Research On Frequency Domain Distributed Algorithm Based On FFT

Distributed adaptive filtering algorithm is an extension of adaptive filter in distributed network.Its purpose is to realize the estimation of unknown target parameters through the information interaction between neighborhood nodes.Therefore,adaptive filtering algorithm can be used as a distributed algorithm and various distributed strategies can be used for parameter estimation.Diffusion least mean square(D-LMS)algorithm based on mean square error(MSE)criterion has been widely studied and applied because of its simplicity and easy implementation.However,for some practical application systems,the tap coefficient of adaptive filter required by adaptive filtering algorithm in time domain is very long,resulting in high computational complexity of the algorithm.Distributed adaptive filtering algorithm also faces the same problem.Frequency domain adaptive filtering(FDAF)algorithm uses fast fourier transform(FFT)to calculate linear convolution in time domain.It can effectively reduce the computational complexity.Therefore,in order to solve the problem of high computational complexity of distributed adaptive filtering algorithm,this thesis introduces frequency domain adaptive filtering algorithm into distributed network.A diffusion constrained frequency domain adaptive filtering(D-CFDAF)algorithm is proposed.In distributed network,in some cases,the information exchange between nodes is not accurate,that is,there is the influence of link noise.In order to reduce the influence of link noise on algorithm performance,a new diffusion average-estimate constrained FDAF(D-A-CFDAF)algorithm using moving average technology is proposed.The convergence of the algorithm is analyzed in the sense of mean and mean square.The algorithm uses a first-order filter to filter the neighborhood estimation to reduce the influence of link noise.Considering the slow convergence rate of DA-CFDAF algorithm in the initial stage,a D-A-CFDAF algorithm with time-varying forgetting factor is proposed.Simulation results show that the proposed algorithm has better performance.As the frequency domain adaptive filtering algorithm has a large delay when the tap coefficient of the filter is too long,a diffusion partitioned-block frequency domain adaptive filter(D-PBFDAF)algorithm is proposed.Then,the stability of the algorithm is analyzed,and the algorithm is applied to the multi-task network.When the priori information of the whole network is unknown,a multi-task D-PBFDAF algorithm with adaptive combination weight coefficients is proposed.Simulation results show that the algorithm has better performance.