Coding in a positioning system
Embodiments describe determining position by selecting a set of digital pseudorandom sequences. The magnitudes of the cross-correlation between any two sequences of the chosen set are below a specified threshold. A subset of digital pseudorandom sequences are selected from the set such that the magnitudes of the autocorrelation function of each member of the subset, within a specified region adjacent to the peak of the autocorrelation function, are equal to or less than a prescribed value. Each transmitter transmits a positioning signal, and at least a portion of the positioning signal is modulated with at least one member of the subset. At least two transmitters of the plurality of transmitters modulate respective positioning signals with different members of the subset of digital pseudorandom sequences.
1. A system comprising at least one processor that is operable to implement a method, the method comprising:
identifying a set of pseudorandom sequences for use in transmitting signals from one or more transmitters to one or more receivers;
identifying a subset of pseudorandom sequences from the set of pseudorandom sequences; and
transmitting a first signal from a first transmitter, wherein at least a portion of the first signal is modulated with a first pseudorandom sequence of the subset;
wherein a magnitude of an autocorrelation function of each member of the set of pseudorandom sequences, within a range adjacent to a peak value of the autocorrelation function, is equal to or less than a prescribed value; and
wherein a magnitude of a cross-correlation function between any pair of pseudorandom sequences in the subset is below a specified threshold.
2. The system of claim 1 , wherein the prescribed value is less than or equal to a maximum magnitude of the cross-correlation function of any pair of pseudorandom sequences in the subset of pseudorandom sequences.
3. The system of claim 1 , wherein the prescribed value is +/−1 times the peak value of the autocorrelation function divided by a non-repeating pseudorandom sequence length.
4. The system of claim 1 , wherein a plurality of magnitudes of the autocorrelation function outside the range exceed the prescribed value.
5. The system of claim 1 , wherein:
the set includes at least 176 pseudorandom sequences;
the subset includes at least three pseudorandom sequences; and
the subset includes no more than ten pseudorandom sequences.
6. The system of claim 1 , wherein the pseudorandom sequences in the set have an alphabet size greater than two.
7. The system of claim 6 , wherein the alphabet size is a power of two.
8. The system of claim 1 , wherein the range adjacent to the peak value of the autocorrelation function includes at least five pseudorandom sequence symbols.
9. The system of claim 1 , wherein the method further comprises:
transmitting a second signal from a second transmitter, wherein at least a portion of the second signal is modulated with a second pseudorandom sequence of the subset;
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
10. The system of claim 9 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the portion of the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the portion of the second signal.
11. The system of claim 1 , wherein the method further comprises:
transmitting a second signal from the transmitter, wherein the second signal is modulated with a second pseudorandom sequence of the subset;
wherein the first signal is modulated with the first pseudorandom sequence of the subset; and
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences.
12. The system of claim 11 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the first signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the second signal.
13. A method comprising:
identifying a set of pseudorandom sequences for use in transmitting signals from one or more transmitters to one or more receivers;
identifying, from the set of pseudorandom sequences, a subset of at least three pseudorandom sequences;
transmitting a positioning signal during a first period of time from a first transmitter, wherein a first portion of the positioning signal is modulated with a first pseudorandom sequence of the subset of pseudorandom sequences, wherein the first pseudorandom sequence has a first length; and
transmitting the positioning signal during a second period of time from the first transmitter, wherein a second portion of the positioning signal is modulated with a second pseudorandom sequence of the subset of pseudorandom sequences, wherein the second pseudorandom sequence has a second length;
wherein the second pseudorandom sequence and the first pseudorandom sequence are different pseudorandom sequences; and
wherein the set and the subset are identified such that:
(i) a magnitude of a first autocorrelation function of each member of the set of pseudorandom sequences, within a first region adjacent to a peak value of the first autocorrelation function, is equal to or less than a first prescribed value, and (ii) a magnitude of a first cross-correlation function between any pair of pseudorandom sequences in the subset is below a first specified threshold; or
(i) a maximum magnitude of a second cross-correlation function between any two pseudorandom sequences of the set of pseudorandom sequences is below a second specified threshold, and (ii) all magnitudes of a second autocorrelation function corresponding to the pseudorandom sequences of the subset, within a second region adjacent to a peak value of the second autocorrelation function, are equal to or less than a second prescribed value.
14. The method of claim 13 , wherein the set of pseudorandom sequences has an alphabet size greater than two (2).
15. The method of claim 14 , wherein the set of pseudorandom sequences is a set of quaternary sequences.
16. The method of claim 14 , wherein the alphabet size is a power of two (2).
17. The method of claim 13 , wherein the first prescribed value is less than or equal to a maximum magnitude of the first cross-correlation function of any pair of pseudorandom sequences in the subset of pseudorandom sequences.
18. The method of claim 13 , wherein the first prescribed value is +/−1 times the peak value of the first autocorrelation function divided by a non-repeating pseudorandom sequence length.
19. The method of claim 13 , wherein the first region adjacent to the peak value of the first autocorrelation function includes at least five pseudorandom sequence symbols.
20. The method of claim 13 , wherein the first pseudorandom sequence consists of a first set of phase angles used to phase modulate the first portion of the positioning signal, and wherein the second pseudorandom sequence consists of a second set of phase angles used to phase modulate the second portion of the positioning signal.