Digital communication using lattice division multiplexing
A wireless data transmission technique includes encoding information bits as a periodic sequence of quadrature amplitude modulation (QAM) symbols, convolving the periodic sequence with a periodic pulse function, thereby generating a filtered periodic sequence, transforming the filtered periodic sequence to a delay-Doppler domain waveform, converting the delay-Doppler domain waveform to a time domain waveform, and transmitting the time domain waveform.
1. A wireless communication method, comprising:
transforming an information signal to a discrete lattice domain signal;
shaping bandwidth and duration of the discrete lattice domain signal by a two-dimensional filtering procedure to generate a filtered information signal, wherein the two-dimensional filtering procedure includes a twisted convolution with a pulse;
generating a time domain signal from the filtered information signal; and
transmitting the time domain signal over a wireless communication channel.
2. The method of claim 1 , wherein the discrete lattice domain includes a Zak domain.
3. The method of claim 1 , wherein the pulse is a separable function of each dimension of the two-dimensional filtering.
4. The method of claim 1 , wherein the time domain signal comprises modulated information signal without an intervening cyclic prefix.
5. The method of claim 4 , wherein the modulated information signal uses quadrature amplitude modulation (QAM) symbols.
6. The method of claim 4 , wherein the modulated information signal is based on an orthogonal time frequency space (OTFS) modulation or an OTFS multicarrier (OTFS-MC) modulation.
7. The method of claim 1 , wherein the pulse is a sinc function.
8. A wireless communication method, implementable by a wireless communication apparatus, comprising:
encoding information bits as a periodic sequence of quadrature amplitude modulation (QAM) symbols;
convolving the periodic sequence with a periodic pulse function, thereby generating a filtered periodic sequence;
transforming the filtered periodic sequence into a delay-Doppler domain waveform;
converting the delay-Doppler domain waveform to a time domain waveform; and
transmitting the time domain waveform.
9. The method of claim 8 wherein the transforming comprises applying a Zak transform.
10. The method of claim 8 , wherein the periodic pulse function comprises a Dirichlet sinc function.
11. The method of claim 8 , wherein the convolving the periodic pulse function comprises applying a tapering window function.
12. The method of claim 8 , wherein the encoding information bits as a periodic sequence includes encoding the information bits as a two-dimensional periodic sequence having a periodicity of N in a first dimension and M in a second dimension, where N and M are integers.
13. A wireless signal transmission apparatus comprising a processor, wherein the processor is configured to implement a method comprising:
transforming an information signal to a discrete lattice domain signal;
shaping bandwidth and duration of the discrete lattice domain signal by a two-dimensional filtering procedure to generate a filtered information signal, wherein the two-dimensional filtering procedure includes a twisted convolution with a pulse;
generating a time domain signal from the filtered information signal; and
transmitting, using transmission circuitry, the time domain signal over a wireless communication channel.
14. The apparatus of claim 13 , wherein the discrete lattice domain includes a Zak domain.
15. The apparatus of claim 13 , wherein the pulse is a separable function of each dimension of the two-dimensional filtering.
16. The apparatus of claim 13 , wherein the time domain signal comprises modulated information signal without an intervening cyclic prefix.
17. The apparatus of claim 16 , wherein the modulated information signal uses quadrature amplitude modulation (QAM) symbols.
18. The apparatus of claim 16 , wherein the modulated information signal is based on an orthogonal time frequency space (OTFS) modulation or an OTFS multicarrier (OTFS-MC) modulation.
19. The apparatus of claim 13 , wherein the twisted convolution between a first function h 1 and a second function h 2 is defined as:
h
1
*
σ
h
2
(
υ
)
=
∫
υ
1
+
υ
2
=
υ
exp
(
j
2
πβ
(
υ
1
,
υ
2
)
)
h
1
(
υ
1
)
h
2
(
υ
2
)
,
wherein β is a polarization form.
20. The apparatus of claim 13 , wherein the pulse is a sinc function.