Title of Invention

METHOD FOR SETTING CYCLIC SHIFT CONSIDERING FREQUENCY OFFSET

Abstract A method for establishing a cyclic shift sequence to provide against the frequency offset is disclosed. The method calculates a distance between a channel response position of the sequence and an alias channel response position caused by a frequency offset, calculates the number of cyclic shifts per group according to the calculated distance, and establishes the cyclic shift (CS)- applying interval. This method easily establishes a cyclic shift (CS) interval at a specific location having no overlapping by considering a channel response of a reception (Rx) sequence and an alias location of this reception (Rx) sequence, although a reception (Rx) signal is shifted by a channel delay spreading or a propagation delay irrespective of categories of a domain generating a sequence, so that it can greatly reduce the number of the detection errors and the false alarm rate. And, if a sequence of the cyclic shift (CS) is allocated to a cell having a frequency offset of more than a predetermined level, the present invention can minimize the influence of a frequency offset on a high-mobility cell.
Full Text [DESCRIPTION]
[invention Title]
METHOD FOR SETTING CYCLIC SHIFT CONSIDERING
FREQUENCY OFFSET
[Technical Field]
The present invention relates to a sequence of a
wireless communication system, and more particularly to a
method for establishing a cyclic shift in consideration of
characteristics of a CAZAC sequence in order to solve the
problem of a frequency offset.
[Background Art]
A Constant Amplitude Zero Auto-Correlation (CAZAC)
sequence is a representative one of various sequences
which have been intensively discussed in the 3GPP LTE.
Channels generally extract a variety of identifiers
(IDs) or information using the CAZAC sequence, for example, synchronization channels (e.g., a primary-SCH, a secondary-SCH, and a BCH) for downlink synchronization,
other synchronization channels (e.g., a RACK) for uplink synchronization, and pilot channels (e.g., a data pilot, and a channel quality pilot). Also, the above-mentioned
CAZAC sequence has been used to perform the scrambling.

Two kinds of methods have been used for the CAZAC
sequence, i.e., a first method for changing a root index
to another, and employing the changed root index, and a
second method for performing a cyclic shift (CS) on a
single root sequence, and employing the CS-result.
If a current root index is changed to a new root
index, a low cross-correlation occurs between the current
root index and the new root index, however, there is no
limitation in designing sequence usages.
In the case of the cyclic shift, zero cross-
correlation exists between the current root index and the
new root index, so that the two root indexes are used
when each of the root indexes require a high rejection
ratio. Specifically, when time-frequency resources are
shared in the same cell and data/control signals are
transmitted, the above-mentioned two root indexes are
adapted to discriminate among different signals or UEs.
A representative example of CAZAC sequences is a
Zadoff-Chu (ZC) sequence, and the Zadoff-Chu sequence can
be defined by the following equation 1:



where "n" is indicative of a sampling index, “Nzc”
is indicative of the length of the ZC sequence, and "u" is
indicative of the root index of the ZC sequence.'
However, if the offset occurs in a frequency
domain in the same manner as in the case where the CAZAC
sequence is transmitted using the OFDM scheme, a
performance or false alarm or throughput may be
excessively deteriorated.
Specifically, if the cyclic shift (CS) is applied
to the CAZAC sequence, the frequency offset or the timing
offset excessively occurs, so that it is difficult to
discriminate between sequences.
iDisclosurel
[Technical Problem]
Accordingly, the present invention is directed to a
method for establishing a cyclic shift (CS) considering a
frequency offset that substantially obviates one or more
problems due to limitations and disadvantages of the
related art.
An object of the present invention is to provide a
method for establishing a cyclic shift (CS) to provide

against a frequency offset, so that it can easily prevent a
sequence (e.g., a CAZAC sequence) from being deteriorated
under the condition that the frequency offset occurs.
Additional advantages, objects, and features of the
invention will be set forth in part in the description
which follows and in part will become apparent to those
having ordinary skill in the art upon examination of the
following or may be learned from practice of the invention.
The objectives and other advantages of the invention may be
realized and attained by the structure particularly pointed
out in the written description and claims hereof as well as
the appended drawings.
[Technical Solution]
To achieve these objects and other advantages and in
accordance with the purpose of the invention, as embodied
and broadly described herein, a method for setting cyclic
shift to be applied to a given sequence against an effect
of a high Doppler frequency higher than a predetermined
value is provided. According to the method, the method
comprises: acquiring a first variable (du) of cyclic shift
corresponding to a Doppler shift of one subcarrier spacing
by using an root index (u) of the given sequence; acquiring
secondary variables comprising a number of group (G)
comprised in the given sequence, a length of the each group

(S) and a number of cyclic shift per the group (P) using
the first variable (du) ; and establishing the cyclic shift
to be applied to the given sequence according to the
secondary variables.
Preferably, the secondary variables further comprise
a number of additional cyclic shifts which are applicable
to the given sequence not based on the group (R).
Preferably, the given sequence is a Zadoff-Chu (ZC)
sequence, and the first variable is acquired by a equation
of,

wherein "u" indicates the root index of the ZC
sequence and “Nzc” corresponds to a length of the ZC
sequence.
And, in this case, the secondary variables are
differently acquired according to a range of the first
variable (du) , and the range of the first variable is
divided by a criteria corresponding to 1/3 of the given
sequence length (Nzc/3) .
And, if the range of the first variable (du) is Ncs
≤ du equations of.



wherein "Ncs" is a predetermined cyclic shift
parameter,' "P" 'corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each
group, "G" corresponds to the number of group and "R"
corresponds to the number of additional cyclic shifts.
On the other hand, if the range of the first
variable (du) is (Nzc/3)≤ du ≤ (Nzc-Ncs)/2, the secondary
variables may be acquired by equations of.

wherein "Ncs" is a predetermined cyclic shift
parameter, "P" corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each
group, "G" corresponds to the number of group and "R"
corresponds to the number of additional cyclic shifts.
And, preferable, said establishing the cyclic shift
is performed as a equation of.


And, the given sequence may be for generating a
random access preamble.
In another aspect of the present invention, there is
provided a method for setting cyclic shift to be applied to
a given sequence, the method comprising: determining
whether the cyclic shift is to be established according to
a restricted sets restricted due to a Doppler shift; and
establishing the cyclic shift to be applied to the given
sequence considering a cyclic shift corresponding to a
Doppler shift of one subcarrier spacing, when the cyclic
shift is determined to be established according to the
restricted sets.
Preferably, when the cyclic shift is determined to
be established according to the restricted sets, said
establishing the cyclic shift to be applied to the given
sequence comprises: acquiring a first variable (du)
indicating the cyclic shift corresponding to the Doppler
shift of one subcarrier spacing by using an root index (u) of the given sequence; acquiring secondary variables
comprising a number of group (G) comprised in the given
sequence, a length of the each group (S) , a number of
cyclic shift per the group (P) using the first variable
(du) and a number of additional cyclic shifts which is

applicable to the given sequence not based on the group (R),
and establishing the cyclic shift to be applied to the
given sequence according to the secondary variables.
Preferably, the given sequence is a Zadoff-Chu (ZC)
sequence, and
the first variable is acquired by a equation of,

wherein "u" indicates the root index of the ZC
sequence and “Nzc” corresponds to a length of the ZC
sequence.
And, the secondary variables may be differently
acquired according to a range of the first variable (du),
and the range of the first variable is divided by a
criteria corresponding to 1/3 of the given sequence length
{Nzc/3).
In this case, if the range of the first variable
(du) is Ncs ≤ du acquired by equations of,


wherein "Ncs" is a predetermined cyclic shift
parameter, "P" corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each
group, "G" corresponds to the number of group and "R"
corresponds to the number of additional cyclic shifts.
On the other hand, if the range of the first
variable (du) is (Nzc/3)≤ du ≤ (Nzc-Ncs)/2, the secondary
variables are acquired by equations of,

wherein "Ncs" is a predetermined cyclic shift
parameter, "P" corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each
group, "G" corresponds to the number of group and "R"
corresponds to the number of additional cyclic shifts.
And, preferably, the cyclic shift ( Cv) is performed
as following equation.

And, the given sequence may be for generating a
random access preamble.

In another aspect of the present invention, there is
provided a method for setting cyclic shift to be applied to
a given sequence, the method comprising: (a) acquiring a
variable of du by a equation of,

wherein "u" indicates an root index of the given
sequence and “Nzc” corresponds to a length of the given
sequence; (b) acquiring variables of G, S, P and R by
equations of,
when a range of the first
variable (du) is Ncs ≤ du of G, S, P and R by equations of,
c
when the range of the
first variable (du) is (Nzc/3)≤ du ≤ (Nzc-Ncs)/2,
wherein "Ncs" is a predetermined cyclic shift

parameter; (c) establishing the cyclic shift by
equation of,
for unrestricted sets
for restricted sets
wherein the restricted sets are a cyclic shift sets
restricted due to a Doppler shift, and the unrestricted
sets are a cyclic shift sets not restricted due to the
Doppler shift.
In another aspect of the present invention, there is
provided a method for transmitting a random access preamble
using cyclic shift, the method comprising; acquiring a root
index (u) of a sequence for the random access preamble from
system information; establishing the cyclic shift to be
applied to the sequence, in said establishing, when the
cyclic shift is determined to be established according to
the restricted sets restricted due to a Doppler shift, the
cyclic shift to be applied to the sequence is established
by considering a cyclic shift corresponding to a Doppler
shift of one subcarrier spacing; generating the sequence
according to the root index (u) with the established cyclic
shift; and transmitting the sequence with the cyclic shift
as the random access preamble.
Preferably, when the cyclic shift is determined to be
established according to the restricted sets, said

establishing the cyclic shift to be applied to the sequence
comprises: acquiring a first variable (du) indicating the
cyclic shift corresponding to the Doppler shift of one
subcarrier spacing by using the root index (u) of the given
sequence; acquiring secondary variables comprising a number
of group (G) comprised in the sequence, a length of the
each group (S), a number of cyclic shift per the group (P)
using the first variable (du) and a number of additional
cyclic shifts which is applicable to the sequence not based
on the group (R) , and establishing the cyclic shift to be
applied to the sequence according to the secondary
variables.
Preferably, wherein the given sequence is a Zadoff-
Chu (ZC) sequence, and the first variable is acquired by a
equation of,

wherein "u" indicates the root index of the ZC
sequence and “Nzc” corresponds to a length of the ZC
sequence.
Preferably, wherein the secondary variables are
differently acquired according to a range of the first
variable (du) , and the range of the first variable is
divided by a criteria corresponding to 1/3 of the given

sequence length (Nzc/3).
More specifically, if the range of the first variable
(du) is Ncs ≤ du acquired by equations of,

wherein "Ncs" is a predetermined cyclic shift
parameter, "P" corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each
group, "G" corresponds to the number of group and "R"
corresponds to the nuinber of additional cyclic shifts.
On the other hand, if the range of the first variable
(du) is (Nzc/3)≤ du ≤ (Nzc-Ncs)/2, the secondary variables
are acquired by equations of,

wherein "Ncs" is a predetermined cyclic shift
parameter, "P" corresponds to the number of cyclic shift
per the group, "S" corresponds to the length of the each

group, "G" corresponds to the number of group and "R"
corresponds to the number of additional cyclic shifts.
And, preferably, wherein the cyclic shift ( Cv ) is
performed as following equation,

It is to be understood that both the foregoing
general description and the following detailed description
of the present invention are exemplary and explanatory and
are intended to provide further explanation of the
invention as claimed.
[Advantageous Effects]
The present invention can easily establish a cyclic
shift (CS) interval at a specific location having no
overlapping by considering a channel response of a
reception (Rx) sequence and an alias location of this
reception (Rx) sequence, although a reception (Rx) signal
is shifted by a frequency offset irrespective of categories
of a domain generating a sequence, so that it can greatly
reduce the number of the detection errors and the false
alarm rate.

And, if a sequence of the cyclic shift (CS) is
allocated to a cell having a frequency offset of more than
a predetermined level, the present invention can minimize
the influence of a frequency offset on a high-mobility cell.
iDescription of Drawings]
The accompanying drawings, which are included to
provide a further understanding of the invention,
illustrate embodiments of the invention and together with
the description serve to explain the principle of the
invention.
In the drawings:
FIG, 1 is a conceptual diagram illustrating the
influence of a frequency offset caused by a pulse shaping
in a frequency domain when a sequence is mapped to a sub-
carrier according to the present invention;
FIG. 2 is a conceptual diagram illustrating
different frequency offset situations existing in a
plurality of cells according to the present invention;
FIG. 3 is a conceptual diagram illustrating a
) sequence allocation method when a sequence is a CAZAC
sequence according to the present invention;
FIG. 4 is a conceptual diagram illustrating aliases
which occur in a time-domain channel response of a

reception sequence due to the frequency offset according
to the present invention;
FIG. 5 is a conceptual diagram illustrating a
method for establishing a new cyclic shift (CS)
applying unit by adding an additional margin to an old
CS-applying unit according to the present invention;
FIGS. 6 and 7 are conceptual diagrams illustrating
application examples of the additional margin of FIG. 5
under the condition that a sequence index is low
according to the present invention;
FIGS. 8 and 9 are conceptual diagram illustrating
exemplary additional margins of FIG. 5 under the
condition that a sequence index is high according to the
present invention;
FIG. 10 shows an example of a single group composed
of P cyclic-shift-sets according to the present
invention;
FIG. 11 is a conceptual diagram illustrating a
method for establishing a cyclic shift (CS) - applying
group and the CS-applying interval of each group
according to the present invention;
FIG. 12 shows locations at which pulses occur by an
interference when the CAZAC index is contained in the
interval of N/3 ~ N/2 according to the present invention;

FIG. 13 is a flow chart illustrating a restricted
cyclic shift set according to one embodiment of the
present invention;
FIG. 14 is a conceptual diagram illustrating a
method for establishing a variable (du) of a cyclic shift
corresponding to the Doppler shift associated with the 1
sub-carrier spacing when the restricted cyclic shift set
is established according to the present invention;
FIG. 15 is a conceptual diagram illustrating a
specific case in which the variable (du) is less than a
basic unit Ncs to which the cyclic shift (CS) is applied
according to the present invention;
FIG. 16 is a conceptual diagram illustrating a
method for calculating a variable establishing the cyclic
shift within the interval of Ncs ≤ du the present invention;
FIG. 17 is a conceptual diagram illustrating a
method for calculating a variable establishing the cyclic
shift within the interval of {Nzc/3) ≤ du according to the present invention;
FIGS. 18 and 19 are conceptual diagrams illustrating
a method for reducing the number of ZCZ preamble sequences
due to an alias response in the case of Nzc=839, Ncs=100,
and du=155 according to the present invention;

FIG. 20 is a conceptual diagram illustrating the
increasing ratio of an available restricted cyclic shift
after the restriction of a start location of the cyclic
shift is removed in the case of Nzc=839 according to the
present invention;
FIG. 21 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=150 according to one embodiment of the present
invention;
FIG. 22 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=399 according to one embodiment of the present
invention;
FIG. 23 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=150 according to another embodiment of the present
invention; and
FIG. 24 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=399 according to another embodiment of the present
invention.
[Mode For Invention]
Reference will now be made in detail to the
preferred embodiments of the present invention, examples of

which are illustrated in the accompanying drawings.
Wherever possible, the same reference numbers will be used
throughout the drawings to refer to the same or like parts.
Prior to describing the present invention, it should
be noted that most terms disclosed in the present invention
correspond to general terms well known in the art, but some
terms have been selected by the applicant as necessary and
will hereinafter be disclosed in the following description
of the present invention. Therefore, it is preferable that
the terms defined by the applicant be understood on the
basis of their meanings in the present invention.
For the convenience of description and better
understanding of the present invention, general structures
and devices well known in the art will be omitted or be
denoted by a block diagram or a flow chart. Wherever
possible, the same reference numbers will be used
throughout the drawings to refer to the same or like parts.
The present invention provides a cyclic shift (CS)
setup method to provide against the frequency offset, so
that it can easily prevent a sequence (i.e., CA2AC
sequence) performance from being deteriorated. For this
purpose, the present invention will disclose the method for
applying the cyclic shift to the CAZAC sequence, and the
influence of the frequency offset of the CAZAC sequence.
The cyclic shift may be applied to the CAZAC

sequence according to two schemes, i.e., a first scheme for
performing the cyclic shift on the sequence, and a method
for multiplying an exponential function of other areas by a
time- or frequency- domain sequence, and performing the
cyclic shift on the multiplied result.
The cyclic shift "d" is applied to the frequency
index "k" in the frequency domain. If the sequence index
of M and the N-length sequence is represented by c(k; d, M,
N) , a method for performing the cyclic shift on the
sequence can be represented by the following equation 2:
[Equation 2]

Where "M" is indicative of an amount of the cyclic
shift, and "mod" is indicative of a modular operator.
A method for applying the cyclic shift by
multiplying an exponential function by the sequence can be
represented by the following equation 3:
[Equation 3]

In the meantime, although each of the above

Equations 2 and 3 shows an exemplary cyclic shift applied
in the frequency domain, the cyclic shift may be applied in
the time-domain sequence sampling index "n" in the time
domain. In this case, an application example of the cyclic
shift can be represented by the following equation 4:
[Equation 4]

where "Cv" is indicative of the degree of the cyclic
shift, '"n" is indicative of a sampling index, “Nzc” is
indicative of the ZC-sequence length, and "u" is indicative
of an root index of the 2C sequence.
The CAZAC sequences can be distinguished from each
other under the condition that different root indexes are
used, however, it should be noted that a difference in
cross-correlation occurs among the CAZAC sequences.
However, in the case of at least two CAZAC sequences
associated with the cyclic shift, the cross-correlation
value between the CAZAC sequences is zero, so that the
above-mentioned CAZAC sequences are used when a high
rejection ratio is required for the two CAZAC sequences.
Specifically, the CAZAC sequence associated with the
cyclic shift share the time-frequency resources within the

same cell, so that they can be used to discriminate among
different signals/UEs during the transmission of
data/control signals.
However, if the frequency offset occurs in the
frequency domain in the same manner as in the case in which
the CAZAC sequence is transmitted using the OFDM scheme,
the present invention may encounter the excessive
deterioration of a performance and false alarm rate.
The following description will disclose an example
in which the sequence is transmitted in the frequency
domain, and another example in which the sequence is
transmitted using the OFDM scheme.
FIG. 1 is a conceptual diagram illustrating the
influence of a frequency offset caused by a pulse shaping
in a frequency domain when a sequence is mapped to a sub-
carrier according to the present invention.
As shown in FIG. 1, each of sequence samples is
mapped to the sub-carrier. If a reception end performs
the signal sampling due to the frequency offset as
denoted by the location of "Interference", signals of
neighboring sub-carriers are mixed within a single sample.
In other words, if the pulse-shaping function is p(x),
the response of an arbitrary sub-carrier can be
represented by the following equation 5:


where "r(k, foff) " is indicative of a reception (Rx)-
frequency response at the k-th sub-carrier location if the
frequency offset is foff, "c(n)" is indicative of a CAZAC
sequence mapped to the sub-carrier by the user equipment
(UE), "p(f)" is indicative of a pulse-shaping function in a
frequency domain, and ωo is indicative of a sub-carrier
spacing.
In the case of the above Equation 5 outputs
only the value c(k). Otherwise, in the case of the
signal of the neighboring sub-carrier may enter the
reception end, so that there arises a performance
deterioration. Due to the performance deterioration caused
by the frequency offset, the probability of encountering
the detection error in the reception end increases, and the
false alarm rate and/or miss-detection may unavoidably
increase in the reception end.
Specifically, provided that the cyclic shift is
applied in the time domain and the CAZAC sequence is
transmitted within the frequency domain, one may not

discriminate among various sequences. And, the above-
mentioned problem may occur in a situation, even when the
CAZAC sequence is transmitted within the time domain as a
form of the timing offset.
In other words, if the frequency offset or the
timing offset occurs, methods for employing the cyclic
shift must unavoidably experience the performance
deterioration. Also, the influence of the frequency offset
is equally applied to a specific case in which the cyclic
shift is applied in the time domain as denoted by Equation
4.
Therefore, there must be newly developed a
technology for preventing a performance of the sequence
(i.e., CAZAC sequence) from being deteriorated under the
condition that the frequency offset occurs.
Specifically, in the case of applying the cyclic
shift to the CAZAC sequence, the frequency offset or the
timing offset excessively occurs, so that the present
invention has difficulty in discriminating among sequences
when the frequency- or timing- offset occupies at least the
half of a single sub-carrier spacing.
However, the degree of the frequency offset and the
degree of the Doppler shift may be different in individual
cells of a cellular mobile communication system.

Therefore, according to one embodiment, the present
invention provides different cyclic shift (CS) setup
methods according to the degree of frequency offsets of the
individual cells, and a detailed description thereof will
hereinafter be described.
FIG. 2 is a conceptual diagram illustrating
different frequency offset situations existing in a
plurality of cells according to the present invention.
Referring to FIG. 2, the present invention may
determine that a specific cell having many high-mobility
UEs in a cellular mobile communication system including
many cells has a high frequency offset. There is every
probability that a UE contained in a cell including
residential districts may be a low-speed UE-, so that the
frequency offset within the cell may be low.
In more detail, FIG. 2 shows cells A and B adjacent
to a high-speed railway, and the cell C distant from the
high-speed railway.
In the case of the cells A and B adjacent to the
high-speed railway, there is every probability that a
plurality of high-speed UEs are contained in a
corresponding cell, so that the present invention has an
advantage in that a sequence which is very resistant to
the frequency offset may be allocated.

For example, in the case of the cell C adjacent to
the residential district distant from the high-speed
railway, the probability of including the high-speed UE
in a corresponding cell is relatively low, so that there
is no need to allocate only the sequence which is very
resistant to the frequency offset.
In the case of the available sequence (e.g., the
CAZAC sequence), first sequences caused by the root
indexes of the individual sequences and second sequences
caused by the cyclic shift applied to the first sequences
may have different frequency offset characteristics.
Therefore, the present invention establishes the
restricted case and the unrestricted case, and provides
the cyclic shift setup methods for the individual cases.
The restricted case indicates that the influence of
the Doppler shift is higher than a predetermined
threshold value so that an unexpected limitation occurs
in the process for establishing a cyclic shift (CS)
applying interval.
The unrestricted case indicates that the influence
of the Doppler shift is equal to or less than the
predetermined threshold value, so that there is no
limitation in the process for establishing the CS-
applying interval.

The method for establishing the cyclic shift will
hereinafter be described in detail.
FIG. 3 is a conceptual diagram illustrating a
sequence allocation method when a sequence is a CAZAC
sequence according to the present invention.
The CAZAC sequence may include a root sequence of
each root CAZAC sequence and a Zero Correlation Zone
(ZCZ) sequence to which different cyclic shifts (also
called circular shifts) are applied.
In more detail, FIG. 3 shows the root sequence for
each root index in Nt root indexes, and the ZCZ-sequence
set to which L cyclic shifts are applied to each root
sequence.
In this case, the ZCZ is indicative of a cyclic
shift - applying interval to which the cyclic shift (CS)
is applied, so that the Node-B is able to discriminate
among RACH signals.
In the meantime, if the CAZAC sequence is used when
the frequency offset exists, the present invention may
have difficulty in discriminating among ZCZ sequences by
the frequency offset. Therefore, the present invention
may determine that the ZCZ sequence is not used in a
predetermined cell having a frequency offset of more than
a predetermined level.

In this way, the threshold value used to decide the
degree of the frequency offset of each cell may be
properly decided according to the number of available
sequences of a corresponding system and the frequency
offset degree of each cell.
If it is determined that the cell has the frequency
offset of more than the predetermined level, the
probability of containing the high-speed UE in this cell
is very high as shown in the cell A or B.
However, if it is determined that the ZCZ sequence
is not used in the cell having the frequency offset of
more than the predetermined level, there may be only Nt
indexes based on the CAZAC indexes, so that the number of
available sequences becomes lower.
If a sequence re-use coefficient becomes lower, one
must allocate sequences according to the cell planning.
However, this allocation based on the cell planning may
unexpectedly increase the complexity in the process for
allocating the sequences to individual cells, so that
another solution may be additionally required on the
condition that the number of available sequences
encounters the problem.
Furthermore, in case of using only Nt sequences and
not using the ZCZ sequence, there may be a problem in
estimating round trip delay or one-way trip delay while

the performance of detecting sequence is enhanced. That
is, there may be a problem of distinguishing the position
of correlation peak varying due to the round trip delay
or one-way trip delay, and a position of correlation peak
varying due to the frequency offset. So, another solution
may be additionally required against this problem.
In the meantime, the above-mentioned problem having
difficulty in discriminating among ZCZ sequences due to
the frequency offset becomes intensified on the condition
that the CAZAC index is very high or is not very low.
In more detail, provided that "k" is indicative of
a frequency-domain index, "N" is indicative of the CAZAC-
sequence length, "M" is indicative of a CAZAC sequence,
and a transmission (Tx) signal is indicative of
"c(k,N,M)", a reception (Rx) signal can be represented by
the following equation 6:
[Equation 6]

where "d" is indicative of the amount of a
frequency-domain delay caused by the frequency offset.
As can be seen from Equation 6, if the CAZAC index
"M" has a very low value, or if the CAZAC index "M" has

the highest value from among a total of Nt sequence
indexes, the influence of the exponential function caused
by the frequency offset is gradually reduced, so that the
influence of the frequency offset in the Rx signal is
gradually reduced.
If the CAZAC sequence is allocated to the cell
having the frequency offset of more than the
predetermined level, the present invention may allocate
only the root sequence. In the case of using the ZCZ
CAZAC sequence due to the insufficient number of root
sequences, the present invention may allow the CAZAC
sequence to employ a specific sequence which is in an
initial predetermined range or the last predetermined
range from among total indexes. In this case, it should
be noted that the term "predetermined range" can be
established in different ways according to system
detection performances.
In the case of comparing the above-mentioned method
with the other method for allowing the ZCZ sequence not
to be used in the cell having the high frequency offset,
the above-mentioned method increases categories or types
of available sequences, so that there is almost no need
to perform the cell planning.
In more detail, if the number of total CAZAC
sequences is Nt as shown in FIG. 3, the sequence to be

used in the cell of the high frequency offset may be set
to CAZAC indexes 0, 1, 2, Nt-2, Nt-1, and Nt.
In the meantime, in the case of using the CAZAC
sequence for the cell having the frequency offset of more
than the predetermined level, there is no need to use
only indexes other than the above-mentioned CAZAC indexes
0, 1, 2, Nt-1, lSIt-2, and Nt. In order to reduce the
interference between the aforementioned CAZAC sequence
and the other sequence used for the cell having the high
frequency offset, the present invention may not use the
sequence index sued for the cell having the high
frequency offset as necessary, resulting in the
implementation of high efficiency.
In the meantime, in the case of using the ZCZ
sequence to guarantee the number of available sequences
in the cell having the high frequency offset and/or to
guarantee the performance of estimating the time delay
occurred in the channel, the present invention
establishes the cyclic shift interval in the restricted
case in consideration of the alias (i.e., Doppler shift)
caused by the frequency offset. As a result, the present
invention prevents the performance deterioration caused
by the frequency offset, and a detailed description
thereof will hereinafter be described.

If the presence of the frequency offset is decided,
the frequency response of the Rx signal can be
represented by the above Equation 6.
In the meantime, Equation 6 shows that a signal
value is transferred from all the neighboring sub-
carriers due to the frequency offset. However, indeed, a
specific component greatly affecting the channel response
of the Rx signal may be set to a part located at both
sides of a corresponding sub-carrier, wherein the part
receives a signal of the neighboring sub-carrier.
Therefore, in the case of considering only the
first order case. Equation 6 may be represented by three
terms, as shown in the following equation 7:
[Equation 7]

In the meantime, the reception end applies a
conjugate complex number c(n) to the Rx signal, so that
the applying result can be represented by the following
equation 8:
[Equation 8]


The pulse-shaping function of Equation 7 can be
easily denoted by a raised cosine- or sine- function.
For the convenience of description, the pulse-
shaping function is represented by constants and
With reference to Equation 8, the channel response
of the Rx signal occurs at three points, i.e., "t"
indicative of a target position in the time domain, "t-M"
indicative of a position shifted to the left side, and
"t+M" indicative of a position shifted to the right side.
It can be recognized that the channel response generated
at the M-shifted position on the basis of the right/left
sides corresponds to the alias of the Rx signal, i.e.,
the Doppler shift component having the 1-subcarrier
spacing.
The above-mentioned phenomenon in which the alias
occurs in the channel response due to the frequency
offset is shown in FIG. 4.
FIG. 4 is a conceptual diagram illustrating aliases
which occur in a time-domain channel response of a

reception sequence due to the frequency offset according
to the present invention.
If the cyclic shift is applied to a sequence used
in a specific cell having a frequency offset of more than
a predetermined level, a single channel response occurs
at the target position in the Rx-channel response of the
corresponding sequence, and two additional aliases may
occur in the Rx-channel response of the corresponding
sequence according to the 1-subcarrier-spacing-sized
Doppler shift.
Therefore, if the CS-appIying interval is
established irrespective of the target position and the
alias positions, an unexpected overlapping occurs between
the channel response and the alias of the Rx sequence due
to the channel delay spreading and the propagation delay,
so that the confusion between the target position and the
alias position may occur among different CS-applying
sequences.
Accordingly, if the restricted case is decided when
the CS-applying interval is established in the CAZAC
sequence, the present invention considers the alias
generated in the channel response, so that it establishes
the CS-applying interval during a specific period in
which the channel response of the Rx sequence does not
overlap with the alias of the above channel response.

FIG. 4 shows an exemplary case in which the M-sized
(where M = sequence index) alias occurs when CAZAC
sequence is generated in a frequency domain. However, if
the CAZAC sequence is generated in the time domain, the
alias generation position caused by the Doppler shift of
the 1-subcarrier spacing may be determined in different
ways.
All the CS-applying cases used for the individual
domains will hereinafter be described in detail.
For the convenience of description and better
understanding of the present invention, FIGS.. 5~11 assume
that the cyclic shift unit is set to To-
FIG. 5 is a conceptual diagram illustrating a
method for establishing a new cyclic shift (CS)
applying unit by adding an additional margin to ah old
CS-applying unit according to the present invention.
The present invention generates a cyclic-shifted
preamble according to the design based on the RACH
component. However, under the environment in which the
OFDM frequency offset exists, the reception end of the
present invention may easily mistake a normal sequence
for another sequence.
In order to prevent the above-mentioned problem
from being generated, the present invention may use an
additional cyclic shift margin as shown in FIG. 5.

Referring to FIG. 5, the delay spread is indicative
of a channel delay spread, and the round trip delay (RTD)
is indicative of a propagation proceeding time of a
physical distance between the user equipment (UE) and the
Node-B. In the case of using the additional cyclic shift
margin, the present invention adjusts the margin size for
each sequence, so that it can reduce the influence of the
frequency offset when the sequence is used.
In the case of implementing the frequency offset
using the additional margin, the cyclic shift unit is
decided by the function of the CAZAC sequence. In other
words, in association with the CAZAC sequence "M", the
cyclic shift unit is represented by the following
equation.9:
[Equation 9]

where To is indicative of a common cyclic shift
unit irrespective of the sequence index, and Tmargin (M) is
indicative of an additional margin used when the sequence
index is M. This margin can be decided by other methods
according to usages of the sequence and the cyclic shift.

Therefore, although it is preferable that the
cyclic shift unit is at least 2M, this additional margin
may be changed to another margin according to the CS-
applying area. The above-mentioned situation is shown in
FIGS. 6 and 7.
FIGS. 6 and 7 are conceptual diagrams illustrating
application examples of the additional margin of FIG. 5
under the condition that a sequence index is low
according to the present invention.
Here, in case of Fig. 5, the interval of M due to
the frequency offset is smaller than the cyclic shift
interval of TO. Even when using this range, we can avoid
the overlapping problem with other sequences. However,
there may be a problem of estimating the information for
the time delay of the transmitted sequence. So, in one
embodiment of this invention, it is preferable not using
this range where the interval of M due to the frequency
offset is smaller than the cyclic shift interval of TQ.
But, there may be a system using this range according to
the requirement of the system.
The oblique-lined part of FIGS. 6 and 7 indicates
the cyclic shift opportunity.
If the signal having no influence of the frequency
offset is located at "t", the pulse affected by the
frequency offset may occur at a single point of the left

side, and may occur at a single point of the right side.
If the signal includes To used as a basic cyclic shift
unit, Tmargin{M) may be set to 2M.
The additional margin is applied to all the indexes,
so that the present invention may define the cyclic shift
highly resistant to the frequency/timing offsets.
However, the higher the sequence index, the higher
the value of Tmargin(M). As a result, the number of
available cyclic shifts is reduced to "1". In order to
prevent the reduction of the cyclic shifts, the present
invention will disclose the case of the high CAZAC index in
detail.
FIGS. 8 and 9 are conceptual diagram illustrating
exemplary additional margins of FIG. 5 under the
condition that a sequence index is high according to the
present invention.
FIG. 8 shows the case in which the CAZAC index "M"
is 2To~3To, and FIG. 9 shows the case in which the CAZAC
index "M" is 3To~4To. Although the case of FIG. 8
considers the basic cyclic shift unit, the cyclic shift
set denoted by the oblique-lined part may be additionally
inserted in the intermediate space. The case of FIG. 9
has a wider space, so that at least two cyclic shifts can
be inserted into this wider space.

FIG. 10 shows an example of a single group composed
of P cyclic-shift sets according to the present invention.
Referring to FIG. 10, if the above-mentioned
explanation is generalized, slots denoted by the oblique-
lined parts are defined in the 3M range in which the
block is constructed by pulses, and the M range is PTo~
(P+l)To, it can be recognized that P cyclic-shift-sets are
constructed.
For the convenience of description, the 3M or 2M+
PTo unit will hereinafter be referred to as a cyclic shift
group. A specific sequence to which the cyclic shift is
applied includes a predetermined number of cyclic shift
groups. The predetermined number of cyclic shifts can be
applied to each cyclic shift group, so that the
predetermined number of cyclic shifts can be applied to
the cyclic shift component caused by the Doppler shift.
FIG. 11 is a conceptual diagram illustrating a
method for establishing a cyclic shift (CS) - applying
group and the CS-applying interval of each group
according to the present invention.
Referring to FIG. 11, units of cyclic shift groups
can be defined in total sequences, and each cyclic shift
group can be defined as shown in FIG. 10. Provided that
the number of cyclic shift groups is G and the number of
cyclic shifts for each group is P, the total number of

available cyclic shifts is P*G. As shown in FIG. 11,
according to one embodiment of the present invention, it
is assumed that the sequence is divided into groups, and
each group searches for a restricted available cyclic
shift in each group.
In the case of using the above-mentioned scheme,
all the available cyclic shifts are defined in the index
range in which the number of cyclic shift groups is "1".
If the sequence length is N, this range having the
sequence length of N corresponds to indexes ranging from
1 ~ N/3 to 2N/3 ~ N-1. In this case, the k~th index has
the same cyclic shift group as that of the (N-k)-th index
and the cyclic shift set.
FIG,"12 shows locations-at-which pulses occur by an
interference when the CAZAC index is contained in the
interval of N/3 ~ N/2 according to the present invention.
A single square of FIG. 12 indicates the cyclic
shift unit. If the CAZAC index is higher than "N/3", all
the consecutive cyclic shift positions (i.e., the cyclic
shift positions defined by To) cannot be used, and they
can be used according to predetermined rules.
A method for establishing the restricted cyclic
shift set according to one embodiment of the present
invention will hereinafter be described."

FIG. 13 is a flow chart illustrating a restricted
cyclic shift set according to one embodiment of the
present invention.
Referring to FIG. 13, if the restricted cyclic
shift set is established in a cell having the frequency
offset of more than a predetermined threshold value, the
present invention provides a method for establishing the
cyclic shift in consideration of the aliasing, so that
there is no confusion between a desired channel response
and this aliasing.
For this purpose, as shown in step S1301 of FIG. 13,
the present invention provides a distance “du” between the
response generated by the Doppler shift and a desired
channel- response using-a- -given sequence root index "u".
In this case, the above distance corresponds to the
cyclic shift generated by the Doppler shift corresponding
to the 1-subcarrier spacing.
A detailed description of the variable “du” will
hereinafter be described in detail.
FIG. 14 is a conceptual diagram illustrating a
method for establishing a variable (du) of a cyclic shift
corresponding to the Doppler shift associated with the 1-
subcarrier spacing when the restricted cyclic shift set
is established according to the present invention.

Referring to FIG. 14(a), if there is no influence
of the Doppler frequency, the peak position generated by
the correlation operation of the reception end is denoted
by "1401". By the delay spread and the round trip delay
(RTD) , the peak position at the reception end appears at
the cyclic shift unit Ncs (1402) used as the cyclic shift
unit basically decided by the system.
In the meantime, in the case of the presence of the
Doppler frequency corresponding to the 1-subcarrier
spacing, the peak position caused by the correlation
operation of the reception end is decided according to
the sequence indexes.
According to the present invention, the distance
between the peak .position based on the Doppler shift
corresponding to the 1-subcarrier spacing ≤ and the ideal
peak position is called “du”.
In other words, FIG. 14 (b) shows the shift of the
reception-end channel response caused by the Doppler
frequency - ≤ . FIG. 14(c) shows the shift of the
reception-end channel response caused by the Doppler
frequency Based on the above-mentioned fact, the
value “du” may be considered to be the cyclic shift caused
by the Doppler shift.

If the restricted cyclic shift is established in
consideration of the cyclic shift corresponding to the
Doppler shift of the 1-subcarrier spacing, the present
invention controls the established restricted cyclic
shift not to be overlapped with the channel response
movement caused by the Doppler shift.
The present invention excludes the reserved areas
"reserved" .of FIGS. 14(a) and 14(b) from the established
cyclic shift interval, so that it can prevent an
unexpected confusion from being generated between channel
responses although the relatively high Doppler shift has
occurred.
Referring back to FIG. 13, the present invention
acquires secondary variables using the acquired variable
“du” of the above step S1301 at step S1302. Namely, the
present invention acquires the number (G) of cyclic shift
groups, the number (P) of cyclic shifts applicable to
each group, and the length (S) of each group from current
sequences (e.g., ZC sequences).
The above-mentioned secondary variables must be
differently established according to sequence indexes,
because the group length is changed to another according
to the sequence indexes. And, the variable “du” is
dependent on the sequence index, so that the present

invention provides a method for establishing secondary
variables according to the range of the variable “du”.
Furthermore, the present invention may apply not
only the above group-based cyclic shift but also an
additional cyclic shift using a specific area which is
not contained in the cyclic shift group within the
sequence range, and a detailed description thereof will
hereinafter be described.
Thereafter, at step S1303, the present invention
establishes the cyclic shift using the acquired secondary
variables of step S1302-
The mathematical relationship between detailed
variables for the cyclic shift application will be
described in detail.
The restricted cyclic shift according to the
present invention has been proposed to prevent the high
Doppler frequency effect from being generated.
The other cyclic shift offset “Coff” different from
the “du” variable will hereinafter be described in detail.
The “Coff” value indicates the degree of an offset
generated by the Doppler shift.
If the offset degree generated by the Doppler shift
is less than the half of the given sequence range, this
offset degree may have the same meaning as that of the du
variable. Otherwise, if the offset degree generated by

the Doppler shift is equal to or higher than the half of
the given sequence range, the resultant value acquired
when the “Coff” value is subtracted from the total
sequence length may correspond to the du variable.
The “Coff” value is dependent on the root index of
the used sequence. The preamble may be generated from
either the time domain or the frequency domain. The
relationship between "off" and "u" values is dependent on
the domain generating the preamble.
If the ZC sequence is generated from the frequency
domain, and the cyclic shift is applied in the time
domain, the present invention may induce the “Coff” value
using the following method, and a detailed description
thereof will hereinafter be described.
It is assumed that the signal energy is propagated
by the value transferred from the neighboring sub-carrier
according to the Doppler frequency. And, it is assumed
that the transferring from the neighboring carrier occurs
at only the sub-carrier position spaced from a current
sub-carrier by one blank, and this case is referred to as
a first order case. In this case, the Rx signal at the
specific sub-carrier is composed of three terms shown in
the following equation 10:
[Equation 10]


Where, the pulse-shaping function "p(f)" may be
denoted by a raised cosine- or sine- function. For the
convenience of description, if constants and c1
are established, the s (n) value can be denoted by s(n) =
For the convenience of
description, if the conjugate of the sequence is
multiplied by the resultant value s(n) , the following
equation 11 can be acquired:
[Equation 11]

+ cic(n+ l)c'(n)
In Equation 11, if "c(n)=x(n)" is denoted by CAZAC,
can be represented by the following equation
12:


Here, "u" indicates the root index, and “Nzc”
indicates the sequence length.
If Equation 12 is applied to Equation 11, it can be
recognized that "s (n)" is composed of three signals. A
first term of the "s(n)" value is indicative of a simple
DC component, a second term is indicative of a complex
exponential wave having the frequency of u/Nzc, and a
third term is indicative of a complex exponential wave
having the frequency of -u/Nzc-
Therefore, the “Coff” value can be represented by
the following equation 13:
[Equation 13]

On the contrary, if the ZC sequence is generated
from the time domain and the cyclic shift is generated
from the time domain, the “Coff” value can be calculated
by the following method.
If the RACH preamble received without having the
frequency offset is set to r(n), the RACH signal received
along with the frequency offset can be represented by the
following equation 14:
[Equation 14]


Where is denoted by , and
indicates the frequency offset denoted by the hertz
(Hz) unit, and fs is indicative of a sampling rate of the
RACH preamble.
The auto-correlation of the value can be
calculated by the equation wherein "u" is
indicative of the index of the ZC sequence
[Equation 15]

In Equation 15, if "Coff,u" is indicative of the
margin of a frequency offset, the auto-correlation of
can be calculated by of the
following equation 16:
[Equation 16]


In Equation 16, " () NZC" is indicative of a modular
operation of the “Nzc” value. If Coff,u’=u * Coff,u is a root
index related with the sampling shifts, and γ is
indicative of a re-sampling ratio replying to the timing
error, the Coff,u’ value can be denoted by

By Equations 15 and 16, the γ value can be denoted
by
The channel response position is called a main lobe,
and the alias response position of a channel affected by
the (+/-) Doppler frequency is called a side lobe.
In more detail, the main lobe is indicative of the
position caused by the 0 offset, and is equal to a normal
channel response position when there is no influence of
the Doppler frequency.
The positive ( + ) side lobe is indicative of the
position caused by the positive ( + ) offset, and is equal
to an alias response position affected by the positive
{ + ) Doppler frequency. The negative (-) side lobe is

indicative of the position caused by the negative (-)
offset, and is equal to an alias response position
affected by the negative (-) Doppler frequency.
As can be seen from Equation 16, it can be
recognized that the main lobe of the auto-correlation
peak occurs at Coff,u=0 or Coff,u’=0- By the above Equation
15, the pair of side-lobes occurs under the condition of
the following equation 17:
[Equation 17]

Therefore, the result of "u*Coff,u - m*Nzc" is equal
to "-1", as represented by "Coff,u = (m*Nzc - l)/u". In this
case, "m" is indicative of the lowest integer capable of
allowing the Coft.u value to be an integer. For example, if
the ZC-sequence length is 839 and the root index is 300,
the "m" value is set to 59, and the Coff,u value is set to
165.
In the case of using the ZC sequence in the time
domain, the Coff value can be defined by the following
equation 18:
[Equation 18]


the index "u" of the CAZAC sequence, so that the Coff
value can be acquired.
Provided that the ZC sequence is used in the
frequency or time area, and the conjugate property
between the Coff and ZC sequences is used, the distance
“du” between the main-lobe and the side-lobe can be
represented by the following equation 21:
[Equation 21]

The present invention provides a variety of methods
in establishing the restricted cyclic shifts, for example,
a first method for establishing the restricted cyclic
shift without using the fixed cyclic shift position, and
a second method for establishing the restricted cyclic
shift using the fixed cyclic shift position.
The first method is associated with the restricted
cyclic shift without considering the pre-defined shift
position. The second method is associated with the
restricted cyclic shift with the consideration of the
pre-defined shift position.

In Equation 18, "m" is indicative of the smallest
positive number capable of allowing the Coff value to be an
integer, and “Nzc” is indicative of the ZC length.
All the indexes "u" is a relative prime of the Nzc
value. Therefore, the positive integer number (Uinv= 1/u)
capable of satisfying the equation (u*Uinv== 1 mod Nzc)
exists. Therefore, the C≤ft.n value can be easily
represented by the following equation 19:
[Equation 19]

In Equation 19, a negative sign (-) is the opposite
of the positive sign ( + ) , so that it can be represented
by the following equation 20:
[Equation 20]

In brief, if the CAZAC sequence is used in the
frequency domain, the CAZAC- sequence index "u" becomes
“Coff” without any change. . If the CAZAC sequence is used
in the time domain, the "(1/u) mod Nzc" is performed on

In regard to the first method, there are a variety
of methods, i.e., a method for directly using the shift
value of the Va-th restricted cyclic shift, and a method
for establishing the cyclic shift interval using the
shift value "Cva"- Namely, the cyclic-shifted sequence
becomes Xu,v(n) =Xu** ( (n+Cva) mod Nzc) as shown in Equation 4.
In regard to the first method, there aire a variety
of methods employing a decimal "Va" for use in the cyclic
shift, for example, a method for establishing the cyclic
shift interval by calculating the shift-index decimal Va
In other words, if the length of the cyclic shift
is set to Ncs, the cyclic-shifted index becomes
"Xu,va(n) =Xu( (n+round(VaNcs) ) mod Nzc)"- In this case,
"round" is indicative of a round-off function.
In regard to the second method, there are a variety
of methods employing the integer "Va" for use in the
cyclic shift, for example, a method for establishing the
cyclic shift interval by calculating the shift-index
integer Va. Namely, the cyclic-shifted sequence becomes
Xu,va(n)=Xu( (n+VaNcs) mod Nzc) •
In the meantime, if the cyclic shift is performed
by the multiple of Ncs, random access preambles, each of
which has the zero correlation zone (ZCZ) area having no
correlation in the u-th root ZC sequence, are defined by
Xu,v(n)=Xu( (n+vNcs) mod Nzc) • This definition is appropriate

for the low/middle cell having no problem in the high
frequency offset. However, if the restricted cyclic shift
is used in the high-mobility cell, the above-mentioned
definition is inappropriate for the high-mobility cell.
Specifically, the available "v" value is restricted, and
the number of available ZCZ preambles is reduced to 1/3
of the ZCZ preambles of a general case.
Embodiments associated with the above-mentioned
cases will hereinafter be described in detail.
Best Mode
This embodiment of the present invention will
disclose a method for establishing the restricted cyclic
shift using only the influence of the Doppler shift,
without using the fixed cyclic shift position.
The present invention assumes that the preamble is
generated using the ZC sequence used as the CAZAC
sequence.
The “du” value of the following equation 22 shows a
specific case in which the ZC sequence is generated in
the frequency domain.


In the case of generating the ZC sequence in the
time domain, the “du” value can be represented by the
following equation 23:
[Equation 23]

In Equation 23, "m" is indicative of the smallest
positive number capable of allowing the “du” value to be
an integer, and Nzc is indicative of the ZC length.
Equation 23 can also be represented by the following
equation 24:
[Equation 24]

Therefore, the v-th cyclic shift of the u-th root
index can be defined by Xu,v (n) =Xu ( (n+Cv) mod Nzc)- In this
case, if the general cyclic shift is decided, the Cv value
can be represented by Cv = v*Ncs. If the restricted cyclic

shift is decided, the Cv value can be represented by the
following equation 25.
[Equation 25]

If the restricted cyclic shift having no pre-
defined shift position is decided, this case is
considered to be a first case (Case 1) , and a detailed
description thereof will hereinafter be described.
The u-th root ZC sequence and the v-th random
access preamble, each of which has the zero correlation
area, are defined by "Xu,v (n) =Xu ( (n+Cv) mod Nzc)"
In this case, "Cv" is denoted by the above equation
25.
In other words, in the case of the unrestricted sets
having a small amount of the Doppler-shift influence, the
present invention may establish the cyclic shift
corresponding to an integer multiple of Ncs equal to the
basic cyclic shift unit.
However, the case of the unrestricted sets less
affected by the Doppler shift may establish the cyclic
shift corresponding to the integer multiple of Ncs.

In association with FIG. 13, the case of the
restricted sets greatly affected by the Doppler shift may
establish the number (G) of cyclic shift groups, the number
(P) of cyclic shifts applicable to each cyclic shift group,
and the number (R) of additional cyclic shifts.
The method for calculating each secondary variable
may be differently decided by the “du” range as previously
stated in FIG. 13.
During the alias distance interval of Ncs≤du the number of cyclic shifts per group is denoted by
, and there are groups, each of
which has the length , and the number of
restricted additional cyclic shifts is denoted by

During the alias distance interval of
the number of cyclic shifts per
group is denoted by , and there are G
groups, each of which has the length
, and the number of restricted

additional cyclic shifts is denoted by

The principles for calculating the above-mentioned
secondary variables will hereinafter be described in
detail.

FIG. 15 is a conceptual diagram illustrating a
specific case in which the variable (du) is less than a
basic unit Ncs to which the cyclic shift (CS) is applied
according to the present invention.
The cyclic shift unit (Ncs) is designed in
consideration of the delay spread and the RTD which are
capable of being generated in the channel. Therefore, if
du is less than Ncs, a peak caused by the delay spread
and/or the RTD within the Ncs range may overlap with the
other peak caused by the Doppler shift, as shown in FIG.
15. Therefore, when establishing the restricted cyclic
shift, this embodiment does not establish the cyclic
shift for the case in which the du value is less than the
Ncs value.


FIG. 16 is a conceptual diagram illustrating a
method for calculating a variable establishing the cyclic
shift within the interval of Ncs ≤ du the present invention.
As shown in FIG. 16, the cyclic shift area generated
by the Doppler frequency occurs in the interval of Ncs ≤ du
the range of a sequence length located at both sides of the
intended cyclic shift.
According to this embodiment, the cyclic shift areas
caused by the Doppler frequency of both sides of the cyclic
shift may be grouped into a single group. Also, the
present invention determines how many Ncs values can be
used without overlapping with others within the “du” range.
The number of restricted cyclic shifts available for each
group may be set to P. Namely, the P value can be
calculated by the following equation 26:

The distance between a specific channel response
1601 and the alias 1601a caused by the Doppler shift is
denoted by “du”. The distance between the specific channel

response 1601 and the other alias 1601b caused by the
Doppler shift is denoted by “du”.
If the P cyclic shifts are applied to each group,
aliases generated in the left area on the basis of the
channel response 1601 are contained in the du range, and
other aliases generated in the right area on the basis of
the channel response 1601 may exist outside of the du range.
In this case, in the case of considering all the
aliasing operations of P channel responses generated in the
right area, a corresponding length corresponds to P • Ncs
(1602) .
Therefore, the length (S) of a single cyclic shift
group may be equal to the sum of the “du” length and the
"P " Ncs" length, and is represented by the following
equation 27:
[Equation 27]

In the meantime, the number of cyclic shift groups
in total sequences may be calculated by dividing the total
sequence length (Nzc) by the group length (S) , and can be
represented by the following equation 28:

[Equation 28]

In the meantime, as shown in FIG. 16, a specific
area 1603 less- than the group length (S) may be left. The
length of the "1603" area corresponds to "Nzc - G • S",
where Nzc is the length of an overall sequence, G is the
number of groups, and S is the group length.
If Nzc - G • S -2du is higher than Ncs, the additional
cyclic shift may also be applied to the above-mentioned
area 1603, and a detailed description thereof is shown at
the "1604" area of FIG. 16. Therefore, provided that the
number of cyclic shifts which are not based on the cyclic
shift group is R, the R value can be represented by the
following equation 29:


FIG. 17 is a conceptual diagram illustrating a
method for calculating a variable establishing the cyclic

shift within the interval of (Nzc/3) ≤ du according to the present invention.
In the area of (Nzc/3) ≤du, differently from the
above-mentioned (2) case (i.e., the aforementioned (2) case
of Ncs ≤ du the aliasing caused by the Doppler shift exceed the total
sequence length Nzc, so that the aliasing may occur between
the channel response of the ideal case and the du range.
For example, the peak located at the "1701" position
of FIG. 17 the aliasing may occur at positions 1701a and
1701b by the (+/-) Doppler shift. Therefore, the number of
cyclic shifts applicable to a single cyclic shift group in
this (3) case is decided by the "Nzc-2du" area (1702)
located at the center of FIG. 17, so that the number P of
restricted cyclic shifts applicable to each group can be
calculated by the following equation 30:
[Equation 30]

In this (3) case, the length S of each cyclic shift
group can be represented by the following equation 31:
[Equation 31]


The variable S is equal to the sum of the length of
the 1702 area (Nzc-2du) and the length of the 1703 area
corresponding to the "P • Ncs" length. The "P • Ncs" length
is variable with the number of cyclic shifts applicable to
each real group located at the right side
In the meantime, the above-mentioned (3) case
determines the number of cyclic shift groups in a given ZC
sequence by considering how many lengths (S, where S = the
length of a specific group) will be permitted in the du
range (1704), whereas the above-mentioned (2) case has
determined the number of cyclic shift groups in such a
given ZC sequence by considering how many lengths (S) will
be permitted in the total sequence length Nzc.
The spacing between a specific channel response and
two aliases of this channel response exceeds the total
sequence range, so that the present invention controls the
individual aliases not to overlap with each other within
the du range. The number of cyclic shift groups can be
represented by the following equation 32:
[Equation 32]


Finally, the cyclic shift group is established in
the du range (1704) as described above, and the 1705 area
having the length shorter" than that of the cyclic shift
group may be left. This length of the 1705 area
corresponds to "du - G • S". If the length of the 1705 area
is longer than Ncs, the additional cyclic shift may be
applied to this length.
Therefore, the number R of additional cyclic shifts
can be represented by
If the length (S) of each cyclic shift group is
higher than "P", the additional cyclic shifts corresponding
to the number of more than "P" may overlap with the ( + /-)
aliasing area in the right area. Therefore, this
embodiment may indicate the number R of additional cyclic
shifts as shown in the following equation 33:
[Equation 33]


Referring to FIG. 17, the Nzc-2du area (1702) located
at the center part must be larger than Ncs, so that the
cyclic shift can be applied to each group. Namely, this
requirement can be represented by Nzc-Zdu > Ncs-
If the above-mentioned requirement is represented in
different ways on the basis of the du value, it can be
recognized that the equation Nzc-Ncs > 2du (i.e., (Nzc-Ncs)/2
>du) must be satisfied. Therefore, this em≤bodiment does
not establish the restricted cyclic shift in the range of
(Nzc - Ncs)/2 ≤du.
Based on the above-mentioned explanation of the
individual intervals, a detailed description of only the
restricted set contained in Equation 25 will hereinafter be
disclosed. Firstly, the restricted set of Equation 25 can
be represented by the following equation 34.
[Equation 34]

The individual terms for use in the above cyclic
shift will hereinafter be described.
In Equation 34, is indicative of a
start point of each cyclic shift group. If the V value is

less than the number P of cyclic shifts for each group,
is indicative of "0". If the " value is
higher than the number P of cyclic shifts for each group
and is less than "2P", is indicative of "S"
corresponding to the length of a single cyclic shift group.
If the " value is higher than "2P" and is less than
3P, is indicative of "2S" corresponding to
the length of two cyclic shift groups.
is indicative of the position
of the cyclic shift applied to each group (or the position
of an additional cyclic shift). In other words, the '
value is shifted to another position by a predetermined
distance Ncs at intervals of the P time.
The V value of Equation 34 (or Equation 25 including
Equation 34) does not discriminate between the groups or
components of the groups, and is indicative of the total
number of cyclic shifts. As a result, the total number of
cyclic shifts can be represented by
Modified Examples

A variety of modified examples applicable to the
present invention will hereinafter be described.
Although the above-mentioned best mode has disclosed
the specific case in which there is no restriction in the
start point of the cyclic shift, the present invention can
be applied to not only the above-mentioned case but also
other restricted cases.
Not only the above-mentioned best mode, but also all
the embodiments capable of being more generally applied to
the present invention will hereinafter be described.
The position at which the alias occurs by the { + )
Doppler frequency is denoted by the "+offset" position, and
the position at the alias occurs by the (-) Doppler
frequency is denoted by "-offset" position.
FIGS. 18 and 19 are conceptual diagrams illustrating
a method for reducing the number of ZCZ preamble sequences
due to an alias response in the case of Nzc=839, Ncs=100,
and du=155 according to the present invention.
The cyclic shift of FIG. 18 can begin at any
position. The cyclic shift of FIG. 19 can be performed at
only the Ncs-multiple position. The Ncs value of FIG. 18 is
equal to that of FIG. 19, however, start positions of the
individual cyclic shifts are different in FIGS. 18 and 19.
In conclusion, the case of FIG. 18 can construct
many more cyclic shifts than those of FIG. 19. In more

detail, the case of FIG. 18 eliminates the restriction of
the start position of the cyclic shift, so that it can
acquire the additional restricted cyclic shift.
FIG. 20 is a conceptual diagram illustrating the
increasing ratio of an available restricted cyclic shift
after the restriction of a start location of the cyclic
shift is removed in the case of Nzc=839 according to the
present invention;
The elimination of the restriction in the cyclic
shift starting may not increase the hardware complexity.
Therefore, the restricted cyclic shift having no
consideration in the pre-defined shift position is
preferred, and the above-mentioned best mode is
established under the aforementioned assumption.
However, the present invention can also be applied
to the restricted cyclic shift having the pre-defined
shift position, so that the following description will
disclose the above-mentioned two cases.
Firstly, the restricted cyclic shift case (i.e..
Case 1) having no consideration in the pre-defined shift
position will hereinafter be described.
Equation 21 indicates the alias distance,
irrespective of the preamble generation domain. The
number of restricted available cyclic shifts per root ZC
sequence is differently decided according to the root

index and the Ncs value, so that different equations for
use in different alias-distance ranges are required.
Specificall, there are two alias-distance ranges in
which there is no discrimination between alias responses.
The range in which the restricted cyclic shift can be
used is set to Ncs≤du≤ (Nzc-Ncs)/2. In this range, the
cyclic shift range and two alias ranges are not
overlapped with each other.
In this case, if the preamble is generated in the
frequency domain, the “du” value is set to "u" as denoted
by du = u. If the preamble is generated in the time
domain, the “du” value is set to "1/u mod Nzc" as denoted
by du = 1/u mod Nzc. The number of restricted cyclic
shifts can be represented by the following equation 35:
[Equation 35]

In Equation 35, "P" is indicative of the number of
restricted cyclic shifts per group, "G" is indicative of
the number of groups generated in a single preamble
sequence, and "R" is indicative of the number of
restricted additional cyclic shifts which is not based on
the additional group.

The available range of the restricted cyclic shift
is denoted by Ncs≤du≤ (Nzc-Ncs)/2. This interval
"Ncs and "(Nzc/3)≤du≤(Nzc-Ncs)/2" on the basis of Nzc/3.
The reason why the alias-distance range is divided
into "Ncs basis of Nzc/3 has already been disclosed.
Therefore, "Ncs≤du≤≤ (Nzc-Ncs)/2" is differently
decided on the basis of "Nzc/3". The range of
Ncs≤du hereinafter be described.
If the start position of the first group is set to
"0", the Vg-th restricted cyclic shift range is defined by
[Cva, start* Cva, end ] in Equations 36 and 37.
The alias occurs at the positions of the following
[Equation 36]


equations 38 and 39:
[Equation 38]

[Equation 39]

In Equation 39, " () NZC" is indicative of a modular
operation.
Firstly, the alias-distance range Ncs≤du (i.e., the alias-distance range 1) has number of
groups. Each group includes number of restricted
cyclic shifts. The length of each group is denoted by
If the available additional cyclic shift
is a positive(+) number, the R value is denoted by

FIG. 21 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=150 according to one embodiment of the present
invention. Each group has three cyclic shifts, and two

additional cyclic shifts exist in the remaining ranges.
In this example, the total number of restricted cyclic
shifts is "5".
According to one embodiment, the present invention
applies the number of calculated groups, the number of
restricted cyclic shifts per group, and the group length
to Equations 36 and 37, and then establishes the cyclic
shift-applying interval in consideration of the above-
mentioned parameters.
Next, in the alias-distance range (Nzc/3) ≤du≤ (Nzc-
Ncs)/2 (i.e., the alias-distance range 2), the number of
available cyclic shifts per group is denoted by
the length of each group is denoted by
and there are G groups (where

The additional cyclic shift is selected from among
the center part and the residual part of the right side.
In this case, the selected cyclic shifts should be the
smallest number of cyclic shifts. Namely, if the R value
is a positive number, the number of additional cyclic
shifts is denoted by The start
position of the Va-th restricted cyclic shift is calculated

by applying the above-mentioned parameters to Equations 36
and 37.
FIG. 22 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=399 according to one embodiment of the present
invention. Each group
There are four groups, each of which has a single
cyclic shift and a single additional cyclic shift. In
this example, the total number of restricted cyclic
shifts is 5.
According to this embodiment, the present invention
applies the number of calculated groups, the number of
restricted cyclic shifts per group, and the group length
to Equations 36 and 37, and then establishes the cyclic
shift-applying interval in consideration of the above-
mentioned parameters.
Indeed, the equal sing (=) between two alias
distance ranges may have no meaning or the relatively-low
importance. For example, in the case of using the ZC
sequence having the length of 839, the (Nzc/3) value is
equal to 279.67 (i.e., (Nzc/3)=279.67), so that the
divided ranges Ncs may have the same results as those of the divided ranges
Ncs≤du≤ {Nzc/3) and (Nzc/3)
Next, the restricted cyclic shift (i.e., Case 2)
considering the pre-defined shift position will hereinafter
be described.
A method for generating the restricted cyclic shift
using the pre-defined shift position is changed to another
method. Each alias-distance range includes not only G
groups, each of which has P cyclic shifts, but also a first
additional cyclic shift out of the R1 groups.
In the case of using the pre-defined shift position,
the present invention has a particular additional cyclic
shift, differently from the other case in which no pre-
defined shift position exists in the alias-distance range
2-area.
In the alias-distance range 2-area, the main region
generally appears in the front samples of the sequence, and
the alias regions generally appear in the rear samples of
the sequence. However, according to the Case 2, the main
region appears in the rear samples of the sequence, and the
alias regions appear in the front samples of the sequence.
The second additional cyclic shift is denoted by R2.
The second additional cyclic shift does not appear in the
alias-distance range 1. The total number of restricted
cyclic shifts can be represented by the following equation
40:

[Equation 40]

Provided that the start position of the first group
is "0", the Va-th restricted cyclic shift is defined in [Cva,
startf Cva, end ] as denoted by Equations 41 and 42:
[Equation 41]

[Equation 42]

The related alias occurs at positions of the
following equations 43 and 44:
[Equation 43]



In Equations 4 3 and 44, ()NZC is indicative of a
modular operation.
In the alias-distance range Ncs≤du the alias-distance range 1), G groups (where,
exists, P restricted cyclic shifts (where,
exists, and the group length is denoted by
If the R1 value is a positive ( + )
number, the number of the first additional cyclic shifts is
denoted by
FIG. 23 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of N2c=839, Ncs=40, and
du=l50 according to another embodiment of the present
invention. In FIG. 23, each group includes three cyclic
shifts and two cyclic shifts. In this example, the total
number of restricted cyclic shifts is "5".
According to this embodiment, the present invention
applies the number of calculated groups, the number of
restricted cyclic shifts per group, and the group length
to Equations 41 and 42, and then establishes the cyclic

shift-applying interval in consideration of the above-
mentioned parameters.
Next, in the alias-distance range (Nzc/3) ≤du≤ (Nzc-
Ncs)/2 (i.e., the alias-distance range 2), the number of
available cyclic shifts per group is denoted by
the length of each group is denoted by
and there are G groups
(where
The first additional cyclic shift is calculated by
the same method as that of the alias-distance range 1. If
the R1 value is a positive number, the number of first
additional cyclic shifts is denoted by

If the R1 value is equal to "0" (i.e., R1=0) , the
presence or absence of a second additional cyclic shift
must be determined. The shape of the second additional
cyclic shift is the opposite of the shape of the
conventional cyclic shift, as shown in the last cyclic
shift of FIG. 23.
The present invention determines whether the alias
range of the second additional cyclic shift is an available
range and

determines whether the cyclic shift interval is available
(i.e., If it is determined that the cyclic
shift interval is available (i.e.,
FIG. 24 is a conceptual diagram illustrating an
exemplary cyclic shift in the case of Nzc=839, Ncs=40, and
du=399 according to another embodiment of the present
invention. In FIG. 24, each group includes three cyclic
shifts and no first additional cyclic shift (i.e., zero
first additional cyclic shift). And, each group further
includes a single additional cyclic shift in which a
relative position of the main region is opposite to that
of. the alias region. This second additional cyclic shift
does not occur when the fixed cyclic shift position is
not used, as shown in FIG. 22, In this example, the
number of total restricted cyclic shifts is "4".
According to this embodiment, the present invention
applies the number of calculated groups, the number of
restricted cyclic shifts per group, and the group length
to Equations 41 and 42, and then establishes the cyclic
shift-applying interval in consideration of the above-
mentioned parameters.
According to another embodiment, a specific system
with the fixed cyclic shift may determine the cyclic shift

according to the following method.
Firstly, the total sequence range is divided by the
cyclic shift value.
Next, the present invention searches for the range
{±u or +(m*Nzc-l)/u) in which the interference caused by
the offset occurs in the first range (i.e., n=l). In this
case, there are a plurality of ranges, each of which has
the interference.
For example, in the case of considering only the
first interference, a maximum number- of interference
generation ranges may be set to "4".
Next, if the first range is not overlapped with all
of the interference ranges caused by the offset, the first
range is set to an available range, and the remaining
ranges caused by the offset is set to a restricted range
(also called a prohibition range) .
The present invention goes to the next range (i.e.,
n=n+l), and repeatedly searches for the range in which the
interference is generated by the offset.
While the present invention searches for the
interference generation range in the n-th range, if an
observation range, several ranges caused by the offset, an
pre-established available range, and pre-established
prohibition ranges are not overlapped with each other, the
present invention determines a current range to be an

available range, and determines the above several ranges
caused by the offset associated with the current range to
be prohibition ranges. If the above-mentioned process is
repeated until reaching the last range, the present
invention may determine the cyclic shift in the system
including the fixed cyclic shift.
According to still another embodiment, the present
invention may apply the aforementioned established cyclic
shift - applying interval to only the high-mobility cell in
a mobile communication system including several cells.
In this case, the present invention may determine
whether a corresponding cell has the high mobility by
determining whether the frequency offset associated with
the cell is higher than a predetermined level after
acquiring the cell information. In this case, the
predetermined level is indicative of a frequency offset
value, which can be readily decided or modified by those
skilled in the art.
Preferably, the present invention may control the
Node-B or the UE to determine whether the corresponding
cell is the high-mobility cell. However, the UE has
difficulty in estimating the frequency offset value of each
of other UEs contained in the cell. Therefore, it is more
preferable that the Node-B determines whether the
corresponding cell is the high-mobility cell in

consideration of several UEs of the cell, and broadcasts
the resultant signal over the broadcast channel.
In the meantime, if it is determined that the
corresponding cell is not indicative of the high-mobility
cell, the present invention may include a process for
allocating a sequence unallocated to the high-mobility cell.
The following description shows that equations are
modified into others under the same condition as that of
the best mode, and a detailed description thereof will
hereinafter be described.
In association with the best mode, the above-
mentioned equations may also be denoted by the following
expression.
and
in the alias-distance
range of Ncs≤du
range of (Nzc/3) ≤du≤ (Nzc-Ncs)/2, the P, S, G, and R values

are denoted by

Next, the case of the' restricted cyclic shift
considering the pre-defined shift position (Case 2) will
hereinafter be described using other equations.
The u-th root ZC sequence having the region of zero
correlation, i.e., the v-th random access preamble, is
defined by Xu,v (n) =Xu ( (n+Cv) mod Nzc) - In this case, the Cv
value is defined by equation 45:
[Equation 45]

for high mobility cell
wherein ,
In this case, the parameters of the high-mobility
cell can be defined by the following explanation.
In more detail, in the alias range of Ncs≤du the P value is denoted by the S value is
denoted by and the G value is
denoted by A first additional cyclic shift

Rl is denoted by and a
second additional cyclic shift R2 is denoted by R2=0.
In the alias range of the P
"value i's" dehote'd by the S value is
denoted by and the G value is
denoted by A first additional restricted cyclic
shift is denoted by a
second additional restricted cyclic shift R2 is denoted by
R2=l in the case of R1=0 and "X - Ncs the X value is denoted by

In the restricted cyclic shift case of
Xu,v(n)=Xu ( (n+Cv) mod Nzc), the method for directly using the
shift value of the v-th restricted cyclic shift has been
disclosed. Differently from the method, another method for
employing the Va value for Va-th restricted cyclic shift so
that the restricted cyclic shift can be applied to the
present invention. In more detail, the similar cyclic
shift can be generated using the equation of


In the case of generating the cyclic shift using the
above-mentioned method, the basic concept is equal to those
of the above-mentioned methods. However, different
equations are applied to the above-mentioned methods.
The case (Case 1) of the restricted cyclic shift
having no consideration in the pre-defined shift position
will be described using other equations.
The index (v) for the cyclic shift is represented by
the following equation 46:
[Equation 46]

In the alias range of the P value is
denoted by the S value is denoted by
and the G value is denoted by
and the additional restricted cyclic
shift R is denoted by

In the alias range of the P
value is denoted by the S value is
denoted by the G value is
denoted by and the R value is denoted by

If the above-
mentioned expression can be represented by other ways. In
more detail, in the alias range of Ncs≤du value is denoted by P=E, the S value is denoted by
the G value is denoted by and
the R value is denoted by
In the alias range of the P
value is denoted by P=F, the S value is denoted by
the G value is denoted by
and the R value is denoted by

Next, the restricted cyclic shift case (Case 2)
considering the pre-defined shift position will be
described using other equations.

The index (v) for the cyclic shift is represented by
the following equation 47:
[Equation 47]

In the alias range of the P value is
denoted by the S value is denoted
by and the G value is denoted by
and the additional restricted cyclic
shift R1 is denoted by
In the alias range of the P
value is denoted by , the S value is
denoted by the G value is
denoted by and the R1 value is denoted by.


If R1=0 and the R2 value can be
represented by R2 =l. In this case, the X value is denoted
by
If and
, in the alias
range of Ncs≤du S value is denoted by S=2F+F', the G value is denoted by
and the R2 value is denoted by
If R1=0 and the R2 value can be
represented by R2=l. In this case, the X value is denoted
by
As described above, according to the above-mentioned
embodiments, in the case of implementing the cyclic shifted
sequence using the CAZAC sequence, the present invention
may define the cyclic shift set capable of removing the
shift ambiguity caused by the frequency- or timing- offset.
Also, in the case of accessing the unsynchronized
channel, the frequency offset or the timing offset is not

adjusted to this unsynchronized channel, so that the
present invention can increase the strength of this channel.
According to the influence range of the pulse-
shaping filter, the present invention may define the cyclic
shift set in which the first-order interference, the
second-order interference, and the higher order
interference are considered.
It should be noted that most terminology disclosed
in the present invention is defined in consideration of
functions of the present invention, and can be differently
determined according to intention of those skilled in the
art or usual practices. Therefore, it is preferable that
the above-mentioned terminology be understood on the basis
of all contents disclosed in the present invention.
It will be apparent to those skilled in the art that
various modifications and variations can be made in the
present invention without departing from the spirit or
scope of the invention. Thus, it is intended that the
present invention cover the modifications and variations of
this invention provided they come within the scope of the
appended claims and their equivalents.
[industrial Applicability!
As apparent from the above description, the present
invention can easily establish a cyclic shift (CS) interval

at a specific location having no overlapping by considering
a channel response of a reception (Rx) sequence and an
alias location of this reception (Rx) sequence, although a
reception (Rx) signal is shifted by a channel delay
spreading or a propagation delay irrespective of categories
of a domain generating a sequence, so that it can greatly
reduce the number of the detection errors and the false
alarm rate.
And, if a sequence of the cyclic shift (CS) is
allocated to a cell having a frequency offset of more than
a predetermined level, the present invention can minimize
the influence of a frequency offset on a high-mobility cell.
The present invention relates to a first method for
allocating a sequence to each cell in consideration of
characteristics of the CAZAC sequence, and a second method
for establishing the cyclic shift to be applied to the
first method. Therefore, the present invention can be
applied to a wireless communication system (e.g., a UE and
a Node-B).
Although the preferred embodiments of the present
invention have been disclosed for illustrative purposes,
those skilled in the art will appreciate that various
modifications, additions and substitutions are possible,
without departing from the scope and spirit of the
invention as disclosed in the accompanying claims.

[CLAIMS]
[claim ll A method for setting cyclic shift to be applied
to a given sequence against an effect of a high Doppler
frequency higher than a predetermined value, the method
comprising:
acquiring a first variable (du) of cyclic shift
corresponding to a Doppler shift of one subcarrier spacing
by using an root index (u) of the given sequence;
acquiring secondary variables comprising a number of
group (G) comprised in the given sequence, a length of the
each group (S) and a number of cyclic shift per the group
(P) using the first variable (du) ; and
establishing the cyclic shift to be applied to the
given sequence according to the secondary variables.
[claim 2] The method according to claim 1, wherein the
secondary variables further comprise a number of additional
cyclic shifts which are applicable to the given sequence
not based on the group (R).
[claim 3] The method according to claim 1 or 2, wherein
the given sequence is a Zadoff-Chu (ZC) sequence, and
the first variable is acquired by a equation of.


wherein "u" indicates the root index of the ZC sequence
and “Nzc” corresponds to a length of the ZC sequence.
[claim 4] The method according to claim 3, wherein the
secondary variables are differently acquired according to a
range of the first variable (du) , and the range of the
first variable is divided by a criteria corresponding to
1/3 of the given sequence length (Nzc/3).
Iciaim 5l The method according to claim 4, wherein:
if the range of the first variable (du) is Ncs ≤ du (Nzc/3}, the secondary variables are acquired by equations
of,

wherein "Ncs" is a predetermined cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and "R" corresponds to

the number of additional cyclic shifts.
[claim 6] The method according to claim 4, wherein:
if the range of the first variable (du) is (Nzc/3)≤ du ≤
(Nzc-Ncs)/2, the secondary variables are acquired by
equations of,

wherein "Ncs" is a predetermined cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and "R" corresponds to
the number of additional cyclic shifts.
[claim 7] The method according to claim 5 or 6, wherein
said establishing the cyclic shift is performed as a
equation of,

I Claim 8l The method according to claim 1, wherein the

given sequence is for generating a random access preamble.
[claim 9] A method for setting cyclic shift to be applied
to a given sequence, the method comprising:
determining whether the cyclic shift is to be
established according to a restricted sets restricted due
to a Doppler shift; and
establishing the cyclic shift to be applied to the
given sequence considering a cyclic shift corresponding to
a Doppler shift of one subcarrier spacing, when the cyclic
shift is determined to be established according to the
restricted sets.
[claim lO] The method according to claim 9, wherein:
when the cyclic shift is determined to be established
according to the restricted sets, said establishing the
cyclic shift to be applied to the given sequence comprises:
acquiring a first variable (du) indicating the cyclic
shift corresponding to the Doppler shift of one subcarrier
spacing by using an root index (u) of the given sequence;
acquiring secondary variables comprising a number of
group (G) comprised in the given sequence, a length of the
each group (S) , a number of cyclic shift per the group (P)
using the first variable (du) and a number of additional

cyclic shifts which is applicable to the given sequence not
based on the group (R), and
establishing the cyclic shift to be applied to the
given sequence according to the secondary variables.
[claim 111 The method according to claim 10, wherein the
given sequence is a Zadoff-Chu (ZC) sequence, and
the first variable is acquired by a equation of.

wherein "u" indicates the root index of the ZC sequence
and “Nzc” corresponds to a length of the ZC sequence.
[claim 121 The method according to claim 11, wherein the
secondary variables are differently acquired according to a
range of the first variable (du) , and the range of the
first variable is divided by a criteria corresponding to
1/3 of the given sequence length (Nzc/3).
[claim 13l The method according to claim 12, wherein:
if the range of the first variable (du) is Ncs ≤ du (Nzc/3) , the secondary variables are acquired by equations
of,


wherein "Ncs" is a predetermined cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and "R" corresponds to
the number of additional cyclic shifts.
[claim 14] The method according to claim 12, wherein:
if the range of the first variable (du) is (Nzc/3)≤ du ≤
(N2C-Ncs)/2, the secondary variables are acquired by
equations of,

wherein "Ncs" is a predetermined cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and "R" corresponds to

the number of additional cyclic shifts.
[ Claim 15 1 The method according to claim 13 or 14,
wherein the cyclic shift is performed as following
equation,

[claim 16] The method according to claim 9, wherein the
given sequence is for generating a random access preamble.
[ Claim 17 1 A method for setting cyclic shift to be
applied to a given sequence, the method comprising:
(a) acquiring a variable of du by a equation of,

wherein "u" indicates an root index of the given
sequence and “Nzc” corresponds to a length of the given
I sequence;
(b) acquiring variables of G, S, P and R by equations
of.


when a range of the first
variable (du) is and acquiring variables
of G, S, P and R by equations of,
when the range of the
first variable (du) is wherein
"Ncs" is a predetermined cyclic shift parameter;
(c) establishing the cyclic shift by equation of,

wherein the restricted sets are a cyclic shift sets
restricted due to a Doppler shift, and the unrestricted
sets are a cyclic shift sets not restricted due to the
Doppler shift.
[ Claim 18 J A method for transmitting a random access
preamble using cyclic shift, the method comprising:
acquiring a root index (u) of a sequence for the random
access preamble from system information;

establishing the cyclic shift to be applied to the
sequence, in said establishing, when the cyclic shift is
determined to be established according to the restricted
sets restricted due to a Doppler shift, the cyclic shift to
be applied to the sequence is established by considering a
cyclic shift corresponding to a Doppler shift of one
subcarrier spacing;
generating the sequence according to.the root index (u)
with the established cyclic shift; and
transmitting the sequence with the cyclic shift as the
random access preamble.
[claim 19] The method according to claim 18, wherein:
when the cyclic shift is determined to be established
according to the restricted sets, said establishing the
cyclic shift to be applied to the sequence comprises:
acquiring a first variable (du) indicating the cyclic
shift corresponding to the Doppler shift of one subcarrier
spacing by using the root index (u) of the given sequence;
acquiring secondary variables comprising a number of
group (G) comprised in the sequence, a length of the each
group (S), a number of cyclic shift per the group (P) using
the first variable (d„) and a number of additional cyclic
shifts which is applicable to the sequence not based on the
group (R), and

establishing the cyclic shift to be applied to the
sequence according to the secondary variables.
[claim 20] The method according to claim 19, wherein the
given sequence is a Zadoff-Chu (ZC) sequence, and
the first variable is acquired by a equation of.

wherein "u" indicates the root index of the ZC sequence
and “Nzc” corresponds to a length of the ZC sequence.
[Claim 21] The method according to claim 20, wherein the
secondary variables are differently acquired according to a
range of the first variable (du), and the range of the
first variable is divided by a criteria corresponding to
1/3 of the given sequence length (N2c/3).
[claim 22] The method according to claim 21, wherein:
if the range of the first variable (du) is Ncs ≤ du (Nzc/3), the secondary variables are acquired by equations
of.



wherein "Ncs" is a predetermined- cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and ≤'R" corresponds to
the number of additional cyclic shifts.
[Claim 23] The method according to claim 21, wherein:
if the range of the first variable (du) is (Nzc/3)≤ du≤
(N2C-Ncs)/2, the secondary variables are acquired by
equations of,

wherein "Ncs" is a predetermined cyclic shift parameter,
"P" corresponds to the number of cyclic shift per the group,
"S" corresponds to the length of the each group, "G"
corresponds to the number of group and "R" corresponds to
the number of additional cyclic shifts.
[claim 24] The method according to claim 22 or 23,

wherein the cyclic shift is performed as following
equation,

A method for establishing a cyclic shift sequence to provide against the frequency offset is disclosed. The method calculates a distance between a channel response position of the sequence and an alias channel response position caused by a frequency offset, calculates the number of cyclic shifts per group according to the calculated distance, and establishes the cyclic shift (CS)- applying interval. This method easily establishes a cyclic shift (CS) interval at a specific location having no overlapping by considering a channel response of a reception (Rx) sequence and an alias location of this reception (Rx) sequence, although a reception (Rx) signal is shifted by a channel delay spreading or a propagation delay irrespective of categories of a domain generating a sequence, so that it can greatly reduce the number of the detection errors and the false alarm rate. And, if a sequence of the cyclic shift (CS) is allocated to a cell having a frequency offset of more than a predetermined level, the present invention can minimize the
influence of a frequency offset on a high-mobility cell.

Documents:

http://ipindiaonline.gov.in/patentsearch/GrantedSearch/viewdoc.aspx?id=UsWsECAPQRICPcRw71PWyQ==&loc=wDBSZCsAt7zoiVrqcFJsRw==


Patent Number 270752
Indian Patent Application Number 2225/KOLNP/2009
PG Journal Number 04/2016
Publication Date 22-Jan-2016
Grant Date 15-Jan-2016
Date of Filing 15-Jun-2009
Name of Patentee LG ELECTRONICS INC.
Applicant Address 20, YEOUIDO-DONG, YEONGDEUNGPO-GU, SEOUL 105-875
Inventors:
# Inventor's Name Inventor's Address
1 HAN, SEUNG HEE LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
2 KWON, YEONG HYEON LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
3 LEE, HYUN WOO LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
4 KIM, DONG CHEOL LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
5 NOH, MIN SEOK LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
6 KWAK, JIN SAM LG INSTITUTE, HOGYE 1(IL)-DONG, DONGAN-GU, ANYANG-SI, GYEONGGI-DO 431-749
7 VUJCIC, DRAGAN 8TER, RUE DES CENDRIERES, 91470 LIMOURS
PCT International Classification Number H04L 27/26
PCT International Application Number PCT/KR2008/000044
PCT International Filing date 2008-01-04
PCT Conventions:
# PCT Application Number Date of Convention Priority Country
1 60/883,754 2007-01-05 U.S.A.