Investigation On Block-Sparse Adaptive Filtering Algorithms

In recent years,with the rapid development of signal processing theory,people's need for identification of unknown systems has become more and more intense.System identification has become the focus and focus of current research.Although scholars at home and abroad have proposed many algorithms for system identification,there are still many problems that need to be solved or require further research.First,there are many unknown systems with prior sparse characteristics in practical system identification applications.For example:high-definition digital TV transmission channels,underwater acoustic communication channels,echo systems,etc.However,traditional adaptive system identification algorithms cannot take advantage of the system's inherent sparse characteristics,which leads to a decrease in algorithm performance.Second,traditional adaptive system identification algorithms are mostly based on the mean square error criterion,and the assumption under this criterion is that the background environment is a Gaussian noise environment,and non-Gaussian impulsive noise environments are not considered.In view of the above problems,the main work of this article is as follows:(1)In the Gaussian environment,for the block sparse characteristics of the network echo system and satellite communication system impulse response,by introducing a mixed l_2,0 norm constraint in the proportionally normalized minimum mean square(PNLMS)algorithm,in order to make full use of the block sparse characteristics,a novel A block sparse proportion normalized least mean square(L20-PNLMS)algorithm based on a mixed l_2,0norm.In order to further improve the performance of the proposed algorithm,an improved proportionally normalized minimum mean square algorithm was developed,and an improved PNLMS(L20-IPNLMS)algorithm with a l_2,0 norm constraint was constructed.In the case of mixed Gaussian noise environment,the mixed l_2,i norm constraint is introduced into the minimum mixed norm algorithm,and a block sparse proportional mixed error criterion(BPNLMMN)algorithm is proposed.The simulation comparison experiment analysis method is used to verify the performance and superiority of the designed L20-PNLMS,L20-IPNLMS and BPNLMMN algorithms for block sparse systems.(2)In the impulsive noise environment,based on the maximum correlation entropy criterion,using the base tracking method,the mixed l_2,1 norm is used to constrain the weight coefficient vector of the adaptive filter(where the l₂ norm function is to divide the weight coefficient of the adaptive filter Update,the function of l₁ norm is to find the sparsity of the system.)A hybrid norm-constrained proportionally normalized maximum correlation entropy(HNC-PNMCC)algorithm is proposed.Through simulation comparison and analysis,the proposed HNC-PNMCC algorithm is used to identify block sparse systems in a simulated mixed Bernoulli distribution impulsive noise environment.(3)Aiming at the problem of decreasing convergence speed of traditional adaptive system identification algorithms under strong correlation signal input and performance degradation under impulsive noise,an affine projection algorithm(APMCC)algorithm based on the maximum correlation entropy criterion is proposed to effectively whiten the input signal and improve the algorithm's performance.Convergence speed;the APMCC algorithm with the gain allocation matrix is implemented to implement the proportional APMCC(PAPMCC)algorithm;the mixed norm constraint weight coefficient vector is introduced into the APMCC algorithm to implement the robust block sparse proportional APMCC(RGS-PAP)algorithm;To improve the flexibility of the algorithm and effectively utilize the inherent sparse characteristics of the system,the l_p norm constraint and variable kernel width technology are introduced into the APMCC algorithm.A variable kernel width ratio APMCC(LP-VPAP)algorithm with l_p norm constraint is proposed.The simulation analysis method was used to verify the superiority of the proposed PAPMCC,RGS-PAP and LP-VPAP algorithms for sparse system identification.