Selection of acquisition sequences for optimal frequency offset estimation
Systems and methods are provided to generate a set of synchronization channel sequences that optimize time and frequency acquisition. A set of root indices of Zadoff-Chu sequences in a first domain (e.g., time domain) that optimize a performance metric or merit factor are identified. An optimal index is determined that also optimizes a performance metric in a reciprocal domain (e.g., frequency domain). Optimal indices satisfy a centro-symmetric relationship with respect to a half-value of sequence length: When 1 is an optimal index, N−1 is also an optimal root index. For sequences of length Q 2 =N, a base sequence generated with an optimal sequence can be utilized to generate at least two disparate optimal sequences through sign-flip, conjugation, and periodic modulation operations.
1. A method, comprising:
identifying, by an apparatus, an optimal root index in a first domain according to a first performance criterion;
determining, by the apparatus, a domain-dual root index for the optimal root index in the first domain and computing a performance metric for the domain-dual root index; and
when the domain-dual root index satisfies a second performance criterion, storing, by the apparatus, the optimal root index;
wherein said step of identifying an optimal root index in a first domain further comprises computing a performance metric for a set of indices in the first domain and wherein the performance metric is
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2. The method of claim 1 , further comprising:
generating a base sequence of length N (a positive integer) with an optimal root index in a first domain; and
associating the base sequence with a first primary synchronization channel (PSC) sequence.
3. The method of claim 2 , further comprising conjugating and sign-flipping the base sequence and associating the result with a second PSC sequence.
4. The method of claim 3 , wherein when κ=√{square root over (N)} is an integer, modulating the base sequence with a x-periodic sequence and associating the result with a third PSC sequence.
5. The method of claim 3 , wherein the base sequence is a Zadoff-Chu sequence.
6. The method of claim 1 , wherein the performance metric is an apparent frequency offset.
7. The method of claim 1 , wherein the first domain is at least one of a time domain or a frequency domain.
8. The method of claim 6 , wherein the dual-domain is one of a frequency domain or a time domain.
9. An apparatus that operates in a wireless communication system, comprising:
a processor configured to compute a performance metric for a set of time-domain root indices; to select an optimal time-domain root index according to a first performance criterion; to determine a frequency-domain root index for the time-domain optimal root index; to compute a performance metric for the frequency-domain root index;
a memory coupled to the processor, wherein the processor is further configured to retain the optimal root index when the frequency-domain root index satisfies a second performance criterion, to generate a Zadoff-Chu base sequence of length N (a positive integer) with the optimal time-domain root index, to associate the Zadoff-Chu base sequence with a first primary synchronization channel (PSC) sequence, to conjugate and sign-flip the Zadoff-Chu base sequence and associate the result with a second PSC sequence, and to modulate the Zadoff-Chu base sequence with a sequence of period κ=√{square root over (N)}, when x is an integer; and to associate the result with a third PSC sequence
wherein the performance metric is
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10. The apparatus of claim 9 , wherein the processor is further configured to identify a disparate time-domain root index according to the first performance criterion when the frequency-domain root index fails to satisfy a second performance criterion.
11. An apparatus, comprising:
means for identifying an optimal root index in a first domain according to a first performance criterion;
means for determining a domain-dual root index for the optimal root index in the first domain and computing a performance metric for the domain-dual root index; and
when the domain-dual root index satisfies a second performance criterion, means for storing the optimal root index;
wherein said means for identifying an optimal root index in a first domain further comprises means for computing a performance metric for a set of indices in the first domain and wherein the performance metric is
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12. The apparatus of claim 11 , wherein the performance metric is an apparent frequency offset.
13. The method of claim 12 , wherein the dual-domain is one of a frequency domain or a time domain.
14. The apparatus of claim 11 , wherein the first domain is at least one of a time domain or a frequency domain.
15. A computer program product including a non-transitory computer-readable medium comprising:
code for causing a computer to identify an optimal root index in a first domain according to a first performance criterion;
code for causing a computer to determine a domain-dual root index for the optimal root index in the first domain and computing a performance metric for the domain-dual root index; and
code for causing a computer to store the optimal root index when the domain-dual root index satisfies a second performance criterion;
wherein said code for causing a computer to identify an optimal root index in a first domain further comprises code for causing a computer to compute a performance metric for a set of indices in the first domain and wherein the performance metric is
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16. The computer program product of claim 15 , wherein the performance metric is an apparent frequency offset.
17. The computer program product of claim 16 , wherein the dual-domain is one of a frequency domain or a time domain.
18. The computer program product of claim 15 , wherein the first domain is at least one of a time domain or a frequency domain.