Systems/methods of sequential modulation of a single carrier frequency by a plurality of elements of a waveform

1. A communications method comprising:

forming a desired spectrum shape for a waveform;

generating the waveform responsive to the desired spectrum shape; and

transmitting and/or receiving information by transmitting and/or receiving at a transmitter and/or at a receiver, a plurality of elements of the waveform sequentially one after another via a single carrier frequency;

wherein generating the waveform responsive to the desired spectrum shape comprises generating a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT); wherein n=1, 2, . . . , N; and NT≦τ; wherein τ denotes a time span of the discrete time-domain waveform U(nT);

wherein transmitting and/or receiving information by transmitting and/or receiving at a transmitter and/or at a receiver, a plurality of elements of the waveform sequentially one after another via a single carrier frequency comprises transmitting and/or receiving the elements of U(nT) sequentially via the single carrier frequency by transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency; and

wherein said forming a desired spectrum shape for a waveform further comprises:

using a first plurality of frequencies over a first time interval; and

using a second plurality of frequencies over a second time interval;

wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.

2. The communications method according to claim 1 , wherein said forming a desired spectrum shape for a waveform is performed at the transmitter.

3. The communications method according to claim 1 , wherein said forming a desired spectrum shape for a waveform is performed at a distance from the transmitter and is then relayed to the transmitter.

4. The communications method according to claim 1 , wherein said forming a desired spectrum shape for a waveform further comprises:

forming the desired spectrum shape to include a first frequency interval comprising a first spectral level that is non-zero and to also include a second frequency interval comprising a second spectral level that is substantially zero.

5. The communications method according to claim 4 , wherein said forming a desired spectrum shape for a waveform further comprises:

forming the desired spectrum shape to also include a third frequency interval comprising a third spectral level that is non-zero;

wherein the second frequency interval that comprises the second spectral level that is substantially zero is situated between the first and third frequency intervals.

6. A communications method comprising:

forming a desired spectrum shape for a waveform to include at least one frequency that provides a frequency content to the waveform and at least one frequency that is excluded from providing a frequency content to the waveform;

generating the waveform responsive to the desired spectrum shape; and

transmitting and/or receiving information by transmitting and/or receiving at a transmitter and/or at a receiver, a plurality of elements of the waveform sequentially one after another via a single carrier frequency;

wherein generating the waveform responsive to the desired spectrum shape comprises generating a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT); wherein n=1, 2, . . . , N; and NT≦τ; wherein τdenotes a time span of the discrete time-domain waveform U(nT);

wherein transmitting and/or receiving information by transmitting and/or receiving at a transmitter and/or at a receiver, a plurality of elements of the waveform sequentially one after another via a single carrier frequency comprises transmitting and/or receiving the elements of U(nT) sequentially via the single carrier frequency by transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency; and

wherein said forming a desired spectrum shape for a waveform further comprises:

using a first plurality of frequencies over a first time interval; and

using a second plurality of frequencies over a second time interval;

wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.

7. The communications method according to claim 6 , wherein said forming a desired spectrum shape for a waveform is performed at the transmitter.

8. The communications method according to claim 6 , wherein said forming a desired spectrum shape for a waveform is performed at a distance from the transmitter and is then relayed to the transmitter.

9. The communications method according to claim 6 , wherein said forming a desired spectrum shape for a waveform further comprises:

forming the desired spectrum shape to include a first frequency interval comprising a first spectral level that is non-zero and to also include a second frequency interval comprising a second spectral level that is substantially zero.

10. The communications method according to claim 9 , wherein said forming a desired spectrum shape for a waveform further comprises:

forming the desired spectrum shape to also include a third frequency interval comprising a third spectral level that is non-zero;

wherein the second frequency interval that comprises the second spectral level that is substantially zero is situated between the first and third frequency intervals.

11. A communications system comprising:

a processor that is configured to form a desired spectrum shape for a waveform and to generate the waveform responsive to the desired spectrum shape; and

a transmitter and/or receiver that is/are configured to transmit and/or receive information by transmitting and/or receiving a plurality of elements of the waveform sequentially one after another via a single carrier frequency;

wherein the waveform comprises a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT); wherein n=1, 2, . . . , N; and NT≦τ; wherein τ denotes a time span of the discrete time-domain waveform U(nT);

wherein the transmitter and/or receiver is/are further configured to transmit and/or receive the elements of U(nT) sequentially via the single carrier frequency by transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency; and

wherein the processor is configured to form the desired spectrum shape to include:

a first plurality of frequencies over a first time interval; and

a second plurality of frequencies over a second time interval;

wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.

12. The communications system according to claim 11 , wherein the processor is configured to form the desired spectrum shape to include:

a first frequency interval comprising a first spectral level that is non-zero and a second frequency interval comprising a second spectral level that is substantially zero.

13. The communications system according to claim 12 , wherein the processor is configured to form the desired spectrum shape to further include:

a third frequency interval comprising a third spectral level that is non-zero;

wherein the second frequency interval that comprises the second spectral level that is substantially zero is situated between the first and third frequency intervals.

14. A communications system comprising:

a processor that is configured to form a desired spectrum shape for a waveform and to generate the waveform responsive to the desired spectrum shape; and

a transmitter and/or receiver that is/are configured to transmit and/or receive information by transmitting and/or receiving a plurality of elements of the waveform sequentially one after another via a single carrier frequency;

wherein the processor is configured to generate the waveform responsive to the desired spectrum shape by generating a discrete time-domain waveform U(nT); wherein n denotes a discrete time index of U(nT); wherein n=1, 2, . . . , N; and NT≦τ; wherein τdenotes a time span of the discrete time-domain waveform U(nT);

wherein the transmitter and/or receiver is/are configured to transmit and/or receive information by transmitting and/or receiving a plurality of elements of the waveform sequentially one after another via a single carrier frequency by transmitting and/or receiving the elements of U(nT) sequentially via the single carrier frequency by transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency;

wherein the processor is configured to form the desired spectrum shape for the waveform to include:

at least one frequency that provides a frequency content to the waveform; and

at least one frequency that is excluded from providing a frequency content to the waveform; and

wherein the processor is further configured to form the desired spectrum shape to include:

a first plurality of frequencies over a first time interval; and

a second plurality of frequencies over a second time interval;

wherein the first plurality of frequencies differs from the second plurality of frequencies in at least one frequency.

15. The communications system according to claim 14 , wherein the processor is further configured to form the desired spectrum shape to include:

a first frequency interval comprising a first spectral level that is non-zero and to also include a second frequency interval comprising a second spectral level that is substantially zero.

16. The communications system according to claim 15 , wherein the processor is further configured to form the desired spectrum shape to further include:

a third frequency interval comprising a third spectral level that is non-zero;

wherein the second frequency interval that comprises the second spectral level that is substantially zero is situated between the first and third frequency intervals.

17. A communications method comprising:

selecting a frequency interval over which a waveform U(nT) is to exist; wherein n denotes a discrete time index and wherein n=1, 2, . . . , N;

allowing at least one frequency that is included in the selected frequency interval to provide a frequency content to the waveform U(nT);

excluding at least one frequency that is included in the selected frequency interval from providing a frequency content to the waveform U(nT);

forming the waveform U(nT) comprising a plurality of elements U(T), U(2T), . . . , U(NT), corresponding to respective integer values 1, 2, . . . , N of the discrete time index n; and

transmitting and/or receiving information by transmitting and/or receiving at a transmitter and/or at a receiver, the plurality of elements U(T), U(2T), . . . , U(NT) of the waveform U(nT) sequentially one after another via a single carrier frequency by first transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency;

wherein said forming the waveform U(nT) further comprises:

generating a first waveform using a first plurality of frequencies over a first time interval; and

generating a second waveform using a second plurality of frequencies over a second time interval;

wherein the second plurality of frequencies differs from the first plurality of frequencies in at least one frequency.

18. The communications method according to claim 17 , wherein said forming the waveform U(nT) comprises:

generating a waveform comprising a first spectral shape that is non-zero over a first plurality of frequencies that is included in said selected frequency interval and a second spectral shape that is substantially zero over a second plurality of frequencies that is also included in said selected frequency interval.

19. The communications method according to claim 17 , wherein said selecting a frequency interval over which a waveform U(nT) is to exist comprises:

identifying frequencies to be used to communicate; and

reducing a measure of interference by preferentially using the identified frequencies while refraining from using other frequencies.

20. The communications method according to claim 17 , wherein said selecting a frequency interval over which a waveform U(nT) is to exist comprises:

selecting a frequency interval that is between 1525 MHz and 1660.5 MHz and excluding a GPS frequency interval that is included therein.

21. The communications method according to claim 17 , wherein said forming the waveform U(nT) comprises:

using a Fourier transform and an inverse Fourier transform.

22. A communications system comprising:

a processor that is configured to select a frequency interval over which a waveform U(nT) is to exist, wherein n denotes a discrete time index and wherein n=1, 2, . . . , N; to allow at least one frequency that is included in the selected frequency interval to provide a frequency content to the waveform U(nT); to exclude at least one frequency that is included in the selected frequency interval from providing a frequency content to the waveform U(nT) and to form the waveform U(nT) comprising a plurality of elements U(T), U(2T), . . . , U(NT), corresponding to respective integer values 1, 2, . . . , N of the discrete time index n; and

a transmitter and/or receiver that is/are configured to transmit and/or receive information by transmitting and/or receiving the plurality of elements U(T), U(2T), . . . , U(NT) of the waveform U(nT) sequentially one after another via a single carrier frequency by first transmitting and/or receiving U(T) via the single carrier frequency, followed by transmitting and/or receiving U(2T) via the single carrier frequency, . . . , followed by transmitting and/or receiving U(NT) via the single carrier frequency;

wherein the processor is further configured to:

generate a first waveform using a first plurality of frequencies over a first time interval; and

generate a second waveform using a second plurality of frequencies over a second time interval;

wherein the second plurality of frequencies differs from the first plurality of frequencies in at least one frequency.

23. The communications system according to claim 22 , wherein the processor is further configured to:

generate a waveform comprising a first spectral shape that is non-zero over a first plurality of frequencies that is included in said selected frequency interval and a second spectral shape that is substantially zero over a second plurality of frequencies that is also included in said selected frequency interval.

24. The communications system according to claim 22 , wherein the processor is further configured to:

identify frequencies to be used to communicate such as to reduce a measure of interference and to preferentially use the identified frequencies and refrain from using other frequencies.

25. The communications system according to claim 22 , wherein the processor is further configured to:

select a frequency interval that is between 1525 MHz and 1660.5 MHz and exclude a GPS frequency interval that is included therein.

26. The communications system according to claim 22 , wherein the transmitter comprises a wireless transmitter.

27. The communications system according to claim 22 , wherein the processor is further configured to form the waveform U(nT) comprising the plurality of elements U(T), U(2T), . . . , U(NT) by using a Fourier transform and an inverse Fourier transform.

28. The communications system according to claim 27 , wherein the Fourier transform provides a spectrum shape that is altered in at least one frequency thereof responsive to an interference concern; and wherein the inverse Fourier transform provides a time-domain waveform responsive to the altered spectrum shape that is used by the processor to form the waveform.