Variable Data Reuse Factor Affine Projection Algorithm

Filtering is one of the most important applications of digital signal processing. The aim of filtering is to extract useful information from signal. Adaptive filter is widely used in areas such as communication, biomedical engineering, automation, speech signal processing and radar. It is a time-variant filter. Adaptive filter has the abilities to learn and adjust there parameters according to the environment. That is quite different from Wiener filter and Kalman filter. Moreover, adaptive filters can process both stationary and unstationary signals without the statistical properties of input signal.Least mean square algorithm is one of the most widespread adaptive algorithms for its simplicity and excellent tracking ability. The problem with least mean square algorithm is that the convergence speed is severely deteriorated when input signal is highly correlated. Affine projection algorithm reuses data to accelerate convergence speech. However, it brings much more computational complexity at the same time. In many applications, affine projection algorithm with larger data-reuse factor is needed to get ideal performance. At the same time, the computational complexity is tremendously increased. Higher computational usually needs higher hardware performance and higher price. Two novel data-reuse factor variable factors are proposed to deal with the confliction between convergence speed and computation complexity in this paper:Affine projection algorithm with variable data-reuse factor and affine projection algorithm with variable data-reuse factor based on regularization factor.Affine projection algorithm with data-reuse factor is derived from traditional affine projection algorithm. The formula of data-reuse factor in the algorithm is originated from forcing the posterior error vector to be equal with noise vector. The result is that the data-reuse factor of affine projection algorithm is adjustable according to the error signal. Affine projection algorithm with data-reuse factor based on regularization factor is derived from regularized affine projection algorithm. The data-reuse factor is also adjusted by error signal. The difference between these two algorithms is that the data-reuse factor is related to step size factor while the later related to step size factor as well as regularization factor. The introduction of regularization factor to our algorithm makes the adjustment of data-reuse factor more flexible, and the performance of algorithm better with regularization factor can not be neglected.The theory of the two proposed algorithms is the same. That is, a large data-reuse factor can be obtained when the error signal is large, which promises fast convergence speed. The data-reuse factor will decrease with the convergence of error signal and reach a much lower level, which promises lower computational complexity. This mechanism solves the confliction among convergence speed and computational complexity. The decreasing of data-reuse factor can result in better steady state performance as well. To sum up, the proposed algorithms in this paper can trade off among computational complexity, convergence speed and steady state misalignment very well.A new, simple variable forgetting factor is also proposed, which is based on the variable data-reuse factor. Between the largest and smallest value, the variable forgetting factor is a power function of data-reuse factor. The new factor promotes the performance of proposed algorithms.System identification is taken as the example to test the performance of the novel algorithms proposed. A large number of simulations are done to show the better performance of the algorithms.