Research On Adaptive Filtering Algorithms And Application

It is well known that adaptive signal processing plays a very important role in many signal processing applications, e.g., the echo cancellation, line enhancement, channel equalization, system identification, and time delay estimation, etc. In the past few decades, many adaptive filtering algorithms have been proposed for these applications. In our work, some of the prob-lems that exist in the existing algorithms have been analyzed. In order to fix these problems, we have conducted research and extension of the adaptive filtering algorithms and applications and major contributions included the following:Firstly, we have proposed a multi-step gradient descent-based variable step size normalized least mean squares (MSGVSS-NLMS) algorithm. The algorithm combines both advantages of variable step size normalized least mean squares (VSS-NLMS) algorithm and momentum least mean squares (MLMS) algorithm. After theoretical analyses, we get the relationship between the step size parameters and algorithm performance of convergence and misadjustment. By us-ing the relationship, we design a reasonable time-varying step size parameter strategy to achieve the filtering process. Analyses show that:when the gradient step size parameter is giv-en, one can change the momentum step size parameter to accelerate the convergence speed, and this accelerating process does not affect the final misadjustment which controlled by the gradi-ent step size parameter. Computer experiments show that the proposed fixed gradient step size and variable gradient step size algorithm can work well and solve the unpredictable misadjustment problem of the conventional VSS-NLMS algorithm.Secondly, we have proposed a variable regularization parameter NLMS algorithm. The tra-ditional adaptive filtering algorithms derivation were analyzed, based on the results of analyses, the choice of a uniform filter update equation as a framework and a new cost function are firstly chosen. Based on such a new performance function, mathematical derivations reveal the influ-ence of the regularization parameter to the convergence and misadjustment of the algorithm. To trade off the conflicting requirements of the fast convergence and low misadjustment of the al-gorithm and using the analytical results, a novel variable regularization parameter method for the NLMS algorithm without any priori knowledge of the system observation noise variance nor its estimate is provided. Furthermore, the relationship between the conventional NLMS and our algorithms is analytically established. The proposed method can also be regarded as a novel variable step size NLMS algorithm. While the simulation results verify the analytical ones, they also show that the performance of the proposed algorithm is superior to those that have been reported in the literature.Finally, we have proposed the method of using the proposed variable regularization param-eter NLMS algorithm to Wi-Fi through-the-wall radar for background interference eliminating. The variable regularization parameter NLMS algorithm has been taken to estimate the channel coefficients at first step, then using the obtained channel estimation to obtain the moving target echo signal by eliminating the background interference in the received signal. A simulative system has been used to verify the validity of the proposed method.