(12) Ulllted States Patent
`Han et al.
`
`(10) Patent N0.:
`(45) Date of Patent:
`
`US 7,746,916 B2
`Jun. 29, 2010
`
`US007746916B2
`
`(54) METHOD AND APPARATUS FOR
`GENERATING AND TRANSMITTING CODE
`SEQUENCE IN AWIRELESS
`COMMUNICATION SYSTEM
`
`(75) Inventors: Seung Hee Han, Seoul (KR); Min Seok
`Noh, Seoul (KR); Yeon Hyeon KWon,
`
`Anyang-Si (KR); Hyllll W00 Lee,
`Anyang-si (KR); Dong Cheol Kim,
`UiWang-si (KR)
`
`(73) Assignee: LG Electronics Inc., Seoul (KR)
`
`( * ) Notice:
`
`Subject to any disclaimer, the term of this
`Patent 15 extended Or adJusted under 35
`U~S-C- 154(1)) by 580 days-
`
`(21) Appl. N0.: 11/563,909
`
`(22) Filed:
`
`NOV‘ 28’ 2006
`_
`_
`_
`Pnor Pubhcatlon Data
`US 2007/0177682 A1
`Aug. 2, 2007
`
`(65)
`
`(30)
`
`(56)
`
`References Cited
`
`U.S. PATENT DOCUMENTS
`7,426,175 B2 *
`9/2008 Zhuang et a1. ............ .. 370/203
`2003/0156624 A1* 8/2003 Koslar ...................... .. 375/131
`ggiygttzlt 31'
`'
`
`1065855
`EP
`1/2001
`10-2007-0103917
`KR
`10/2007
`9605668
`WO
`2/1996
`2003049295
`WO
`6/2003
`W0 03/075500
`W0
`9/2003
`W0 WO 2005/104412
`11/2005
`OTHER PUBLICATIONS
`Texas Instruments “On allocation of Uplink Pilot Sub-Channels in
`Eutra SC-FDMA”, 3GPP TSG-RAN WGl, El-050922, Aug. 29,
`2005.
`_
`_
`* c1ted by exammer
`Primary ExamineriDavid C Payne
`Assistant ExamineriAdolf DsouZa
`(74) Attorney, Agent, or FirmiLee, Hong, Degerman, Kang
`& Waimey
`
`Foreign Application Priority Data
`
`(57)
`
`ABSTRACT
`
`Nov. 28, 2005
`Jul. 4, 2006
`Jul. 7, 2006
`
`(KR) .................... .. 10-2005-0114306
`(KR) .................... .. 10-2006-0062467
`(KR) .................... .. 10-2006-0064091
`
`(51) Int. Cl.
`(2006.01)
`H04B 1/00
`(52) US. Cl. ..................... .. 375/142; 370/203; 370/208;
`375/131; 375/140; 375/146; 375/148
`(58) Field of Classi?cation Search ............... .. 370/203;
`375/131, 142
`See application ?le for complete search history.
`
`A method of generating a code sequence in a Wireless com
`munication system is disclosed- More speci?cally, the
`method includes recognizing a desired length of the code
`sequence, generating a code sequence having a length differ
`ent from the desired length, and modifying the length of the
`generated code sequence to equal the desired length. Here,
`the step of modifying includes discarding at least one element
`of the generated code sequence or inserting at least one null
`element to the generated code sequence
`
`11 Claims, 18 Drawing Sheets
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`US. Patent
`
`Jun. 29, 2010
`
`Sheet 1 0f 18
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`US 7,746,916 B2
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`U.S. Patent
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`Jun. 29, 2010
`
`Sheet 2 of 18
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`US 7,746,916 B2
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`US. Patent
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`Jun. 29, 2010
`
`Sheet 3 0f 18
`
`US 7,746,916 B2
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`FIG. 3
`
`Start
`
`F
`
`Generate code sequence having length M _n_ 8301
`based on code generating algorithm
`
`1
`
`Generate code sequence having length N
`by removing (M-N) number of elements
`from each code sequence for N
`number of code sequence (M>N )
`
`~ S302
`
`}
`End
`
`SAMSUNG 1026-0004
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`

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`US. Patent
`
`Jun. 29, 2010
`
`Sheet 4 0f 18
`
`US 7,746,916 B2
`
`FIG. 4
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`sequence 0
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`US. Patent
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`Jun. 29, 2010
`
`Sheet 5 0f 18
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`US 7,746,916 B2
`
`FIG. 5
`
`sequence 0
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`Time Index
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`US. Patent
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`Jun. 29, 2010
`
`Sheet 6 6f 18
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`US 7,746,916 B2
`
`FIG. 6
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`SAMSUNG 1026-0007
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`

`
`U.S. Patent
`
`Jun. 29, 2010
`
`Sheet 7 of 18
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`US 7,746,916 B2
`
`FIG. 7
`
`100
`
`—- Conventional (§F=103i)
`—— Present Embodiment (N=1024
`
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`0,9
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`
`Value of Correlation
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`SAM SU NG 1026-0008
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`SAMSUNG 1026-0008
`
`

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`US. Patent
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`Jun. 29, 2010
`
`Sheet 8 0f 18
`
`US 7,746,916 B2
`
`FIG. 8
`
`Required CAZAC length=L
`
`U
`
`Generated CAZAC length=X>L, X=prime number
`
`Truncated CAZAC length=L
`
`FIG. 9
`
`Required CAZAC length=L
`
`qIEHBI'HtBd CAZAC length=X<L, X=prime numbe;
`
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`C1
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`SAMSUNG 1026-0009
`
`

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`US. Patent
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`Jun. 29, 2010
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`Sheet 9 0f 18
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`US 7,746,916 B2
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`FIG. 10
`
`Original CAZAC seq.
`
`M
`
`Delaycd CAZAC seq. W
`
`SAMSUNG 1026-0010
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`

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`US. Patent
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`Jun. 29, 2010
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`Sheet 10 0f 18
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`US 7,746,916 B2
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`FIG. 11
`
`Required SBQUBHCE length, L
`
`|
`
`'
`
`Delayed CAZAC sequence length, L
`
`.
`
`'
`
`SAMSUNG 1026-0011
`
`

`
`US. Patent
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`Jun. 29, 2010
`
`Sheet 11 0f 18
`
`US 7,746,916 B2
`
`FIG. 12
`
`[i
`
`Required sequence length, L
`
`:i
`
`[120
`l
`
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`
`A CAZAC sequence with prime length XZL
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`Basie CAZAC sequence length, X; L
`
`T Truncated CAZAC sequence length, L .4
`
`SAMSUNG 1026-0012
`
`

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`US. Patent
`
`Jun. 29, 2010
`
`Sheet 12 0f 18
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`US 7,746,916 B2
`
`FIG. 13
`
`}_
`
`Required sequence length, L
`
`:
`
`A CAZAC sequence with prime length X; L I
`Ff
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`L Truncated CAZAC sequence length, L
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`padding
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`SAMSUNG 1026-0013
`
`

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`US. Patent
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`Jun. 29, 2010
`
`Sheet 13 0f18
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`US 7,746,916 B2
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`FIG. 14
`
`Required sequence length, L
`
`A CAZAC sequence with prime length XéL
`r:
`
`[140
`
`1
`
`[140
`
`2
`
`Basic CAZAC sequence length, XQL
`Generated CAZAC sequence length, L
`
`SAMSUNG 1026-0014
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`

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`US. Patent
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`Jun. 29, 2010
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`Sheet 14 0f 18
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`US 7,746,916 B2
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`FIG. 15
`
`generated CAZAC 1ength=L
`
`C2
`
`t?////////////¢7/I$ W
`
`Padding
`
`padding
`
`SAMSUNG 1026-0015
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`

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`US. Patent
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`Jun. 29, 2010
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`Sheet 15 0f 18
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`US 7,746,916 B2
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`FIG. 16
`
`Transmitting End
`TrnnsmittingUnit
`L
`_.___Y
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`Y
`
`Sequence
`Selection
`Unit
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`SIP
`C
`overter
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`Receiving End
`
`1602
`
`1603
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`1601
`
`FIG. 1'?
`
`Basic Code Sequence Generation Unit
`
`Code
`Sequence
`Generation
`Unit
`
`Circular
`Cl _ Shi?
`Application
`Unit
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`5
`
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`Unit
`
`Code Sequence Length Adjustment Unit
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`Unit
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`1702a
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`1701
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`SAMSUNG 1026-0016
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`US. Patent
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`Jun. 29, 2010
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`Sheet 16 6f 18
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`US 7,746,916 B2
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`FIG. 1B
`
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`
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`
`SAMSUNG 1026-0017
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`U.S. Patent
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`Jun. 29, 2010
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`Sheet 17 of 18
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`US 7,746,916 B2
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`FIG. 19
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`SAMSUNG 1026-0018
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`US. Patent
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`Jun. 29, 2010
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`Sheet 18 0f 18
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`US 7,746,916 B2
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`FIG. 20
`
`:_
`Required CAZAC length=L
`Puwerper tone=11 ///r7/L
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`US 7,746,916 B2
`
`1
`METHOD AND APPARATUS FOR
`GENERATING AND TRANSMITTING CODE
`SEQUENCE IN A WIRELESS
`COMMUNICATION SYSTEM
`
`This application claims the bene?t of Korean Application
`No. P2005-114306, ?led on Nov. 28, 2005, Korean Applica
`tion No. P2006-62467, ?led on Jul. 4, 2006, and Korean
`Application No. P2006-64091, ?led on Jul. 7, 2006, Which
`are hereby incorporated by reference.
`
`BACKGROUND OF THE INVENTION
`
`2
`attained by the structure particularly pointed out in the Written
`description and claims hereof as Well as the appended draW
`ings.
`To achieve these objects and other advantages and in accor
`dance With the purpose of the invention, as embodied and
`broadly described herein, a method of generating a code
`sequence in a Wireless communication system includes rec
`ogniZing a desired length of the code sequence, generating a
`code sequence having a length different from the desired
`length, and modifying the length of the generated code
`sequence to equal the desired length. Here, the step of modi
`fying includes discarding at least one element of the gener
`ated code sequence or inserting at least one null element to the
`generated code sequence.
`In another aspect of the present invention, method of gen
`erating a code sequence in a Wireless communication system
`includes a recogniZing a desired length of a ?rst code
`sequence, generating a second code sequence having a length
`different from the desired length of the ?rst code sequence,
`and modifying the length of the second code sequence to
`equal the desired length of the ?rst code sequence. Here, the
`step of modifying includes discarding at least one element of
`the modi?ed code sequence if the length of the modi?ed code
`sequence is longer than the desired length of the ?rst code
`sequence or inserting at least one null element to the modi?ed
`code sequence if the length of the modi?ed second code
`sequence is shorter than the desired length of the ?rst code
`sequence.
`In a further aspect of the present invention, an apparatus for
`generating a code sequence in a Wireless communication
`system includes a sequence selection unit for recogniZing a
`desired length of the code sequence, generating a code
`sequence having a length different from the desired length,
`and modifying the length of the generated code sequence to
`equal the desired length, Wherein the sequence selection unit
`discards at least one element of the generated code sequence
`or inserts at least one null element to the generated code
`sequence in modifying the length of the generated code
`sequence, and a transmitting unit for transmitting the modi
`?ed generated code sequence via at least one antenna.
`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.
`
`1. Field of the Invention
`The present invention relates to a method of generating and
`transmitting code sequence, and more particularly, to a
`method and apparatus for generating and transmitting code
`sequence in a Wireless communication system.
`2. Discussion of the RelatedArt
`Usually, a pilot signal or a preamble of a Wireless commu
`nication system is referred to as a reference signal used for
`initial synchronization, cell search, and channel estimation.
`Further, the preamble is comprised of a code sequence, and
`the code sequence is further comprised of orthogonal or
`quasi-orthogonal Which represent good correlation proper
`ties.
`For example, a Hadamard matrix of 128x128 is used in a
`portable intemet (PI) to insert the code sequence to the fre
`quency domain. In so doing, 127 types of code sequences are
`used.
`Although the Hadmard code sequence and a poly-phase
`Constant Amplitude Zero Auto-Correlation (CAZAC) code
`sequence are orthogonal codes, a number of codes used to
`maintain orthogonality is limited. For example, a number of
`N orthogonal codes in a N><N Hadamard matrix is N, and a
`number of N orthogonal codes that can be expressed by the
`CAZAC codes is N and a prime number smaller than N
`(David C. Chu, “Polyphase Codes With Good Periodic Cor
`relation Properties,” Information Theory IEEE Transaction
`on, vol. 18, issue 4, pp. 531-532, July 1972). With respect to
`CAZAC sequence types, GCL CAZAC and Zadoff-Chu
`CAZAC are often used.
`If the code sequence is generated using the Hadamard
`codes, N number of sequence types corresponding to the
`entire length of the codes is generated. HoWever, the if the
`code sequence is generated using the CAZAC codes, only
`half or N/ 2 number of sequence types are generated.
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`SUMMARY OF THE INVENTION
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`
`Accordingly, the present invention is directed to a method
`and apparatus for generating and transmitting code sequence
`in a Wireless communication system that substantially obvi
`ates one or more problems due to limitations and disadvan
`tages of the related art.
`An object of the present invention is to provide a method of
`generating a code sequence in a Wireless communication
`system.
`Another object of the present invention is to provide an
`apparatus for generating a code sequence in a Wireless com
`munication system.
`Additional advantages, objects, and features of the inven
`tion 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
`
`50
`
`55
`
`60
`
`65
`
`The accompanying draWings, Which are included to pro
`vide a further understanding of the invention and are incor
`porated in and constitute a part of this application, illustrate
`embodiment(s) of the invention and together With the descrip
`tion serve to explain the principle of the invention. In the
`draWings;
`FIG. 1 illustrates a structure of an apparatus for transmit
`ting data using Orthogonal Frequency Division Multiplexing
`(OFDM) or OFDM Access (OFDMA) scheme;
`FIG. 2 illustrates a structure of an apparatus for receiving
`data using OFDM/OFDMA scheme;
`FIG. 3 is a How diagram illustrating adjusting a code
`sequence;
`FIG. 4 illustrates cross-correlation properties of the gener
`ated code sequence;
`FIG. 5 illustrates a generated CAZAC sequence
`
`SAMSUNG 1026-0020
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`US 7,746,916 B2
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`4
`
`aNs5q7NxN
`
`using N (:l024);
`FIG. 6 illustrates a cross-correlation properties cumulative
`distribution function (CDF) of the code sequences that can be
`generated according to the code sequence
`
`aN55q7MxN
`
`and the CAZAC sequence
`
`“N
`
`XN
`
`5:-,q_N
`
`when N:l024;
`FIG. 7 illustrates the cross-correlation properties CDF of
`the code sequences that can be generated based on the
`CAZAC sequence generated using the prime number of
`N:103l and a code sequence set
`
`aN55q7MxN
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`having length of 1024 (seven (7) elements removed);
`FIG. 8 illustrates a method ofgenerating CAZAC sequence
`using a length required by a communication system;
`FIG. 9 illustrates a method of generating a CAZAC
`sequence using a padding portion;
`FIG. 10 illustrates an exemplary application of circular
`shift;
`FIG. 11 is an exemplary diagram illustrating application of
`circular shift to the generated code sequence after the ele-
`ments of the code sequence are removed;
`FIG. 12 is an exemplary diagram illustrating application of
`circular shift to the generated code sequence prior to remov- 45
`ing the elements of the code sequence;
`FIG. 13 is an exemplary diagram illustrating application of
`circular shift to the generated code sequence after a padding
`portion is attached;
`FIG. 14 is an exemplary diagram illustrating application of 50
`circular shift to the generated code sequence prior to attach-
`ing a padding portion;
`FIG. 15 is an exemplary diagram of a padding portion of
`the code sequence in which the padding portion is used as a
`lower bandwidth guard interval;
`FIG. 16 is a structural diagram for transmitting the code
`sequence. Depending on whether the transmission ofthe code
`sequence is made in a downlink direction or an uplink direc-
`tion, the structure can be in different form;
`FIG. 17 is a structural diagram illustrating a basic code
`sequence generation unit and a code sequence length adjust-
`ment unit;
`FIG. 18 illustrates cross-correlation characteristics of the
`
`55
`
`60
`
`code sequence;
`FIG. 19 illustrates cross-correlation characteristics of the
`
`65
`
`code sequence; and
`
`FIG. 20 is an exemplary diagram illustrating boosting the
`power of the generated code sequence.
`
`DETAILED DESCRIPTION OF THE INVENTION
`
`Reference will now be made in detail to the preferred
`embodiments ofthe present invention, examples ofwhich are
`illustrated in the accompanying drawings. Wherever pos-
`sible, the same reference numbers will be used throughout the
`drawings to refer to the same or like parts.
`FIG. 1 illustrates a structure of an apparatus for transmit-
`ting data using Orthogonal Frequency Division Multiplexing
`(OFDM) or OFDM Access (OFDMA) scheme. FIG. 2 illus-
`trates a structure of an apparatus for receiving data using
`OFDl\/I/OFDMA scheme.
`
`In FIG. 1, trafiic data and control data are multiplexed at a
`muxer 11. Here, the trafiic data is used to provide service from
`a transmitting end to a receiving end, and the control data is
`used to facilitate transmission from the transmitting end to the
`receiving end. The discussion relating to the present invention
`regarding the code sequence which relates to a type of a code
`sequence of the control data. The code sequence can be used
`for initial synchronization, cell search, or channel estimation.
`Depending on the communication system,
`the code
`sequence can be used in various forms. For example, the code
`sequence in an IEEE 802.16 wideband wireless access system
`can be used in a preamble or a pilot signal format, and in a
`multi-input, multi-output (MIMO) system, the code sequence
`can be used as a midarnble format.
`
`After being processed at the muxer 11, the multiplexed
`traffic and control data is then channel coded by a channel
`coding module 12. Charmel coding is used to allow the receiv-
`ing end to correct error that can occur during transmission by
`adding parity bits. Examples of charmel coding include con-
`volution coding, turbo coding, and low density parity check
`(LDPC) coding.
`Thereafter, the channel coded data is modulated by a digital
`modulation module 13 in which data symbols are mapped
`using algorithms such as a quadrature phase shift keying
`(QPSK) or a 16-quadrature amplitude modulation (16 QAM).
`The mapped data symbols are then processed by a subchannel
`modulation module 14 through which the data symbols are
`mapped to each subcarrier of the OFDM system or OFDMA
`system. Then, the data symbols mapped to subcarriers are
`processed by an inverse fast Fourier transform (IFFT) module
`15 which transform the data symbols into a signal in a time
`domain. The transformed data symbols are then processed
`through a filter 16 and further processed through a digital-to-
`analog conversion (DAC) module 17 where the filtered data
`symbols are converted to analog signals. Lastly, the analog
`signals are converted into a radio frequency (RF) by a RF
`module 18 which is then transmitted via an antenna 19 to the
`
`receiving end.
`Based on the type of generated code (e.g., CAZAC code),
`the steps of charmel coding and/or symbol mapping can be
`omitted. FIG. 2 illustrates a receiving end whose processes
`are inverse to those of the transmitting end.
`A code sequence is used for transmitting control informa-
`tion, which includes identification (ID) and synchronization
`information, to classify types of sequences in a communica-
`tion system. In order for more effective reception of the
`control information using code sequence, the code sequence
`can be adjusted or modified. Further, the code sequence can
`be applied to all of the channels that use code sequence for
`control signaling such as a random access channel (RACH),
`
`SAM SU NG 1026-0021
`
`SAMSUNG 1026-0021
`
`

`
`US 7,746,916 B2
`
`5
`downlink/uplink reference symbol, charmel quality inforrna-
`tion
`(CQI),
`and Acknowledgement
`(ACK)/Negative
`Acknowledgement (NACK).
`FIG. 3 is a flow diagram illustrating adjusting a code
`sequence. More specifically, a length of the code sequence is
`defined as N, a number of codes in the code sequence is
`defined as NMLN, and a code sequence set defined as
`
`aNs5q7NxN -
`
`In operation, the code sequence set
`
`aNs5q7NxN
`
`having Nseq N number of codes can be extended to a code
`sequence set
`
`aN55q7MxN
`
`having NMLM number of codes.
`Equation
`
`61N55qiNxN
`
`is a matrix ofNseq
`
`iN><N of
`
`Nmrl
`1
`0
`_
`aN55qiNxN — [“Ns5q_NxN aN5gq7NxN"- HNWLNXN]
`
`T
`
`k
`» and HNWLNXN
`
`is a row vector of
`
`a*Ns,q_N.N = La*Ns,q_NXN<0>a*N,,q_N.N<1>. . .a*NmLN.N<N -1) J.
`
`Furthermore,
`
`k
`HNWLNXN ("J
`
`5
`
`1 0
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`.
`.
`indicates n(:0, l, 2,
`seq
`N iN—l) code sequence.
`Referring to FIG. 3, a code sequence set
`
`.
`
`, N—l) element of k(:0,
`
`l, 2,
`
`55
`
`6
`Noise (PN) code, and a Constant Amplitude Zero Auto-Cor-
`relation (CAZAC) code, among others to be used for initial
`synchronization, cell search, and channel estimation in the
`wireless communication system. The code sequence set hav-
`ing length M per each code type can be generated by various
`schemes as discussed. As for the CAZAC code, the value of
`length M is a smallest prime number greater than the value of
`length N, preferably.
`Subsequently, a code sequence set
`
`6lNmLMxN,
`
`having NMLM number of code sequences, can be generated
`where a resulting length of the code sequence is length N.
`More specifically, the code sequence set
`
`6lN55q_MxM ,
`
`having NMLM number of code sequences where each code
`sequence has length M (from step S301), can have elements
`of the code sequence removed. That is, elements which com-
`prise each code sequence can be removed from the code
`sequence allowing the length of the code sequence to be
`adjusted or shortened. Here, M—N number of elements can be
`removed from the code sequence whose length corresponds
`to length M. By removing elements from the code sequence
`with length M, a code sequence having length N can be
`generated. As discussed, N is smaller than M. Consequently,
`a code sequence set
`
`HNSW Mx/v,
`
`having NSeqiMnumber of code sequences in which each code
`sequence has length N, can be generated (S302).
`A code sequence is used for transmitting control informa-
`tion, which includes identification (ID) and synchronization
`information, to classify types of sequences in a communica-
`tion system. Currently in 3"’ Generation Partnership Project
`(3GPP) Long Term Evolution (LTE), a CAZAC sequence is
`being considered.
`The CAZAC sequence can be used by channels to output
`various IDs and information. The charmels include charmels
`
`for downlink synchronization (e.g., primary synchronization
`channel, secondary synchronization charmel, and broadcast
`channel), uplink synchronization (e.g., random access chan-
`nel), and pilot channels (e.g., data pilot and channel quality
`pilot). Further, the CAZAC sequence can be used in scram-
`bling as well as channels that use code sequence such as
`RACH.
`
`6lN55q_MxM ,
`
`Although there are various types ofthe CAZAC sequences,
`there are two types of often used CAZAC sequences—GCL
`CAZAC and Zadoff-Chu CAZAC. The Zadoff-Chu CAZAC
`
`60
`
`sequence can be defined by the following equations.
`
`having NMLM number of code sequence(s) where each code
`sequence has length M, can be generated based on the code
`generation algorithm based on code type in which a value of 65
`length M is a natural number greater than a value of length N
`(S301). Here, the code types include Hadamard code, Pseudo
`
`c(k; N, M): exp(
`
`J/7rMk(k + 1)
`N
`
`] (for odd N)
`
`[Equation 11
`
`SAM SU NG 1026-0022
`
`SAMSUNG 1026-0022
`
`

`
`US 7,746,916 B2
`
`8
`In Equation 6, A and M are natural numbers, and index(A)
`(:0, 1, 2, .
`.
`.
`, NSeqiM—1) is an index ofA in ascending order.
`In order to extend the CAZAC sequence where N:1024, a
`smallest prime number greater than 1024 is used. That is, the
`smallest prime number greater than 1024 is 1031 . As such, the
`code sequence set
`
`10
`
`61/\/seq WM
`
`7
`
`-continued
`
`c(k; N, M) = exp(
`
`J/7r/VI/(2
`N
`
`] (for even N)
`
`[Equation 2]
`
`Here, k denotes sequence index, N denotes a length of
`CAZAC to be generated, and M denotes sequence ID.
`Ifthe Zadoff-Chu CAZAC sequence and the GCL CAZAC
`sequence are expressed by c(k;N,M) as shown in Equations 1
`and 2, then the sequences have the following three (3) char-
`acteristics as presented in following equations.
`
`|c(k; N, M)| = 1 (for all k, N, M)
`
`[Equation 3]
`
`15
`
`RM_N(d) =
`’
`
`1,
`0,
`
`d = 0
`f
`)
`( or
`(for d ¢ 0)
`
`RMl,M2;N(d) = p (for all M1, M2 and N)
`
`[E
`
`t‘
`qua ion
`
`4]
`
`[Equation 5]
`
`20
`
`According to Equation 3, the CAZAC sequence always has
`a size of 1, and the CAZAC sequence of Equation 4 has an
`auto-correlation function denoted by a delta function. Here,
`the auto-correlation is based on circular correlation. Further,
`Equation 5 is a cross-correlation which is constant if N is a
`prime number,
`If the length to be applied in the wireless communication
`system for generating the CAZAC sequence is denoted by L,
`a method for generating the CAZAC sequence sets N of
`Equations 1 and 2 to equal L (N:L)—identified as step (1).
`Step (2) canbe identified by a methodwhere a value ofN is set
`to be a prime number greater than a value of length L for
`generating the CAZAC sequence.
`Referring to the characteristics of the generated CAZAC
`sequence having a specified length of L, if L is not a prime
`number, the generated CAZAC sequence can include M:1,
`2,
`.
`.
`. L—1 number of codes, some of which are repeated
`codes. In other words, the number of different codes is less
`than L—1 number of codes. On the contrary, if L is a prime
`number, there is L—1 number of different codes. The above
`descriptions may also be applied to other types of code
`sequences and are not
`limited to Zadoff-Chu CAZAC
`sequence.
`the following technique has been considered.
`Further,
`More specifically, if the length of code to be applied to the
`system is not a prime number, and there are a large number of
`codes to be used, a smallest prime number greater than L was
`selected. Using the selected prime number,
`the CAZAC
`sequence was generated, and discards or removes at least one
`element of the generated CAZAC sequence for use. This
`technique is different than the technique introduced with
`respect to step 1.
`For example, assume that a number of codes of a CAZAC
`code sequence (N) is 1024. The following equation can be
`used to express an algorithm for generating a Zadoff-Chu
`CAZAC code.
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`where M:1031 is applied to Equation 6.
`Since M (:1031) is a prime number, NSeqiM:1030. Fur-
`thermore, A can be referred to as a seed value used to generate
`a code sequence maintaining CAZAC properties. If M is a
`prime number, a total of M—1 number of code sequences can
`be generated. In other words, for example, if M:1024, a total
`of 512 (:1024/2 or N/2) number of code sequences are gen-
`erated. However, if M:1031, a total of 1030 number of code
`sequences (M—1) are generated. Moreover, the cross-correla-
`tion properties of the generated code sequence are better if M
`is a prime number than a composite number.
`In order to adjust or modify the CAZAC code sequence set
`
`aN55q7MxM
`
`where M:1031 to a code sequence set
`
`aN55q7MxM
`
`whose length is N:1024, M—N number of elements can be
`removed from index n:N, .
`.
`.
`, M—1, generating a code
`sequence set
`
`aN55q7MxN ,
`
`In determining the value of M, although the number ofcode
`sequences can increase with increase in value of N, it is
`preferable to determine the value of M based on the code
`sequence whose length is N that promotes maintenance of
`good correlation properties. In case of the CAZAC code,
`optimum correlation properties can be attained if the value of
`length M is the smallest prime number greater than the value
`of length N.
`If the code sequence set
`
`aN55q7MxN
`
`“index(A) (n) =
`
`VA7m(n + 1)
`exp[Iz
`M
`,A7m2
`exp 1;
`M
`
`,
`], when M 18 odd
`,
`,when M is even
`
`generated using length N:1024 is compared with the code
`sequence set
`
`60
`
`[Equation 6]
`
`aN5CgiMxN ,
`
`wheren=0, 1,2,... ,M—1
`
`65
`
`a total number code sequences of the former can be repre-
`sented by N/2 or 512 (:1024/2) code sequences having an
`
`SAM SU NG 1026-0023
`
`SAMSUNG 1026-0023
`
`

`
`US 7,746,916 B2
`
`9
`, N/2-1 (N:l024), and a total number ofcode
`.
`.
`index 0, 1,2, .
`sequences of the latter can be represented by M—l or 1030
`having an index 0, 1,2, .
`.
`.
`, M—2 (M:l03l).
`FIG. 4 illustrates cross-correlation properties of the gener-
`ated code sequence. More specifically, the cross-correlation
`properties of
`
`a*Nm]_M.N<k = 1. 2.
`
`.N..q_M -1)
`
`associated with the remaining NMLM ( l 02 9) code sequences
`for
`
`0
`aN55q7MxN
`
`code sequence of the code sequence set
`
`61/\/seq Mm-
`
`The figure illustrates this with respect to amplitude, code
`index, and time index.
`Further, FIG. 5 illustrates a generated CAZAC sequence
`
`aNs5q7NxN
`
`using N(:l024). More specifically,
`cross-correlation properties of
`
`the figures illustrate
`
`a*Nmq_M.N<k = 1. 2.
`
`.N..q_M -1)
`
`regarding the remaining NSeqiN(5l 1) code sequences. The
`figure illustrates this with respect to amplitude, code index,
`and time index. Between FIG. 4 and FIG. 5, the cross-corre-
`lation properties of the generated code sequence of FIG. 4 are
`better.
`
`FIG. 6 illustrates a cross-correlation properties cumulative
`distribution function (CDF) of the code sequences that can be
`generated according to the code sequence
`
`61/\/seq M;/v
`
`and the CAZAC sequence
`
`aNs5q7NxN
`
`when N:l024.
`
`FIG. 7 illustrates the cross-correlation properties CDF of
`the code sequences that can be generated based on the
`CAZAC sequence generated using the prime number of
`N:l03l and a code sequence set
`
`10
`
`aN55q7MxN
`
`having length of 1024 (seven (7) elements removed). The
`performance lines of FIGS. 4-7 indicate that
`the code
`sequence set with seven (7) elements removed has equivalent
`cross-correlation properties compared to the original code
`sequence set.
`As discussed, the codes in addition to the CAZAC code are
`available, such as the PN code and the Hadamard code. The
`discussion with respect to the CAZAC code sequence can
`also be applied to the PN code and the Hadamard code. With
`respect to the PN code, a modular shift register generator is
`used to generate the code sequences. If a number of shift
`registers generated is represented by N, a code sequence
`having a length of 2N—l is generated. Thereafter, a value ‘‘I’’
`is added to the shift register, resulting in a length 2N+1— l, and
`then, adjust the length to equal 2N.
`With respect to the Hadamard codes, a number of code
`sequences, which equal the length ofthe code sequence, make
`up a code sequence. However, for example, if M number of
`code sequences having length N is required (M>N), then M
`number of code sequences having length M are generated,
`followed by removing a specified number of elements to
`make the length of the code sequence equal length N.
`FIG. 8 illustrates a method ofgenerating CAZAC sequence
`using a length required by a communication system. That is,
`the required (or desired) length of the CAZAC sequence can
`be represented by length L. Further, the codes types can be
`extended. However, since a generated code sequence can be
`truncated or have elements discarded to correspond to the
`desired length L, the auto-correlation and cross-correlation
`properties of the truncated code sequence can experience
`deterioration. Similarly, even if a code sequence portion is
`added/attached to the generated code sequence (e.g., zero-
`padding or cyclic prefix) to correspond to the desired length
`L, the auto-correlation and cross-correlation properties can
`experience deterioration. Here, auto-correlation properties
`relate to the auto-correlation value being 1 when the delay is
`0. Otherwise, the auto-correlation value is 0 when the delay is
`a value other than 0. Further, the cross-correlation properties
`having a constant value is negatively affected.
`Assuming that the code sequence having poor auto-corre-
`lation and cross-correlation properties are removed,
`the
`remaining number of code sequences may be less than L—l.
`In order to attain a desired length and a maximum number
`of CAZAC sequence types corresponding to the desired
`length, a smallest prime number, X, greater than the desired
`length, L, O(>L) can be selected. Although the CAZAC
`sequence can be generated using X, due to deterioration ofthe
`correlation properties, the correlations properties of CAZAC
`sequence as shown in Equations 4 and 5 carmot be attained.
`Further, when selecting a length of the generated code
`sequence, the length that is nearest to the desired length L
`which is between a smallest prime number larger than the
`desired length or a largest prime number smaller than the
`desired length can