Research On Adaptive Filtering Algorithms For Sparse Impulse Response And Their Applications

Advances in information technology have influnced every apsect of humman being's life. They have changed our socity profoundly. How to conviniently and efficiently retrieve, analyze and use information is a key problem of morden information technology. Digital signal processing technology processes the input signals using the characteristics of time discret system in order to use the information included in the signals. The adaptive signal processing technology is one of the important aspects of digital signal processing technology and has widely applied in many fields such as communication, control, etc. Adaptive filter dynamically adjusts its coefficients according to a certain adaptive algorithm so it can deal with the systems where the exact system characteristic is unknow in advance, or the system is time-varying.In recent years, with the increase of demand, the length of adaptive filter was doubled. As a result, traditional adaptive algorithms encounter many new challenges. First, the convergence speed of adaptive filter becomes slow with the increase of the filter length. Second, computational complexity of adaptive algorithm becomes too heavy to be implemented in resource-limited applications or in real-time applications. Third, convergence accuracy of adaptive filter is degraded. Many approaches have been proposed to solve these problems. Recently, a new perspective of adaptation process, proportionate adaptation, was developed and investigated widely. This new method is based on a fact, that long adaptive filters are sparse in nature. That is, although these filters have hundereds or thousands coefficients, only a small portion of them have noticeable value while most of the others are zeros. This dissertation is engaged to sduty the various proportionate adaptive algorithms, in order to improve theire convergence speed, convergence accuracy and computational complexity.First, the MPNLMS algorithm is improved. A simplified derivation of MPNLMS algorithm is provided in a concise process. A method is proposed to determine its convergence criterion. Based on this criterion, a new segment function is proposed to approximate the mu-law function. Consequently the fast convergence speed of MPNLMS algorithm is retained. Then, computational complexity of proportionate adaptive algorithms is reduced by removing some redundant operations, while the convergence speed is not degraded. The original proportionate adaptive algorithms are only effective for sparse impulse responses. In an application where the sparsity of target impulse response varies with the environment, the performance of proportionate adaptive algorithms is not guaranteed. This dissertation proposes to introduce the measure of the sparsity into the algorithms. It then adjusts the related parameters of proportionate adaptive algorithms according to the sparsity. The convergence speed of the related algorithms is improved for any impulse response with different sparsity.Second, by analyzing the convergence process of proportionate adaptive algorithm using a block method, a new perspective is provided for proportionate adaptation. Then, a new method is proposed to determine the proportionate step size. All existing proportionate adaptive algorithms exploit the shape of target impulse response to determine their proportionate step size. This method is effective in the initial period of adaptation. But after the adaptive filter has converged to certain degree, this method will result in slow convergence of the small coefficients because they cannot obtain reseonable step size. Consequently, the convergence speed in the second period is degraded. The analysis reveals that, the optimal proportionate step gain should be determined according to the difference between the target impulse response and the current estimate of adaptive filter. This discovery implies a new way to pursuit faster proportionate adaptive algorithms. In this dissertation, it is proposed to determine the proportionate step gain according to the coefficients difference between the current estimate and a past estimate. In the initial period, this method is identical to the original proportionate algorithms. Thereafter, this method can assign similar proportionate step gain for all the coefficients so the overall convergence is improved. This method is not only effective for sparse impulse response, but also for non-sparse impulse response and it is unnecessary to adjust any parameter.Third, a variable step-size method is proposed for proportionate adaptive algorithms in order to improve their convergence accuracy. This method can keep fast convergence speed of proportionate adaptive algorithms, and it can achieve very low steady-state misalignment at the same time. The step-size parameter is one of the most important parameters of adaptive algorithms. It has great influence on convergence speed and the steady-state misalignment of adaptive algorithms. However, the requirements of fast convergence and low steady-state misalignment are conflict for constant step-size adaptive algorithms. For a constant global step-size algorithm, a step-size parameter has to be selected before start of algorithm, by compromising these two conflict requirements. In this dissertation, a variable step-size is proposed for proportionate adaptive algorithms to solve this problem. By taking into account the disturbance signal, it is proposed to force the a posterior error to be the disturbance signal, instead of to be zero. Then, a new optimization criterion is established. Based on this criterion, a step-size control approach for proportionate NLMS algorithm is proposed. This method uses a large global step-size when the output error is large to accuralate the convergence speed. After the adaptive filter has converged to certain degree, the output error becomes small, so the global step-size becomes small to achieve low steady-state misalignment. For the the correlated input signal, for example, speech signals, affine projection algorithm (APA) has faster convergence speed than the NLMS algorithm. The proposed variable step-size method is then extended to the proportionate APA. In this case, it is necessary to introduce a diagonal variable step-size matrix. By forcing the the a posterior error vector to be the disturbance signal vector, after the similar process, a variable step-size method is achieved for PAPA. Simulation results verify the effectiveness of the proposed algorithms.