Ternary sequences with power of two exponent dimensionalities suitable for channel estimation
Methods, systems, and devices for channel estimation in a location tracking system are described. The methods, system, and devices may include tools and techniques for determining and/or designing perfect or semi-perfect sequences (including preamble sequences) for implementation in a location tracking system. Sequences having 2's exponent dimensionality, such as ternary sequences, may be determined and employed, which may help reduce implementation complexity and/or operating power consumption. Sequences may be determined using mean square error and/or maximum autocorrelation peak performance metrics.
1. A method to perform channel estimation, comprising:
selecting, in a time domain, an initial real sequence comprising perfect circular autocorrelation;
performing, in the time domain, an initial modification to a length of the initial real sequence;
determining a phase response of a frequency domain version of the modified initial real sequence;
converting the phase response to a time domain response; and
transmitting, at a transmitter, a preamble generated based at least in part on the time domain response.
2. The method of claim 1 , further comprising:
quantitizing the time domain response to a predetermined number of levels with an optimal threshold; and
iteratively calculating a performance metric based at least in part on the initial modified length and the quantitized time domain response.
3. The method of claim 2 , wherein the quantitizing comprises applying a three level quantitization.
4. The method of claim 2 , further comprising:
determining whether to perform an additional modification to the length of the initial real sequence based at least in part on each of the iterative calculations of the performance metric, the length of the initial real sequence being 2 d −1, where d is a dimensionality of the preamble.
5. The method of claim 4 , wherein the performance metric comprises a mean square error function.
6. The method of claim 4 , wherein the performance metric comprises a maximum autocorrelation peak metric.
7. The method of claim 4 , further comprising:
determining to perform the additional modification when a minimum mean square error is reached.
8. The method of claim 1 , wherein performing the initial modification comprises adding an element within the initial real sequence.
9. A system for performing channel estimation, comprising:
means for selecting, in a time domain, an initial real sequence comprising perfect circular autocorrelation;
means for performing, in the time domain, an initial modification to a length of the initial real sequence;
means for determining a phase response of a frequency domain version of the modified initial real sequence;
means for converting the phase response to a time domain response; and
means for transmitting a preamble generated based at least in part on the time domain response.
10. The system of claim 9 , further comprising:
means for quantitizing the time domain response to a predetermined number of levels with an optimal threshold; and
means for iteratively calculating a performance metric based at least in part on the initial modified length and the quantitized time domain response.
11. The system of claim 10 , wherein the quantitizing comprises applying a three level quantitization.
12. The system of claim 10 , further comprising:
means for determining whether to perform an additional modification to the length of the initial real sequence based at least in part on each of the iterative calculations of the performance metric, the length of the initial real sequence being 2 d −1, where d is a dimensionality of the preamble.
13. The system of claim 12 , wherein the performance metric comprises a mean square error function.
14. The system of claim 12 , wherein the performance metric comprises a maximum autocorrelation peak metric.
15. The system of claim 12 , further comprising:
means for determining to perform the additional modification when a minimum means square error is reached.
16. The system of claim 9 , wherein performing the initial modification comprises adding an element within the initial real sequence.
17. An apparatus for performing channel estimation, comprising:
a transmitter;
a processor;
memory in electronic communication with the processor; and
instructions stored in the memory, the instructions being executable by the processor to:
select, in a time domain, an initial real sequence comprising perfect circular autocorrelation;
perform, in the time domain, an initial modification to a length of the initial real sequence;
determine a phase response of a frequency domain version of the modified initial real sequence;
convert the phase response to a time domain response; and
transmit, using the transmitter, a preamble generated based at least in part on the time domain response.
18. The apparatus of claim 17 , wherein the instruction are further executable by the processor to:
quantitize the time domain response to a predetermined number of levels with an optimal threshold; and
iteratively calculate a performance metric based at least in part on the initial modified length and the quantitized time domain response.
19. The apparatus of claim 18 , wherein the instructions executable by the processor to quantitize comprise instructions executable by the processor to apply a three level quantitization.
20. The apparatus of claim 18 , wherein the instructions are further executable by the processor to:
determine whether to perform an additional modification to the length of the initial real sequence based at least in part on each of the iterative calculations of the performance metric, the length of the initial real sequence being 2 d −1, where d is a dimensionality of the preamble.
21. The apparatus of claim 20 , wherein the performance metric comprises a mean square error function.
22. The apparatus of claim 20 , wherein the performance metric comprises a maximum autocorrelation peak metric.
23. The apparatus of claim 20 , wherein the instructions are further executable by the processor to determine to perform the additional modification when a minimum mean square error is reached.
24. The apparatus of claim 17 , wherein the instructions executable by the processor to perform the initial modification comprise instructions executable by the processor to add an element within the initial real sequence.
25. A computer-program product for channel estimation, the computer-program product comprising a non-transitory computer-readable medium storing instructions executable by a processor to:
select, in a time domain, an initial real sequence comprising perfect circular auto correlation;
perform, in the time domain, an initial modification to a length of the initial real sequence;
determine a phase response of a frequency domain version of the modified initial real sequence;
convert the phase response to a time domain response; and
transmit, at a transmitter, a preamble generated based at least in part on the time domain response.
26. The computer-program product of claim 25 , wherein the instructions are further executable by the processor to:
quantitize the time domain response to a predetermined number of levels with an optimal threshold; and
iteratively calculate a performance metric based at least in part on the initial modified length and the quantitized time domain response.
27. The computer-program product of claim 26 , wherein the instructions executable by the processor to quantitize comprise instructions executable by the processor to apply a three level quantitization.
28. The computer-program product of claim 26 , wherein the instructions are further executable by the processor to:
determine whether to perform an additional modification to the length of the initial real sequence based at least in part on each of the iterative calculations of the performance metric, the length of the initial real sequence being 2 d −1, where d is a dimensionality of the preamble.
29. The computer-program product of claim 28 , wherein the performance metric comprises a mean square error function.
30. The computer-program product of claim 28 , wherein the performance metric comprises a maximum autocorrelation peak metric.