Affine Projection Algorithm, The Number Of Step Length And Step In The Study

Digital Signal Processing technology has been developed a lot in modem society. Filtering is a kind of signal processing technology; after processing the input signals, the output signal contains the useful content. Filter is one of representative digital signal processing system which could be divided into time invariant system and time variable system. The time invariant system coefficients and structure are fixed while that of the time variable system will be changed with time. The filtering is one kind of time variable system.With the development of very large scale integration, the adaptive filter is widely used in communication, automatic engineer and echo cancellation. The filter with the learning and adaptive ability, variates the coefficients with time and environment, and also it can process the steady and no steady signal without the statistic information.Least mean square algorithm is widely used for the simply structure, low compute complex. It is one of random gradient algorithms with the steady gradient during the iteration. While the input signal of high correlated will worse the algorithm convergence speed.To solve the mentioned problem, affine projection algorithm is proposed by Ozeki and Umeda. The algorithm reusing the input signal improves the convergence speed with the high correlated input signal. However, it brings with much more computational complexity and high steady convergence error at the same time. Some scholars proposed variable step size affine projection and variable order affine projection algorithm. The representative algorithms are VSAPA and E-APAThe step size of affine projection algorithm is controlled according to the conditions on fast convergence speed, and a new variable step size affine projection algorithm is proposed. The step size of the algorithm is adjusted automatically with the variation of the output error to reduce the steady-state MSE. When the algorithm is used in system identification, faster convergence rate and lower mean square error is obtained.Via changing the condition of the Affine Projection Algorithm, a new Affine Projection Algorithm (APA) with Evolving Order is proposed by equalizing the posterior error to the system noise. The order of the proposed algorithm is proportional to the ratio between the square of L2norm of the error vector and system noise power. And the scale factor can be adjusted by the regularization factor. The order is large at the beginning and small when the algorithm has converged. Simulations show that the proposed algorithm has fast convergence rate, low steady state misalignment and computational complexity.The paper proposed two new variable parameter APA algorithms in different views. And also the comprehensive algorithm of the VSAPA and E-APA can be used to trade off among computational complexity, convergence speed and steady state misalignment.