Systems and methods for pseudo-random coding
Systems and methods for improving performance in terrestrial and satellite positioning systems are disclosed. Signal processing systems and methods are described for selecting, from among a set of codes, certain codes having desired autocorrelation and/or cross-correlation properties. Systems and methods for generating, encoding, transmitting, and receiving signals using the selected codes are also described.
1. A method for selecting codes to be used within positioning signals sent from one or more transmitters, the method comprising:
identifying a set of codes, wherein a magnitude of an autocorrelation function of each member of the set of codes, within a specified zonal region adjacent to a peak of the autocorrelation function, is below a first prescribed value;
identifying a subset of codes, from among two or more subsets of codes in the identified set of codes, that optimizes a performance criterion, wherein the performance criterion is associated with a relationship between members within the subset of codes;
transmitting, from a first transmitter, a first positioning signal that is modulated with a first code of the identified subset of codes; and
transmitting, from a second transmitter, a second positioning signal that is modulated with a second code of the identified subset of codes.
2. The method of claim 1 , wherein the subset of codes is identified from the set such that magnitudes of a cross-correlation function of any pair of codes within the subset of codes are equal to or less than a second prescribed value.
3. The method of claim 1 , wherein the subset of codes that optimizes the performance criterion minimizes a maximum magnitude of a cross-correlation between all pairs of non-identical codes of that subset of codes as compared to the other subsets of codes of the two or more subsets of codes.
4. The method of claim 3 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation.
5. The method of claim 3 , wherein said first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation.
6. The method of claim 1 , wherein a set of frequency offset modulated (FOM) signals is generated, wherein each signal of the set of FOM signals is generated by modulating a respective signal of the FOM signals with a code of the identified set of codes, and further modulating the respective signal of the FOM signals with a carrier whose frequency is chosen from among a set of offsets relative to a base offset frequency.
7. The method of claim 6 , wherein the performance criterion includes a minimization of the maximum magnitude of the cross-correlation between all pairs of FOM signals, wherein each pair has different codes and wherein frequency offsets associated with each pair are within a specified range.
8. The method of claim 7 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation between the FOM signals.
9. The method of claim 7 , wherein the first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation between said FOM signals.
10. The method of claim 1 , wherein the method further comprises:
selecting the first code from the subset of codes prior to transmitting the first positioning signal; and
selecting the second code from the subset of codes prior to transmitting the second positioning signal.
11. The method of claim 10 , wherein the second positioning signal is transmitted at an offset frequency relative to the first positioning signal.
12. The method of claim 1 , wherein each subset of codes of the two or more subsets of codes contain an equal number of codes.
13. The method of claim 1 , wherein each subset of codes of the two or more subsets of codes include respective numbers of codes that are within a range of sizes.
14. The method of claim 1 , wherein the performance criterion is associated with a relationship between all pairs of signals that are modulated with different members within the subset of codes and further modulated with carrier frequencies that are chosen from among a set of offsets relative to a base frequency.
15. The method of claim 1 , wherein a cross-correlation condition associated with the codes within the identified subset of codes is preferred over the cross-correlation condition associated with the other subsets of codes of the two or more subsets of codes.
16. The method of claim 1 , wherein the subset of codes optimizes the performance criterion when a cross-correlation magnitude associated with the subset of codes is less than a cross-correlation magnitude associated with the other subsets of codes.
17. The method of claim 1 , wherein the subset of codes optimizes the performance criterion when a result achieved by codes within the subset of codes in relation to the performance criterion is preferred over other results achieved by codes within the other subsets of codes in relation to the performance criterion.
18. One or more non-transitory processor-readable media embodying program instructions that, when executed by one or more processors, cause the one or more processors to implement a method for selecting codes to be used within positioning signals sent from one or more transmitters, the method comprising:
identifying a set of codes, wherein a magnitude of an autocorrelation function of each member of the set of codes, within a specified zonal region adjacent to a peak of the autocorrelation function, is below a first prescribed value;
identifying a subset of codes, from among two or more subsets of codes in the identified set of codes, that optimizes a performance criterion, wherein the performance criterion is associated with a relationship between members within the subset of codes;
transmitting, from a first transmitter, a first positioning signal that is modulated with a first code of the identified subset of codes; and
transmitting, from a second transmitter, a second positioning signal that is modulated with a second code of the identified subset of codes.
19. The one or more non-transitory processor-readable media of claim 18 , wherein the subset of codes is identified from the set such that magnitudes of a cross-correlation function of any pair of codes within the subset of codes are equal to or less than a second prescribed value.
20. The one or more non-transitory processor-readable media of claim 18 , wherein the subset of codes that optimizes the performance criterion minimizes a maximum magnitude of a cross-correlation between all pairs of non-identical codes of that subset of codes as compared to the other subsets of codes of the two or more subsets of codes.
21. The one or more non-transitory processor-readable media of claim 20 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation.
22. The one or more non-transitory processor-readable media of claim 20 , wherein said first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation.
23. The one or more non-transitory processor-readable media of claim 18 , wherein a set of frequency offset modulated (FOM) signals is generated, wherein each signal of the set of FOM signals is generated by modulating a respective signal of the FOM signals with a code of the identified set of codes, and further modulating the respective signal of the FOM signals with a carrier whose frequency is chosen from among a set of offsets relative to a base offset frequency.
24. The one or more non-transitory processor-readable media of claim 23 , wherein the performance criterion includes a minimization of the maximum magnitude of the cross-correlation between all pairs of FOM signals, wherein each pair has different codes and wherein frequency offsets associated with each pair are within a specified range.
25. The one or more non-transitory processor-readable media of claim 24 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation between the FOM signals.
26. The one or more non-transitory processor-readable media of claim 24 , wherein the first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation between said FOM signals.
27. The one or more non-transitory processor-readable media of claim 18 , wherein the method further comprises:
selecting the first code from the subset of codes prior to transmitting the first positioning signal; and
selecting the second code from the subset of codes prior to transmitting the second positioning signal.
28. The one or more non-transitory processor-readable media of claim 27 , wherein the second positioning signal is transmitted at an offset frequency relative to the first positioning signal.
29. The one or more non-transitory processor-readable media of claim 18 , wherein each subset of codes of the two or more subsets of codes contain an equal number of codes.
30. The one or more non-transitory processor-readable media of claim 18 , wherein each subset of codes of the two or more subsets of codes include respective numbers of codes that are within a range of sizes.
31. The one or more non-transitory processor-readable media of claim 18 , wherein the performance criterion is associated with a relationship between all pairs of signals that are modulated with different members within the subset of codes and further modulated with carrier frequencies that are chosen from among a set of offsets relative to a base frequency.
32. The one or more non-transitory processor-readable media of claim 18 , wherein a cross-correlation condition associated with the codes within the identified subset of codes is preferred over the cross-correlation condition associated with the other subsets of codes of the two or more subsets of codes.
33. The one or more non-transitory processor-readable media of claim 18 , wherein the subset of codes optimizes the performance criterion when a cross-correlation magnitude associated with the subset of codes is less than a cross-correlation magnitude associated with the other subsets of codes.
34. The one or more non-transitory processor-readable media of claim 18 , wherein the subset of codes optimizes the performance criterion when a result achieved by codes within the subset of codes in relation to the performance criterion is preferred over other results achieved by codes within the other subsets of codes in relation to the performance criterion.
35. A system for selecting codes to be used within positioning signals sent from one or more transmitters, wherein the system comprises a network of transmitters that includes:
a first transmitter configured to transmit a first positioning signal that is modulated with a first code of a subset of codes identified from among two or more subsets of codes in an identified set of codes; and
a second transmitter configured to transmit a second positioning signal that is modulated with a second code of the identified subset of codes,
wherein a magnitude of an autocorrelation function of each member of the identified set of codes, within a specified zonal region adjacent to a peak of the autocorrelation function, is below a first prescribed value, and
wherein the identified subset of codes optimizes a performance criterion associated with a relationship between members within the subset of codes.