Modulation and equalization in an orthonormal time-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 of wireless transmission, comprising:
applying a two-dimensional spreading to an input data;
applying a fast Fourier transform (FFT) and a first and a second time-frequency tiling to an output of the two-dimensional spreading, wherein the two-dimensional spreading and the FFT together perform a series of data spreading operations using a spreading kernel; and
outputting a waveform resulting from an output of the second time-frequency tiling over a channel.
2. The method of claim 1 , wherein the spreading kernel comprises a unitary matrix.
3. The method of claim 1 , wherein the series of data spreading operations includes a two-dimensional cyclic convolution with the spreading kernel.
4. The method of claim 3 , wherein the two-dimensional cyclic convolution is implemented using a two-dimensional FFT multiplication using a two-dimensional Discrete Fourier Transform of the spreading kernel followed by a two-dimensional inverse Fourier transform.
5. The method of claim 3 , wherein the series of data spreading operations includes cyclic shifting a kernel matrix along column direction by an amount corresponding to a time shift.
6. The method of claim 1 , wherein the output of the second time-frequency tiling comprises a two-dimensional matrix whose columns correspond to a symbol time slice that utilizes full available transmission bandwidth.
7. The method of claim 6 , wherein time gaps are interposed between columns of the two-dimensional matrix.
8. The method of claim 1 , wherein the output of the second time-frequency tiling comprises a two-dimensional matrix whose columns correspond frequency bins.
9. The method of claim 8 , wherein time gaps are interposed between columns of the two-dimensional matrix.
10. A non-transitory computer readable medium including program instructions for execution by a processor in a signal transmitter; the program instructions, upon execution, causing the processor to implement a method comprising:
applying a two-dimensional spreading to an input data;
applying a fast Fourier transform (FFT) and a first and a second time-frequency tiling to an output of the two-dimensional spreading, wherein the two-dimensional spreading and the FFT together perform a series of data spreading operations using a spreading kernel; and
outputting a waveform resulting from an output of the second time-frequency tiling over a channel.
11. An apparatus for wireless transmission, comprising a processor configured to ready program code from a memory and implement a method, comprising:
applying a two-dimensional spreading to an input data;
applying a fast Fourier transform (FFT) and a first and a second time-frequency tiling to an output of the two-dimensional spreading, wherein the two-dimensional spreading and the FFT together perform a series of data spreading operations using a spreading kernel; and
outputting a waveform resulting from an output of the second time-frequency tiling over a channel.
12. The apparatus of claim 11 , wherein the spreading kernel comprises a unitary matrix.
13. The apparatus of claim 11 , wherein the series of data spreading operations includes a two-dimensional cyclic convolution with the spreading kernel.
14. The apparatus of claim 13 , wherein the two-dimensional cyclic convolution is implemented using a two-dimensional FFT multiplication using a two-dimensional Discrete Fourier Transform of the spreading kernel followed by a two-dimensional inverse Fourier transform.
15. The apparatus of claim 13 , wherein the series of data spreading operations includes cyclic shifting a kernel matrix along column direction by an amount corresponding to a time shift.
16. The apparatus of claim 11 , wherein the output of the second time-frequency tiling comprises a two-dimensional matrix whose columns correspond to a symbol time slice that utilizes full available transmission bandwidth.
17. The apparatus of claim 16 , wherein time gaps are interposed between columns of the two-dimensional matrix.
18. The apparatus of claim 11 , wherein the output of the second time-frequency tiling comprises a two-dimensional matrix whose columns correspond frequency bins.
19. The apparatus of claim 18 , wherein time gaps are interposed between columns of the two-dimensional matrix.