Time-domain Least Mean Square Research Articles

Cancellation for frequency offset in OFDM system based on TF-LMS algorithm

In an orthogonal frequency division multiplexing (OFDM) system, a time and frequency domain least mean square algorithm (TF-LMS) was proposed to cancel the frequency offset (FO). TF-LMS algorithm is composed of two stages. Firstly, time domain least mean square (TD-LMS) scheme was selected to pre-cancel the frequency offset in the time domain, and then the interference induced by residual frequency offset was eliminated by the frequency domain mean square (FD-LMS) scheme in frequency domain. The results of bit error rate (BER) and quadrature phase shift keying (QPSK) constellation figures show that the performance of the proposed suppression algorithm is excellent.

Adaptive inverse control of random vibration based on the filtered-X LMS algorithm

Random vibration control is aimed at reproducing the power spectral density (PSD) at specified control points. The classical frequency-spectrum equalization algorithm needs to compute the average of the multiple frequency response functions (FRFs), which lengthens the control loop time in the equalization process. Likewise, the feedback control algorithm has a very slow convergence rate due to the small value of the feedback gain parameter to ensure stability of the system. To overcome these limitations, an adaptive inverse control of random vibrations based on the filtered-X least mean-square (LMS) algorithm is proposed. Furthermore, according to the description and iteration characteristics of random vibration tests in the frequency domain, the frequency domain LMS algorithm is adopted to refine the inverse characteristics of the FRF instead of the traditional time domain LMS algorithm. This inverse characteristic, which is called the impedance function of the system under control, is used to update the drive PSD directly. The test results indicated that in addition to successfully avoiding the instability problem that occurs during the iteration process, the adaptive control strategy minimizes the amount of time needed to obtain a short control loop and achieve equalization.

Wavelet transform domain adaptive FIR filtering

This paper presents and studies two new wavelet transform domain least mean square (LMS) algorithms. The algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their Cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity. The procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation. The first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process. It then computes the Cholesky factor of that matrix and uses its inverse to whiten the input. The complexity of this first approach is O[N log/sup 2/ (N)]. In contrast, the second approach computes a sparse estimate of the Cholesky factor of the wavelet domain correlation matrix of the input process directly. This second approach has a computational complexity of O[N log (N)] floating-point operations. However, it requires a more complex bookkeeping procedure. Both algorithms have a convergence rate that is faster than that of time-domain LMS and discrete Fourier transform (DFT) or discrete cosine transform (DCT)-based LMS procedures. The paper compares the two procedures and analyzes their mean and mean square performance.

Wavelet transform based adaptive filters: analysis and new results

In this paper the wavelet transform is used in an adaptive filtering structure. The coefficients of the adaptive filter are updated by the help of the least mean square (LMS) algorithm. First, the wavelet transform based adaptive filter (WTAF) is described and it is analyzed for its Wiener optimal solution. Then the performance of the WTAF is studied by the help of learning curves for three different convergence factors: (1) constant convergence factor, (2) time-varying convergence factor, and (3) exponentially weighted convergence factor. The exponentially weighted convergence factor is proposed to introduce scale-based variation to the weight update equation. It is shown for two different sets of data that the rate of convergence increases significantly for all three WTAF structures as compared to that of time-domain LMS. The high convergence rates of the WTAF give us reason to expect that it will perform well in tracking rapid changes in a signal.

Frequency-domain implementation of Griffiths–Jim adaptive beamformer

It is well known that the drawback of the time-domain least-mean-square (LMS) algorithm proposed by Widrow [Proc. IEEE 63, 719–720 (1975)] in adaptive filter applications is that its convergence speed decreases as the eigenvalue spread of the input autocorrelation matrix increases. However, this problem can be overcome by employing the transform-domain LMS method [Narayan et al., IEEE Trans. ASSP 31, 609–615 (1983)] which first transforms input time-domain signals into another transform-domain signals through DFT or some orthogonal transforms and then uses the self-orthogonalizing algorithm [Gitlin and Magee, IEEE Trans. Commun. 25, 666–672 (1977)] to optimize the variable weights of an adaptive filter. This method has been shown to offer great improvement in convergence rate over the time-domain LMS method. The objective of this paper is to apply the frequency-domain LMS algorithm with the self-orthogonalizing technique, called FLMS, to the Griffiths–Jim adaptive beamformer to accelerate the convergence rate for real-time processing of adaptive array signals. It is shown that the two minimum mean-square errors of the beamformer implemented in the time and frequency domains are identical. Computer simulations show that the adaptive beamformer using the FLMS exhibits faster convergence behavior and better performance of nulling jammers than that using the LMS, especially for the larger eigenvalue spread.