Data modulation schemes based on the Zak transform
One example wireless communication method includes transforming an information signal to a discrete sequence, where the discrete sequence is a Zak transformed version of the information signal, generating a first ambiguity function corresponding to the discrete sequence, generating a second ambiguity function by pulse shaping the first ambiguity function, generating a waveform corresponding to the second ambiguity function, and transmitting the waveform over a wireless communication channel. Another communication method includes 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, generating, using a Zak transform, a time domain signal from the filtered information signal, and transmitting the time domain signal over a wireless communication channel.
1. A method for wireless communication, comprising:
transforming an information signal to a discrete sequence, wherein the discrete sequence is a Zak transformed version of the information signal;
generating a first ambiguity function corresponding to the discrete sequence;
generating a second ambiguity function by pulse shaping the first ambiguity function;
generating a waveform corresponding to the second ambiguity function; and
generating the waveform for transmission over a wireless communication channel.
2. The method of claim 1 , wherein the waveform comprises a uniform temporal power profile.
3. The method of claim 1 , wherein the first ambiguity function is a discrete ambiguity function supported on a discrete lattice.
4. The method of claim 3 , wherein the second ambiguity function is a continuous ambiguity function, and wherein the pulse shaping is based on a pulse that is localized on the discrete lattice.
5. A method for wireless communication, comprising:
obtaining a waveform from an information signal, wherein the waveform corresponds to a second ambiguity function that is a pulse shaped version of a first ambiguity function, wherein the first ambiguity function corresponds to a discrete sequence, and wherein the discrete sequence is a Zak transformed version of the information signal; and
transmitting the waveform over a wireless channel.
6. The method of claim 5 , wherein the waveform comprises a uniform temporal power profile.
7. The method of claim 5 , wherein the first ambiguity function is a discrete ambiguity function supported on a discrete lattice.
8. The method of claim 7 , wherein the second ambiguity function is a continuous ambiguity function, and wherein the pulse shaping is based on a pulse that is localized on the discrete lattice.
9. The method of claim 5 , wherein the discrete sequence is quasi-periodic.
10. A wireless communication apparatus comprising a processor configured to:
transform an information signal to a discrete sequence, wherein the discrete sequence is a Zak transformed version of the information signal;
generate a first ambiguity function corresponding to the discrete sequence;
generate a second ambiguity function by pulse shaping the first ambiguity function;
generate a waveform corresponding to the second ambiguity function; and
generate the waveform for transmission over a wireless communication channel.
11. The wireless communication apparatus of claim 10 , wherein the waveform comprises a uniform temporal power profile.
12. The wireless communication apparatus of claim 10 , wherein the first ambiguity function is a discrete ambiguity function supported on a discrete lattice.
13. The wireless communication apparatus of claim 12 , wherein the second ambiguity function is a continuous ambiguity function, and wherein the pulse shaping is based on a pulse that is localized on the discrete lattice.