Modulation and equalization in an orthonormal time-frequency shifting communications system
A method for modulating data for transmission within a communication system. The method includes establishing a time-frequency shifting matrix of dimension N×N, wherein N is greater than one. The method further includes combining the time-frequency shifting matrix with a data frame to provide an intermediate data frame. A transformed data matrix is provided by permuting elements of the intermediate data frame. A modulated signal is generated in accordance with elements of the transformed data matrix.
1. A method for wireless communication, comprising:
transforming a data frame with N 2 data symbols into a time frequency shifted (TFS) data matrix with N 2 elements, wherein each of the N 2 elements carries information corresponding to all N 2 data symbols;
generating, based on a feedback signal, a pre-equalized TFS data matrix by performing a pre-equalization operation on the TFS data matrix;
generating N composite waveforms based on modulating each column of the pre-equalized TFS data matrix; and
transmitting each of the N composite waveforms as a pre-equalized orthonormal time frequency space (OTFS) signal.
2. The method of claim 1 , wherein modulating a column of the pre-equalized TFS data matrix comprises:
separating each element of the column into real and imaginary components;
filtering the real and imaginary components to generate filtered real and imaginary components; and
controlling, using the filtered real and imaginary components, an operation of a cosine and sine generator, respectively.
3. The method of claim 1 , wherein the N composite waveforms comprise N 2 summation-symbol-weighted cyclically time shifted and cyclically frequency shifted waveforms.
4. The method of claim 1 , wherein the generating the pre-equalized TFS data matrix comprises:
receiving the feedback signal;
generating, based on the feedback signal, a pre-distortion transfer function that corresponds to a wireless channel; and
configuring, based on the pre-distortion transfer function, the pre-equalization operation.
5. The method of claim 4 , wherein the wireless channel comprises an echo reflection, and wherein the pre-equalization operation comprises an anti-echo cancellation waveform.
6. The method of claim 4 , wherein the wireless channel comprises a frequency shift, and wherein the pre-equalization operation comprises a compensatory reverse frequency shift.
7. The method of claim 1 , wherein the transmitting each of the N composite waveforms comprises transmitting over a plurality of time blocks or a plurality of frequency blocks.
8. A method for wireless communication, comprising:
receiving each of N orthonormal time frequency space (OTFS) signals;
constructing, based on the N OTFS signals, a received data matrix;
generating an equalized data matrix with N 2 elements by performing an equalization operation on the received data matrix; and
transforming the equalized data matrix into a data frame with N 2 data symbols, wherein each of the N 2 elements carries information corresponding to all N 2 data symbols.
9. The method of claim 8 , wherein the equalization operation comprises a linear equalization operation.
10. The method of claim 8 , wherein the equalization operation comprises a decision feedback least means square (DF-LMS) equalization operation.
11. The method of claim 8 , further comprising:
transmitting, based on the equalization operation, a feedback signal that corresponds to a wireless channel.
12. The method of claim 11 , wherein at least one of the N OTFS signals experiences an echo reflection in the wireless channel, and wherein the feedback signal comprises an indication of an anti-echo cancellation waveform.
13. The method of claim 11 , wherein at least one of the N OTFS signals experiences a frequency shift in the wireless channel, and wherein the feedback signal comprises an indication of a compensatory reverse frequency shift.
14. A device for wireless communication, comprising:
a processor; and
a memory that comprises instructions stored thereupon, wherein the instructions when executed by the processor configure the processor to:
transform a data frame with N 2 data symbols into a time frequency shifted (TFS) data matrix with N 2 elements, wherein each of the N 2 elements carries information corresponding to all N 2 data symbols;
generate, based on a feedback signal, a pre-equalized TFS data matrix by performing a pre-equalization operation on the TFS data matrix;
generate N composite waveforms based on modulating each column of the pre-equalized TFS data matrix; and
transmit each of the N composite waveforms as a pre-equalized orthonormal time frequency space (OTFS) signal.
15. The device of claim 14 , wherein the processor is further configured, as part of the modulating a column of the pre-equalized TFS data matrix, to:
separate each element of the column into real and imaginary components;
filter the real and imaginary components to generate filtered real and imaginary components; and
control, using the filtered real and imaginary components, an operation of a cosine and sine generator, respectively.
16. The device of claim 14 , wherein the N composite waveforms comprise N 2 summation-symbol-weighted cyclically time shifted and cyclically frequency shifted waveforms.
17. The device of claim 14 , wherein the processor is further configured, as part of the generating the pre-equalized TFS data matrix, to:
receive the feedback signal;
generate, based on the feedback signal, a pre-distortion transfer function that corresponds to a wireless channel; and
configure, based on the pre-distortion transfer function, the pre-equalization operation.
18. The device of claim 17 , wherein the wireless channel comprises an echo reflection, and wherein the pre-equalization operation comprises an anti-echo cancellation waveform.
19. The device of claim 17 , wherein the wireless channel comprises a frequency shift, and wherein the pre-equalization operation comprises a compensatory reverse frequency shift.
20. The device of claim 14 , wherein the transmitting each of the N composite waveforms comprises transmitting over a plurality of time blocks or a plurality of frequency blocks.