Research On Affine Projection Subband Adaptive Algorithms

The field of Digital Signal Processing has developed so fast since the 1980s,the reason for this is that a growing number of practical technology can be used in digital signal processing algorithms.When dealing with signals whose statistical properties are unknown,the traditional algorithms do not process these signals efficiently.The solution is to use an adaptive filter that automatically changes its characteristics by optimizing the internal parameters.The adaptive filtering algorithms are essential in the field of signal processing applications.Adaptive filter are widely used in system identification fields,such as acoustic echo cancellation,active noise control.Least mean square(LMS)algorithm is widely used for the simply structure,low compute complex.While the input signal of highly correlated will worse the algorithm convergence speed.To solve this problem,the affine projection algorithm(APA)and subband adaptive filtering(SAF)algorithms has been proposed.To optimize the performance of convergence speed and steady-state misadjustment,we make improvements on the basis of combination of the APA and SAF,we develop a new algorithm to further enhance the tracking ability by using variable step size and proportional.First,we are briefly generalizing the basic idea of the traditional AP algorithm,normalized subband adaptive(NSAF)algorithm and their improved algorithms.When the input signal is colored signal,especially in the highly background noise environment,for the problem of tracking ability with the improved affine projection and subband adaptive filtering algorithm greatly decline.We develop an improved affine projection subband adaptive filtering(IAPSAF)algorithm,in order to further illustrate the effectiveness of the algorithm,the new algorithm are analyzed with steady state.Secondly,when the input signal is related signal,NSAF is much faster than the normalized least mean square(NLMS)algorithm on the convergence speed,and computational complexity is relatively close to both of them,especially in the long impulse response.Based on this feature,acoustic echo cancellation becomes an important application of NSAF.However,due to the use of fixed step,we need to solve the tradeoff between the convergence rate and steady-state misadjustment in the NSAF algorithm.Benefit from the convex combination ideas,we develop a combined step size affine projection subband adaptive filtering(CSS-IAPSAF)algorithm based on proposed IAPSAF.It is worth mentioning that compared to the convex combination algorithms,the proposed algorithm only requires a single filter update,thus significantly reduces the computational cost.Finally,in the acoustic echo cancellation,the proportionate normalized least mean square(PNLMS)algorithm was put forward based on the sparse characteristic of impulse response,The basic idea is according to different step size proportional update for each tap weight vector,make the algorithm have faster convergence rate and low steady state misadjustment in this application.When the input signal correlation is higher,proportionate normalized subband adaptive(PNSAF)algorithm shows the faster convergence speed.Based on this thought,and to further improve the IAPSAF's performance with sparse impulse response at the same time,we develop an improved proportionate APSAF(IP-APSAF)algorithm,and we compared to other improved proportionate algorithm,not only has faster convergence speed,but also has a lower steady state misadjustment.The simulations verify the effectiveness of the various improved affine projection subband adaptive filtering algorithms.