Abstract: A method includes: generating a trellis; generating one or more predicted symbols using a first non-linear model; computing and saving two or more branch metrics using a priori log-likelihood ratio (LLR) information, a channel observation, and the one or more predicted symbols; if alpha forward recursion has not yet completed, generating alpha forward recursion state metrics using a second non-linear model; if beta backward recursion has not yet completed, generating beta backward recursion state metrics using a third non-linear model; if sigma forward recursion has not yet completed, generating sigma forward recursion state metrics using the branch metrics, the alpha state metrics, and the beta backward recursion state metrics; generating extrinsic information comprising a difference of a posteriori LLR information and the a priori LLR information; computing and feeding back the a priori LLR information; and calculating the a posteriori LLR information.

Abstract: A method includes: generating a trellis; generating one or more predicted symbols using a first non-linear model; computing and saving two or more branch metrics using a priori log-likelihood ratio (LLR) information, a channel observation, and the one or more predicted symbols; if alpha forward recursion has not yet completed, generating alpha forward recursion state metrics using a second non-linear model; if beta backward recursion has not yet completed, generating beta backward recursion state metrics using a third non-linear model; if sigma forward recursion has not yet completed, generating sigma forward recursion state metrics using the branch metrics, the alpha state metrics, and the beta backward recursion state metrics; generating extrinsic information comprising a difference of a posteriori LLR information and the a priori LLR information; computing and feeding back the a priori LLR information; and calculating the a posteriori LLR information.

Abstract: A method includes: generating a trellis; generating one or more predicted symbols using a first non-linear model; computing and saving two or more branch metrics using a priori log-likelihood ratio (LLR) information, a channel observation, and the one or more predicted symbols; if alpha forward recursion has not yet completed, generating alpha forward recursion state metrics using a second non-linear model; if beta backward recursion has not yet completed, generating beta backward recursion state metrics using a third non-linear model; if sigma forward recursion has not yet completed, generating sigma forward recursion state metrics using the branch metrics, the alpha state metrics, and the beta backward recursion state metrics; generating extrinsic information comprising a difference of a posteriori LLR information and the a priori LLR information; computing and feeding back the a priori LLR information; and calculating the a posteriori LLR information.

Abstract: A method for pre-coding a digital signal in a transmitter associated with a digital communications system to remove non-linear distortions. The method converts digital bits to be transmitted to a transmit constellation including symbols defining a plurality of the bits and subtracting a modeled constellation from the transmit constellation to provide a pre-coded constellation. The method performs a modulo operation on the pre-coded constellation to limit the number of symbols that are transmitted at any particular point in time and models the pre-coded constellation after the modulo operation using a Volterra series model, where a plurality of terms in the Volterra series are separately modeled and each modeled term of the constellation is added together to provide the modeled constellation. The method filters the pre-coded constellation to interpolate a symbol sequence in the constellation and shape the constellation and converts the shaped constellation to an analog signal to be transmitted.

Abstract: A system and method of improving the modulation of GPS signal transmission is disclosed. Two alternative approaches are proposed: the Barrier Approximation and the Augmented Lagrangian Method. While both techniques can solve the problem with a substantially smaller error threshold, the Augmented Lagrangian Method further addresses potential ill-conditioning associated with nonconvex optimization. A formula for the lower bound on the constellation's amplitude is devised for any given arbitrary power profile. Lastly, additional results for multiplexing three, four, and five codes in GPS are presented. This invention also explores advantages and disadvantages for different solving strategies used. A discussion on how to generalize these techniques to non-POCET signal constellations is also included.

Abstract: An apparatus and method for optimizing the performance of satellite communication system receivers by using the Soft-Input Soft-Output (SISO) BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm to detect a transmitted information sequence is disclosed. A Sliding Window technique is used with a plurality of reduced state sequence estimation (RSSE) equalizers to execute the BCJR algorithm in parallel. A serial data stream is converted into a plurality of data blocks using a serial-to-parallel converter. After processing in parallel by the equalizers, the output blocks are converted back to a serial data stream by a parallel-to-serial converter. A path history is determined using maximum likelihood (ML) path history calculation.

Abstract: An apparatus and method for optimizing the performance of satellite communication system receivers by using the Soft-Input Soft-Output (SISO) BCJR (Bahl, Cocke, Jelinek and Raviv) algorithm to detect a transmitted information sequence is disclosed. A Sliding Window technique is used with a plurality of reduced state sequence estimation (RSSE) equalizers to execute the BCJR algorithm in parallel. A serial data stream is converted into a plurality of data blocks using a serial-to-parallel converter. After processing in parallel by the equalizers, the output blocks are converted back to a serial data stream by a parallel-to-serial converter. A path history is determined using maximum likelihood (ML) path history calculation.

Abstract: A method for pre-coding a digital signal in a transmitter associated with a digital communications system to remove non-linear distortions. The method converts digital bits to be transmitted to a transmit constellation including symbols defining a plurality of the bits and subtracting a modeled constellation from the transmit constellation to provide a pre-coded constellation. The method performs a modulo operation on the pre-coded constellation to limit the number of symbols that are transmitted at any particular point in time and models the pre-coded constellation after the modulo operation using a Volterra series model, where a plurality of terms in the Volterra series are separately modeled and each modeled term of the constellation is added together to provide the modeled constellation. The method filters the pre-coded constellation to interpolate a symbol sequence in the constellation and shape the constellation and converts the shaped constellation to an analog signal to be transmitted.

Abstract: A blind equalizer apparatus includes a decision-directed (DD) least mean squares (LMS) blind equalizer. A blind equalizer apparatus includes: a DD LMS blind equalizer, wherein: the blind equalizer uses a finite impulse response filter with tap weights that are adaptively updated using a filter tap update algorithm, wherein blind equalization of one of an in-phase (I) channel and a quadrature (Q) channel is carried out by maximizing the Euclidean distance of binary modulated waveforms, wherein the blind equalizer averages a block to compute an independent phase estimate for a block, wherein the blind equalizer computes an error variable for a block from the phase estimate for the block, wherein the blind equalizer uses the phase estimate and alternating I/Q one dimensional/binary slicing to make a hard decision, and wherein the blind equalizer uses the hard decision to derive an error variable that is used to update the filter tap weights.

Abstract: A method includes: generating a trellis; generating one or more predicted symbols using a first non-linear model; computing and saving two or more branch metrics using a priori log-likelihood ratio (LLR) information, a channel observation, and the one or more predicted symbols; if alpha forward recursion has not yet completed, generating alpha forward recursion state metrics using a second non-linear model; if beta backward recursion has not yet completed, generating beta backward recursion state metrics using a third non-linear model; if sigma forward recursion has not yet completed, generating sigma forward recursion state metrics using the branch metrics, the alpha state metrics, and the beta backward recursion state metrics; generating extrinsic information comprising a difference of a posteriori LLR information and the a priori LLR information; computing and feeding back the a priori LLR information; and calculating the a posteriori LLR information.

Abstract: A method and system for providing adaptive coded modulation in LEO satellite communication system is provided. The received power signal at the receiver is predicted by the LEO satellite transmitter without using channel feedback from the receiver. The receiver rapidly detects changes in transmission rate and changes its demodulation rate in tandem with the LEO satellite. Certain conditions that vary slowly, such as local weather and ground moisture level, are provided to the transmitter from the receiver at a much slower rate than that used in normal data communications.

Abstract: A method for optimizing a constellation for M-ary amplitude phase shift keying (M-APSK) that provides signal modulation for transmitting a series of digital bits in an analog signal by a transmitter to be received by a receiver over a communications channel. The method includes identifying symbol-wise mutual information of a transmitted constellation, where the symbol-wise mutual information includes a conditional probability density function. The method identifies an unconstrained capacity that defines an ultimate performance limit of the constellation, and minimizes a difference between a rate of the symbol-wise mutual information and a rate of the unconstrained capacity to determine the number of rings, the number of symbols in each ring and the ring ratio in the constellation.

Abstract: A method for removing distortions in a transmitted signal transmitted by a high power amplifier in a satellite communications system. The method characterizes the high power amplifier to define a series of Volterra coefficients and uses those coefficients in an equalizer in a receiver in the communications system to remove the distortions. The equalizer is a non-linear soft interference cancellation and minimum mean square error equalizer that employs three processing operations including parallel soft interference cancellation, minimum mean square error filtering and a priori log-likelihood ratio calculations.

Abstract: A method for removing distortions in a transmitted signal transmitted by a high power amplifier in a satellite communications system. The method characterizes the high power amplifier to define a series of Volterra coefficients and uses those coefficients in an equalizer in a receiver in the communications system to remove the distortions. The equalizer is a non-linear soft interference cancellation and minimum mean square error equalizer that employs three processing operations including parallel soft interference cancellation, minimum mean square error filtering and a priori log-likelihood ratio calculations.

Abstract: A blind equalizer apparatus includes a decision-directed (DD) least mean squares (LMS) blind equalizer. A blind equalizer apparatus includes: a DD LMS blind equalizer, wherein: the blind equalizer uses a finite impulse response filter with tap weights that are adaptively updated using a filter tap update algorithm, wherein blind equalization of one of an in-phase (I) channel and a quadrature (Q) channel is carried out by maximizing the Euclidean distance of binary modulated waveforms, wherein the blind equalizer averages a block to compute an independent phase estimate for a block, wherein the blind equalizer computes an error variable for a block from the phase estimate for the block, wherein the blind equalizer uses the phase estimate and alternating I/Q one dimensional/binary slicing to make a hard decision, and wherein the blind equalizer uses the hard decision to derive an error variable that is used to update the filter tap weights.