Research On Proportionate Adaptive Algorithms For Sparse System Identification

With the rapid development of science and technology, the research methods of various disciplines further tend to be quantified. In scientific experiments and production practice, the complex objects usually require quantifying and ascertaining their inherent laws by observation and calculation, which generates system identification problem. System identification has important applications in the field of signal processing, communications and control, etc. It essentially estimates or determines the characteristic, unit impulse response and transfer function of the system based on the input and output signals of the system.However, in practice, many unknown systems have sparse characteristic, which only a few coefficients have a significant value and the other coefficients are zero or very small values in hundreds of coefficients. For such system, the traditional adaptive algorithms, such as least mean square (LMS) algorithm and its variations do not exploit sparsity, which leads to slow convergence rate. In recent years, some algorithms utilizing sparse characteristic of impulse response have been proposed, and these algorithms have achieved improved performance for sparse system identification. The proportional normalized least mean square (PNLMS) algorithm and its variations are one of the most notable algorithms. To further improve the performance of algorithms for sparse system identification, the paper dedicated to the research of various improved proportionate adaptive algorithm that is very necessary.First, the basic idea of the traditional LMS, PNLMS algorithms and their improved algorithms are briefly generalized. The advantages and disadvantages of the PNLMS algorithm and its variations are analyzed. When the input signal is related signals, the convergence rate of improved PNLMS (IPNLMS) algorithm greatly decline. The paper gets DIPNLMS by introducing the decorrelation principle, which improves the convergence perpormanc of IPNLMS algorithm. In order to further solve the tradeoff between the convergence rate and steady-state misadjustment in the fixed step-size DIPNLMS algorithm, we develop an adaptive convex combination DIPNLMS (CDIPNLMS) algorithm.Secondly, proportional affine projection algorithm (PAPA) is an extended form of PNLMS algorithm in the time domain. The PAPA has a faster convergence rate for dealing with the relevant input signals, but it has high computational complexity. To reduce the computational complexity, C. Paleologu proposed memory PAPA (MPAPA). However, unreasonable calculation method of proportional step-size parameter in MPAPA leads to slow convergence rate at late stage. To overcome this problem, the effective method is using the absolute value of the difference between the current tap weight estimate and the system tap weight as the step-size at each tap. Unfortunately, the system tap weights are unknown in practical application. Here, we choose the previous tap weight estimates as the unknown system tap weights. However, the calculating method of proportional step-size parameter is not always proportional to the actual magnitude of the filter weights exactly, which leads to slow convergence rate. To this end, the paper introduces individual activation factors method into WMPAPA, thus IAF-WMPAPA is proposed. Fortunately, IAF-WMPAPA achieves good recognition results for high sparse systems.Finally, when the input signals are related, the normalized subband adaptive filtering (NSAF) algorithm greatly accelerates the convergence rate of the normalized LMS (NLMS) algorithm. The proportional NSAF (PNSAF) algorithm shows a faster convergence rate than NSAF algorithm for sparse system identification. To identify highly sparse systems under actual conditions, the method of individual activation factor is incorporated into PNSAF algorithm, developing an individual activation factors PNSAF (IAF-PNSAF) algorithm. It greatly accelerates the convergence rate of the PNSAF. However, in order to solve the tradeoff between the convergence rate and steady-state misadjustment in the fixed step-size IAF-PNSAF algorithm, we develop an adaptive convex combination IAF-PNSAF (CIAF-PNSAF) algorithm to solve the problem of selecting step-size parameter. The CIAF-PNSAF algorithm obtains fast convergence rate and small steady-state misadjustment.The simulations verify the effectiveness of the various improved proportional adaptive filtering algorithms.