm uses a fixed step size in its coefficient update recursion inheriting the limitation in the fullupdate algorithm of having to compromise between fast convergence speed and low level of steady state error. This problem above can be tackled by changing fixed step-size μ in Equation (1) to time-varying step-size μðnÞ, which is adjusted based on a criterion that tries to measure the proximity of the adaptive filter parameters to the optimal ones
In order to compare the performance of each algorithm fairly, the algorithms mentioned above are all placed in the same experimental environment, and the parameters of each algorithm are selected to meet the needs of the experiment
Summary
The least-mean-square (LMS) algorithm is widely used in many fields, such as system identification [1, 2], echo cancellation [3], adaptive channel equalization [4], adaptive antenna array [5], and adaptive spectral line enhancement [6], due to its good robustness, low computational complexity, and simple structure. It is well known that the convergence rate and steady-state error of the algorithm are directly related to the adaptation step size of a conventional LMS algorithm. The convergence rate increases with the increase of the adaption step size, but the steady-state error changes in the opposite direction [7]. The adaptive step size is a contradiction in the iterations, and variable step-size (VSS) LMS algorithm, which is adjusted according to the proximity between the actual value and the optimal value in the iterations, is proposed solving this contradiction. The convergence condition of the leaky LMS algorithm with variable step size is analyzed, and the quantization range of step size is given.
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