Research On Theory And Method Of Combined-step-size Adaptive Filtering

Combinations of adaptive filters have high computational burdens due to the two or several adaptive filters running at the same time.Meanwhile,they also have poor convergence or tracking behavior at the intersection of the large step size filter and the small step size filter.To overcome these drawbacks,this paper proposes a new concept of combined-step-size?CSS?,studies the design method of CSS,proposes a series of CSS adaptive filtering algorithms,and forms the theory and method of CSS adaptive filtering.The proposed CSS scheme has lower computational complexity than the conventional combination scheme of adaptive filters because it only requires one filter run at every moment.Because the proposed CSS plays the role of variable step size,the convergence or tracking behavior of the proposed CSS adaptive filter is much better than that of the traditional combination of adaptive filters.The proposed CSS scheme provides a new design scheme and idea for variable step size design.The major contributions of this dissertation are as follows:1?In order to reduce the computational complexity of combination of least mean square?LMS?adaptive filters and improve its convergence or tracking behavior,a CSS-LMS adaptive filter is developed.The proposed CSS-LMS adaptive filter uses a combining factor to adaptively combine two different step sizes of one LMS adaptive filter,where the large step size affords a fast convergence or tracking rate and the small one offers a small steady-state error.The combining factor is defined as the output of a sigmoidal activation function and it updates indirectly by using the stochastic gradient descent method to minimize the L₂-norm of the system output error.In order to quickly obtain the fast convergence or tracking rate of the large step size and the small steady-state error of the small one,the sigmoid activation function is modified by using enlarged,shifted and truncated methods.Based on the proposed new concept of CSS,the CSS normalized LMS?CSS-NLMS?adaptive filter and the CSS proportionate NLMS?CSS-PNLMS?/CSS improved proportionate NLMS?CSS-IPNLMS?adaptive filter are also proposed for reducing the computational complexities of combination of the corresponding adaptive filters and improving their convergence or tracking behavior.Simulations have demonstrated that the proposed CSS-LMS family adaptive filters obtain the superior convergence or tracking performance than the combinations of LMS family adaptive filters.2?Based on the proposed new concept of CSS,a CSS affine projection?AP?family adaptive filtering algorithms are developed.The proposed CSS-AP family algorithms include the CSS-AP algorithm,CSS proportionate AP?CSS-PAP?/CSS improved proportionate AP?CSS-IPAP?algorithm,CSS affine projection sign?CSS-APS?algorithm,and CSS proportionate APS?CSS-PAPS?/CSS improved proportionate APS?CSS-IPAPS?algorithm.Except that the computational complexities of the proposed CSS-AP family algorithms are much lower than those of the traditional combination algorithms of AP family adaptive filters,their computational complexities are comparable to those of the original AP family algorithms.Especially when the projection order is very large,the additional computational complexities of the proposed CSS-AP family algorithms are very slight.Simulation results show that the proposed CSS-AP family algorithms have faster convergence or tracking rates than the traditional combination algorithms of AP family adaptive filters.Furthermore,the proposed CSS-APS algorithm presents superior performance than the variable step size APS algorithm.3?In order to avoid the high computational burden of the exponential term of the generalized maximum correntropy criterion?GMCC?algorithm and produce smaller steady-state error,a maximum Versoria criterion?MVC?algorithm is proposed by maximizing the generalized Versoria function.Then,its CSS variant is also developed for producing better filter performance.To accelerate the convergence rate of the MVC algorithm for the correlated input signals,an affine projection Versoria?APV?algorithm is derived by maximizing the summation of Versoria-cost-reusing with a constraint on the square of the L₂-norm of the filter weight vector difference.Its computational complexity,stability,and steady-state excess mean-square error analyses are carried out and a fast recursive filtering technique is introduced to reduce its complexity.A CSS-APV algorithm is then proposed for solving the tradeoff problem of fast convergence rate and small steady-state error of the APV algorithm.For the sparsity of communication transmission channel,a CSS proportionate APV/CSS improved proportionate APV algorithm is proposed to estimate the impulse response of sparse transmission channels.In this section,all combining factors of CSSs are updated indirectly by using the stochastic gradient method to maximize the Versoria cost function.Simulation results show that the proposed Versoria family algorithms achieve good performance in terms of the convergence or tracking rate and the steady-state error.4?To address the tradeoff between the fast convergence rate and small steady-state error of the variable step-size?VSS?normalized subband adaptive filter?NSAF?with a fixed parametric step-size scaler?SSS?and improve its tracking performance in abrupt change scenarios,a combined-step-size?CSS?NSAF with a variable-parametric SSS?VPSSS?is proposed and its stability is analyzed.The combining factor of the CSS-VPSSS-NSAF algorithm is updated indirectly by using the stochastic gradient method to minimize the L₁-norm of the subband error vector or system output error.Simulation results show that the proposed CSS-VPSSS-NSAF algorithm without the reset algorithm still achieves better tracking performance than the VSS-SSS-NSAF algorithm with the reset algorithm.Utilizing the saturation property of the Versoria cost function,a CSS variable-parametric Versoria-based NSAF?VPV-NSAF?algorithm is proposed and its stability is analyzed.Simulations show that the proposed CSS-VPV-NSAF algorithm performs much better than the VSS sign subband adaptive filter algorithm and CSS-VPSSS-NSAF algorithm.5?The bias-compensated?BC?normalized maximum correntropy criterion?NMCC?algorithm encounters the conflicting requirement of fast convergence rate and small steady-state error.In order to overcome this drawback,a CSS BC normalized MVC?CSS-BC-NMVC?algorithm is proposed,which is obtained by combining the CSS scheme and the Versoria cost function.Its stability is then analyzed.For improving the robustness of the BC-NSAF algorithm in the presence of non-Gaussian impulsive interferences,by utilizing the Versoria cost function with the saturation property which can suppress the non-Gaussian impulsive interferences effectively,a CSS BC V-NSAF?CSS-BC-V-NSAF?algorithm is presented and its stability is analyzed.Simulation results have verified that the proposed CSS-BC-NMVC algorithm has good robustness and produces faster convergence rate and smaller steady-state error than the BC-NMCC algorithm.Also,the proposed CSS-BC-V-NSAF algorithm not only solves the tradeoff problem between fast convergence rate and small steady-state error of the BC-NSAF algorithm,but also overcomes the disadvantage that the BC-NSAF algorithm loses robustness in the presence of non-Gaussian impulsive interferences.