Research On Filtering Algorithms Based On Combined Affine Projection Sign

Adaptive filters are widely used and can track channels in real time,which plays an indelible role in signal processing direction.In addition to the hardware conditions of the adaptive filter,the core of the whole component is the adaptive filter algorithm,which gives the soul of the filter and makes it possible for the filter.Different algorithms de-termine the performance of the filter.In addition,environmental factors can also lead to changes in the performance of the filter.If the algorithm has good strong anti-interference to the unknown environment and makes the filtering performance（steady-state error,con-vergence rate,etc.）meet the expectation,which indicates that the algorithm has strong robustness.People are always looking for an algorithm whose convergence speed and steady-state error are in line with expectations,but the two are often relative.And,in or-der to overcome this problem,one of the popular ideas is the convex combination.For the algorithm adjusted by the step parameter,the large step size is able to accelerate the con-vergence speed,while the small step size can improve the filtering accuracy.The convex combination method is able to maintain the filtering accuracy of those original algorithms and improve the convergence speed of proposed algorithms.The typical algorithms are the combined affine projection sign algorithm（CAPSA）and the combined-step-size affine projection sign algorithm（CSS-APSA）.There are a large number of long sparse channels in the communication system,where a large number of weight coefficients are zero or close to zero,and only a small amount of weight coefficients have significant values.The traditional adaptive filter adopts a global step size parameter,and all the channel weight coefficients are the same fixed parameter,so that the convergence speed of the algorithm is affected by the minimum parameter,and it takes more iterations for a larger weight coefficient to converge to its optimal value,so its convergence performance is not very ideal.researchers put forward various improved algorithms to solve this problem?among those algorithms the proportional improvement is a uesful method.Improving the affine projection sign algorithm（APSA）is the most typical one and the memory-improved proportionate APSA（MIP-APSA）is derived.In addition,there are a large number of non-gaussian impulse noises in the real environment,which will make those algorithms extremely sensitive and lead to performance（conver-gence speed or filtering accuracy）deterioration.The problem may be effectively improved by choosing the appropriate error criterion,among which the minimum?₁-norm criterion and generalized correntropy induced metric（GCIM）have better effects.Based on the above problems,this paper studies APSA-type algorithms.The main work and contribu-tion points of full text are as follows:1)Based on the existing algorithms of CAPSA and CSS-APSA,a simplified CSS-APSA（SCSS-APSA）was proposed from the consideration and practical analysis of the mixing factors related to their performance.Similar to the idea of CSS-APSA algorithm improving the CAPSA,we further improved the CSS-APSA and got the modified CSS-APSA algorithm（MCSS-APSA）.And on the basis of the idea of simplification,the sim-plified method is applied to the MCSS-APSA,so the simplified MCSS-APSA（SMCSS-APSA）is derived.2)In this paper,the minimum?₁-norm criterion and GCIM have been successfully applied in adaptive filtering fields,on account of their robustness in Non-Gaussion noise environment.The MIP-APSA-type algorithms were improved based on generalized cor-relation induction metric,and called as GCI-M-IP-APSA which has good filtering perfor-mance under the condition of large strong impulse noise and sparse channel.Moreover,a simplified GCI-M-IP-APSA（SGCI-M-IP-APSA）is also proposed to reduce the com-putational complexity.What's more,in order to solve the poor convergence behavior in non-stationary situations,we apply an adaptive convex combination for SGCI-M-IP-APSA.In the whole paper,the simulation software matlab-r2014a was used to carry out ef-fective experiments.With the help of experimental results and theoretical analysis,the modified Algorithms（MAs）proposed in this paper were well verified to have better fil-tering performance.