Abstract: A channel impulse response is determined for a channel by receiving a signal from the channel, and by determining a least squares estimate of the channel impulse response. The received signal contains a training sequence and unknown data. The least squares estimate of the channel impulse response is determined by multiplying the received signal by a stored quantity. The stored quantity is based on (i) a stored replica of the training sequence, and (ii) an assumed covariance matrix that is based on a noise variance and an initial channel impulse response that assumes a unit physical channel.

Abstract: In forming a current channel estimate from a received signal y, the received signal y is decoded to form data s, a convolution matrix ?is formed from a first portion of the data s, a matrix F1 is formed from a second portion the data s such that the second portion of the data s includes data that is less recent that the data in the first portion of the data s, a matrix F2 is formed from a third portion the data s such that the third portion of the data s includes data that is more recent than the data in the first portion of the data s, a predicted channel estimate hpred is determined, and a conjugate gradient algorithm is performed to determine the current channel estimate. The conjugate gradient algorithm is based on the received signal y, the matrix ?, the matrices F1 and F2, the predicted channel estimate hpred, and a previous channel estimate h1.

Abstract: In forming a channel estimate, a received signal y is decoded to form data s, a convolution matrix ? is formed from the data s, a matrix F is formed from the data s such that the matrix F results from the forming of the matrix ? as a convolution matrix, and a conjugate gradient algorithm is performed to determine the channel estimate. The conjugate gradient algorithm is based on the received signal y, the matrix ?, and the matrix F.

Abstract: An impulse response of a channel is estimated by correlating a received signal with a stored vector. The received signal contains a training sequence having a length Ltr, the stored vector has a length Lsv, Ltr/n=Lsv, and n is greater than two. The signal is received by a device. The vector is determined based on the training sequence and an ideal channel. The ideal channel is an idealized form of a channel through which the device receives the signal. A plurality of correlations may be performed where each correlation provides a substantially noise-free estimate of the impulse response of a different portion of the channel. The correlations are combined to provide an estimate of the impulse response of the channel.

Abstract: A channel impulse response for a channel is determined by determining an initial channel impulse response estimate based upon a stored training sequence and a received signal, by thresholding the initial channel impulse response estimate, by estimating a noise variance for the channel based upon the stored training sequence, the thresholded initial channel impulse response estimate, and the received signal, by determining an inverse of a covariance matrix based on the estimated noise variance and the thresholded initial channel impulse response estimate, by updating the channel impulse response based on the inverse covariance matrix, the stored training sequence, and the received signal, and by thresholding the updated channel impulse response estimate.

Abstract: Initial values of the tap weights for the taps of a linear equalizer are determined based on a channel impulse response of a channel so that the values corresponding to the weights of the equalizer taps achieve optimum initialization of the equalizer. These values are determined through use of a nested summation where the number of summations is dependent upon the number of multi-paths characterizing the channel.

Abstract: The tap weights of an equalizer are initialized in response to a received relatively short training sequence, and new tap weights for the equalizer are thereafter successively calculated in response to relatively long sequences of received symbols and corresponding sequences of decoded symbols. These new tap weights are successively applied to the equalizer.

Abstract: A response of a channel may be estimated by correlating a received signal and a training sequence, by forming a matrix ? based on a desired shape for the peaks of the correlation, by extracting a vector y from the received signal, and by estimating the channel response from a least-squares solution based on the matrix ?, the vector y, and a matrix formed from the elements of the known training sequence.

Abstract: A received signal having a series of T-spaced symbols having more than two levels is sampled at a rate that produces successive samples SP, SC, and SN substantially equally spaced by T/2. An output representing the difference between the sign of the sample SN and the sign of the sample SP is generated, and the value of the sample SC is offset so that the value of the sample SC approaches zero. The offset value of the sample SC and the generated output are multiplied together in order to provide a timing error signal. The sampling of the received signal is controlled in accordance with the timing error signal.

Abstract: In forming a current channel estimate from a received signal y, the received signal y is decoded to form data s, a convolution matrix ?is formed from a first portion of the data s, a matrix F1 is formed from a second portion the data s such that the second portion of the data s includes data that is less recent that the data in the first portion of the data s, a matrix F2 is formed from a third portion the data s such that the third portion of the data s includes data that is more recent than the data in the first portion of the data s, a predicted channel estimate hpred is determined, and a conjugate gradient algorithm is performed to determine the current channel estimate. The conjugate gradient algorithm is based on the received signal y, the matrix ?, the matrices F1 and F2, the predicted channel estimate hpred, and a previous channel estimate h1.

Abstract: In forming a channel estimate, a received signal y is decoded to form data s, a convolution matrix ? is formed from the data s, a matrix F is formed from the data s such that the matrix F results from the forming of the matrix ? as a convolution matrix, and a conjugate gradient algorithm is performed to determine the channel estimate. The conjugate gradient algorithm is based on the received signal y, the matrix ?, and the matrix F.

Abstract: A channel impulse response is determined for a channel by receiving a signal from the channel, and by determining a least squares estimate of the channel impulse response. The received signal contains a training sequence and unknown data. The least squares estimate of the channel impulse response is determined by multiplying the received signal by a stored quantity. The stored quantity is based on (i) a stored replica of the training sequence, and (ii) an assumed covariance matrix that is based on a noise variance and an initial channel impulse response that assumes a unit physical channel.

Abstract: A channel impulse response for a channel is determined by determining an initial channel impulse response estimate based upon a stored training sequence and a received signal, by thresholding the initial channel impulse response estimate, by estimating a noise variance for the channel based upon the stored training sequence, the thresholded initial channel impulse response estimate, and the received signal, by determining an inverse of a covariance matrix based on the estimated noise variance and the thresholded initial channel impulse response estimate, by updating the channel impulse response based on the inverse covariance matrix, the stored training sequence, and the received signal, and by thresholding the updated channel impulse response estimate.

Abstract: The tap weights of an equalizer are initialized in response to a received relatively short training sequence, and new tap weights for the equalizer are thereafter successively calculated in response to relatively long sequences of received symbols and corresponding sequences of decoded symbols. These new tap weights are successively applied to the equalizer.

Abstract: An impulse response of a channel is estimated by correlating a received signal with a stored vector. The received signal contains a training sequence having a length Ltr, the stored vector has a length Lsv, Ltr/n=Lsv, and n is greater than two. The signal is received by a device. The vector is determined based on the training sequence and an ideal channel. The ideal channel is an idealized form of a channel through which the device receives the signal. A plurality of correlations may be performed where each correlation provides a substantially noise-free estimate of the impulse response of a different portion of the channel. The correlations are combined to provide an estimate of the impulse response of the channel.

Abstract: A received signal having a series of T-spaced symbols having more than two levels is sampled at a rate that produces successive samples SP, SC, and SN substantially equally spaced by T/2. An output representing the difference between the sign of the sample SN and the sign of the sample SP is generated, and the value of the sample Sc is offset so that the value of the sample SC approaches zero. The offset value of the sample Sc and the generated output are multiplied together in order to provide a timing error signal. The sampling of the received signal is controlled in accordance with the timing error signal.

Abstract: A response of a channel may be estimated by correlating a received signal and a training sequence, by forming a matrix &Ggr; based on a desired shape for the peaks of the correlation, by extracting a vector y from the received signal, and by estimating the channel response from a least-squares solution based on the matrix &Ggr;, the vector y, and a matrix formed from the elements of the known training sequence.

Abstract: Initial values of the tap weights for the taps of a linear equalizer are determined based on a channel impulse response of a channel so that the values corresponding to the weights of the equalizer taps achieve optimum initialization of the equalizer. These values are determined through use of a nested summation where the number of summations is dependent upon the number of multi-paths characterizing the channel.