Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
A variable step-size affine projection algorithm
Digital Signal Processing
Convergence behavior of affine projection algorithms
IEEE Transactions on Signal Processing
A variable step size LMS algorithm
IEEE Transactions on Signal Processing
Fast exact variable order affine projection algorithm
Signal Processing
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This paper proposes a two-stage affine projection algorithm (APA) with different projection orders and step-sizes. The proposed algorithm has a high projection order and a fixed step-size to achieve fast convergence rate at the first stage and a low projection order and a variable step-size to achieve small steady-state estimation errors at the second stage. The stage transition moment from the first to the second stage is determined by examining, from a stochastic point of view, whether the current error reaches the steady-state value. Moreover, in order to prevent the sudden drop of convergence rate on switching from a high projection order to a low projection order, a matching step-size method has been introduced to determine the initial step-size of the second stage by matching the mean-square errors (MSEs) before and after the transition moment. In order to continuously reduce steady-state estimation errors, the proposed algorithm adjusts the step-size of the second stage by employing a simple algorithm. Because of the reduced projection orders and variable step-size in the steady-state, the algorithm achieves improved performance as well as extremely low computational complexity as compared to the existing APAs with selective input vectors and APAs with variable step-size.