Mean-Square Analysis of Affine Projection Algorithm and Study for the Performance Improvement

DoctorThis dissertation introduces mean-square analysis of affine projection algorithm(APA).The proposed analysis shows improved prediction of the MSD learning behavior of APA than the previous literature for the convergence rate and steady-state error.In the case of mean-sqaure error(MSE) anlysis, the exact relations of the same numober of the projection order(M) of APA are discovered.The accurate analysis gives us a chance to improve the APA by scheduling/varying step-size/regularization factor based on geometric/algebraic interpretations than the previous algorithms which have the similar strategies.Chapter 2 presents an improved mean-square deviation (MSD) analysis of the standard affine projection algorithm (APA) based on two distinctive features.First, the propagation model of the error covariance includes the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputssuch a cross-correlation has merely been considered previously.Second, the analysis based on n most recent accumulated iterations, rather than a typical analysis based on a current single iteration, is suggested to reveal a previously unseen phenomenon, where n denotes the tap-length of the filter.Simulation results are in better agreement with the proposed theoretical results, than the previous theoretical ones, over a wide range of parameters such as tap-length, projection order, and step-size.Chapter 3 presents the M exact relations based on the results from Chapter 2 by pre-/post-multiplying input matrix which has the tap-length(n) by M.Chapter 4 and 5 improve the APA and the normalized least-mean-square(NLMS) algorithm based on the geometric interpretations.An approach for scheduling the step sizes of an adaptive filter using the affine projection algorithm (APA) is proposed so that its mean-square deviation (MSD) learning curve can be guided along a pre-designed trajectory in Chapter 4.This approach eliminates the parameter-tuning process and does not require estimating unmeasurable stochastic quantities.Furthermore, a step-size lower bound is derived in random-walk-modeled environments that leads the adaptive filter to achieve the smallest steady-state MSD, while in stationary environments, the closer to zero the step size is, the smaller the steady-state MSD.For efficient memory usage in practice, the schedule is modified from full-table step sizes to a few down-sampled step sizes without performance degradation.The proposed algorithm also demonstrates greater robustness over different signal-to-noise ratios than the existing variable-step-size APAs.Chapter 5 proposes a new algorithm that schedules a regularization factor in the normalized least-mean-squares (NLMS) algorithm by analyzing the mean-square deviation learning behavior, which makes the proposed algorithm have both a faster convergence rate and a lower steady-state error for various input signals with almost no additional computation in the NLMS framework.Chapter 6 describes how to set up the step size of the affine projection algorithm (APA) based on mean-square deviation analysis, namely algebraic interprestion.The analysis considers the cross-correlation between the current weight error vector and the prior measurement noises associated with the reused inputs vectors for better prediction of the learning behavior of the APA.With the predetermined step size based on the analysis, the proposed approach eliminates the parameter-tuning process and the derived algorithm achieves both the fast convergence rate and the low steady-state error.In a simulation, the proposed algorithms exhibits fast convergence and produces small steady-state error not only for a white signal but also for various colored input signals for a properly chosen projection order.It is shown that they are also robust against uncertain signal-to-noise ratios