Transmit pre-coding

1. A method for receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal transmitted by a user device in a wireless network, the method comprising:

determining a plurality of subcarrier frequencies allocated to the user device;

converting the OFDM signal to a plurality of frequency-domain values corresponding to the plurality of subcarrier frequencies; and

decoding the plurality of frequency-domain values to recover a plurality of data symbols encoded by the user device on the plurality of subcarrier frequencies;

wherein decoding employs a plurality of codes that are inverse to, complex-conjugate of, or complementary to a set of complex-valued codes that the user device employs to shape the OFDM signal into a superposition of cyclic-shifted pulse waveforms that each has one of the plurality of data symbols modulated thereon.

2. The method of claim 1 , wherein each of the plurality of codes employed for decoding comprises a different vector of linear phase offsets.

3. The method of claim 1 , wherein the cyclic-shifted waveforms have cyclic shifts that cause the cyclic-shifted waveforms to be orthogonal, and each of the plurality of codes employed for decoding comprises a set of linear phase offsets that corresponds to one of the cyclic shifts.

4. The method of claim 1 , wherein the complex-valued codes cause the cyclic-shifted waveforms to be Sinc waveforms, and the plurality of codes is configured to decode the Sinc waveforms.

5. The method of claim 1 , wherein the plurality of subcarrier frequencies has a frequency spacing f s , and the plurality of cyclic-shifted waveforms are periodic over a symbol interval T s =1/f s .

6. The method of claim 1 , wherein converting the OFDM signal to a plurality of frequency-domain values uses a discrete Fourier transform.

7. The method of claim 1 , further comprising removing at least one of a guard interval, a cyclic prefix, and a cyclic postfix from the OFDM signal before converting the OFDM signal to the plurality of frequency-domain values.

8. The method of claim 1 , wherein converting the OFDM signal to the plurality of frequency-domain values provides for orthogonal frequency division multiple access for the user device and at least one other user device.

9. The method of claim 1 , wherein an m th one of the plurality of codes is expressed as a set of N code chips for a set of integers n={0, . . . , N−1}, wherein each code chip is expressed by e i2πnm/N , wherein i is the square root of −1, and π is Pi.

10. An apparatus for receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal transmitted by a user device in a wireless network, the apparatus comprising:

at least one processor; and

a non-transitory computer-readable memory communicatively coupled to the at least one processor, the non-transitory computer-readable memory including a set of instructions stored thereon and executable by the at least one processor for:

determining a plurality of subcarrier frequencies allocated to the user device;

converting the OFDM signal to a plurality of frequency-domain values corresponding to the plurality of subcarrier frequencies; and

decoding the plurality of frequency-domain values to recover a plurality of data symbols encoded by the user device on the plurality of subcarrier frequencies;

wherein decoding employs a plurality of codes that are inverse to, complex-conjugate of, or complementary to a set of complex-valued codes that the user device employs to shape the OFDM signal into a superposition of cyclic-shifted pulse waveforms that each has one of the plurality of data symbols modulated thereon.

11. The apparatus of claim 10 , wherein each of the plurality of codes employed for decoding comprises a different vector of linear phase offsets.

12. The apparatus of claim 10 , wherein the cyclic-shifted waveforms have cyclic shifts that cause the cyclic-shifted waveforms to be orthogonal, and each of the plurality of codes employed for decoding comprises a set of linear phase offsets that corresponds to one of the cyclic shifts.

13. The apparatus of claim 10 , wherein the complex-valued codes cause the cyclic-shifted waveforms to be Sinc waveforms, and the plurality of codes is configured to decode the Sinc waveforms.

14. The apparatus of claim 10 , wherein the plurality of subcarrier frequencies has a frequency spacing f s , and the plurality of cyclic-shifted waveforms are periodic over a symbol interval T s =1/f s .

15. The apparatus of claim 10 , wherein converting the OFDM signal to a plurality of frequency-domain values uses a discrete Fourier transform.

16. The apparatus of claim 10 , wherein the non-transitory computer-readable memory further includes instructions stored thereon and executable by the at least one processor for removing at least one of a guard interval, a cyclic prefix, and a cyclic postfix from the OFDM signal before converting the OFDM signal to the plurality of frequency-domain values.

17. The apparatus of claim 10 , wherein converting the OFDM signal to the plurality of frequency-domain values provides for orthogonal frequency division multiple access for the user device and at least one other user device.

18. The apparatus of claim 10 , wherein an m th one of the plurality of codes is expressed as a set of N code chips for a set of integers n=, {0, . . . , N−1}, wherein each code chip is expressed by e i2πnm/N , wherein i is the square root of −1, and π is Pi.

19. A computer program product for receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal transmitted by a user device in a wireless network, the computer program product comprising a non-transitory computer readable storage device having computer readable program code stored therein, said program code containing instructions executable by one or more processors of a computer system for:

determining a plurality of subcarrier frequencies allocated to the user device;

converting the OFDM signal to a plurality of frequency-domain values corresponding to the plurality of subcarrier frequencies; and

decoding the plurality of frequency-domain values to recover a plurality of data symbols encoded by the user device on the plurality of subcarrier frequencies;

wherein decoding employs a plurality of codes that are inverse to, complex-conjugate of, or complementary to a set of complex-valued codes that the user device employs to shape the OFDM signal into a superposition of cyclic-shifted pulse waveforms that each has one of the plurality of data symbols modulated thereon.

20. The computer program product of claim 19 , wherein each of the plurality of codes employed for decoding comprises a different vector of linear phase offsets.

21. The computer program product of claim 19 , wherein the cyclic-shifted waveforms have cyclic shifts that cause the cyclic-shifted waveforms to be orthogonal, and each of the plurality of codes employed for decoding comprises a set of linear phase offsets that corresponds to one of the cyclic shifts.

22. The computer program product of claim 19 , wherein the complex-valued codes cause the cyclic-shifted waveforms to be Sinc waveforms, and the plurality of codes is configured to decode the Sinc waveforms.

23. The computer program product of claim 19 , wherein the plurality of subcarrier frequencies has a frequency spacing f s , and the plurality of cyclic-shifted waveforms are periodic over a symbol interval T s =1/f s .

24. The computer program product of claim 19 , wherein converting the OFDM signal to a plurality of frequency-domain values uses a discrete Fourier transform.

25. The computer program product of claim 19 , wherein the non-transitory computer-readable storage device further includes instructions stored therein and executable by the one or more processors for removing at least one of a guard interval, a cyclic prefix, and a cyclic postfix from the OFDM signal before converting the OFDM signal to the plurality of frequency-domain values.

26. The computer program product of claim 19 , wherein converting the OFDM signal to the plurality of frequency-domain values provides for orthogonal frequency division multiple access for the user device and at least one other user device.

27. The computer program product of claim 19 , wherein an m th one of the plurality of codes is expressed as a set of N code chips for a set of integers n={0, . . . , N−1}, wherein each code chip is expressed by e i2πnm/N , wherein i is the square root of −1, and π is Pi.