Research On Variable Design Parameter Subband Adaptive Filters

Adaptive filters find widespread applications in areas such as communications, radar, sonar, image processing, and biomedical engineering. An adaptive filter is closely related to its structure, algorithm, and applications. The performance of an adaptive filter depends on its structure and algorithm. The transversal filter structure based least mean square (LMS) algorithm proposed by Widrow and Hoff is one of the most popular adaptive filtering algorithms owing to its low computational complexity, good stability, and ease implementation. However, when the input signal of the adaptive filter is highly correlated, the LMS algorithm converges slowly.Subband adaptive filtering technique is one of the effective methods which can increase the convergence rate of the LMS algorithm. A subband adaptive filter (SAF) partitions and then decimates the input signal via a filter bank. Compared to the correlation of the fullband input signal, the correlation of the subband input signals is low, and therefore adaptive filtering in subbands can increase the convergence rate of the adaptive filter. In the conventional SAF, each subband employs an individual adaptive subfilter. This structure generates aliasing components in the output of the adaptive filter, which causes high steady-state misalignment (or misadjustment) in the conventional SAF.In order to solve the problem of aliasing components in the conventional SAF, Lee and Gan have proposed a new SAF structure, which is called multiband structure by the authors. In the multiband structure, each subband employs the same fullband adaptive filter. The proposed normalized subband adaptive filter (NSAF) based on the multiband structure has a good convergence performance because of its inherent decorrelating and least perturbation properties. Similar to other adaptive filters, the faster the convergence rate of the NSAF is, the higher the steady-state misalignment is; on the contrary, the slower the convergence rate of the NSAF is, the lower the steady-state misalignment is. The users of adaptive filters have to take a tradeoff between convergence rate and steady-state misalignment by selecting appropriate design parameter(s), such as step-size parameter, regularization parameter. Therefore, the NSAF can not simultaneously obtain both fast convergence rate and low steady-state misalignment.Based on the application of adaptive filtering in system identification, from several different points of view, this dissertation presents five variable design parameters, including variable step-size parameter, variable regularization matrix?, variable step-size matrix, variable regularization matrix?, and variable combining parameter, to solve the problem of tradeoff between convergence rate and steady-state misalignment in the NSAF. In the process of deriving the variable design parameters, two different principles are employed, i.e., the principle of largest decrease of normalized square deviation (MSD) and the principle of cancellation of system noise. In addition, this dissertation also presents an L1-norm minimization based sign subband adaptive filter (SSAF), and then incorporate a variable regularization parameter into the SSAF to enhance its robustness. It can be seen that the variable regularization parameter SSAF is more robust and has a lower computational complexity than the NSAF.Simulation results show that the variable design parameter methods presented in this dissertation can solve the problem of tradeoff between convergence rate and steady-state misalignment and thus improve the whole performance of the NSAF.