Zero correlation zone sequences for communication system
View Patent ↗The present disclosure provides for the construction and use of a set of Zero-Correlation-Zone (ZCZ) Concatenated Complementary Pair (CCP) sequences with zero-correlation-zone range greater than one or with zero-correlation-zone range equal to one and the sequence set size greater than two. Complementary pair sequences A and B are selected and, for each member of the set of ZCZ CCP sequences, sign sequences p A and p B are combined with the complementary pair sequences to form a member ZCZ CCP sequence of the set. A ZCZ CCP sequence modified by propagation over a communication channel may be identified by cross-correlation with ZCZ CCP sequences of the set. A set of sign sequences may be constructed by recursive expansion from an initial set or found by a computer search. The sequences may be used in a transceiver of a portable electronic device or other communication device.
1. A method for constructing a set of sequences for use in a transceiver of a communication system, the method comprising:
selecting sequences A and B of length N that form a complementary pair; and
for each member i of a set of sequences:
selecting a pair of sign sequences p A i and p B i of length L/2 and
combining the pair of sign sequences p A i and p B i with the complementary pair sequences A and B, respectively, to form the member i sequence;
selecting one or more sequences of the set of sequences for use in the transceiver of the communication system, and
storing the one or more sequences in a memory of the transceiver,
where the pairs of sign sequences p A i and p B i are selected such that the set of sequences comprises a set of Zero-Correlation-Zone (ZCZ) Concatenated Complementary Pair (CCP) sequences, of length L×N with zero-correlation-zone range greater than one, and where the ZCZ CCP sequences facilitate communication.
2. The method of claim 1 , where the pairs of sign sequences are selected such that the cross correlations between the member i sign sequence p A i of the set of ZCZ CCP sequences and a member j sign sequence p B j are zero at lag=0 and at least one of lag=1 and lag=−1 for each member i and member j of the set of ZCZ CCP sequences.
3. The method of claim 1 , where combining the sign sequences p A i and p B i with the complementary pair sequences A and B comprises:
forming a first Kronecker tensor product p A i {circle around (×)} A and a second Kronecker tensor product p B i {circle around (×)} B; and
interleaving blocks of length N of the first and second Kronecker tensor products.
4. The method of claim 1 , where combining the sign sequences p A i and p B i with the complementary pair sequences A and B comprises:
modulating the sequence A by a sign of the sign sequence p A i for each sign of the sign sequence p A i ;
modulating the sequence B by a sign of the sign sequence p B i for each sign of the sign sequence p B i ; and
interleaving the sign modulated sequence A with the sign modulated sequence B in blocks of length of N.
5. The method of claim 1 , where combining the sign sequences p A i and p B i with the complementary pair sequences A and B comprises:
alternately concatenating the complementary pair sequence A, modulated by a sign of the sign sequence p A , and the complementary pair sequence B, modulated by a sign of the sign sequence p A .
6. The method of claim 1 , where the sequence A and the sequence B are binary Golay complementary sequences.
7. The method of claim 1 , where the transceiver comprises a transmitter of a mobile electronic device, the method further comprising:
transmitting the one or more sequences from the transmitter of the mobile electronic device.
8. The method of claim 1 , where the transceiver comprises a receiver of a mobile electronic device, the method further comprising:
receiving in the receiver of the mobile electronic device a sequence transmitted over a communication channel; and
correlating the received sequence with the one or more sequences.
9. A method for constructing a set of sequences for use in a transceiver of a communication system, the method comprising:
selecting sequences A and B of length N that form a complementary pair; and
for each member i of a set of sequences:
selecting a pair of sign sequences p A i and p B i of length L/2 and
combining the pair of sign sequences p A i and p B i with the complementary pair sequences A and B, respectively, to form the member i sequence; and
selecting one or more sequences of the set of sequences for use in the transceiver of the communication system,
where the pairs of sign sequences p A i and p B i are selected such that the set of sequences comprises a set of Zero-Correlation-Zone (ZCZ) Concatenated Complementary Pair (CCP) sequences, of length L×N with zero-correlation-zone range greater than one, and where the ZCZ CCP sequences facilitate communication,
where:
the pair of sign sequences p A i and p B i for set member i of the set of sequences satisfy a first condition that:
the sign sequence p A i is uncorrelated with the sign sequence p B i at lag=0 and at lag=−1; and
the sign sequences p A i and B j , for set member i and different set member j, satisfy a second condition that:
the cross-correlation of the sign sequence p A i with the sign sequence p A j is zero at lag=0,
the cross-correlation of the sign sequence p B i with the sign sequence hd j B is zero at lag=0,
the cross-correlation of the sign sequence p A i with the sign sequence p B j is zero at lag=0 and lag=−1, and
the cross-correlation of the sign sequence p B i with the sign sequence p A j is zero at lag=0 and lag=1.
10. The method of claim 9 , where selecting sign sequences p A i and p B i comprises:
searching a plurality of sign sequences of length L/2; and
identifying a set of sign sequences for which:
for each set member i of the set of sequences, the pair of sign sequences p A i and p B i satisfy the first condition; and
for each pair of set members i and j, i≠j, the sign sequences p A i , p B i , p A j and p B j satisfy the second condition.
11. A transceiver implemented method for transmitting information over a communication channel in a training sequence for estimating properties of the communication channel, the method comprising:
retrieving sequences A and B that form a complementary pair from a memory of the transceiver;
selecting a pair of sign sequences p A i and p B i from a set of pairs of sign sequences dependent upon the information to be transmitted;
combining the sign sequences p A i and p B i with the complementary pair sequences A and B, respectively, to form a zero correlation zone (ZCZ) concatenated complementary pair (CCP) sequence; and
transmitting ZCZ CCP sequence as the training sequence,
where the pairs of sign sequences are configured such that their combination with complementary pair sequences A and B form a set of ZCZ CCP sequences that facilitate communication, and
where combining the sign sequences p A i and p B i with the complementary pair sequences A and B comprises:
alternately concatenating the complementary pair sequence A, modulated by a sign of the sign sequence p A , and the complementary pair sequence B, modulated by a sign of the sign sequence p A .
12. The method of claim 11 , where the set of pairs of sign sequences comprises more than two pairs of sign sequences.
13. The method of claim 11 , where the sum of the cross-correlation of the sign sequence p A i with the sign sequence p A j and the cross-correlation of the sign sequence p B i with the sign sequence p B j is equal to zero at lag=0 for sign sequences of a set member i and a different set member j.
14. The method of claim 11 , where the zero-correlation-zone range is greater than one.
15. A receiver of a wireless communication system operable to identify a transmitted training sequence of a set of training sequences in a training sequence field in a signal frame that is propagated over a communication channel, the receiver comprising:
a memory operable to store complementary pair sequences A and B, first sign sequence p A (1) and second sign sequence p B (1) ,
a first zero correlation zone (ZCZ) Concatenated Complementary Pair (CCP) sequence generator, operable to generate a first ZCZ CCP sequence of a set of sequences having a zero correlation zone greater than one;
a second ZCZ CCP sequence generator, operable to generate a second ZCZ CCP sequence of the set of sequences having a zero correlation zone greater than one;
a first correlator, operable to produce a first cross-correlation between the first ZCZ CCP sequence and the propagated signal frame;
a second correlator, operable to produce a second cross-correlation between the second ZCZ CCP sequence and the propagated signal frame; and
a comparator, operable to identify the transmitted training sequence by comparing the first cross-correlation and the second cross-correlation,
where the transmitted training sequence facilitates communication, and
where the first ZCZ CCP sequence generator is operable to alternately combine the complementary pair sequence A with the first sign sequence p A (1) and the complementary pair sequence B with the second sign sequence p A (1) to generate the first ZCZ CCP sequence.
16. The receiver of claim 15 , further comprising a memory operable to store the first and second ZCZ CCP sequences.
17. A receiver of a wireless communication system operable to identify a transmitted training sequence of a set of training sequences in a training sequence field in a signal frame that is propagated over a communication channel, the receiver comprising:
a first zero correlation zone (ZCZ) Concatenated Complementary Pair (CCP) sequence generator, operable to generate a first ZCZ CCP sequence of a set of sequences having a zero correlation zone greater than one;
a second ZCZ CCP sequence generator, operable to generate a second ZCZ CCP sequence of the set of sequences having a zero correlation zone greater than one;
a first correlator, operable to produce a first cross-correlation between the first ZCZ CCP sequence and the propagated signal frame;
a second correlator, operable to produce a second cross-correlation between the second ZCZ CCP sequence and the propagated signal frame; and
a comparator, operable to identify the transmitted training sequence by comparing the first cross-correlation and the second cross-correlation,
where the transmitted training sequence facilitates communication,
where:
the first sequence comprises a plurality of concatenated sub-sequences, each sub-sequence being a sequence A of a complementary pair modulated by a sign of a first sign sequence p A (i) , concatenated with a sequence B of the complementary pair modulated by a sign of a second sign sequence p B (i) ; and
the second sequence comprises a plurality of concatenated sub-sequences, each sub-sequence being the sequence A of the complementary pair modulated by a sign of a third sign sequence p A (j) , concatenated with the sequence B of the complementary pair modulated by a sign of a fourth sign sequence p B (j) ,
where the first, second third and fourth sign sequences are found by performing a computerized search.
18. The receiver of claim 17 , where
the first, second, third and fourth sign sequences satisfy a first condition that:
the first sign sequence p A (i) is uncorrelated with the second sign sequence p B (i) at lag 0 and at lag=−1; and
the third sign sequence p A (j) p A (j) is uncorrelated with the fourth sign sequence p B (j) at lag 0 and at lag=−1; and
the first, second, third and fourth sign sequences satisfy a second condition that:
the first sign sequence p A (i) is uncorrelated with the third sign sequence p A (j) at lag 0;
the second sign sequence p B (j) is uncorrelated with the fourth sign sequence p B (j) at lag 0;
the cross-correlation of the first sign sequence p A (i) with the fourth sign sequence p B (j) is zero at lag=0 and at lag=−1; and
the cross-correlation of the second sign sequence p B (i) with the third sign sequence p A (j) is zero at lag=0 and at lag=1.
19. The receiver of claim 17 , where the complementary pair sequences A and B comprise Golay sequences.
20. A non-transitory computer-readable medium having computer-executable instructions that, when executed by a processor of a transceiver , cause the processor to:
receive a signal frame containing a training sequence;
generate a first Zero-Correlation-Zone (ZCZ), concatenated complementary pair (CCP) sequence comprising a plurality of concatenated sub-sequences, each sub-sequence being a sequence A of a complementary pair, modulated by a sign of a first sign sequence p A (1) , alternately concatenated with a sequence B of the complementary pair, modulated by a sign of a second sign sequence p B (1) ;
generate a second ZCZ CCP sequence comprising a plurality of concatenated sub-sequences, each sub-sequence being the sequence A of the complementary pair, modulated by a sign of a third sign sequence p A (2) ; concatenated with the sequence B of the complementary pair, modulated by a sign of a fourth sign sequence p B (2) ;
produce a first cross-correlation between the first ZCZ CCP sequence and the training sequence;
produce a second cross-correlation between the second ZCZ CCP sequence and the training sequence; and
identify the training sequence by comparing the first cross-correlation and the second cross-correlation
where:
the first, second, third and fourth sign sequences satisfy a first condition that:
the first sign sequence p A (1) is uncorrelated with the second sign sequence p B (1) at lag 0 and at lag=−1, and
the third sign sequence p A (2) is uncorrelated with the fourth sign sequence p B (2) at lag 0 and at lag=−1; and
the first, second, third and fourth sign sequences satisfy a second condition that:
the first sign sequence p A (1) is uncorrelated with the third sign sequence p A (2) at lag 0;
the second sign sequence p B (1) is uncorrelated with the fourth sign sequence p B (2) at lag 0;
the cross-correlation of the first sign sequence p A (1) with the fourth sign sequence p B (2) is zero at lag=0 and at lag=−1; and
the cross-correlation of the second sign sequence p B (1) with the third sign sequence p A (2) is zero at lag=0 and at lag=−1.
21. The non-transitory computer-readable medium of claim 20 , where the computer-executable instructions that, when executed by a processor, cause the processor to generate a first ZCZ CCP sequence comprise computer-executable instructions to access a first ZCZ CCP sequence stored in a memory.
22. The non-transitory computer-readable medium of claim 20 , where the computer-executable instructions that, when executed by a processor, cause the processor to generate the first ZCZ CCP sequence, comprise computer-executable instructions to:
access the complementary pair sequences A and B, the first sign sequence p A (1) and the second sign sequence p B (1) stored in a memory; and
alternately combine the complementary pair sequence A with the first sign sequence p A (1) , and the complementary pair sequence B with the second sign sequence p A (1) to generate the first ZCZ CCP sequence.