Frequency-domain Block LMS Algorithm Research Articles

Mean-square performance of the modified frequency-domain block LMS algorithm

The mean weight vector of the normalized frequency-domain block least-mean-square (NFBLMS) algorithm cannot converge to the optimal solution in the mean-square error sense for the non-causal and under-modeling cases. A modified frequency-domain block least-mean-square (MFBLMS) algorithm was proposed to resolve this problem, which was claimed to have optimal steady-state performance. In this paper, we present a comprehensive statistical analysis of the MFBLMS algorithm in both the full- and under-modeling conditions. We first present the equivalent time-domain expressions for the update equation and the error vector of the MFBLMS, which allows us to carry out the performance analysis completely in the time domain. The analytical model for both the mean and mean-square performance of the MFBLMS are provided without assuming a specific input distribution, and the closed-form solution of the step-size bound is given. It is found that the upper step-size bound of the MFBLMS algorithm is much smaller than that of the NFBLMS algorithm for the correlated inputs, and the MFBLMS algorithm does not always achieve a better steady-state performance than the NFBLMS algorithm. Simulation results agree with our theoretical analysis quite well.

Convergence analysis of the modified frequency-domain block LMS algorithm with guaranteed optimal steady state performance

Although the bin-normalized frequency domain block LMS (NFBLMS) algorithm has theoretically very fast convergence speed, it suffers from convergence to a biased steady state solution when causality is not met or when the adaptive filter is of deficient length. A modified FBLMS (MFBLMS) algorithm with guaranteed optimal steady state performance has been proposed, but the theoretical analysis on its convergence properties has not been presented. This paper analyzes the convergence behavior of the algorithm by using the theory of asymptotically equivalent matrices. The eigenvalues of the matrix controlling the convergence behavior is proven to have the tendency to be equally distributed, and a theoretical eigenvalue spread is derived based on the first-order autoregressive (AR) signal model, which is significantly lower than that of the time domain LMS (TDLMS) algorithm. Therefore the convergence speed of the MFBLMS is significantly higher than that of the TDLMS algorithm for colored reference signal. Simulations are carried out to validate the convergence behavior predicted from the theoretical analysis.

A Step Size Control Method for Deficient Length FBLMS Algorithm

In many practical situations, where the length of the system impulse response is extremely long, the adaptive filter usually works in an under-modeling situation. In our previous work, we found that for deficient-length frequency-domain block least-mean-square (FBLMS) algorithm, the steady-state solution depends on the step size selected. The deficient length-FBLMS algorithm will converge to the Wiener solution only if the same step size is selected for each frequency bin. Numerous variable step-size methods for FBLMS algorithm have been proposed. However, almost all of them cannot converge to the Wiener solution in the under-modeling situation. In this letter, a step size control method for deficient-length FBLMS algorithm is proposed. Effectiveness of the proposed algorithm is demonstrated through computer simulations.

A modified frequency-domain block LMS algorithm with guaranteed optimal steady-state performance

The bin-normalized frequency-domain block LMS (FBLMS) algorithm has low computational burden and potential fast convergence; however, it suffers from a biased steady-state solution when the reference signal lags behind the desired signal or the adaptive filter is of insufficient length. This paper proposes a unified framework for the FBLMS algorithm, which can be used to comprehensively analyze its steady-state behavior. Furthermore, a modified FBLMS algorithm with guaranteed optimal steady-state performance is proposed based on the framework. Simulations are carried out to demonstrate the benefit of the proposed algorithm.

Research on the Interference Cancellation Based on Adaptive Algorithms

The adaptive interference cancellation algorithms(AICA) is proposed in this paper. The Matlab simulation results of the performance of six different kinds of AICA are presented. According to the comparison of the simulation results, especially the usage of resource, convergence rate and effects of cancellation, the NLMS adaptive interference cancellation algorithm and frequency-domain block LMS algorithm are selected, which are suitable for the further design on FPGA. By simulating the functions by Modelsim, and analyzing the PSD curve and the constellation of output signals, the adaptive interference cancellation algorithm system based on frequency-domain block LMS have achieved expected effect. The frequency-domain block LMS adaptive echo interference cancellation system has better flatness on the in-band PSD curve and better convergence effect on the constellation. Therefore, frequency-domain block LMS adaptive interference cancellation algorithm is chosen as the design with high performance-price ratio. The more points there are, the more obvious advantages it will perform.

Steady-State Solution of the Deficient Length Constrained FBLMS Algorithm

In almost all analyses of the frequency-domain block least mean-square (FBLMS) algorithm, the length of the adaptive filter is assumed to be equal to that of the unknown system impulse response. However, in many practical situations, where the length of the system impulse response is extremely long, the adaptive filter usually works in an under-modeling situation. The analysis results for the sufficient length FBLMS algorithm are not applicable to the deficient length case. In this correspondence, the steady-state solution of the deficient length constrained FBLMS algorithm is analyzed. Simulations illustrate the accuracy of the theoretical results.

Research on the Adaptive Algorithm for Interference Cancellation

A adaptive interference cancellation algorithm was proposed in this paper. The MATLAB simulation results of the performance of five different kinds of adaptive interference cancellation algorithm were presented. According to the comparison of the simulation results, especially the usage of resource, convergence rate and effects of cancellation, the frequency-domain block LMS algorithm was selected suitable for the further design on FPGA. By simulating the functions by modelsim, and analyzing the PSD curve and the constellation of output signals, the adaptive interference cancellation algorithm system based on frequency-domain block LMS achieved expected effect. The better in-band flatness of the PSD curve and the higher convergence rate on constellation were obtained. Therefore, the frequency-domain block LMS adaptive interference cancellation algorithm is chosen as the design with high performance-price ratio.

Analysis of the frequency-domain block LMS algorithm

We present a new analysis of the frequency-domain block least-mean-square (FBLMS) algorithm. An earlier analysis uses a mapping of the frequency-domain information to the time-domain before proceeding with the analysis of the algorithm. We present a direct analysis of the FBLMS algorithm in the frequency domain. As compared with the previous analysis, the new analysis is easier to follow. It is also more rigorous than the previous works and gives a better insight to the effect of various processing components in the algorithm structure on its convergence behavior. In particular, we show how the transformation of input samples to the frequency domain, combined with the effect of the involved windowing matrices, and step-normalization affect the convergence behavior of both constrained and unconstrained versions of the FBLMS algorithm. We also report a procedure for derivation of misadjustment equations of various versions of the FBLMS algorithm.

Generalized sliding FFT and its application to implementation of block LMS adaptive filters

This paper has two contributions. First, the concept of the generalized sliding fast Fourier transform (GSFFT) as an efficient implementation of the hopping FFT is introduced. Application of the GSFFT is broad and not limited to what has been considered in this paper. The frequency domain block LMS (FBLMS) adaptive filters are then revised, and their implementations for block lengths less than the length of the adaptive filter are studied. The GSFFT and the available pruned FFTs are used to give an efficient implementation of these filters. In the particular case of the block length equal to one, where the FBLMS algorithm reduces to the frequency domain LMS (FLMS) algorithm, it is shown that the latter can be implemented with the order of M complexity, where M is the length of the adaptive filter. >

Performance analysis of frequency-domain block LMS adaptive digital filters

The performance of the frequency-domain block least-mean-square (FBLMS) adaptive digital filters, whose filter weights are updated efficiently using the fast Fourier transform, is investigated. In particular, the convergence of the unconstrained FBLMS algorithm with reduced complexity, which is obtained by removing the constraint that has been known to be required in adjusting the frequency-domain weights based on overlap-save sectioning, is analyzed. The performance of the self-orthogonalizing FBLMS algorithm with improved convergence speed, in which different convergence factors normalized by frequency-domain power estimates are used for different frequency components of the weights, is also studied. >

Performance of a class of adaptive data-driven echo cancellers

A study is made of the performance of a class of adaptive data-driven echo cancellers (DDECs). The authors first investigate the interrelationship in a unified framework among the system equations of various data-driven echo cancellers. As a result, they obtain a new DDEC algorithm that consists of only one real-valued adaptive structure. The authors analyze and compare the convergence behavior of DDECs. They analyze their complexities when the least-mean-square (LMS) algorithm and the frequency-domain block LMS algorithm are used for adjusting the canceller weights. The results show that the echo canceller structure realized in the frequency domain has advantages in convergence rate and in implementation complexity as compared to existing DDEC structures. >