Adaptive filtering algorithm design for improving the performance of a family of affine projection algorithm

DoctorThis dissertation proposes the various methods to improve the performance of a family of affine projection algorithm. First, we introduce the previous invented adaptive filtering algorithms. Least mean squares (LMS) algorithm, normalized least mean squares (NLMS) algorithm, and affine projection algorithm (APA) are derived by using the cost functions based on the square value of the error signal. Second, we propose an APA based on the concept of reuse time of the current input vector. Reuse time is defined as the survival period of an input vector, during which the input vector is continuously reused in the subsequent update equations. The algorithm consists of two key procedures: assignment and reduction. The assignment procedure assigns a fundamental reuse-time or zero to the individual reuse time of each current input vector only once by checking whether the current input vector has enough information for update, which eliminates the repetitive selection procedure for input vectors. The reduction procedure gradually decreases the fundamental reuse time by examining, from a stochastic point of view, whether the current error reaches the steady-state value, which indirectly controls the number of input vectorsthis leads to fast convergence and small estimation errors. Through these two procedures, the proposed algorithm achieves not only improved performance but also extremely low computational complexity.Third, we propose an APA that determines its projection order using a pseudo-fractional method.The pseudo-fractional method adjusts the projection order by comparing the averages of the accumulated squared errors.The method relaxes the constraint of the conventional APA that the projection order must be integral, and it includes both the integral projection order and the fractional projection order.Experimental results show that the proposed algorithm achieves a faster convergence rate and a smaller steady-state estimation error than the existing algorithms.Fourth, we propose a non-periodic-partial-update affine projection algorithm with data-selective updating.The proposed algorithm employs two update concepts: non-periodic partial update and data-selective update.The former plays a role in adjusting the length of the update period, and the latter in reducing computational complexity.Thus, the algorithm requires two key procedures of length assignment and state decision.The length assignment procedure determines the length of the update period by checking whether the current input vectors have enough information with an update period assignment criterion.The state decision procedure stochastically determines whether the adaptive filter has reached a steady state.When the current state of the adaptive filter is confirmed as a transient state by the decision procedure, the algorithm updates all filter coefficients with an update period assigned by the length assignment procedure.Through these two procedures, the proposed algorithm not only achieves good performance, especially for colored input signals, in terms of the convergence rate and steady-state estimation errors but also provides a substantial reduction in the number of updates.Fifth, we propose a NLMS algorithm that automatically determines the number of orthogonal correction factors (OCF) by using a pseudo-fractional method, which relaxes the constraint that the number of OCF in the NLMS algorithm must be integral and introduces the concept of a pseudo-fractional OCF number in the adaptation rule.The pseudo-fractional OCF number is adjusted by using the difference between the averages of the accumulated squared-output errors.The experimental results show that the proposed algorithm has not only a fast convergence rate but also a small steady-state estimation error with low computational complexity in comparison to existing algorithms with multiple input vectors.Sixth, we propose a new variable step-size NLMS algorithm with OCF.The proposed scheme for the step size is based on a mean square deviation analysis for the tap weight and its estimate at each iteration.The experimental results show that the proposed algorithm has faster convergence and a smaller steady-state error than do existing algorithms with multiple input vectors.Seventh, we propose a two-stage 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 (MSE) 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.Finally, we propose a novel scheme for obtaining an optimal step size and proposes a criterion for decrementing the projection order, which would lead to fast convergence and a small steady-state estimation error with low computational complexity.The scheme is based on an analysis of the mean square deviation (MSD) for the tap weight and its estimated value at each iteration.The criterion is obtained by calculating the steady-state MSD.The experimental results show that the proposed algorithm has faster convergence and a smaller steady-state error than the existing affine projection algorithms with a variable step size or variable projection order