Abstract: An apparatus and method of applying a fast algorithm to a pilot-based channel estimation process includes receiving, in a receiver, a signal comprising information bits transmitted in a wireless channel, executing a pilot-based channel estimation process running on a decision-directed turbo estimation procedure having a p structure for a vector of pilots and an upper bound N for a channel spread based on a feedback of detected information bits via OFDM, encoding the detected information bits, re-encoding the detected information bits at a decoder output, re-constructing and subtracting an ICI term from the received signal, modulating the detected information bits, estimating channel symbols in a per-carrier basis based on a diagonal matrix of a full matrix involved in the pilot-based channel estimation, and performing training of the wireless channel based on an entire vector of the channel symbols.

Abstract: An apparatus and method of applying a superfast algorithm to a pilot-based channel estimation process includes receiving a signal comprising information bits transmitted in a wireless channel, executing the pilot-based channel estimation process having p structures for a vector of pilot structures and an upper bound N for a channel spread, determining a result of a matrix inversion of a channel correlation matrix for an error channel estimation offline without performing a matrix inversion, storing pilot information of the received signal for channel recovery in a transform domain, representing the Toeplitz inverse by a FFT representation, detecting and estimating nonzero taps of a channel impulse response of the wireless channel, obtaining a non-structured minimum mean-square-error (MMSE) estimate as a first estimate of locations of the nonzero taps, and replacing the non-structured MMSE estimate by an estimate computed by a tap detection algorithm.

Abstract: An apparatus and method of applying a superfast algorithm to a pilot-based channel estimation process includes receiving a signal comprising information bits transmitted in a wireless channel, executing the pilot-based channel estimation process having p structures for a vector of pilot structures and an upper bound N for a channel spread, determining a result of a matrix inversion of a channel correlation matrix for an error channel estimation offline without performing a matrix inversion, storing pilot information of the received signal for channel recovery in a transform domain, representing the Toeplitz inverse by a FFT representation, detecting and estimating nonzero taps of a channel impulse response of the wireless channel, obtaining a non-structured minimum mean-square-error (MMSE) estimate as a first estimate of locations of the nonzero taps, and replacing the non-structured MMSE estimate by an estimate computed by a tap detection algorithm.

Abstract: An apparatus and method of applying a fast algorithm to a pilot-based channel estimation process includes receiving, in a receiver, a signal comprising information bits transmitted in a wireless channel, executing a pilot-based channel estimation process running on a decision-directed turbo estimation procedure having a p structure for a vector of pilots and an upper bound N for a channel spread based on a feedback of detected information bits via OFDM, encoding the detected information bits, re-encoding the detected information bits at a decoder output, re-constructing and subtracting an ICI term from the received signal, modulating the detected information bits, estimating channel symbols in a per-carrier basis based on a diagonal matrix of a full matrix involved in the pilot-based channel estimation, and performing training of the wireless channel based on an entire vector of the channel symbols.

Abstract: A receiver and method of enhancing transmitted data signals in a wireless communications system includes wirelessly transmitting and receiving a data signal over a wireless channel in the communications system; providing known channel parameters corresponding to the wireless channel; expressing the data signal as an input data vector; replacing indexes in the input data vector having a magnitude greater than one into indexes in the input data vector having a unit norm; creating an output data vector; and calculating a dot product of (i) the input data vector comprising replaced indexes; and (ii) the output data vector, wherein the calculating process equalizes the data signal received by a receiver in the presence of Doppler frequency shifts of the data signal.

Abstract: Directly computing Feed Forward Equalizer (FFE) coefficients and Feed Back Equalizer (FBE) coefficients of a Decision Feedback Equalizer (DFE) from a channel estimate. The FBE coefficients have an energy constraint. A recursive least squares problem is formulated based upon the DFE configuration, the channel estimate, and the FBE energy constraint. The recursive least squares problem is solved to yield the FFE coefficients. The FFE coefficients are convolved with a convolution matrix that is based upon the channel estimate to yield the FBE coefficients. A solution to the recursive least squares problem is interpreted as a Kalman gain vector. A Kalman gain vector solution to the recursive least squares problem may be determined using a Fast Transversal Filter (FTF) algorithm.

Abstract: A receiver and method of enhancing transmitted data signals in a wireless communications system includes wirelessly transmitting and receiving a data signal over a wireless channel in the communications system; providing known channel parameters corresponding to the wireless channel; expressing the data signal as an input data vector; replacing indexes in the input data vector having a magnitude greater than one into indexes in the input data vector having a unit norm; creating an output data vector; and calculating a dot product of (i) the input data vector comprising replaced indexes; and (ii) the output data vector, wherein the calculating process equalizes the data signal received by a receiver in the presence of Doppler frequency shifts of the data signal.

Abstract: Multi-Input-Multi-Output (MIMO) Optimal Decision Feedback Equalizer (DFE) coefficients are determined from a channel estimate h by casting the MIMO DFE coefficient problem as a standard recursive least squares (RLS) problem and solving the RLS problem. In one embodiment, a fast recursive method, e.g., fast transversal filter (FTF) technique, then used to compute the Kalman gain of the RLS problem, which is then directly used to compute MIMO Feed Forward Equalizer (FFE) coefficients gopt. The complexity of a conventional FTF algorithm is reduced to one third of its original complexity by choosing the length of a MIMO Feed Back Equalizer (FBE) coefficients bopt (of the DFE) to force the FTF algorithm to use a lower triangular matrix. The MIMO FBE coefficients bop are computed by convolving the MIMO FFE coefficients gopt with the channel impulse response h. In performing this operation, a convolution matrix that characterizes the channel impulse response h extended to a bigger circulant matrix.

Abstract: Optimal Decision Feedback Equalizer (DFE) coefficients are determined from a channel estimate h by casting the DFE coefficient problem as a standard recursive least squares (RLS) problem, e.g., the Kalman gain solution to the RLS problem. A fast recursive method, e.g., fast transversal filter (FTF) technique, for computing the Kalman gain is then directly used to compute Feed Forward Equalizer (FFE) coefficients gopt. The complexity of a conventional FTF algorithm is reduced to one third of its original complexity by choosing the length of a Feed Back Equalizer (FBE) coefficients bopt (of the DFE) to force the FTF algorithm to use a lower triangular matrix. The FBE coefficients bopt are then computed by convolving the FFE coefficients gopt with the channel impulse response h. In performing this operation, a convolution matrix that characterizes the channel impulse response h extended to a bigger circulant matrix.

Abstract: Directly computing Feed Forward Equalizer (FFE) coefficients and Feed Back Equalizer (FBE) coefficients of a Decision Feedback Equalizer (DFE) from a channel estimate. The FBE coefficients have an energy constraint. A recursive least squares problem is formulated based upon the DFE configuration, the channel estimate, and the FBE energy constraint. The recursive least squares problem is solved to yield the FFE coefficients. The FFE coefficients are convolved with a convolution matrix that is based upon the channel estimate to yield the FBE coefficients. A solution to the recursive least squares problem is interpreted as a Kalman gain vector. A Kalman gain vector solution to the recursive least squares problem may be determined using a Fast Transversal Filter (FTF) algorithm.

Abstract: Multi-Input-Multi-Output (MIMO) Optimal Decision Feedback Equalizer (DFE) coefficients are determined from a channel estimate h by casting the MIMO DFE coefficient problem as a standard recursive least squares (RLS) problem and solving the RLS problem. In one embodiment, a fast recursive method, e.g., fast transversal filter (FTF) technique, then used to compute the Kalman gain of the RLS problem, which is then directly used to compute MIMO Feed Forward Equalizer (FFE) coefficients gopt. The complexity of a conventional FTF algorithm is reduced to one third of its original complexity by choosing the length of a MIMO Feed Back Equalizer (FBE) coefficients bopt (of the DFE) to force the FTF algorithm to use a lower triangular matrix. The MIMO FBE coefficients bop, are computed by convolving the MIMO FFE coefficients gopt with the channel impulse response h. In performing this operation, a convolution matrix that characterizes the channel impulse response h extended to a bigger circulant matrix.

Abstract: Optimal Decision Feedback Equalizer (DFE) coefficients are determined from a channel estimate h by casting the DFE coefficient problem as a standard recursive least squares (RLS) problem, e.g., the Kalman gain solution to the RLS problem. A fast recursive method, e.g., fast transversal filter (FTF) technique, for computing the Kalman gain is then directly used to compute Feed Forward Equalizer (FFE) coefficients gopt. The complexity of a conventional FTF algorithm is reduced to one third of its original complexity by choosing the length of a Feed Back Equalizer (FBE) coefficients bopt (of the DFE) to force the FTF algorithm to use a lower triangular matrix. The FBE coefficients bopt are then computed by convolving the FFE coefficients gopt with the channel impulse response h. In performing this operation, a convolution matrix that characterizes the channel impulse response h extended to a bigger circulant matrix.