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This paper proposes a new method of reducing the steady-state error for the Affine Projection Algorithm (APA) using Error Reduction Factor (ERF) to yield Error Reduction Affine Projection Algorithm (ER-APA). The proposed method is very simple but highly effective. In the paper, we analyze the ER-APA for calculating theoretical filter convergence. Through experiments, it is shown that the ER-APA sufficiently...
This paper proposes an adaptation algorithm named Adaptive Step-Size q-Normalized Least Mean Modulus-Newton Algorithm (ASS-qNLMM-NewtonA) in which the normalizing factor is a generalized norm called “q-norm” of the filter input. Two types of impulse noise are considered: one is found in observation noise and another at filter input. Analysis of the ASS-qNLMM-NewtonA is developed to theoretically calculate...
This paper proposes and develops a statistical analysis of Affine Projection Normalized Correlation Algorithm (AP-NCA) which is a combination of the Affine Projection Algorithm (APA) and Normalized Correlation Algorithm (NCA) for use in complex-domain adaptive filters. For impulse noise, two types are considered: one is found in observation noise and another at filter input. Through experiments with...
This paper proposes a new adaptation algorithm named Adaptive Step-Size p-Modulo Correlation Phase Algorithm (ASS-pModuloCPhiA) for adaptive filters used in digital QAM systems. The algorithm employs “p-modulus” of the correlation between the error and filter input, and an adaptive step-size control algorithm. The ASS-pModuloCPhiA achieves significant improvement in filter convergence speed of the...
This paper develops a statistical analysis of the Affine Projection Algorithm (APA) for adaptive filters to theoretically calculate filter convergence behavior. Assuming that the number of tap weights of the adaptive filter is sufficiently large, we derive simple difference equations that only require matrix computations. In experiments with some examples, it is observed that simulated and theoretically...
This paper first proposes to combine the Sign Algorithm (SA) with an estimate of the inverse covariance matrix of the filter input calculated using the Newton's method. We further propose a new adaptive step-size (ASS) control algorithm to improve the filter convergence speed, yielding an adaptation algorithm named Adaptive Step-Size Sign-Newton (ASS-Sign-Newton) algorithm. A performance analysis...
This paper proposes a new adaptation algorithm named Normalized Recursive Least Adaptive Threshold Nonlinear Errors (NRLATNE) algorithm for complex-domain adaptive filters which makes the filters fast convergent for correlated filter inputs and robust against two types of impulse noise: one is found in additive observation noise and another at filter input. Analysis of the proposed NRLATNE algorithm...
This paper proposes Variable Step-Size Least Mean Modulus Algorithm (VSS-LMMA) for robust filtering in impulsive noise environments. The VSS-LMMA for use in adaptive filters in digital QAM systems is basically the LMMA combined with a new simple variable step-size control algorithm to improve the convergence speed of the LMMA while preserving its robustness against additive impulsive observation noise...
In this paper, stability conditions in terms of the upper bounds of the step size and of the initial value of the Mean Squared Error (MSE) are derived for FIR adaptive filters with non-quadratic error criteria, where "rth power" of the error is used in the correlation multiplier for tap weight adaptation. Simple formulae of the upper bounds for the Least Mean Fourth Algorithm (LMFA) (r =...
This paper first reviews an adaptation algorithm named Recursive Least Moduli (RLM) algorithm for complex-domain adaptive filters. The RLM algorithm achieves significant improvement in the filter convergence speed when the filter input is strongly correlated. Stochastic models are presented for two types of impulse noise found in adaptive filtering systems: one in observation noise and another at...
This paper proposes an adaptation algorithm named Recursive Least Normalized Correlation Norms (RLNCN) algorithm for adaptive filters, based on a cost function of a quantity named Normalized Correlation Norm (NCN) which generically yields a family of normalized type algorithms. The RLNCN algorithm achieves a significant improvement in filter convergence speed, while it preserves robustness against...
This paper proposes a new adaptation algorithm named Normalized Recursive Least Moduli (NRLM) algorithm which employs “p-modulus” of error and “q-norm” of filter input. p-modulus and q-norm are generalization of the modulus and norm used in complex-domain adaptive filters. The NRLM algorithm with p-modulus and q-norm makes adaptive filters fast convergent and robust against two types of impulse noise:...
This paper proposes normalized recursive least moduli (NRLM) algorithm for complex-domain adaptive filters in which the normalizing factor is q-norm of filter input. Stochastic models are given for two types of impulse noise found in adaptive filtering systems: one in observation noise and another at filter input. We first review q-norm and normalized least mean modulus (NLMM) algorithm, and then...
This paper first reviews Correlation Phase Algorithm (CPhiA) for adaptive filters in the complex-number domain with colored Gaussian reference inputs. Stochastic models are presented for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. To improve the filter convergence speed for a strongly correlated filter reference input, we combine the...
This paper first describes Correlation Phase Algorithm (CPhiA) for adaptive filters to be used in digital QAM systems. We present stochastic models for two types of impulse noise intruding adaptive filters: one in observation noise and another at filter input. Performance analysis of the CPhiA in the presence of both types of impulse noise is fully developed to derive difference equations for calculating...
This paper proposes a new adaptation algorithm named normalized correlation-Newton (NC-Newton) algorithm and a novel variable q-norm control method (NC-Newton-Varq-norm) for complex-domain adaptive filters. First, stochastic models are presented for two types of impulse noise intruding adaptive filters: one is present in observation noise and another at filter input. After reviewing q-norm and NC-Newton...
This paper first revisits least mean modulus (LMM) algorithm for complex-domain adaptive filters, presents a mathematical model for impulsive observation noise called CGN, and reviews recursive least moduli (RLM) algorithm that combines the LMM algorithm with recursive estimation of inverse covariance matrix of filter inputs. The RLM algorithm is effective in making the convergence of an adaptive...
This paper first reviews least mean modulus-Newton (LMM-Newton) algorithm that combines LMM algorithm for complex-domain adaptive filters with simple recurrent calculation of the inverse covariance matrix of the filter reference input process. The LMM-Newton algorithm is effective in improving the convergence of an adaptive filter with a strongly correlated input, while preserving the robustness of...
This paper first reviews least mean modulus-Newton (LMM-Newton) algorithm for complex-domain adaptive filters. The LMM-Newton algorithm is effective in making the convergence of an adaptive filter with a highly correlated input as fast as that for the LMM algorithm with a White & Gaussian filter input. However, the filter convergence for the LMM-Newton algorithm is still much slower than for the...
This paper derives a new adaptation algorithm named signed correlation algorithm with recursive estimation of signed data covariance (SCA-RESDC) that combines signed correlation algorithm (SCA) for complex-domain adaptive filters with recursive estimation of signed data covariance matrix of a strongly correlated filter reference input process. The SCA-RESDC achieves significant improvement in filter...
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