Tomlinson-Harashima precoding in an OTFS communication system

1. A method for signal transmission using precoded symbol information, the method comprising:

estimating a two-dimensional model of a communication channel in a delay-Doppler domain wherein the two-dimensional model of the communication channel is a function of time delay and frequency shift;

determining a perturbation vector in a delay-time domain wherein the delay-time domain is related to the delay-Doppler domain by an FFT operation;

modifying user symbols based upon the perturbation vector so as to produce perturbed user symbols;

determining, using a delay-time model of the communication channel, a set of Tomlinson-Harashima precoders corresponding to a set of fixed times in the delay-time domain;

generating precoded user symbols by applying the Tomlinson-Harashima precoders to the perturbed user symbols; and

providing, based upon the precoded user symbols, a modulated signal for transmission over the communication channel.

2. The method of claim 1 wherein the applying includes using FFT operations to apply the Tomlinson-Harashima precoders to the perturbed user symbols.

3. The method of claim 1 wherein the determining a set of Tomlinson-Harashima precoders includes performing a decomposition of the delay-time model of the communication channel.

4. The method of claim 3 in which the decomposition comprises an LQD decomposition where L is a lower triangular matrix, D is a diagonal matrix, and Q is a unitary matrix.

5. The method of claim 1 wherein the estimating the two-dimensional model of the communication channel includes:

receiving at least a first pilot signal wherein the first pilot signal occupies a first predetermined coordinate position in a time-frequency plane,

determining a first time shift of the first pilot signal and a first frequency shift of the first pilot signal.

6. A communication apparatus, comprising:

a plurality of antennas;

a processor configured to:

estimate a two-dimensional model of a communication channel in a delay-Doppler domain wherein the two-dimensional model of the communication channel is a function of time delay and frequency shift;

determine a perturbation vector in a delay-time domain wherein the delay-time domain is related to the delay-Doppler domain by an FFT operation;

modify user symbols based upon the perturbation vector so as to produce perturbed user symbols;

determine, using a delay-time model of the communication channel, a set of Tomlinson-Harashima precoders corresponding to a set of fixed times in the delay-time domain;

generate precoded user symbols by applying the Tomlinson-Harashima precoders to the perturbed user symbols; and

a transmitter configured to provide, based upon the precoded user symbols, a modulated signal to the plurality of antennas for transmission over the communication channel.

7. The communication apparatus of claim 6 wherein the processor is further configured to use FFT operations to apply the Tomlinson-Harashima precoders to the perturbed user symbols.

8. The communication apparatus of claim 6 wherein the processor is further configured to determine the set of Tomlinson-Harashima precoders by performing a decomposition of the delay-time model of the communication channel.

9. The communication apparatus of claim 8 where the decomposition comprises an LQD decomposition where L is a lower triangular matrix, D is a diagonal matrix, and Q is a unitary matrix.

10. The communication apparatus of claim 6 wherein the processor, as part of estimating the two-dimensional model of the communication channel, is further configured to:

receive at least a first pilot signal wherein the first pilot signal occupies a first predetermined coordinate position in a time-frequency plane, and

determine a first time shift of the first pilot signal and a first frequency shift of the first pilot signal.