A method for signal transmission using precoded symbol information involves estimating a two-dimensional model of a communication channel in a delay-Doppler domain. A perturbation vector is determined in a delay-time domain wherein the delay-time domain is related to the delay-Doppler domain by an FFT operation. User symbols are modified based upon the perturbation vector so as to produce perturbed user symbols. A set of Tomlinson-Harashima precoders corresponding to a set of fixed times in the delay-time domain may then be determined using a delay-time model of the communication channel. Precoded user symbols are generated by applying the Tomlinson-Harashima precoders to the perturbed user symbols. A modulated signal is then generated based upon the precoded user symbols and provided for transmission over the communication channel.

Sampling circuitry for receiving an analog signal from photodetector circuitry and generating a sample analog signal. Equalization circuitry for generating an equalized signal comprising first and second sample values corresponding with a cursor tap and a first postcursor tap, and one or more third sample values corresponding with taps other than the cursor tap and the first postcursor tap. In the equalized signal, amplitudes of the first and second sample values are substantially equal while the third sample values are attenuated relative to the first and second sample values. The first and second sample values correspond with two or more first symbols of a first alphabet. Data slicer and modulo circuitry to generate a data signal based on the equalized signal and perform a modulo operation on the two or more first symbols and to generate one or more second symbols. The second symbols are according to a second alphabet.

Systems and methods of precoded faster than Nyquist (FTN) signalling are provided. In the transmitter, Tomlinson-Harashima Preceding (THP) is applied to produce precoded symbols. The THP is based on inter-symbol interference (ISI) due to using faster than Nyquist (FTN) signalling. An inverse modulo operation is not performed in the receiver. Instead, in the receiver, FTN processing is performed based on a matched filter output by determining log a-posteriori probability ratio LAPPR values computed for an n.sup.th bit b.sub.n of a k.sup.th received symbol and pre-computed a-priori probabilities of an extended constellation for a given pulse shape h(t) and FTN acceleration factor combination.

A communication method, a communications apparatus, and a storage medium are disclosed, to reduce a probability that consecutive bit errors occur in a communications system. A received to-be-sent signal is modulated to obtain a modulated signal, and N rounds of operations are further performed on the modulated signal to obtain an encoded signal. An output of the 1.sup.st-round operation in the N rounds of operations is determined based on the modulated signal and an output that is of the N.sup.th-round operation and that is processed by a first delay circuit, and an output of the i.sup.th-round operation in the N rounds of operations is determined based on an output of the (i−1).sup.th-round operation and an output that is of the N.sup.th-round operation and that is processed by a second delay circuit, where i is an integer greater than 1 and less than or equal to N.

A method for signal transmission using precoded symbol information involves estimating a two-dimensional model of a communication channel in a delay-Doppler domain. A perturbation vector is determined in a delay-time domain wherein the delay-time domain is related to the delay-Doppler domain by an FFT operation. User symbols are modified based upon the perturbation vector so as to produce perturbed user symbols. A set of Tomlinson-Harashima precoders corresponding to a set of fixed times in the delay-time domain may then be determined using a delay-time model of the communication channel. Precoded user symbols are generated by applying the Tomlinson-Harashima precoders to the perturbed user symbols. A modulated signal is then generated based upon the precoded user symbols and provided for transmission over the communication channel.

A transmitter for transmitting an output signal includes first and second filter structures. The first filter structure includes a first combiner to extend a first data signal by a first reference signal to obtain a first extended data signal, and a first IIR filter for filtering the first extended data signal to obtain a first filtered data signal. The second filter structure includes a second combiner to extend a second data signal by a second reference signal, and a second IIR filter for filtering the second extended data signal. The transmitter includes a multiplexer for combining the first and second filtered data signals to obtain the output signal. A system response of the first IIR filter based on the first reference signal corresponds to a system response of the second IIR filter based on the second reference signal.

Methods, systems, and devices for spectral sharing wireless systems, wherein multiple user devices share time and frequency resources for uplink and/or downlink transmissions, are described. One example method includes transmitting transmission symbols from the network station to at least one user device by processing through a first precoder and a pre-compensation stage, wherein the pre-compensation stage is selected to have the transmission symbols receivable at the at least one user device to appear as if the transmission symbols are processed by a second precoder different from the first precoder.

Systems and methods for channel estimation are disclosed. In one aspect, supercomplementary sets (SCSs) of sequences are defined and more optionally, but more particularly, supercomplementary zero-sum cross-correlation (SZC) sequence blocks are created from the SCSs and transmitted to a receiver. The receiver receives a signal that includes the SCSs or SZC sequence block(s) deformed by a channel frequency offset (CFO). The receiver may correlate the signal with the known SCS or SZC to create a signal with minimal or no side lobes from which the CFO may be removed and a channel estimate formed. Based on the channel estimate, a distance between transmitter and receiver may be determined and used for other purposes, such as the provision of location-based services.

A method for signal transmission using precoded symbol information involves estimating a two-dimensional model of a communication channel in a delay-Doppler domain. A perturbation vector is determined in a delay-time domain wherein the delay-time domain is related to the delay-Doppler domain by an FFT operation. User symbols are modified based upon the perturbation vector so as to produce perturbed user symbols. A set of Tomlinson-Flarashima precoders corresponding to a set of fixed times in the delay-time domain may then be determined using a delay-time model of the communication channel. Precoded user symbols are generated by applying the Tomlinson-Flarashima precoders to the perturbed user symbols. A modulated signal is then generated based upon the precoded user symbols and provided for transmission over the communication channel.

A method of operation for an Ethernet transceiver is disclosed. The method includes entering a training sequence. The training sequence includes transferring uncoded two-level symbols to a link partner; exchanging updated precoder coefficients with the link partner; and directly following exchanging updated precoder coefficients, transferring multi-level symbols to the link partner. The multi-level symbols being encoded consistent with the exchanged updated precoder coefficients and having greater than two symbol levels.