Performance Analysis Of Frequency-domain Adaptive Filter

Adaptive filtering technology is a filtering technology that realizes the optimal filtering under the premise that the prior statistical knowledge of the signal to be received is unknown,with the help of a certain filtering algorithm to self-learn the changes of the external non-stationary environment.Because the operation is simpler and easier to implement,the Least Mean Square(LMS)algorithm is the most widely used algorithm among many adaptive filtering algorithms.But when the weight coefficient of the filter is increased,the computational complexity of the LMS algorithm will also increase,especially in some applications that require thousands of weight coefficients to model the system.Even it will be difficult to implement in resource-constrained systems.In order to solve the problem of computational complexity of adaptive filter,Ferrara initially proposed the frequency-domain adaptive filtering(FDAF)algorithm based on Fourier Transform(FFT)and overlap-save method.However,the fixed step size makes the filter always unable to get fast convergence and low steady-state error simultaneously,no matter it is the time-domain LMS algorithm or the FDAF algorithm.To solve the contradiction,the convex combination of LMS(CLMS)algorithm is developed.By connecting two independent filters in parallel,the combined filter can obtain a fast convergence speed and a low steady-state mean square error(MSE).Combining the FDAF and CLMS algorithms,the convex combination of overlap-save frequency-domain adaptive filters(COSFDAF)algorithm was developed to improve the ability of adaptive filters to identify large systems.Based on the above adaptive algorithms,differing from working out the state recursions of the mean weight-error vector and weight-error covariance matrix to analyze the performance of adaptive filter,a new and more simplified method to analyze the performance of the frequency-domain adaptive filter is proposed in this paper.The analysis is implemented in frequency-domain directly,that is,it is not convert frequency domain into time domain by using inverse Fourier transform(IFFT),which makes the analysis process easier to understand.This paper mainly includes the following aspects:(1)Based on the separation hypothesis,the performance of the FDAF algorithm in stationary and non-stationary environments is analyzed.And the analytical expression of the steady-state mean square error,the steady-state tracking mean square error and the optimal step size in the tracking environment of the FDAF algorithm are given.In addition,the theoretical analysis of the transient performance for FDAF algorithm is given.The transient performance expressions under the white and the related input signal are obtained.Computer simulation results verify the correctness of the theoretical analysis.(2)Simulation results show that the COSFDAF algorithm has superior performance in terms of convergence speed and steady-state mean square error in both the steady-state performance and tracking performance,which can converge to the a smaller steady-state mean square error.According to the performance analysis of the convex combination of time-domain adaptive filters and the proposed method in this paper,the steady-state performance and tracking performance are derived.And the analysis for the transient performance of the COSFDAF algorithm under the white and the related input signal is presented.Computer simulation results verify the correctness of the theoretical analysis.