Abstract: An error between the rate fsym at which data are received and the rate fs at which the data are sampled in is determined by processing a received signal with a nonlinear operator, performing a DFT on the processed signal to produce a plurality of DFT bins each characterized by a respective frequency, determining a dominant spectral component k0 from at least two of the DFT bins whose frequencies are substantially close to the frequency of the dominant spectral component k0, and determining the data rate fsym from the dominant spectral component k0.

Abstract: Constrained tap weights of a decision feedback equalizer are determined according to the channel impulse response of a channel and a constraint function. The constraint function is differentiable and is an approximation of a non-differentiable tap weight constraint function. The tap weight constraint function may have a constraint value M that is a function of a mean squared error of the estimated mean squared error at the output of the decision feedback 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 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 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: Constrained tap weights of a decision feedback equalizer are determined according to the channel impulse response of a channel and a constraint function. The constraint function is differentiable and comprises an approximation of a non-differentiable tap weight constraint function. The tap weight constraint function may have a constraint value M that is a function of a mean squared error of the estimated means squared error at the output of the decision feedback equalizer.

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: An error between the rate fsym at which data are received and the rate fs at which the data are sampled in is determined by processing a received signal with a nonlinear operator, performing a DFT on the processed signal to produce a plurality of DFT bins each characterized by a respective frequency, determining a dominant spectral component k0 from at least two of the DFT bins whose frequencies are substantially close to the frequency of the dominant spectral component k0, and determining the data rate fsym from the dominant spectral component k0.

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.