Fuyun Ling

A recursive modified Gram-Schmidt algorithm for least- squares estimation

This paper presents a recursive form of the modified Gram-Schmidt algorithm (RMGS). This new recursive least-squares (RLS) estimation algorithm has a computational complexity similar to the conventional RLS algorithm, but is more robust to roundoff errors and has a highly modular structure, suitable for VLSI implementation. Its properties and features are discussed and compared to other LS estimation algorithms.

Adaptive Lattice Decision-Feedback Equalizers--Their Performance and Application to Time-Variant Multipath Channels

This paper presents two types of adaptive lattice decisionfeedback equalizers (DFE), the least squares (LS) lattice DFE and the gradient lattice DFE. Their performance has been investigated on both time-invariant and time-variant channels through computer simulations and compared to other kinds of equalizers. An analysis of the self-noise and tracking characteristics of the LS DFE and the DFE employing the Widrow-Hoff least mean square adaptive algorithm (LMS DFE) are also given. The analysis and simulation results show that the LS lattice DFE has the faster initial convergence rate, while the gradient lattice DFE is computationally more efficient. The main advantages of the lattice DFEs are their numerical stability, their computational efficiency, the flexibility to change their length, and their excellent capabilities for tracking rapidly time-variant channels.

Numerically robust least-squares lattice-ladder algorithms with direct updating of the reflection coefficients

New time-recursive equations are derived for the reflection coefficients and the ladder gains in the a priori and a posteriori forms of the exact least-squares (LS) lattice-ladder filtering algorithms. The numerical accuracy of the LS lattice-ladder algorithms obtained by use of these new direct time update equations is analyzed and compared to the accuracy resulting from the conventional LS lattice-ladder algorithms. The analysis and a number of simulation results which are presented lead us to conclude that the new a priori and a posteriori forms of the LS lattice-ladder algorithms yield superior performance.

Corrections to 'The LMS algorithm with delayed coefficient adaptation'

The analysis in an earlier paper (see Trans. Acoust. Speech and Signal Processing, vol.37, no.9, p.1397-405, 1989) is improved by correcting an error in the derivation of the system equation. After the correction, the system equation is modified, and thus, so are the related analytical results. >

Efficient least-squares lattice algorithms based on Givens rotation with systolic array implementations

LS (least squares) lattice algorithms based on Givens rotation, called Givens-lattice algorithms, are presented. They are derived by exploiting the relationship between the Givens algorithms and the RMGS (recursive modified Gram-Schmidt) algorithm. It is shown that the Givens-lattice algorithms are suitable for LS estimation of time-series signals and are computationally more efficient than the recently derived fast QR algorithm for the same purpose. Systolic array implementation of Givens-lattice algorithms using the same basic processing cells in the systolic arrays for the original Givens algorithm is discussed. Computer simulation results are given.<<ETX>>

On training fractionally spaced equalizers using intersymbol interpolation

The use of an intersymbol interpolation method in training fractionally spaced equalizers (FSEs) is investigated. It is shown that the optimal interpolation filter depends on the amplitude frequency response of the transmitter filter and the channel. Using a nonoptimal interpolation filter increases the stead-state mean-square error of the FSE. An interpolated complex FSE (CFSE) using a stochastic gradient, or LMS, adaptive algorithm has very little advantage over an LMS CFSE with symbol-rate updating. However, an interpolated LMS phase-splitting FSE (PS-FSE) has a convergence speed that is twice as fast as a conventional PS-FSE. Special precautions for evaluating the performance of interpolated FSEs are discussed, and a novel evaluation scheme is proposed. >

Convergence characteristics of LMS and LS adaptive algorithms for signals with rank-deficient correlation matrices

The author investigates the convergence characteristics of the last mean square (LMS) and the recursive least squares (RLS) adaptive algorithms when the correlation matrix of the input signal does not have a full rank. It is shown that the initial convergence rate of the LMS algorithm is inversely proportional to the rank of correlation matrix, or equivalently, the number of nonzero eigenvalues. The same conclusion holds for the RLS algorithms if the minimum norm solution (MNS) is used in each iteration. A simple time-recursive method to obtain approximate MNSs in each iteration is presented and proven. The effect of additive noise is discussed.<<ETX>>

A flexible, numerically robust array processing algorithm and its relationship to the givens transformation

The development of systolic array processors is very important for real-time adaptive array processing applications. In this paper a numerically robust algorithm, based on the modified Gram-Schmidt (MGS) method, is presented. The algorithm can be efficiently realized using a systolic architecture and is capable of handling both exponential and finite memory windows in order to cope with time-varying data. Finally, the relation of these algorithms to similar schemes based on the Givens transformation is investigated.

A new complex system identification method and its application to echo canceller fast initialization

A method is proposed for estimating the impulse response of a complex system based on its complex input and only the real part of its output. A unique periodic white complex testing sequence is constructed, and it is then sent to the system to be estimated. An important feature of the testing sequence is that its real and imaginary parts are mutually orthogonal, i.e. their cross-correlation is zero. Due to this orthogonality, the effects of the systems real imaginary parts are ideally decoupled. The cross-correlation between the complex testing sequence and the systems real part output yields an accurate estimate of the systems complex impulse response. In applications where the unknown systems impulse response is sparse, it is possible to squeeze it and choose a considerably small period for the sequence to reduce complexity. An effective algorithm for this purpose is presented. The application of this new method to fast training of the Nyquist echo cancellers in data modems is described. It is shown that using these techniques, fast and accurate estimation can be achieved efficiently.<<ETX>>

Finite word-length effects in recursive least squares algorithms with application to adaptive equalization

In this paper we provide a summary of recent and new results on finite word length effects in recursive least squares adaptive algorithms. We define the numerical accuracy and numerical stability of adaptive recursive least squares algorithms and show that these two properties are related to each other, but are not equivalent. The numerical stability of adaptive recursive least squares algorithms is analyzed theoretically and the numerical accuracy with finite word length is investigated by computer simulation. It is shown that the conventional recursive least squares algorithm gives poor numerical accuracy when a short word length is used. A new form of a recursive least squares lattice algorithm is presented which is more robust to round-off errors compared to the conventional form. Optimum scaling of recursive least squares algorithms for fixedpoint implementation is also considered.AnalyseOn présente un résumé des nouveaux résultats concernant les effets de la précision finie dans les algorithmes adaptatifs des moindres carrés récursifs. Pour ces algorithmes, on définit la piécision numérique, la stabilité numérique et l’on montre que ces deux propriétés sont liées sans être équivalentes. La stabilité numérique est analysée théoriquement et la précision numérique sur des mots de longueur finie est examinée par simulation sur ordinateur. On montre que l’algorithme récursif classique des moindres carrés atteint une faible précision numérique lorsque des mots de longueur faible sont utilisés. On présente une nouvelle forme d’algorithme des moindres carrés en treillis qui se montre plus résistant aux erreurs d’arrondi que l’algorithme classique. On considère aussi une normalisation optimale des algorithmes des moindres carrés récursifs pour une implantation en virgule fixe.