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Autocorrelation Matrix

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M. Barton – One of the best experts on this subject based on the ideXlab platform.

  • Performance of SVD-based fractionally spaced equalizers in data transmission systems
    IEEE Transactions on Signal Processing, 1994
    Co-Authors: M. Barton

    Abstract:

    An algorithm is presented for implementing a complex fractionally spaced equalizer (CFSE) that uses the least-mean-square (LMS) algorithm and singular value decomposition (SVD). SVD is used to reduce the eigenvalue spread of the Autocorrelation Matrix of the CFSE tap inputs. It is shown that SVD accelerates the convergence of the CFSE in proportion to the receiver oversampling factor but maintains the steady-state excess mean square error (MSE) at approximately the same level as that of the CFSE that does not have an SVD-based receiver prefilter. The authors choice of a prefilter from the Autocorrelation Matrix of the received signal will facilitate easier and faster tracking of the principal components in an adaptive environment. >

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  • ICASSP – An alternative realization of the SVD-based FSE
    International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: M. Barton

    Abstract:

    An investigation is conduced of the noise threshold performance of the singular-value-decomposition (SVD)-based least-mean-square (LMS) adaptive algorithm when the Autocorrelation Matrix of the input signal is not truly rank deficient and when low-rank approximation techniques are used to prefilter the channel output adaptively. It is shown that SVD improves the input SNR (signal-to-noise ratio) and reduces the eigenvalue spread of the Autocorrelation Matrix, but these improvements fall short of the amount required to significantly improve the convergence characteristics of the LMS fractionally spaced equalizer operating in low SNRs. The results show some improvement in the initial convergence rate of the algorithm, while the excess mean-squared error (MSE) remains essentially unchanged. >

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G Vazquezgrau – One of the best experts on this subject based on the ideXlab platform.

  • recursive bayes risk parameter estimation from the cyclic Autocorrelation Matrix
    International Conference on Acoustics Speech and Signal Processing, 1994
    Co-Authors: J Ribasagarra, G Vazquezgrau

    Abstract:

    We present a new method for recursively estimating the frequency and timing parameters of a second order cyclostationary signal with known cyclic Autocorrelation Matrix (CAM). This problem appears in the context of radar as well as asynchronous communications in highly non-stationary environments (e.g. telemetry) due to the Doppler effect. The parameters evolution is modelled by a zero-order random walk. The estimates are obtained from the instantaneous CAM (ICAM) of the signal. While nonlinear Kalman filter theory is a possible approach to this problem, Bayes risk theory is used instead. In this way the Riccati equation and gain matrices become independent of the estimates, thus allowing a look-up table solution. The folded normal density (FND) is assumed as parameters’ prior. The prior is recursively updated in mean (estimates) and variance. By comparing the obtained equations with linear Kalman filter equations we show that with few modifications a first-order random walk model can be easily incorporated to cope with highly non-stationary frequency evolution. >

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G. Vazquez-grau – One of the best experts on this subject based on the ideXlab platform.

  • ICASSP (4) – Recursive Bayes risk parameter estimation from the cyclic Autocorrelation Matrix
    Proceedings of ICASSP '94. IEEE International Conference on Acoustics Speech and Signal Processing, 1
    Co-Authors: J. Riba-sagarra, G. Vazquez-grau

    Abstract:

    We present a new method for recursively estimating the frequency and timing parameters of a second order cyclostationary signal with known cyclic Autocorrelation Matrix (CAM). This problem appears in the context of radar as well as asynchronous communications in highly non-stationary environments (e.g. telemetry) due to the Doppler effect. The parameters evolution is modelled by a zero-order random walk. The estimates are obtained from the instantaneous CAM (ICAM) of the signal. While nonlinear Kalman filter theory is a possible approach to this problem, Bayes risk theory is used instead. In this way the Riccati equation and gain matrices become independent of the estimates, thus allowing a look-up table solution. The folded normal density (FND) is assumed as parameters’ prior. The prior is recursively updated in mean (estimates) and variance. By comparing the obtained equations with linear Kalman filter equations we show that with few modifications a first-order random walk model can be easily incorporated to cope with highly non-stationary frequency evolution. >

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