| 1. |
- Ljung, Lennart, 1946-, et al.
(författare)
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Application of Fast Kalman Estimation to Adaptive Equalization
- 1977
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Ingår i: Proceedings of the 1977 IEEE Symposium on Information Theory. - Linköping : Linköping University. ; , s. 38-39
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.
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| 2. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Application of Fast Kalman Estimation to Adaptive Equalization
- 1978
-
Ingår i: IEEE Transactions on Communications. - : IEEE Communications Society. - 0090-6778 .- 1558-0857. ; 26:10, s. 1439-1446
-
Tidskriftsartikel (refereegranskat)abstract
- Very rapid initial convergence of the equalizer tap coefficients is a requirement of many data communication systems which employ adaptive equalizers to minimize intersymbol interference. As shown in recent papers by Godard, and by Gitlin and Magee, a recursive least squares estimation algorithm, which is a special case of the Kalman estimation algorithm, is applicable to the estimation of the optimal (minimum MSE) set of tap coefficients. It was furthermore shown to yield much faster equalizer convergence than that achieved by the simple estimated gradient algorithm, especially for severely distorted channels. We show how certain "fast recursive estimation" techniques, originally introduced by Morf and Ljung, can be adapted to the equalizer adjustment problem, resulting in the same fast convergence as the conventional Kalman implementation, but with far fewer operations per iteration (proportional to the number of equalizer taps, rather than the square of the number of equalizer taps). These fast algorithms, applicable to both linear and decision feedback equalizers, exploit a certain shift-invariance property of successive equalizer contents. The rapid convergence properties of the "fast Kalman" adaptation algorithm are confirmed by simulation.
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| 3. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Fast Calculation of Gain Matrices for Recursive Estimation Schemes
- 1977
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A sequence of vectors {x(t)} with dimension N is given, such that x(t+1) is obtained from x(t) by introducing p new elements, deleting p old ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Npoperations and memory locations, in contrast to the conventional way which requires proportional-to-N 2operations and memory locations. A non-symmetric case is also treated.
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| 4. |
- Ljung, Lennart, 1946-, et al.
(författare)
-
Fast Calculation of Gain Matrices for Recursive Estimation Schemes
- 1978
-
Ingår i: International Journal of Control. - : Taylor & Francis. - 0020-7179 .- 1366-5820. ; 27:1, s. 1-19
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Tidskriftsartikel (refereegranskat)abstract
- A sequence of vectors {x(t)} with dimension N is given, such that x(t+1) is obtained from x(t) by introducing p new elements, deleting p old ones, and shifting the others in some fashion. The sequence of vectors $ is sought. This paper presents a method of calculating these vectors with proportional-to-Npoperations and memory locations, in contrast to the conventional way which requires proportional-to-N 2operations and memory locations. A non-symmetric case is also treated.
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