WO2009028876A2 - Method for generating sequence in wireless communication system - Google Patents

Abstract

A method of generating a sequence includes deciding a length of an initial sequence according to allocated radio resources, deciding a random seed according to the length of the initial sequence, generating an iterated sequence by iterating the initial sequence by predetermined times, and selecting the iterated sequence when the iterated sequence satisfies a threshold. Cell planning is facilitated since the number of sequences can be increased under the same radio resource.

Description

Description

METHOD FOR GENERATING SEQUENCE IN WIRELESS COMMUNICATION SYSTEM

Technical Field

[1] The present invention relates to wireless communication, and more particularly, to a method of generating sequences in a wireless communication system such that a correlation characteristic and a cubic metric (CM) characteristic are guaranteed and the number of the sequences is increased in allocated radio resources. Background Art

[2] Third generation partnership project (3GPP) mobile communication systems based on a wideband code division multiple access (WCDMA) radio access technique are widely spread all over the world. High-speed downlink packet access (HSDPA) that can be defined as a first evolutionary stage of WCDMA provides 3GPP with wireless access technique that is highly competitive in the mid-term future. However, since requirements and expectations of users and service providers are continuously increased and developments of competing radio access techniques are continuously in progress, new technical evolutions in 3GPP are required to secure competitiveness in the future.

[3] One of systems that have been considered in systems subsequent to the third generation is an orthogonal frequency division multiplexing (OFDM) system that is able to attenuate inter-symbol interference with low complexity. The OFDM is adapted to map serially input data symbols into subcarriers and transmit the subcarriers. Sub- carriers keep orthogonality with each other in the frequency domain. Each orthogonal subcarrier experiences independent frequency selective fading and can have minimized inter-symbol interference. Orthogonal frequency division multiple access (OFDMA) refers to a multiple access scheme using the OFDM as a modulation method. The OFDMA provides each user with at least one orthogonal subcarrier. Generally the subcarriers are allocated to respective users independently.

[4] In the wireless communication system, sequences are widely used. A sequence is used to carry information or used for signal detection, channel estimation, multiplexing and so on. In the OFDM/OFDMA, a transmitter maps the elements of a sequence to the subcarriers in order to transmit sequence. A good correlation characteristic of the sequence is needed to improve detection performance in a receiver.

[5] In general, the length of a sequence depends on allocated radio resources since the amount of radio resources allocated to one user is limited. The number of available sequences is limited under the length of a base sequence. This is because orthogonality needs to be guaranteed between sequences in order to distinguish a user or signal from other users or signals. The number of orthogonal sequences to be generated from the base sequence generally depends on the length of the base sequence.

[6] To increase the number of available sequences in a given length is required to increase the capacity of the wireless communication system because the number of users, which can be allocated at once, is determined according to the number of available sequences.

[7] A variety of methods for increasing the number of sequences in a given length have been disclosed. According to Korean Patent Application No. 10-2005-0126307, sequences are generated by iterating a specific sequence once or more and masking the iterated sequence with an orthogonal code.

[8] In the wireless communication system, sequences need to have a good correlation characteristic to improve detection performance in a receiver and a good peak- to-average power ratio (PAPR)/cubic metric (CM) characteristic to reduce power consumption in a transmitter.

[9] There is a need for a method of generating sequences, in which the correlation characteristic and the PAPR/CM characteristic are taken into consideration and the number of sequences can be increased in a given length. Disclosure of Invention Technical Problem

[10] A method is sought for generating sequences, which can increase the number of sequences while keeping the PAPR/CM characteristic.

Technical Solution

[11] In an aspect, a method of generating a sequence in a wireless communication system includes deciding a length of an initial sequence according to allocated radio resources, deciding a random seed according to the length of the initial sequence, generating an iterated sequence by iterating the initial sequence by predetermined times, and selecting the iterated sequence when the iterated sequence satisfies a threshold.

[12] In another aspect, a method of generating a sequence in a wireless communication system includes deciding a length of an initial sequence according to allocated radio resources, deciding a random seed according to the length of the initial sequence, generating an iterated sequence by iterating the initial sequence by predetermined times, and selecting the iterated sequence when the iterated sequence satisfies a first threshold and a second threshold.

[13] In still another aspect, a method of generating a sequence in a wireless communication system includes generating a sequence, and selecting the sequence when the sequence satisfies a first threshold and a second threshold, wherein the first threshold is based on a CM and the second threshold is based on a cross correlation. Advantageous Effects

[14] Cell planning is facilitated since the number of sequences can be increased under the same radio resource. Since a mean cross-correlation value between sequences is small and cross-correlation exceeding a specific value is not generated, good BLER characteristic can be obtained. Brief Description of the Drawings

[15] FIG. 1 is a block diagram showing a wireless communication system.

[16] FIG. 2 is a flowchart illustrating a method of generating sequence in accordance with an embodiment of the present invention.

[17] FIG. 3 is a flowchart illustrating a method of generating an iterated sequence.

[18] FIG. 4 is a graph showing a probability density function (PDF) and a cumulative distribution function (CDF) of a sequence generated in 1 resource block.

[19] FIG. 5 is a graph showing the comparison of a generated sequence and a CDF of a

Zadoff-Chu (ZC) sequence by cyclic copy and truncation.

[20] FIG. 6 is a graph showing a PDF and CDF of a sequence generated in 1 resource block.

[21] FIG. 7 is a graph showing the comparison of a generated sequence and a CDF of a

ZC sequence by cyclic copy and truncation.

[22] FIG. 8 is a graph showing a PDF and CDF of a sequence generated in 1 resource block.

[23] FIG. 9 is a graph showing the comparison of a generated sequence and a CDF of a

ZC sequence by cyclic copy and truncation.

[24] FIG. 10 is a graph showing a PDF and CDF of a sequence generated in 1 resource block.

[25] FIG. 11 is a graph showing the comparison of a generated sequence and a CDF of a

ZC sequence by cyclic copy and truncation.

[26] FIG. 12 is a graph showing a PDF and CDF of a sequence generated in 2 resource blocks.

[27] FIG. 13 is a graph showing the comparison of a generated sequence and a CDF of a

ZC sequence by cyclic copy and truncation. Mode for the Invention

[28] FIG. 1 is a block diagram showing a wireless communication system. The wireless communication system is widely deployed all over the world in order to provide various communication services such as voice, packet data, etc.

[29] Referring to FIG. 1, a wireless communication system includes a user equipment

(UE) 10 and a base station (BS) 20. The UE 10 can be fixed or mobile and can be referred to as another terminology, such as a mobile station (MS), a user terminal (UT), a subscriber station (SS), a wireless device or the like. The BS 20 generally is a fixed station that communicates with the UE 10 and can be referred to as another terminology, such as an evolved-NodeB (e-NB), a base transceiver system (BTS), access point or the like. There are one or more cells within the coverage of the BS 20. Downlink means a communication from the BS 20 to the UE 10, and uplink means a communication from the UE 10 and the BS 20.

[30] A wireless communication system can be an orthogonal frequency division multiplexing (OFDM) / orthogonal frequency division multiple access (OFDMA) based system. The OFDM employs a plurality of orthogonal subcarriers. The OFDM employs an orthogonality characteristic between inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT). In a transmitter, data experiences IFFT and is then transmitted. In a receiver, FFT is performed on a received signal in order to restore original data. A transmitter uses IFFT so as to combine multiple subcarriers, and a receiver uses corresponding FFT so as to split multiple subcarriers.

[31] A sequence used in the wireless communication system needs to have orthogonality with excellent auto-correlation and cross-correlation. A sequence having orthogonality is called an orthogonal sequence. An example of the orthogonal sequence is a constant amplitude zero auto-correlation (CAZAC) sequence.

[32] One example of the CAZAC sequence is a Zadoff Chu (ZC) sequence. A ZC sequence c(k) having a length of N can be expressed as shown:

[33] MathFigure 1

[Math.l]

[34] where 0≤k<N-l, and M is a root index and is a natural number less than or equal to

N. N is a relatively prime to M. This means that, once N is determined, the number of root indices is equal to the number of available ZC sequences.

[35] The ZC sequence c(k) has the following three characteristics.

[36] MathFigure 2

[Math.2]

| c(A-)| = l for all k, N, M

[37] MathFigure 3 [Math.3]

[38] MathFigure 4

[Math.4]

R _{M M}. _j^d)= const for all M₁ M₂

[39] Equation 2 shows that the ZC sequence always has a magnitude of 1'. Equation 3 shows that auto-correlation of the ZC sequence is indicated by a Dirac-delta function. The auto-correlation is based on circular correlation. Equation 4 shows that cross correlation is always constant.

[40] The ZC sequence can keep its characteristic even after experiencing discrete Fourier transform (DFT) or inverse discrete Fourier transform (IDFT). Thus, the ZC sequence can be easily applied to not only OFDM/OFDMA systems, but also single carrier- frequency division multiple access (SC-FDMA) systems that perform DFT spreading at the IFFT front end.

[41] In general, when frequency division multiple access (FDMA) such as OFDMA is used, a basic radio resource allocation unit is used to allocate radio resources. Hereinafter, it is assumed that the radio resource allocation unit in the frequency domain is called a resource block, and one resource block includes 12 subcarriers. Accordingly, a ZC sequence of the length 12 can be mapped to one resource block.

[42] The number of ZC sequences with different root indices from a base ZC sequence having the length 12 is 4. This is because when the length of the base ZC sequence is not a prime number, the number of the ZC sequences to be generated from the base ZC sequence depends on the number of prime numbers less than or equal to the length. In other words, when the length N of the base ZC sequence is a prime number, the number of the ZC sequences to be generated from the base ZC sequence is N-I.

[43] There are various methods for increasing the number of ZC sequences whose length is not a prime number.

[44] For an example, there is a method of generating a truncated sequence. When N is not a prime number, a ZC sequence having a length which is a prime number greater than N is generated. The generated ZC sequence is truncated as long as N. This is disadvantageous in that it deteriorates auto-correlation and cross-correlation and increases the PAPR/CM, but is advantageous in that it can greatly increase a total number of sequences.

[45] For another example, there is a method of generating a ZC sequence having a length which is the greatest prime number among natural numbers smaller than N which is not a prime number. The generated ZC sequence is made into a ZC sequence having the length N through zero-padding. Zero-padding is performed from a first element, corresponding to the greatest prime number among natural numbers smaller than N, to an Nth element. This can deteriorate auto-correlation and cross-correlation and increase the PAPR/CM. Deterioration can also occur even in channel estimation in zero-padded subcarriers.

[46] For still another example, there is a method of, when N is not a prime number, generating a ZC sequence having a length which is the greatest prime number among natural numbers smaller than N and then performing cyclic copy. A ZC sequence having the length N is generated by cyclically copying the front part of the generated ZC sequence to the end of the ZC sequence. This can deteriorate auto-correlation and cross-correlation, but can increase the number of sequences. Further, this is advantageous in that it can generate sequences of many indices with a low PAPR/CM.

[47] In the above, it can be said that the method of generating sequences by employing truncation or cyclic copy is superior to the method using zero-padding. However, when it is assumed that a sequence, having a lower CM as compared with a case where data is modulated using quadrature phase shift keying (QPSK), is used, even though the method of increasing the number of sequences is used, the number of indices of a sequence having a small CM as compared with a case where data is modulated using QPSK still is not sufficient since only 6 root indices for one resource block are obtained. For two resource blocks, 8 root indices are obtained by using the truncation method and 12 root indices are obtained by using the cyclic copy method. Insufficient number of sequences makes cell planning very complicated, and is not appropriate to be used in control channels in which many control signals are multiplexed.

[48] Hereinafter, how to increase the number of sequences having lower CM as compared with a case where data is modulated using QPSK and how to improve cross-correlation characteristic are disclosed.

[49] FIG. 2 is a flowchart illustrating a method of generating sequence in accordance with an embodiment of the present invention.

[50] Referring to FIG. 2, in step SI lO, the length N of a sequence to be obtained is decided and a random seed suitable for the length is decided. The length N of the sequence depends on the size of an allocated resource block. For example, assuming that one resource block which is composed of twelve subcarriers is allocated to the sequence and the length N is 12. The random seed is a value having a complex number that can randomly be generated and can use a QPSK constellation point, a random complex number, one of the elements of the ZC sequence shown in Equation 1 or the like.

[51] In step S 120, the sequence is iterated as many as predetermined times such that the sequence has a flat attribute in the time domain and frequency domain. This is described later on with reference to FIG. 3. The iterated and generated sequence is referred to as an iterated sequence.

[52] In step S 130, a CM for the iterated sequence is calculated. The CM of the iterated sequence is compared with a first threshold (Th_CM)-

[53] In step S 140, when the CM of the iterated sequence is greater than the first threshold

(Th_CMX a random seed is selected again and a new iterated sequence is generated. The first threshold (Th_CM) can use a CM of QPSK.

[54] In step S 150, when the CM of the sequence is smaller than the first threshold (Th_CMX it is determined whether cross-correlation between sequences fulfills a predetermined maximum allowable cross-correlation in consideration of the entire circular shift of a selected root sequence. The iterated sequence has a characteristic of a CAZAC sequence and hence the iterated sequence becomes a root sequence. Although the root sequence is cyclically shifted, orthogonality between sequences is maintained. The maximum allowable cross-correlation becomes a second threshold. If, as a result of the determination, the maximum allowable cross-correlation is not fulfilled, a random seed is selected again. If, as a result of the determination, the maximum allowable cross- correlation is fulfilled, the sequence is selected as a desired sequence.

[55] As a result of comparing an iterated sequence and at least one threshold, if threshold is satisfied, the iterated sequence is selected and, if threshold is not satisfied, a new iterated sequence is generated. In the case in which a threshold is based on CM, an iterated sequence guarantees a desired CM. If a threshold is based on a cross-correlation value of an iterated sequence, the iterated sequence may not have a cross- correlation value higher than the threshold.

[56] A generated sequence has a low mean cross-correlation as compared with an existing sequence, and there is no sequence having a value higher than a maximum allowable cross-correlation between sequences. In addition, even in the number of sequences, the number of sequences smaller than QPSK CM is more than that of existing ZC sequences.

[57] FIG. 3 is a flowchart illustrating a method of generating an iterated sequence.

[58] Referring to FIG. 3, in step S121, it is assumed that an initial sequence is C₁ where T denotes an iteration number, a capital letter 'C denotes a sequence in the frequency domain, and a small letter 'c' denotes a sequence in the time domain. The initial sequence having a length N can be expressed as shown below.

[59] MathFigure 5

[Math.5]

Q= (C₁( I), C₁^) ,..., C,(JV) } [60] For example, when a random seed is selected as a QPSK constellation point, the random seed becomes cχ«) e { i +_/-, i -i, - i +/-, - i -7 } , » - i , ..,_Jv

[61] In step S 122, the sequence C₁ is normalized to thereby obtain a normalized frequency domain sequence as shown below. [62] MathFigure 6

[Math.6]

[63] In step S 123, IDFT is performed on the normalized frequency domain sequence to thereby obtain a time domain sequence C₁. [64] MathFigure 7

[Math.7]

[65] In step S 124, the time domain sequence C₁ is normalized to obtain a normalized time domain sequence as shown below. [66] MathFigure 8

[Math.8]

[67] In step S 125, the iteration number i is iterated until it becomes greater than a maximum iteration number M. In step S 126, if the iteration number i is smaller than the maximum iteration number M, i=i+l is set. DFT is performed on the normalized time domain sequence in order to obtain a frequency domain sequence. The frequency domain sequence is set as an initial sequence and the iteration number i is iterated.

[68] After significant iterations such as M=IOOO are performed, a generated sequence shows almost the same characteristic as that of a CAZAC sequence. The sequence that is iterated as many times as the maximum iteration number becomes an iterated sequence which can be a frequency domain sequence or a time domain sequence depending on a system.

[69] FIG. 4 is a graph showing a PDF and a CDF of a sequence generated in 1 resource block. FIG. 5 is a graph showing the comparison of a generated sequence and a CDF of a ZC sequence by cyclic copy and truncation. A maximum allowable correlation error is set to 0.45 and six cyclic shifts are considered.

[70] The total number of root sequences is 10 and a mean cross-correlation is 0.2284. The generated root sequences X(k) are shown below, where k denotes an index.

[71] X(l)={-0.15873+0.22068i, 0.035374-0.28679i, 0.11742+0.2698i, 0.10738+0.27987i,

-0.04899-0.29821, 0.070514-0.28384i, -0.24076+0.13367i, -0.011174+0.30043i, - 0.25501+0.085944i, -0.27306+0.12834i, -0.16354+0.22155i, -0.052915-0.28462i}

[72] X(2)={0.23797-0.16203i, 0.26094-0.12206i, 0.071584+0.27915i,

0.067116+0.2800U, -0.28943+0.000047i, 0.25133+0.14295i, -0.21729+0.19096i, 0.27046-0.10317i, 0.28152-0.062703i, 0.25388-0.13587i, -0.073194-0.27999i, - 0.15275+0.24525i}

[73] X(3)={0.28694+0.03294i, -0.22501+0.1806i, -0.28573+0.040449i,

0.15599-0.24276i, 0.27449-0.088874i, -0.23643-0.16573i, -0.10448+0.26926i, 0.11775+0.26341i, 0.050489+0.28417i, -0.13283+0.25648i, 0.28245-0.060202i, - 0.17434+0.2302H}

[74] X(4)={0.2063+0.20192i, 0.18756-0.21943i, 0.07412-0.279i, -0.10845+0.26754i,

0.26587-0.11244i, -0.14483-0.2497 Ii, 0.2878-0.022593i, -0.28866+0.0031165i, - 0.16794-0.23479i, -0.26664-0.11064i, -0.11027-0.26678i, 0.28479+0.04724i}

[75] X(5)={0.1436+0.2507 Ii, -0.20283+0.20506i, -0.0062058-0.28852i,

0.11578+0.26473i, 0.1576+0.2421i, 0.20808-0.20032i, 0.20622-0.20237i, - 0.24974-0.14429i, 0.28849+0.0037839i, -0.09146-0.27359i, 0.18219+0.22357i, 0.2079+0.2004i}

[76] X(6)={-0.20697-0.2229i, -0.12815-0.27148i, -0.13014-0.26249i, -0.17945+0.24427i,

0.26364+0.062527i, -0.13053+0.26129i, -0.27076-0.051977i, -0.26009+0.15053i, 0.25114-0.10358i, -0.16689+0.23444i, -0.26792+0.062897i, 0.22855-0.17327i}

[77] X(7)={ -0.056939-0.28299i, 0.17579+0.22897i, 0.062398+0.28186i,

0.27798+0.077837i, 0.24839+0.147 Ii, -0.15521+0.24339i, -0.17566+0.22908i, 0.2881 l+0.018175i, 0.17767-0.22752i, -0.075565+0.2786i, 0.14506-0.24959i, - 0.28652+0.0353i}

[78] X(8)={-0.24276+0.15626i, 0.27564-0.085709i, 0.23624+0.16586i, -

0.052283-0.28389i, -0.02292+0.28777i, -0.049912-0.28435i, -0.15424-0.24403i, 0.087943+0.27493i, -0.2783 l+0.076733i, -0.24831-0.14728i, -0.20154-0.20663i, - 0.25095-0.14263i}

[79] X(9)={-0.12994+0.25789i, 0.28237+0.059535i, 0.12165-0.26179i,

0.048903-0.28424i, -0.15757-0.24176i, 0.21592-0.1916H, 0.23557-0.1664H, 0.22349+0.18312i, -0.28816-0.017187i, -0.090474-0.27423i, 0.028545+0.28752i, - 0.099097-0.27113i}

[80] X(10)={-0.23151+0.17251i, 0.16971-0.23354i, 0.27804-0.077621i, - 0.041718+0.28569i, -0.23121+0.17277i, -0.14172+0.25149i, -0.28509+0.045268i, - 0.041329+0.28566i, 0.17416+0.23022i, 0.16958-0.2336i, -0.28514+0.04513 Ii, 0.28594+0.039635i}

[81] FIG. 6 is a graph showing a PDF and CDF of a sequence generated in 1 resource block. FIG. 7 is a graph showing the comparison of a generated sequence and a CDF of a ZC sequence by cyclic copy and truncation. A maximum allowable correlation error is set to 0.45 and six cyclic shifts are taken into consideration.

[82] The total number of root sequences is 15 and a mean cross-correlation is 0.2410. The generated root sequences X(k) are shown below.

[83] X(l)={-0.15291-0.24459i, -0.17052-0.23283i, 0.10444+0.26903i, -

0.06483+0.28108i, 0.24716-0.14946i, -0.22461-0.18142i, 0.28767-0.026757i, 0.28582+0.039498i, 0.26586+0.11213i, 0.22233+0.18449i, 0.1171-0.2639H, 0.080392+0.27742i}

[84] X(2)={-0.060124+0.28227i, 0.022597+0.28788i, -0.27455+0.088962i,

0.23908-0.16193i, 0.2745-0.089105i, 0.022597+0.28788i, 0.060525-0.28219i, 0.008601 l+0.2886i, 0.2745-0.089105i, 0.24466-0.15333i, -0.27455+0.088962i, 0.008601 l+0.2886i}

[85] X(3)={-0.16292-0.2383i, 0.093207+0.27321i, 0.12492-0.26025i, -

0.28784+0.021944i, 0.093207+0.2732H, -0.12492+0.26025i, -0.28784+0.021944i, - 0.093207-0.2732H, 0.28784-0.021944i, -0.16292-0.2383i, -0.093207-0.27321i, - 0.28784+0.021944i}

[86] X(4)={0.18173+0.22429i, -0.23359-0.16962i, 0.18907+0.21814i, 0.16019-0.24015i,

-0.285 l l+0.045237i, -0.27543+0.08645i, 0.056536+0.28308i, 0.12788+0.2588 Ii, - 0.13363+0.25589i, -0.030096+0.287 Ii, -0.27343-0.09258 Ii, 0.020561-0.28794i}

[87] X(5)={0.18185-0.2242i, 0.068446+0.28044i, 0.18185-0.2242i, 0.13638+0.25443i,

0.10324+0.26958i, -0.25443+0.13638i, -0.28509-0.045385i, 0.28044-0.068446i, - 0.28509-0.045385i, -0.25443+0.13638i, 0.10324+0.26958i, 0.13638+0.25443i}

[88] X(6)={0.16404-0.23754i, 0.23928+0.16149i, -0.10648-0.26832i, 0.17109+0.2325 Ii,

-0.28414+0.0509761, -0.21126-0.19673i, 0.25174-0.14128i, 0.15002-0.24663i, - 0.24203+0.15734i, 0.21563+0.19193i, 0.27948-0.072292i, 0.28612-0.038349i}

[89] X(7)={-0.28038+0.068695i, -0.20029+0.20789i, -0.0053723-0.28863i, -

0.24684-0.14969i, 0.061502-0.28205i, 0.27426-0.090079i, -0.28544-0.043096i, - 0.17767-0.22752i, -0.2865 l-0.035253i, 0.17136+0.2323 Ii, -0.13024+0.25763i, 0.24293-0.15595i}

[90] X(8)={-0.28592+0.039821i, -0.11488-0.26483i, 0.10847-0.26752i,

0.039821+0.28592i, 0.26483-0.11488i, 0.2277-0.17744i, 0.17744+0.2277i, - 0.11488-0.26483i, 0.17744+0.2277i, 0.2277-0.17744i, 0.26483-0.11488i, - 0.26752-0.10847i} [91] X(9)={0.13663-0.25374i, -0.24862-0.144i, 0.07163 l-0.28042i, 0.24894-0.14764i,

0.27762-0.073973i, -0.27603+0.082816i, 0.069176+0.27927i, 0.28996+0.0022032i, 0.16015+0.24109i, 0.05723-0.28372i, 0.20659-0.20348i, -0.14856+0.24639i}

[92] X(10)={-0.23559-0.16683i, -0.20756-0.20063i, 0.17472+0.2298i, 0.17809+0.2272i,

0.17934+0.22621i, -0.10771+0.26783i, -0.28637+0.036412i, 0.20756+0.20063i, - 0.02668 l+0.28744i, 0.26402-0.11673i, -0.23216-0.17156i, 0.2331+0.17028i}

[93] X(l l)={0.0037813-0.28865i, 0.071056+0.27979i, 0.24791-0.1479i,

0.25958+0.1263 Ii, 0.12411-0.26063i, -0.23196-0.17184i, 0.28525+0.044319i, 0.287-0.03102i, -0.28553+0.042512i, -0.21963-0.18734i, 0.054822-0.28342i, - 0.27988-0.070713i}

[94] X(12)={-0.28862-0.0058334i, -0.045786+0.28502i, -0.10954+0.26709i, -

0.26791+0.1075 Ii, 0.2085-0.19965i, 0.27205+0.096565i, 0.28862+0.0058334i, - 0.27572+0.085494i, 0.20026+0.20792i, 0.26335+0.11825i, -0.098657-0.27129i, 0.034232+0.28664i}

[95] X(13)={0.28856+0.0082257i, -0.028199-0.28729i, 0.1514-0.24579i, -

0.22475-0.18117i, 0.28856+0.0082257i, 0.10406+0.26927i, 0.13716+0.25401i, - 0.28729+0.028199i, 0.28856+0.0082257i, 0.18117-0.22475i, -0.28856-0.0082257i, 0.26927-0.10406i}

[96] X(14)={0.037806+0.28619i, 0.12555+0.25994i, 0.28358+0.054014i, -

0.26882+0.1052H, -0.088743+0.2747i, 0.27653-0.082869i, 0.06041+0.28228i, - 0.26408+0.1166i, -0.0019584-0.28867i, -0.28854-0.0089168i, 0.11043-0.26672i, - 0.1314+0.25703i}

[97] X(15)={0.2828+0.046047i, 0.23466+0.16703i, -0.066145-0.28003i, -

0.18428-0.21989i, -0.23175-0.17252i, 0.22279+0.18597i, -0.090966-0.27468i, - 0.24309-0.15616i, 0.2901-0.022214i, -0.28758-0.035748i, 0.176-0.22924i, 0.27973+0.067385i}

[98] FIG. 8 is a graph showing a PDF and CDF of a sequence generated in 1 resource block. FIG. 9 is a graph showing the comparison of a generated sequence and a CDF of a ZC sequence by cyclic copy and truncation. A maximum allowable correlation error is 0.5 and 12 cyclic shifts are taken into consideration.

[99] The total number of root sequences is 11 and a mean cross-correlation is 0.2412. The generated root sequences X(k) are shown below.

[100] X(l)={0.23196+0.17182i, 0.04799 l+0.28464i, -0.2626+0.11993i, -

0.042449-0.28555i, 0.17016+0.23318i, 0.17942-0.22616i, 0.28022-0.06942i, - 0.24593-0.15118i, -0.082339+0.27668i, 0.24725+0.14897i, -0.23179+0.17206i, 0.22468+0.18128i}

[101] X(2)={ -0.2006-0.207561, 0.038132-0.28523i, -0.011562+0.28913i, -

0.22227-0.18559i, 0.14142+0.25078i, -0.26607+0.10966i, -0.2073 l+0.20094i, - 0.22284-0.18508i, -0.28918-0.011295i, 0.22766+0.17593i, 0.2508-0.14135i, -

0.22279-0.18513i} [102] X(3)={-0.10102+0.27662i, -0.26623-0.12048i, -0.18528+0.22597i, -

0.12417-0.26703i, 0.28067+0.068289i, -0.11756-0.2595 Ii, -0.27954-0.041434i,

0.18902+0.21839i, -0.25987+0.12606i, -0.22696+0.16836i, 0.18072+0.22024i,

0.25343+0.1386i} [103] X(4)={-0.0040032-0.28863i, -0.094284-0.27284i, -0.23252-0.17107i,

0.21813+0.18907i, -0.25405+0.13708i, 0.12746+0.25903i, -0.28833+0.013931i, -

0.072299-0.27947i, 0.28437-0.049694i, -0.20226-0.20596i, -0.28749+0.026263i,

0.22941-0.17526i} [104] X(5)={0.27901+0.074133i, -0.16803-0.23546i, -0.27768-0.078935i, -

0.27615-0.082519i, 0.054265-0.28396i, -0.27685-0.083182i, 0.13932+0.25244i, -

0.16552-0.23579i, -0.13376-0.25627i, 0.25173-0.14107i, -0.043012+0.28502i,

0.24989-0.14472i} [105] X(6)={0.1419+0.2514i, 0.11372-0.26533i, 0.023074+0.28775i, -0.15351-0.24447i,

0.21515-0.19248i, -0.22593-0.1797i, -0.28341-0.054892i, -0.27632+0.08359i, -

0.23409-0.1689H, 0.14372-0.25036i, 0.21516-0.19245i, -0.26476+0.11503i} [106] X(7)={-0.28863-0.0052039i, -0.28739-0.027182i, 0.21252+0.19537i,

0.13369-0.25586i, -0.18402-0.22243i, 0.27743+0.07976 Ii, -0.18593-0.22082i,

0.2039 l-0.20434i, 0.1971-0.2109H, 0.25475+0.13578i, -0.28867+0.00028528i, -

0.12245-0.26142i} [107] X(8)={-0.17523-0.2294i, -0.17277-0.23126i, -0.093515+0.2731 Ii,

0.24044+0.15976i, 0.28625+0.03729i, 0.20662+0.20159i, 0.25822+0.12906i, -

0.23916+0.16167i, 0.24928+0.14558i, -0.20204-0.20618i, 0.28262+0.0588 Hi, -

0.024601+0.28763i} [108] X(9)={ -0.25472+0.1035 Ii, 0.26122+0.15144i, 0.16638+0.24802i, -

0.22601-0.17052i, -0.26051+0.1123i, -0.29172+0.0098473i, 0.2812-0.062398i,

0.19194+0.24877i, 0.11916+0.26854i, 0.19771-0.20257i, 0.15312+0.22989i,

0.24247-0.12238i} [109] X(IO)=(0.18967-0.20177i, 0.28232-0.0012105i, -0.057968-0.2884i,

0.26672+0.16278i, -0.15054+0.24598i, -0.056908+0.28612i, -0.17579-0.22423i,

0.036096+0.2806 Ii, 0.1121+0.27748i, -0.2973-0.056232i, -0.11733+0.24836i,

0.039147+0.26804i} [110] X(l l)={0.084818-0.27466i, 0.22407-0.18574i, -0.02665+0.28921i, -

0.27035-0.1027i, 0.20207+0.20505i, 0.28895+0.03096i, 0.19502+0.20994i, -

0.27079-0.10792i, -0.016493+0.28807i, 0.22409-0.18183i, 0.072974-0.27735i,

0.28519-0.012043i} [111] FIG. 10 is a graph showing a PDF and CDF of a sequence generated in 1 resource block. FIG. 11 is a graph showing the comparison of a generated sequence and a CDF of a ZC sequence by cyclic copy and truncation. A maximum allowable correlation error is set to 0.53 and 12 cyclic shifts are taken into consideration.

[112] The total number of root sequences is 12 and a mean cross-correlation is 0.2339. The generated root sequences X(k) are shown below.

[113] X(l)={0.23498+0.16726i, 0.17016-0.23313i, 0.19887+0.2091 Ii, -

0.062537-0.28163i, -0.18266+0.22354i, -0.27718-0.081306i, 0.078986-0.27775i, - 0.16899+0.234H, -0.25952+0.12699i, -0.21364-0.19432i, -0.22035-0.1865i, - 0.27597+0.084304i}

[114] X(2)={ -0.28368-0.0534741, 0.24115-0.15868i, 0.15226-0.24526i, -

0.2763 l-0.083595i, 0.28272+0.0583 Hi, 0.26017+0.12507i, 0.020076+0.28798i, 0.16726+0.23528i, 0.17557-0.22914i, 0.26678+0.11028i, 0.048097-0.28464i, - 0.055142+0.28336i}

[115] X(3)={-0.066747+0.28085i, -0.008545+0.28855i, -0.05001-0.2843 Ii, -

0.027816-0.28733i, 0.26515-0.11414i, -0.18816-0.21893i, -0.2166-0.19084i, 0.008545-0.28855i, -0.22751+0.17769i, 0.20079-0.20741i, 0.25793+0.12963i, 0.04477-0.28518i}

[116] X(4)={ -0.27098-0.099512i, 0.064818-0.2813i, 0.24475-0.15308i, 0.26198-0.12125i, -0.18373+0.22266i, -0.23454-0.1683i, 0.095773+0.27233i, 0.28183+0.062513i, - 0.15508-0.24348i, 0.26028+0.12484i, -0.046835-0.28485i, -0.027524-0.28736i}

[117] X(5)={0.2864-0.036168i, 0.12247-0.26141i, 0.098248+0.27144i, 0.22809+0.17694i, -0.15834-0.24137i, 0.014009+0.28834i, -0.25113+0.14237i, 0.27603+0.084504i, 0.25494-0.13543i, 0.27824+0.076903i, -0.21379-0.19398i, 0.05871 l-0.28264i}

[118] X(6)={-0.1936+0.21413i, -0.14105+0.25187i, 0.071056-0.27979i, -

0.014514-0.2883H, 0.23847-0.16269i, -0.1267+0.25938i, -0.22096-0.18577i, - 0.16507+0.23683i, -0.098146+0.27148i, -0.2876+0.02488 Ii, 0.21775+0.18952i, - 0.21886-0.18823i}

[119] X(7)={-0.19226+0.21565i, -0.10832+0.26766i, 0.26686-0.11097i,

0.043339+0.28519i, -0.28669-0.031952i, 0.11023-0.26717i, 0.035359-0.28657i, - 0.24152+0.15854i, 0.2155+0.19159i, -0.17427+0.22999i, 0.17705+0.22786i, - 0.28786+0.016909i}

[120] X(8)={0.094901-0.27281i, 0.056686+0.28314i, 0.26884-0.10528i, 0.11391+0.2655i, -0.2788 l-0.075239i, -0.0843-0.2761i, -0.071016-0.27969i, -0.28554-0.040859i, - 0.26925+0.10397i, 0.21841-0.18863i, -0.18468-0.22165i, -0.27459+0.089066i}

[121] X(9)={-0.28716-0.02649i, 0.18431-0.22204i, -0.16677-0.2355i, 0.22178-0.18432i, - 0.23658-0.16579i, 0.026388+0.28753i, 0.1022+0.2703 Ii, -0.2876+0.022559i, 0.052646-0.28364i, 0.26341+0.11887i, -0.099908-0.2709 Ii, -0.18561-0.22138i}

[122] X(10)={ -0.020433-0.288i, 0.2074-0.20101i, 0.25008+0.1438i, 0.12536-0.25995i, 0.21865+0.18837i, 0.27851-0.075154i, -0.1483+0.24784i, 0.054802-0.28347i, 0.24165-0.1583H, -0.099593-0.2708 Ii, -0.28736+0.026107i, -0.058928+0.2828 li}

[123] X(l l)={-0.27763+0.079382i, 0.26574+0.11258i, 0.27327-0.093218i, -

0.035502-0.28641i, 0.21322+0.1947i, 0.26573+0.1126i, 0.27469-0.088973i, 0.26574+0.11258i, -0.2788+0.075194i, -0.035502-0.28641i, -0.20876-0.1995i, 0.26573+0.1126i}

[124] X(12)={0.28567+0.041768i, -0.028328-0.28743i, 0.23062+0.17348i, -

0.28574+0.040408i, 0.18321-0.22328i, 0.23153-0.17246i, -0.20979-0.19845i, - 0.24183+0.15738i, -0.035376-0.28645i, -0.22756-0.17753i, 0.28229+0.059716i, 0.28867-0.0080144i}

[125] FIG. 12 is a graph showing a PDF and CDF of a sequence generated in 2 resource blocks. FIG. 13 is a graph showing the comparison of a generated sequence and a CDF of a ZC sequence by cyclic copy and truncation. A maximum allowable correlation error is set to 0.4 and 12 cyclic shifts are taken into consideration.

[126] The total number of root sequences is 37 and a mean cross-correlation is 0.1768. But the mean cross-correlation of the ZC sequence by cyclic copy is 0.1919 and the number of the he ZC sequence by cyclic copy having lower CM than QPSK CM is 12. The mean cross-correlation of the ZC sequence by truncation is 0.1886 and the number of the he ZC sequence by truncation having lower CM than QPSK CM is 8.

[127] The generated root sequences X(k) are shown below.

[128] X(l)={-0.02298-0.20283i, 0.19749-0.051615i, 0.16537-0.11966i, -

0.099786-0.17807i, -0.14593-0.14272i, 0.20412-0.0010156i, 0.12097+0.16442i, 0.14976-0.1387i, 0.01427l+0.20362i, 0.10526+0.17489i, 0.0099325-0.20388i, 0.029298-0.20201i, 0.16334-0.12242i, 0.18796+0.079621i, 0.037723-0.2006Ii, 0.15734+0.13004i, -0.029409-0.20199i, -0.20294+0.021999i, 0.14539+0.14327i, - 0.18096-0.094454i, 0.0043073-0.20408i, -0.064455+0.19368i, -0.20158+0.032109i, - 0.05433+0.19676i}

[129] X(2)={0.097439+0.17849i, -0.01184-0.2039H, 0.20303+0.0201Hi,

0.14734+0.14394i, -0.188+0.078636i, -0.18486+0.088648i, -0.19331-0.0524H, 0.0038263-0.20522i, -0.20203+0.019376i, -0.19478-0.052794i, -0.074875-0.18829i, - 0.19092+0.071672i, 0.171-0.11238i, -0.20164+0.023233i, 0.033223+0.2010H, - 0.2031+0.007369Ii, 0.18948+0.075187i, -0.054474+0.19456i, -0.032861-0.20308i, 0.15037+0.13747i, 0.2041l-0.032083i, -0.13055-0.15863i, -0.20687+0.016826i, - 0.10392+0.17789i}

[130] X(3)={0.040296-0.20003i, 0.20139-0.033096i, -0.16064-0.12585i,

0.093692-0.18096i, 0.19317+0.066812i, -0.19461-0.060965i, -0.085538+0.18568i, - 0.20104-0.036315i, -0.11448+0.169i, 0.01428-0.20372i, 0.0090754+0.20379i, - 0.008568l+0.20405i, 0.19712-0.052765i, -0.2035l+0.015076i, 0.021323+0.20296i, 0.13308+0.1544i, 0.050742+0.1978 Ii, 0.20293+0.019545i, -0.20426+0.0036716i, - 0.13805-0.15007i, -0.11168+0.1707 Ii, 0.11242+0.17063i, -0.18166+0.093985i, - 0.20203+0.0295131}

[131] X(4)={-0.18975-0.075267i, -0.20117-0.034562i, 0.14823-0.14034i, -

0.17566+0.10399i, -0.19773+0.050664i, -0.021659+0.20296i, -0.20409-0.0044547i, - 0.2024 l-0.026327i, -0.11834+0.16633i, 0.14863-0.1399H, 0.20129-0.033942i, - 0.2041 l+0.0019806i, 0.19993-0.041148i, 0.14736-0.14126i, 0.20413-0.00031004i, - 0.18107+0.094229i, -0.14364+0.14502i, -0.19164+0.07029i, 0.15219+0.13605i, 0.041251-0.19992i, 0.13013+0.15726i, -0.1508-0.13758i, -0.18346-0.089506i, 0.028535+0.20213i}

[132] X(5)={0.1982+0.048813i, 0.034387-0.20124i, 0.18458+0.087123i,

0.072229-0.19097i, 0.18782-0.079775i, 0.13058+0.15692i, -0.031103-0.20176i, 0.13002+0.15737i, -0.19468-0.061456i, -0.072577-0.19074i, 0.17569-0.10393i, 0.17085+0.11166i, 0.12442+0.16182i, 0.0084529-0.20389i, 0.11185-0.17075i, - 0.1565-0.13098i, -0.19255-0.067763i, -0.15683+0.1306H, 0.18518+0.086004i, - 0.12113-0.16436i, -0.13238+0.15535i, -0.17315+0.10808i, 0.084612-0.18581i, - 0.13603-0.15223i}

[133] X(6)={0.20414+0.017378i, 0.16596-0.12317i, 0.13918-0.14926i, -

0.18107-0.094806i, 0.20267+0.01003i, 0.1991-0.045596i, 0.10195+0.17627i, - 0.18901-0.071264i, 0.068821+0.19608i, -0.056006-0.19406i, 0.19231-0.071568i, - 0.12204-0.1585Ii, -0.043006-0.2i, 0.2008l-0.0039021i, -0.14734+0.13622i, - 0.00040864+0.20342i, -0.048758-0.198i, -0.11281-0.17459i, -0.15608+0.12736i, - 0.086666-0.18488i, -0.01406+0.20646i, 0.12422+0.15438i, 0.0066837-0.2073i, 0.13188-0.16496i}

[134] X(7)={0.16687-0.11781i, -0.18995+0.075867i, 0.13557+0.15152i,

0.022979-0.20289i, -0.1943-0.062327i, -0.13216+0.15562i, -0.089475+0.18339i, 0.17488-0.10287i, 0.0037561-0.20437i, 0.1977-0.050115i, 0.19305+0.06894H, - 0.16905+0.11537i, -0.17427+0.10417i, -0.040829-0.20075i, 0.083838+0.18699i, - 0.19779+0.050257i, 0.12895-0.15792i, -0.04927+0.19728i, 0.012309-0.20372i, - 0.10696-0.17514i, -0.010549-0.20418i, -0.083878-0.18506i, -0.027845-0.20227i, - 0.19499-0.060725i}

[135] X(8)={0.1607+0.12586i, 0.068952-0.19213i, 0.087423-0.18446i, 0.17294+0.10844i, 0.096161-0.18005i, 0.14866+0.13988i, 0.14743-0.14117i, 0.16582+0.11903i, - 0.12815-0.15888i, 0.19497+0.06044i, -0.14536-0.1433Ii, -0.19634-0.055846i, 0.11263+0.17024i, 0.20405-0.0053374i, 0.18158-0.093257i, 0.15237+0.13584i, - 0.13231+0.15544i, -0.11904+0.16582i, 0.04098-0.19997i, -0.1751-0.1049H, 0.12369+0.16238i, -0.1683+0.1155Ii, -0.19887+0.046001i, 0.20268+0.024198i}

[136] X(9)={0.13114+0.15643i, 0.2038-0.01149i, -0.20067-0.037401i, 0.035385+0.20103i, -0.0026405+0.2041 Ii, 0.10963+0.17219i, -0.11953-0.16547i, - 0.1988+0.046316i, 0.058049-0.1957i, -O.O8O1O8+0.18775i, -0.18837+0.07864i, - 0.18522+0.085793i, 0.20094+0.035898i, 0.098514+0.17878i, 0.090713-0.18286i, 0.20348+0.016227i, 0.19654-0.055116i, 0.12563+0.16088i, -0.079516+0.188i, 0.19971+0.042205i, -0.15846-0.12867i, 0.073041-0.19061i, 0.19808+0.04929i, - 0.20262+0.0247 Hi}

[137] X(10)={ -0.062607-0.19349i, -0.17835-0.097502i, 0.064072-0.19438i,

0.021427+0.20329i, 0.033528-0.20159i, -0.19466-0.057615i, 0.19041-0.074193i, 0.13969-0.14677i, -0.18067+0.094552i, -0.013198+0.20376i, 0.20339+0.013755i, 0.05757+0.196i, 0.16165-0.12475i, 0.074444+0.19142i, -0.14577+0.14437i, 0.2047 l+0.0064597i, 0.017048+0.20396i, -0.17416-0.1034H, -0.20197+0.025499i, 0.17084+0.11153i, 0.17263+0.11128i, 0.16738+0.11557i, 0.20277+0.034147i, 0.016624+0.20318i}

[138] X(l l)={-0.031697+0.20164i, 0.20046-0.038529i, -0.20214+0.028414i,

0.1752+0.10472i, 0.1203+0.1649Ii, -0.16181+0.12446i, 0.022041+0.20293i, 0.19982-0.041617i, -0.16361-0.12206i, 0.19709+0.053056i, -0.14087+0.14772i, 0.2041l+0.00070613i, -0.037628-0.20065i, 0.053276-0.19705i, 0.052749-0.19718i, 0.062088-0.19447i, 0.16998+0.11303i, -0.19778+0.050494i, 0.0050407+0.20405i, 0.12325+0.16274i, 0.07436+0.19009i, -0.10594-0.17448i, 0.1056-0.17469i, 0.078666+0.18836i}

[139] X(12)={-0.12244-0.16332i, -0.14838-0.14018i, -0.1133+0.16979i, -

0.20389+0.0098389i, -0.067524+0.19263i, 0.062878-0.1942i, 0.0070122+0.204i, - 0.090667-0.18288i, -0.14718+0.14144i, -0.10838+0.17297i, 0.20198+0.029482i, 0.1033-0.17606i, -0.19276-0.067153i, 0.20171+0.031301i, 0.18195-0.092522i, - 0.038028+0.20055i, -0.018176+0.20331i, -0.19722+0.052653i, 0.031675+0.20165i, 0.20133-0.03366i, 0.02934l-0.202i, 0.18326+0.089912i, -0.20199+0.029428i, - 0.10515-0.17496i}

[140] X(13)={0.1685-0.11522i, -0.025467-0.20253i, 0.0026446-0.2041Ii,

0.14913+0.13938i, 0.0015185+0.20412i, 0.19+0.074622i, 0.20166+0.031617i, 0.15486+0.13299i, 0.1779-0.10008i, 0.13472+0.15335i, -0.029467-0.20199i, - 0.19737+0.052077i, 0.025472-0.20253i, 0.19084+0.072421i, 0.036412-0.20085i, - 0.037905+0.20057i, 0.07472+0.18996i, -0.19207-0.069102i, -0.14755+0.14105i, 0.19537+0.05914i, -0.20345-0.016616i, -0.057283-0.19592i, 0.18095+0.094475i, - 0.023265+0.20279i}

[141] X(14)={0.16924+0.1128i, 0.047141-0.19847i, -0.056892-0.19585i, -

0.10991-0.17265i, -0.19517+0.058503i, 0.20152+0.031584i, -0.059094-0.19503i, - 0.039806+0.2002H, 0.18144+0.093917i, -0.1661-0.11824i, -0.12046-0.16466i, - 0.19908-0.041912i, -0.072498-0.19189i, 0.16104-0.1262i, 0.2005+0.03846i, - 0.090161-0.18355i, 0.18756+0.080998i, -0.20319+0.021072i, 0.19371-0.063716i, 0.14363+0.1448i, 0.19422+0.062809i, -0.17596+0.10277i, 0.13314-0.1548 Ii, 0.2045+0.010661i}

[142] X(15)={0.19442-0.062177i, 0.20344+0.016637i, -0.11316+0.16989i,

0.081131+0.18731i, -0.18502+0.086218i, -0.20407-0.0049093i, 0.094004+0.18119i, 0.094417+0.18098i, 0.18882+0.077546i, -0.16257-0.12344i, -0.18913-0.076782i, - 0.10299+0.17624i, 0.038663-0.20043i, 0.13712-0.15121i, -0.0027695+0.2041 Ii, - 0.15164-0.13664i, -0.12637-0.1603 Ii, 0.0019099+0.20412i, -0.20387-0.010186i, - 0.10201+0.1768 Ii, -0.16513-0.11999i, 0.043829+0.19936i, 0.14266-0.146i, - 0.00041919+0.20412i}

[143] X(16)={-0.19936+0.043861i, 0.15288+0.13525i, -0.18697-0.081901i, -

0.016495+0.20346i, -0.041058-0.19995i, -0.14025+0.1483 Ii, -0.045609-0.19896i, 0.20409-0.0039735i, -0.039484+0.20027i, 0.069512-0.19192i, 0.19203+0.069215i, 0.11028+0.17177i, 0.077712+0.18875i, -0.16665-0.11787i, -0.19692-0.053761i, 0.15312+0.13499i, 0.18597-0.084148i, 0.11616-0.16785i, -0.20188+0.0302i, - 0.14905+0.13946i, -0.20053+0.03815i, -0.12936+0.1579i, 0.11484+0.16875i, - 0.023408+0.20278i}

[144] X(17)={0.12891+0.15813i, -0.14804-0.14025i, 0.19213-0.070684i,

0.20112-0.033485i, -0.20233+0.025199i, 0.056451-0.19654i, -0.19567+0.056854i, - 0.19471+0.06153H, 0.17651+0.10219i, -0.19918+0.046514i, 0.013429+0.20393i, - 0.18894-0.076248i, -0.16419-0.12084i, -0.071021+0.19156i, 0.20444-0.0036066i, 0.021767+0.20223i, -0.11331+0.16997i, -0.14688+0.1421 Ii, -0.017461-0.20329i, - 0.19668-0.05534i, -0.20044+0.037576i, -0.17547+0.10399i, 0.20373-0.013857i, 0.10472-0.17545i}

[145] X(18)={0.02302+0.20321i, 0.055972+0.19615i, 0.012719+0.20347i, -

0.13543-0.15126i, -0.19836+0.041117i, 0.18738+0.082934i, -0.088903+0.18485i, - 0.17375-0.10973i, -0.19387-0.064448i, -0.13925+0.15129i, -0.044809+0.19858i, 0.070332-0.19514i, -0.047455+0.19562i, 0.13918-0.14783i, -0.064867-0.1924H, 0.12502-0.164i, 0.20042-0.041152i, -0.20253+0.0035307i, 0.17612+0.10549i, - 0.077043+0.1897i, -0.051838-0.19659i, -0.20131+0.006551 Ii, -0.19823+0.046156i, 0.10233-0.17806i}

[146] X(19)={0.023113+0.20299i, -0.20384-0.0032565i, 0.17614-0.10432i, -

0.17184+0.11127i, 0.20148-0.030462i, 0.1248+0.16173i, -0.1355+0.15237i, - 0.070325-0.1918H, -0.11795-0.16649i, -0.00637 l l+0.20363i, 0.1796+0.096236i, - 0.14059-0.14767i, -0.0025122+0.20426i, 0.1933-0.06593i, 0.059361+0.19546i, - 0.13898-0.1495i, -0.14139+0.14692i, -0.15686+0.13122i, -0.15846-0.12805i, 0.0054043-0.2043 Ii, 0.019588-0.20309i, -0.16574-0.11977i, -0.17056-0.11189i, - 0.20184+0.027917i} [147] X(20)={0.18466-0.084459i, 0.18935+0.080303i, -0.11125-0.16764i, -

0.19155-0.0775i, -0.025262-0.20259i, -0.18194+0.095432i, 0.1319-0.1562i, 0.029263+0.20108i, 0.19712-0.04989i, -0.1897-0.07295 Ii, -0.18381+0.089405i, - 0.039001+0.2015 Ii, 0.083852-0.18996i, 0.038523-0.19794i, 0.19761+0.047952i, 0.16769-0.11793i, 0.12677-0.1559i, 0.12028+0.16503i, -0.14839-0.14266i, 0.15665+0.12952i, 0.18052+0.09659 Ii, 0.20323+0.013293i, -0.018535+0.20291i, - 0.047247-0.1992i}

[148] X(21)={0.095798-0.1788i, 0.094404+0.18108i, -0.083021-0.18666i, -

0.077599-0.18854i, -0.08566-0.18572i, -0.15218+0.13668i, -0.16277-0.12204i, - 0.062665+0.1953 Ii, 0.10408-0.176i, -0.059722-0.19593i, 0.051718-0.19789i, - 0.064188-0.1939H, 0.14736+0.14152i, -0.17352+0.10653i, -0.18458-0.086697i, - 0.018709-0.20527i, -0.20299-0.0071094i, 0.15877+0.12881i, 0.19418-0.062093i, - 0.12458-0.16197i, 0.16533+0.11785i, 0.19913-0.046579i, 0.18605+0.081199i, - 0.15757+0.12916i}

[149] X(22)={0.20257+0.025168i, 0.12153-0.16397i, 0.16662+0.11794i, -

0.14829+0.14022i, 0.074481-0.19002i, -0.19807+0.049352i, -0.01639+0.20347i, 0.17585-0.10365i, 0.081939+0.18697i, -0.17476-0.10542i, -0.15491-0.13294i, 0.099424+0.17827i, 0.14613-0.14252i, -0.12946+0.15779i, -0.018402-0.20331i, 0.15935-0.12754i, 0.044293-0.1993i, -0.1704-0.1124H, -0.18325-0.089962i, - 0.1964-0.055599i, -0.075908+0.18948i, -0.16021-0.12656i, -0.015357-0.20355i, - 0.1267-0.16006i}

[150] X(23)={-0.19814-0.049076i, -0.20263-0.02465i, -0.12753+0.15938i,

0.10243-0.17657i, 0.19175-0.069994i, 0.20394+0.0086637i, -0.11 l-0.1713i, 0.13868+0.14978i, -0.09376+0.18132i, -0.20408-0.0044368i, -0.20376+0.0122i, 0.03198+0.2016i, 0.092877-0.18177i, -0.20297-0.021689i, 0.1831-0.090234i, - 0.068135+0.19242i, -0.10247-0.17654i, 0.17368-0.10724i, -0.017388-0.20338i, 0.20409+0.0037074i, -0.09419-0.18109i, -0.19553-0.058613i, 0.1247-0.1616H, 0.08167-0.18707i}

[151] X(24)={-0.11606-0.16791i, 0.097793-0.17918i, -0.12496-0.1614H,

0.062499-0.19433i, -0.17002+0.11298i, 0.1868+0.082318i, -0.078666-0.18837i, - 0.16879-0.1148i, -0.027268+0.20228i, -0.17381-0.10702i, 0.062335-0.19437i, 0.023464-0.20277i, 0.11304+0.16997i, -0.078052-0.1886i, -0.18198+0.092531i, - 0.076715+0.18916i, -0.20402-0.0065168i, 0.15253+0.13566i, 0.088544+0.18393i, 0.1848+0.086738i, -0.16713+0.117151, -0.12326-0.1627i, -0.078703-0.18832i, - 0.072529+0.19079i}

[152] X(25)={0.132+0.15899i, -0.17637-0.10205i, -0.17369-0.1065 Ii, 0.19472-0.060717i, 0.19268-0.064517i, -0.2025 l+0.020152i, -0.18846+0.077143i, 0.19941-0.04852i, 0.16698-0.11806i, 0.19964-0.042093i, -0.16048-0.1257i, 0.002896 l+0.20072i, 0.088732+0.18299i, -0.14584+0.14QIi, 0.13709+0.15354i, 0.14672-0.141 Hi, 0.18608+0.080369i, 0.1793-0.093469i, 0.19805+0.050544i, 0.20306+0.0044748i, - 0.16048+0.1317i, 0.14812-0.14382i, -0.020922+0.20429i, -0.18221-0.094444i}

[153] X(26)={0.13362-0.15363i, 0.17668+0.10376i, 0.11876+0.16923i, -

0.12704-0.15989i, -0.1553-0.1346i, 0.11542-0.16764i, -0.078585+0.18514i, 0.19911-0.033756i, -0.024284-0.20204i, -0.19879+0.043559i, -0.20359-0.03669 Ii, 0.09668+0.17879i, -0.068739-0.19292i, 0.014848+0.20395i, -0.06421+0.19525i, 0.016118+0.2048i, -0.14917+0.14086i, -0.047804+0.19686i, -0.17386-0.10903i, - 0.045869-0.1973 Ii, -0.15687+0.12994i, -0.0288 l-0.20085i, -0.098522+0.18045i, - 0.10626+0.17197i}

[154] X(27)={-0.056453-0.19781i, -0.08725-0.18548i, -0.12725+0.1573i,

0.077533+0.18845i, -0.14095-0.14759i, -0.18892+0.07675 Ii, 0.18928-0.074892i, 0.20513-0.016255i, 0.068525+0.19096i, 0.16519+0.12105i, -0.16626-0.11897i, 0.13395-0.15544i, -0.17946-0.096341i, -0.0037015-0.20208i, 0.019691-0.2027i, 0.19852-0.044148i, -0.1533-0.13444i, 0.11689-0.16867i, 0.17645-0.099725i, - 0.1996+0.042812i, 0.10449-0.17642i, -0.063757+0.19536i, 0.19586+0.056479i, 0.17583+0.10412i}

[155] X(28)={0.092101-0.18473i, 0.19523-0.056136i, -0.12369-0.16083i,

0.07396-0.19189i, 0.20269-0.023323i, 0.20244-0.021519i, 0.18505-0.08617i, - 0.093224+0.1801i, -0.18629+0.083992i, -0.070167-0.19076i, -0.15797-0.13025i, - 0.10422+0.17542i, 0.08691+0.18329i, 0.056852-0.19663i, -0.077984-0.18796i, 0.19909-0.056344i, -0.19852+0.052219i, -0.10796-0.17319i, 0.16738+0.11812i, - 0.1086-0.17254i, 0.0050828+0.20429i, 0.013258-0.20235i, 0.098273+0.17954i, 0.20075+0.022774i}

[156] X(29)={0.11193-0.17118i, 0.02144-0.20284i, -0.01327+0.2036i, -0.11785-0.16624i, -0.11989-0.16553i, -0.11147-0.17096i, 0.19116+0.071958i, 0.18128+0.093603i, 0.18031+0.096137i, -0.14644+0.14214i, 0.19295+0.067635i, 0.18139+0.09465H, - 0.15668+0.13032i, 0.095828-0.18005i, 0.088635+0.18355i, -0.13978+0.1488 Ii, 0.072338+0.19053i, 0.14563-0.14272i, -0.19661-0.054561i, 0.20354-0.018395i, - 0.1489-0.139H, 0.16017+0.12685i, 0.13528+0.1532i, 0.1723-0.10941i}

[157] X(30)={-0.094784-0.18189i, -0.20619-0.0081193i, -0.19691+0.052881i, -

0.035364-0.19998i, -0.19948+0.027245i, 0.20523+0.03357i, 0.13444+0.15385i, 0.064319+0.19151i, -0.011107+0.20322i, -0.017658-0.20428i, 0.015798+0.20337i, - 0.16647+0.11827i, 0.11249-0.17327i, -0.16431+0.12492i, 0.12179+0.1592H, - 0.086771+0.18842i, -0.11405+0.17443i, 0.08953-0.17979i, 0.15195+0.13283i, 0.046484-0.19777i, -0.20239-0.026605i, -0.004958l+0.20544i, -0.15518+0.13022i, 0.029391-0.19838i}

[158] X(31)={0.1379-0.1505i, 0.20412-0.00045434i, 0.1056+0.17469i, 0.11104+0.17128i, -0.19599-0.057035i, -0.19457-0.061715i, 0.098396+0.17884i, -0.1896+0.07563 Ii, 0.14184-0.14679i, 0.18204-0.09234i, -0.13707+0.15126i, 0.20246+0.02602 Ii, 0.079974-0.1878 Ii, -0.045876-0.1989i, 0.035536-0.20101i, 0.033764-0.2013 Ii, - 0.20338-0.01743 Ii, -0.17999+0.096278i, 0.1966-0.054926i, -0.12739-0.15949i, 0.15609-0.13154i, -0.19118-0.071537i, 0.2014-0.033248i, -0.18771-0.080202i}

[159] X(32)={-0.039248-0.20032i, -0.12405-0.1621i, 0.17337+0.10775i,

0.079495+0.188OH, -0.19977+0.041945i, -0.065971+0.19317i, 0.19945-0.043425i, 0.098087-0.1790H, 0.11031-0.17175i, -0.14473-0.14395i, -0.061102+0.19476i, 0.20094+0.03593 Ii, 0.034017+0.20127i, -0.20314+0.019979i, -0.019574-0.20318i, 0.0077542+0.20398i, 0.10384-0.17574i, 0.17064+0.11202i, -0.02685-0.20235i, 0.19793+0.049903i, 0.16242-0.12364i, 0.14308-0.14558i, 0.18947-0.075945i, 0.16101+0.12547i}

[160] X(33)={-0.20208-0.028808i, -0.16549+0.1195i, -0.10163-0.17702i, -

0.19469-0.061337i, -0.092444-0.18199i, -0.1163+0.16775i, -0.092909+0.18175i, - 0.073176+0.19056i, 0.054701-0.19666i, 0.19023-0.074017i, 0.20402+0.0064539i, - 0.17562-0.10404i, 0.11886+0.16595i, 0.01689-0.20342i, -0.075798+0.18953i, - 0.14768-0.14092i, -0.028257-0.20216i, -0.11895+0.16588i, 0.19249-0.067935i, 0.20304+0.021058i, -0.20089-0.036165i, -0.20181+0.030661i, 0.16569+0.11922i, - 0.15809+0.12913i}

[161] X(34)={0.17825+0.099474i, -0.060434-0.19497i, 0.10876+0.17273i,

0.16091-0.1256i, -0.2035 l+0.015852i, -0.15132+0.137i, -0.20315+0.01987i, - 0.09986+0.17803i, 0.047284+0.19857i, -0.13919-0.1493H, 0.12329-0.16268i, - 0.10106+0.17735i, 0.10284+0.17632i, 0.10953+0.17225i, -0.0040835-0.20408i, 0.19294-0.066636i, 0.15671+0.1308i, 0.19444-0.062125i, 0.19371+0.064359i, - 0.13254+0.15524i, -0.12291+0.16297i, -0.019376-0.2032i, 0.034528+0.20118i, - 0.1833+0.089812i}

[162] X(35)={0.0398+0.20023i, -0.019734+0.2032i, -0.18489+0.086498i,

0.12844+0.15865i, 0.17419-0.10636i, -0.20353-0.01555i, -0.20033+0.039246i, 0.13415+0.15381i, 0.15963-0.1272i, 0.19693+0.053766i, 0.11891-0.16594i, 0.16749+0.11664i, -0.053791-0.19687i, -0.14167-0.14696i, 0.017057-0.20344i, 0.16931-0.11395i, -0.11153+0.17097i, 0.035341-0.20104i, -0.043073+0.1995 Ii, 0.081331-0.18723i, 0.07369-0.19038i, 0.14035+0.14825i, 0.050488-0.19779i, 0.17867-0.098753i}

[163] X(36)={0.20411-0.002051 Ii, 0.058094-0.19575i, 0.16816+0.11565i, -

0.19005+0.074553i, -0.1764+0.10265i, -0.19368+0.064466i, 0.19674+0.054556i, 0.031173+0.20175i, -0.13798-0.15043i, 0.049696-0.19797i, 0.20396-0.0076632i, 0.10069-0.1775 Ii, 0.18341-0.089497i, -0.094961+0.1808 Ii, 0.15258-0.13557i, 0.062659-0.19427i, -0.078503-0.1884i, -0.18206-0.09222i, 0.20198-0.029308i, 0.057834-0.19575i, -0.031235+0.20178i, 0.071267-0.19124i, -0.17701+0.10184i, 0.20312+0.019718i}

[164] X(37)={-0.10533-0.17484i, -0.20407-0.0033903i, -0.096465-0.1799 Ii,

0.04891+0.19814i, 0.19879-0.046166i, -0.11674+0.16746i, 0.0071485-0.204i, 0.20363-0.013768i, -0.18017+0.095954i, -0.07606+0.18942i, -0.094254+0.18107i, 0.10782+0.17338i, -0.13008+0.15726i, -0.2041-0.0043899i, 0.12558+0.16093i, 0.19981+0.042147i, 0.10942-0.17238i, 0.18425+0.08781 Ii, -0.17422+0.10635i, - 0.20402-0.0039024i, -0.076896+0.1890H, -0.029016-0.20209i, -0.1788-0.098568i, 0.10944+0.17232i}

[165] The number of sequences having a CM lower than a QPSK CM can be increased, facilitating cell planning. Further, a mean cross-correlation value between sequences is small and cross-correlation exceeding a specific value is not generated. Accordingly, a block error rate (BLER) characteristic can be improved.

[166] A generated sequence can be used for various purposes requiring an orthogonal code in wireless communication systems. A generated sequence can be used for a reference signal, a synchronization code, a scrambling code and so on.

[167] A generated sequence can be used in a downlink control channel or an uplink control channel. For example, a generated sequence can be applied to an acknowledgement (ACK)/negative- acknowledgement (NACK) signal or a spreading code of a channel quality indicator (CQI).

[168] The present invention can be implemented with hardware, software, or combination thereof. In hardware implementation, the present invention can be implemented with one of an application specific integrated circuit (ASIC), a digital signal processor (DSP), a programmable logic device (PLD), a field programmable gate array (FPGA), a processor, a controller, a microprocessor, other electronic units, and combination thereof, which are designed to perform the aforementioned functions. In software implementation, the present invention can be implemented with a module for performing the aforementioned functions. Software is storable in a memory unit and executed by the processor. Various means widely known to those skilled in the art can be used as the memory unit or the processor.

[169] While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims. The exemplary embodiments should be considered in descriptive sense only and not for purposes of limitation. Therefore, the scope of the invention is defined not by the detailed description of the invention but by the appended claims, and all differences within the scope will be construed as being included in the present invention.

Claims

Claims

[1] A method of generating a sequence in a wireless communication system, the method comprising: deciding a length of an initial sequence according to allocated radio resources; deciding a random seed according to the length of the initial sequence; generating an iterated sequence by iterating the initial sequence by predetermined times; and selecting the iterated sequence when the iterated sequence satisfies a threshold.

[2] The method of claim 1, wherein the iterated sequence is iterated by transforming the initial sequence to a time domain sequence and transforming the time domain sequence to a frequency domain sequence.

[3] The method of claim 2, wherein the initial sequence is normalized before transforming to the time domain sequence.

[4] The method of claim 2, wherein the time domain sequence is normalized before transforming to the frequency domain sequence.

[5] The method of claim 1, wherein the threshold is based on a cubic metric (CM).

[6] The method of claim 1, wherein the threshold is based on a cross correlation.

[7] A method of generating a sequence in a wireless communication system, the method comprising: deciding a length of an initial sequence according to allocated radio resources; deciding a random seed according to the length of the initial sequence; generating an iterated sequence by iterating the initial sequence by predetermined times; and selecting the iterated sequence when the iterated sequence satisfies a first threshold and a second threshold. [8] The method of claim 7, wherein the first threshold is based on a CM and the second threshold is based on a cross correlation. [9] A method of generating a sequence in a wireless communication system, the method comprising: generating a sequence; and selecting the sequence when the sequence satisfies a first threshold and a second threshold, wherein the first threshold is based on a CM and the second threshold is based on a cross correlation. [10] The method of claim 9, wherein generating the sequence comprising: deciding a length of a initial sequence according to allocated radio resources; deciding a random seed according to the length of the initial sequence; and generating the sequence by iterating the initial sequence by predetermined times.