Systems and methods for pseudo-random coding
Systems and methods for improving performance in terrestrial and satellite positioning systems. 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 computer-implemented method for decoding positioning signals received from one or more transmitters, the method comprising:
receiving a first positioning signal from a first transmitter, wherein at least a portion of the first positioning signal is encoded with a first code;
receiving a second positioning signal from a second transmitter, wherein at least a portion of the second positioning signal is encoded with a second code,
wherein the first code and the second code are members of a subset of at least two codes from 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,
wherein the subset of codes optimizes a performance criterion that is associated with a relationship between members within the subset of codes; and
determining positioning information using the first positioning signal received from the first transmitter and using the second positioning signal received from the second transmitter.
2. The method of claim 1 , wherein magnitudes of a cross-correlation function of any pair of codes within the subset of codes are 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 the 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 the first positioning signal and the second positioning signal are members of a set of frequency offset modulated (FOM) signals, wherein each signal of the set of FOM signals is generated by modulating that signal 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 in the set of FOM signals, wherein frequency offsets associated with each of the pairs of FOM signals in the set of FOM signals 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 each of the pairs of 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 each of the pairs of the FOM signals.
10. The method of claim 1 , wherein the second positioning signal is offset in frequency relative to the first positioning signal.
11. The method of claim 1 , wherein the subset of codes optimizes the performance criterion with respect to at least one additional subset of codes in the set of codes, and wherein each of the subset of codes and the at least one additional subset of codes include an equal number of codes.
12. The method of claim 1 , wherein the subset of codes optimizes the performance criterion with respect to at least one additional subset of codes in the set of codes, and wherein the subset of codes and the at least one additional subset of codes include respective numbers of codes that are within a range of sizes.
13. 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.
14. 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 one or more other subsets of codes in the set of codes.
15. 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 one or more other subsets of codes in the set of codes.
16. 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 one or more other subsets of codes in the set of codes in relation to the performance criterion.
17. The method of claim 1 , wherein the positioning information includes a first time of arrival of the first positioning signal, and a second time of arrival of the second positioning signal.
18. The method of claim 1 , wherein the positioning information includes a first location of the first transmitter, and a second location of the second transmitter.
19. 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 decoding positioning signals received from one or more transmitters, the method comprising:
receiving a first positioning signal from a first transmitter, wherein at least a portion of the first positioning signal is encoded with a first code;
receiving a second positioning signal from a second transmitter, wherein at least a portion of the second positioning signal is encoded with a second code,
wherein the first code and the second code are members of a subset of at least two codes from 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,
wherein the subset of codes optimizes a performance criterion that is associated with a relationship between members within the subset of codes; and
determining positioning information using the first positioning signal received from the first transmitter and using the second positioning signal received from the second transmitter.
20. The non-transitory processor-readable media of claim 19 , wherein magnitudes of a cross-correlation function of any pair of codes within the subset of codes are less than a second prescribed value.
21. The non-transitory processor-readable media of claim 19 , 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.
22. The non-transitory processor-readable media of claim 21 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation.
23. The non-transitory processor-readable media of claim 21 , wherein the first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation.
24. The non-transitory processor-readable media of claim 19 , wherein the first positioning signal and the second positioning signal are members of a set of frequency offset modulated (FOM) signals, wherein each signal of the set of FOM signals is generated by modulating that signal with a carrier whose frequency is chosen from among a set of offsets relative to a base offset frequency.
25. The non-transitory processor-readable media of claim 24 , wherein the performance criterion includes a minimization of the maximum magnitude of the cross-correlation between all pairs of FOM signals in the set of FOM signals, wherein frequency offsets associated with each of the pairs of FOM signals in the set of FOM signals are within a specified range.
26. The non-transitory processor-readable media of claim 25 , wherein the first prescribed value is equal to or less than one-half of the maximum magnitude of the cross-correlation between each of the pairs of the FOM signals.
27. The non-transitory processor-readable media of claim 25 , wherein the first prescribed value is equal to or less than one-tenth of the maximum magnitude of the cross-correlation between each of the pairs of the FOM signals.
28. The non-transitory processor-readable media of claim 19 , wherein the second positioning signal is offset in frequency relative to the first positioning signal.
29. The non-transitory processor-readable media of claim 19 , wherein the subset of codes optimizes the performance criterion with respect to at least one additional subset of codes in the set of codes, and wherein each of the subset of codes and the at least one additional subset of codes include an equal number of codes.
30. The non-transitory processor-readable media of claim 19 , wherein the subset of codes optimizes the performance criterion with respect to at least one additional subset of codes in the set of codes, and wherein the subset of codes and the at least one additional subset of codes include respective numbers of codes that are within a range of sizes.
31. The non-transitory processor-readable media of claim 19 , 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 non-transitory processor-readable media of claim 19 , wherein a cross-correlation condition associated with the codes within the identified subset of codes is preferred over the cross-correlation condition associated with one or more other subsets of codes in the set of codes.
33. The non-transitory processor-readable media of claim 19 , 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 one or more other subsets of codes in the set of codes.
34. The non-transitory processor-readable media of claim 19 , 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 one or more other subsets of codes in the set of codes in relation to the performance criterion.
35. The non-transitory processor-readable media of claim 19 , wherein the positioning information includes a first time of arrival of the first positioning signal, and a second time of arrival of the second positioning signal.
36. The non-transitory processor-readable media of claim 19 , wherein the positioning information includes a first location of the first transmitter, and a second location of the second transmitter.