Synthesizing coherent correlation sums at one or multiple carrier frequencies using correlation sums calculated at a coarse set of frequencies
View Patent ↗Techniques are provided for synthesizing a long coherent I and Q correlation integral at a particular frequency by synthetically combining a sequence of shorter correlation integrals at the same or different frequency. Techniques are also provided for acquiring a carrier-modulated signal with an unknown shift of the carrier frequency, and possibly some additional unknown signal parameters. These techniques involve synthesizing coherent correlation sums at a fine frequency resolution, using coherent correlation sums that are calculated at a coarse frequency resolution. This approach allows for coherent processing of the received signal over an arbitrarily long time interval, while avoiding the excessive computational requirements of traditional methods.
1. A method for detecting a sampled signal having a carrier frequency that is within a frequency range and a delay within a delay range relative to a reference signal, comprising:
determining a plurality of coarse frequencies within the frequency range;
dividing the sampled signal into a plurality of data blocks, the number of data blocks being a function of the number of the plurality of coarse frequencies;
determining a plurality of fine frequencies, each fine frequency being a function of the number of the plurality of coarse frequencies and the number of data blocks;
calculating a first set of correlation sums for each data block, each correlation sum in the first set being based on the reference signal, one of a predetermined number of delays within the delay range and one of the plurality of the coarse frequencies;
calculating a second set of correlation sums, each correlation sum in the second set being a function of the first set of correlation sums and a selected one of the plurality of the fine frequencies; and
based on the second set of correlation sums, determining the carrier frequency and the delay.
2. A method as in claim 1 , wherein the plurality of coarse frequencies is determined based on a sampling frequency of the sampled signal and the frequency range.
3. A method as in claim 1 , wherein the plurality of coarse frequencies is a function of a predetermined angular phase value.
4. A method as in claim 3 , wherein the predetermined angular phase value is determined from a predetermined signal-to-noise ratio.
5. A method as in claim 1 , wherein the first set of correlation sums comprise an in-phase component and a quadrature component.
6. A method as in claim 1 , wherein the second set of correlation sums is calculated by weighting one or more of the correlation sums from the first set of correlation sums by a function of the selected fine frequency.
7. A method as in claim 1 , wherein the sampled signal is modulated by a set of data bits, and wherein the first and second sets of correlation sums are calculated using coherent integration, taking into account the values of the data bits.
8. A method as in claim 7 , wherein the sampled signal corresponds to signals transmitted from a set of global positioning system (GPS) satellite vehicles.
9. A method of claim 1 , wherein an interval between two closest fine frequencies is less than an interval between two closest coarse frequencies.
10. A method as in claim 1 , wherein the number of data blocks is also selected based on a measure of computational complexity.
11. A method as in claim 1 , wherein the plurality of coarse frequencies is determined based on an intermediate frequency employed by a receiver and a Doppler shift associated with a position and a motion of a global positioning satellite vehicle relative to the receiver.
12. A computer readable medium, comprising instructions executable by a computer to implement a method for detecting a sampled signal having a carrier frequency that is within a frequency range and a delay within a delay range relative to a reference signal, wherein the method comprises:
determining a plurality of coarse frequencies within the frequency range;
dividing the sampled signal into a plurality of data blocks, the number of data blocks being a function of the number of the plurality of coarse frequencies;
determining a plurality of fine frequencies, each fine frequency being a function of the number of the plurality of coarse frequencies and the number of data blocks;
calculating a first set of correlation sums for each data block, each correlation sum in the first set being based on the reference signal, one of a predetermined number of delays within the delay range and one of the plurality or the coarse frequencies;
calculating a second set of correlation sums, each correlation sum in the second set being a function of the first set of correlation sums and a selected one of the plurality of the fine frequencies; and
based on the second set of correlation sums, determining a selected fine frequency and a selected delay.
13. A computer readable medium as in claim 12 , wherein the plurality of coarse frequencies is determined based on a sampling frequency of the sampled signal and the frequency range.
14. A computer readable medium as in claim 12 , wherein the plurality of coarse frequencies is a function of a predetermined angular phase value.
15. A computer readable medium as in claim 14 , wherein the predetermined angular phase value is determined from a predetermined signal-to-noise ratio.
16. A computes readable medium as in claim 12 , wherein the first set of correlation sums comprise an in-phase component and a quadrature component.
17. A computer readable medium as in claim 12 , wherein the second set of correlation sums is calculated by weighting one or more of the correlation sums from the first set of correlation sums by a function of the selected fine frequency.
18. A computer readable medium as in claim 12 , wherein the sampled signal is modulated by a set of data bits, and wherein the first and second sets of correlation sums are calculated using coherent integration, taking into account the values of the data bits.
19. A computer readable medium as in claim 18 , wherein the sampled signal corresponds to signals transmitted from a set of global positioning system (GPS) satellite vehicles.
20. A computer readable medium as in claim 12 , wherein an interval between two closest fine frequencies is less than an interval between two closest coarse frequencies.
21. A computer readable medium as in claim 12 , wherein the number of data blocks is also selected based on a measure of computational complexity.
22. A computer readable medium as in claim 12 , wherein the plurality of coarse frequencies is determined based on an intermediate frequency employed by a receiver and a Doppler shift associated with a position and a motion of a global positioning satellite vehicle relative to the receiver.