Method and apparatus for using an unique index set for PSC sequence in a wireless communication system
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). 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. Evaluating a primary synchronization channel having length N of 63, an optimal pair of root indices of (28, 31, 32) and (31, 33, 35) provide a five-fold improvement in frequency offset error over conventional single index set of (25, 29, 34).
1. A method for transmitting a synchronization channel for enabling accurate remote determination of frequency offset and time offset in a wireless communication system, comprising:
determining a first optimal root index of a Zadoff-Chu (ZC) sequence having a frequency offset error below a predetermined threshold;
determining a second optimal root index having a desirable attribute;
selecting the first root index for a primary synchronization channel; and
generating and transmitting the primary synchronization channel.
2. The method of claim 1 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises (28, 31, 32) and the second optimal root index comprises (31, 33, 35).
3. The method of claim 1 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises (31, 32, 44) and the second optimal root index comprises (31, 32, 46).
4. The method of claim 1 , wherein determining the first and second optimal root indices further comprises:
computing a performance metric for a set of time-domain root indices;
selecting an optimal time-domain root index according to a first performance criterion;
determining a frequency-domain root index for the time-domain optimal root index;
computing a performance metric for the frequency-domain root index; and
retaining the optimal root index when the frequency-domain root index that satisfies a second performance criterion.
5. The method of claim 4 , wherein generating and transmitting the primary synchronization channel further comprises:
generating a Zadoff-Chu base sequence of length N (a positive integer) with the selected optimal time-domain root index;
associating the Zadoff-Chu base sequence with a first primary synchronization channel (PSC) sequence; and
conjugating and sign-flipping the Zadoff-Chu base sequence and associating the result with a second PSC sequence;
modulating the Zadoff-Chu base sequence with a sequence of period κ=√{square root over (N)}, when κ is an integer and associating the result with a third PSC sequence,
wherein the performance metric is
∑
k
=
-
N
/
2
1
(
kl
λ
(
k
)
)
-
2
+
∑
k
=
1
N
/
2
-
1
(
kl
λ
(
k
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)
-
2
,
where l λ (k)=−λk(mod N)−N/2.
6. The method of claim 1 , wherein the predetermined threshold is 200 Hz.
7. At least one processor for transmitting a synchronization channel for enabling accurate remote determination of frequency offset and time offset in a wireless communication system, comprising:
a first module for determining a first optimal root index of a Zadoff-Chu (ZC) sequence having a frequency offset error below a predetermined threshold;
a second module for determining a second optimal root index having a desirable attribute;
a third module for selecting the first root index for a primary synchronization channel; and
a fourth module for generating and transmitting the primary synchronization channel.
8. The at least one processor of claim 7 , further comprising the first module for determining that the first optimal root index comprises (28, 31, 32) and the second module for determining that second optimal root index comprises (31, 33, 35) for a ZC sequence of selected length N of 63.
9. The at least one processor of claim 7 , further comprising the first module for determining that the first optimal root index comprises (31, 32, 44) and the second module for determining that second optimal root index comprises (31, 32, 46) for a ZC sequence of selected length N of 63.
10. The at least one processor of claim 7 , wherein the first and second modules for determining respectively the first and second optimal root indices each is further for,
computing a performance metric for a set of time-domain root indices;
selecting an optimal time-domain root index according to a first performance criterion;
determining a frequency-domain root index for the time-domain optimal root index;
computing a performance metric for the frequency-domain root index; and
retaining the optimal root index when the frequency-domain root index that satisfies a second performance criterion.
11. The at least one processor of claim 10 , wherein the fourth module for generating and transmitting the primary synchronization channel is further for,
generating a Zadoff-Chu base sequence of length N (a positive integer) with the selected optimal time-domain root index;
associating the Zadoff-Chu base sequence with a first primary synchronization channel (PSC) sequence;
conjugating and sign-flipping the Zadoff-Chu base sequence and associating the result with a second PSC sequence; and
modulating the Zadoff-Chu base sequence with a sequence of period κ=√{square root over (N)}, when κ is an integer and associating the result with a third PSC sequence,
wherein the performance metric is
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k
=
-
N
/
2
1
(
kl
λ
(
k
)
)
-
2
+
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k
=
1
N
/
2
-
1
(
kl
λ
(
k
)
)
-
2
,
where l λ (k)=−λk(mod N)−N/2.
12. The At least one processor of claim 7 , wherein the predetermined threshold is 200 Hz.
13. A computer program product for transmitting a synchronization channel for enabling accurate remote determination of frequency offset and time offset in a wireless communication system, comprising:
computer-readable storage medium, comprising:
code for causing a computer to determine a first optimal root index of a Zadoff-Chu (ZC) sequence having a frequency offset error below a predetermined threshold;
code for causing the computer to determine a second optimal root index having a desirable attribute;
code for causing the computer to select the first root index for a primary synchronization channel; and
code for causing the computer to generate and transmitting the primary synchronization channel.
14. An apparatus for transmitting a synchronization channel for enabling accurate remote determination of frequency offset and time offset in a wireless communication system, comprising:
means for determining a first optimal root index of a Zadoff-Chu (ZC) sequence having a frequency offset error below a predetermined threshold;
means for determining a second optimal root index having a desirable attribute;
means for selecting the first root index for a primary synchronization channel; and
means for generating and transmitting the primary synchronization channel.
15. The apparatus of claim 14 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises (28, 31, 32) and the second optimal root index comprises (31, 33, 35).
16. The apparatus of claim 14 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises (31, 32, 44) and the second optimal root index comprises (31, 32, 46).
17. The apparatus of claim 14 , wherein the means for determining the first and second optimal root indices further comprises:
means for computing a performance metric for a set of time-domain root indices;
means for selecting an optimal time-domain root index according to a first performance criterion;
means for determining a frequency-domain root index for the time-domain optimal root index;
means for computing a performance metric for the frequency-domain root index; and
means for retaining the optimal root index when the frequency-domain root index that satisfies a second performance criterion.
18. The apparatus of claim 17 , wherein generating and transmitting the primary synchronization channel further comprises:
generating a Zadoff-Chu base sequence of length N (a positive integer) with the selected optimal time-domain root index;
associating the Zadoff-Chu base sequence with a first primary synchronization channel (PSC) sequence; and
conjugating and sign-flipping the Zadoff-Chu base sequence and associating the result with a second PSC sequence;
modulating the Zadoff-Chu base sequence with a sequence of period κ=√{square root over (N)}, when κ is an integer and associating the result with a third PSC sequence,
wherein the performance metric is
∑
k
=
-
N
/
2
1
(
kl
λ
(
k
)
)
-
2
+
∑
k
=
1
N
/
2
-
1
(
kl
λ
(
k
)
)
-
2
,
where l λ (k)=−λk(mod N)−N/2.
19. The apparatus of claim 14 , wherein the predetermined threshold is 200 Hz.
20. An apparatus for transmitting a synchronization channel for enabling accurate remote determination of frequency offset and time offset in a wireless communication system, comprising:
a processor for determining a first optimal root index of a Zadoff-Chu (ZC) sequence having a frequency offset error below a predetermined threshold, for determining a second optimal root index having a desirable attribute, for selecting the first root index for a primary synchronization channel; and generating the primary synchronization channel; and
a transmitter for transmitting the primary synchronization channel.
21. The apparatus of claim 20 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises (28, 31, 32) and the second optimal root index comprises (31, 33, 35).
22. The apparatus of claim 20 , wherein for a ZC sequence of selected length N of 63, the first optimal root index comprises, (31, 32, 44) and the second optimal root index comprises (31, 32, 46).
23. The apparatus of claim 20 , wherein determining the first and second optimal root indices further comprises the processor for computing a performance metric for a set of time-domain root indices, for selecting an optimal time-domain root index according to a first performance criterion, for determining a frequency-domain root index for the time-domain optimal root index, and for computing a performance metric for the frequency-domain root index, and
a memory for retaining the optimal root index when the frequency-domain root index that satisfies a second performance criterion.
24. The apparatus of claim 23 , wherein generating and transmitting the primary synchronization channel further comprises:
generating a Zadoff-Chu base sequence of length N (a positive integer) with the selected optimal time-domain root index;
associating the Zadoff-Chu base sequence with a first primary synchronization channel PSC) sequence;
conjugating and sign-flipping the Zadoff-Chu base sequence and associating the result with a second PSC sequence; and
modulating the Zadoff-Chu base sequence with a sequence of period κ=√{square root over (N)}, when κ is an integer and associating the result with a third PSC sequence,
wherein the performance metric is
∑
k
=
-
N
/
2
1
(
kl
λ
(
k
)
)
-
2
+
∑
k
=
1
N
/
2
-
1
(
kl
λ
(
k
)
)
-
2
,
where l λ (k)=−λk(mod N)−N/2.
25. The apparatus of claim 20 , wherein the predetermined threshold is 200 Hz.