# Patent

## Title
Method for sequencing the ZC sequences of the RACH

## Abstract

A method for sequencing the ZC sequences of the RACH is provided, wherein, the method for sequencing the ZC sequences comprises: setting the logical index of each ZC sequence as α, and the physical index of each ZC sequence as u, wherein 1≦u≦N−1,0≦α≦N−2, N is the length of each ZC sequence and N=839; creating the physical indices u corresponding to the logical indices α=0, 1, . . . , 837, sequencing the ZC sequences of the RACH according to the created mapping relationship between the logical indices and the physical indices.

## Background
FIELD OF THE INVENTION
The present invention relates to communication field, in particular to a method for sequencing the ZC sequences of the random access channel.
BACKGROUND OF THE INVENTION
In the Long Term Evolution (LTE for short) system, cyclic shift sequences of Zadoff-Chu (ZC for short) sequences are used as the preamble by the Random Access Channel (RACH for short). These cyclic shift sequences are also referred to as Zero Correlation Zone (ZCZ for short) sequences.
In practical systems, after a mobile phone is powered on, downlink synchronization is first performed, and then the detection of the Broadcast Channel (BCH for short) is initiated. A base station informs, via the BCH channel, the mobile phone of the index and the step length of the cyclic shift of the first ZC sequence available for the RACH of the current cell. According to the index, the mobile phone makes use of certain mapping rule to calculate the serial number of the corresponding ZC sequence, and then, generates usable ZCZ sequences according to the step length of the cyclic shift and a certain “cyclic shift limitation rule” (the mobile phone is under a high speed circumstance).
If the number of the ZCZ sequences is smaller than a certain threshold Q, the mobile phone automatically increments the sequence index, and continuously generates the ZCZ sequences using the next ZC sequence, until the total number of the ZCZ sequences is larger than or equal to Q. Finally, the mobile phone randomly selects one sequence from all the generated usable ZCZ sequences as a preamble to be sent.
In the high speed circumstance, the frequency offset caused by Doppler Effect will generate, during the process of the preamble detection, a correlation peak alias, which will lead to a timing offset and a false detection. This problem is settled in the LTE system through limiting the use of some cyclic shifts according to a certain rule, which is the above mentioned “cyclic shift limitation rule”.
Meanwhile, the cyclic shift limitation rule also limits the maximum cyclic shift NCS corresponding to each ZC sequence, and this maximum cyclic shift directly determines the maximum cell radius supported by each ZC sequence. Assuming that the distance between the correlation peak and the correlation peak alias thereof is du, the relation between the maximum cyclic shift NCS and du is:

NCS=min(du,NZC−2·du)  (1)

Wherein, NZC is the length of a ZC sequence, du can be calculated by the following formula:




  
    
      
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Wherein, u is the serial number of the ZC sequence, and m is the minimum positive integer which makes




  
    
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a positive integer.

The mapping process between the indices and the serial numbers of the ZC sequences is actually the process of re-sequencing the ZC sequences. Wherein, the generation formula of the ZC sequences is shown as Equation (3) (0≦u≦NZC−1), and the serial number of the ZC sequence is the serial number used in the generation of each ZC sequence. The index of the sequence is the sequence number of each ZC sequence in a queue of sequenced ZC sequences, where the ZC sequences are sequenced according to a certain criterion.




  
    
      
        
          
            
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At present, there are mainly two sequencing methods: one is to sequence according to the cubic metric (CM for short, it is a standard for measuring the Peak-to-Average Power Ratio of the emitted data, the larger the CM is, the higher the Peak-to-Average Power Ratio is) of the ZC sequences, and the other is to sequence according to the maximum cell radius supported by each ZC sequence under a high speed circumstance.
The first method is advantageous in that network planning of the ZC sequences can be conveniently performed according to the CM of a root sequence so as to assign the sequences with smaller CMs to the cells with larger radius, and the sequences with similar CMs to the same cell. Its shortcoming lies in that sequence fragments will be generated under the high speed circumstance, which will cause the waste of the sequences. In other words, during the process of generating the ZCZ sequences with the continuous incrementation of the sequence index, if the maximum cell radius supported by a ZC sequence is smaller than the radius of the current cell, this sequence neither could be used by the current cell, nor it could be used by other cells having radiuses smaller than the maximum cell radius supported by this ZC sequence (this is because that the index is continuously incremental, as shown in FIG. 1).
The second method is advantageous in avoiding the generation of the sequence fragments, that is disadvantageous in that the CMs of the ZC sequences assigned to a cell differs greatly from each other so that sequence planning can not be performed according to the CM.
A patent application of the present applicant with an application number of 200710135732.1 provides a method and device for sequencing the ZC sequences of the random access channel, which can not only prevent sequence fragments from being generated in the high speed circumstance, but also perform sequence planning and assigning according to the CM character of the sequences. The method comprises the following steps:
step 1, the sequences are sequenced according to the CM values of the sequences;
step 2, the sequencing result of step 1 is grouped according to a particular CM value (for example, the grouping may be performed according to the CM value of QPSK (about 1.2 dB));
step 3, the sequences in each group are sequenced, according to the maximum cell radius supported by the sequences under the high speed circumstance, for a second time to obtain the final sequencing result.
The present invention modifies the sequencing method and device provided by the patent application with the application number of 200710135732.1. The present invention not only inherits all the advantages of the application, but also performs a better sequence planning and assigning according to the CM character of the sequence, so that sequences with similar CMs are assigned to the same cell.
SUMMARY OF THE INVENTION
In view of the above mentioned one or more problems, the present invention provides a method for sequencing the ZC sequences of the random access channel.
The present invention provides a method for sequencing the ZC sequences of the random access channel. The method for sequencing the ZC sequences of the random access channel according to the present invention comprises: step 1, according to Cubic Metric, CM, of Quadrature Phase Shift Keying, OPSK, ZC sequences of the RACH are divided into a low CM group and a high CM group, to make the index of each ZC sequence within the low CM group smaller or larger than the index of each ZC sequence within the high CM group; step 2, according to the maximum cell radius or maximum cyclic shift supported by the ZC sequences under high speed circumstance, the ZC sequences within the low CM group and within the high CM group are respectively divided into S sub-groups using S−1 maximum cyclic shift thresholds, wherein S is a positive integer; and step 3, according to the CMs of the ZC sequences, the sequences are sequenced within each sub-group, to make the ZC sequences in adjacent sub-groups within the low CM group and within the high CM group have different sequencing and the ZC sequences in adjacent sub-groups between the low CM group and the high CM group have the same sequencing, wherein the last sub-group within the low CM group and the first sub-group within the high CM group are adjacent with each other while the first sub-group within the low CM group and the last sub-group within the high CM group are adjacent with each other.
The CMs of the ZC sequences within the low CM group is not larger than the CM of QPSK; and the CMs of the ZC sequences within the low CM group is larger than the CM of QPSK.
In step 3, the sequences are sequenced from high to low or from low to high.
The index of the sequence within sub-group i is set smaller than the index of the sequences within sub-group i+1, wherein 1≦i≦S−1, the ith maximum cyclic shift threshold is Th_Ncs(i), and Th_Ncs(i)<Th_Ncs(i+1), wherein, 1≦i≦S−2 and i is a positive integer; as for the low CM group, when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(i−1) and less than Th_Ncs(i); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is less than Th_Ncs(1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group is not less than Th_Ncs(S−1); or when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(i−1) and not larger than Th_Ncs(i); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not larger than Th_Ncs(1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−1); and as for the high CM group, when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(S−i) and less than Th_Ncs(S−i+1); when i=11, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(S−1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is less than Th_Ncs(1); or when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−i) and not larger than Th_Ncs(S−i+1); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not larger than Th_Ncs(1).
The index of the sequence within sub-group i is set smaller than the index of the sequence within sub-group i+1, wherein 1≦i≦S−1, the ith maximum cyclic shift threshold is Th_Ncs(i), and Th_Ncs(i)<Th_Ncs(i+1), wherein, 1≦i≦S−2 and i is a positive integer; as for the low CM group, when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(i−1) and less than Th_Ncs(S−i+1); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(S−i); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is less than Th_Ncs(1); or when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−i) and not larger than Th_Ncs(S−i+1); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not larger than Th_Ncs(1); and as for the high CM group, when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(i−1) and less than Th_Ncs(i); when i=1, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is less than Th_Ncs(1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not less than Th_Ncs(S−1); or when 1<i<S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(i−1) and not larger than Th_Ncs(i); when i=11, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is not larger than Th_Ncs(1); when i=S, the maximum value of the maximum cyclic shift supported by each ZC sequence within sub-group i is larger than Th_Ncs(S−1).
The maximum cyclic shift is NCS=min(du,NZC−2·du), wherein, du is the distance between the correlation peak alia and correlation peek, NZC is the length of the ZC sequence.
The distance between the correlation peak alias and correlation peak




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wherein u is the serial number of the ZC sequence, m is the minimum positive integer which makes





  
    
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a positive integer.

The present invention also provides a method for sequencing the ZC sequences of the RACH, the method for sequencing the ZC sequences of the RACH according to the present invention comprises: setting the logical index of each ZC sequence as α, and the physical index of each ZC sequence as u, wherein 1≦u≦N−1, 0≦α≦N−2, N is the length of each ZC sequence and N=839; creating the physical indices u corresponding to the logical indices α=0, 1, . . . , 837, the physical indices u are: 129, 710, 140, 699, 120, 719, 210, 629, 168, 671, 84, 755, 105, 734, 93, 746, 70, 769, 60, 779, 2, 837, 1, 838, 56, 783, 112, 727, 148, 691, 80, 759, 42, 797, 40, 799, 35, 804, 73, 766, 146, 693, 31, 808, 28, 811, 30, 809, 27, 812, 29, 810, 24, 815, 48, 791, 68, 771, 74, 765, 178, 661, 136, 703, 86, 753, 78, 761, 43, 796, 39, 800, 20, 819, 21, 818, 95, 744, 202, 637, 190, 649, 181, 658, 137, 702, 125, 714, 151, 688, 217, 622, 128, 711, 142, 697, 122, 717, 203, 636, 118, 721, 110, 729, 89, 750, 103, 736, 61, 778, 55, 784, 15, 824, 14, 825, 12, 827, 23, 816, 34, 805, 37, 802, 46, 793, 207, 632, 179, 660, 145, 694, 130, 709, 223, 616, 228, 611, 227, 612, 132, 707, 133, 706, 143, 696, 135, 704, 161, 678, 201, 638, 173, 666, 106, 733, 83, 756, 91, 748, 66, 773, 53, 786, 10, 829, 9, 830, 7, 832, 8, 831, 16, 823, 47, 792, 64, 775, 57, 782, 104, 735, 101, 738, 108, 731, 208, 631, 184, 655, 197, 642, 191, 648, 121, 718, 141, 698, 149, 690, 216, 623, 218, 621, 152, 687, 144, 695, 134, 705, 138, 701, 199, 640, 162, 677, 176, 663, 119, 720, 158, 681, 164, 675, 174, 665, 171, 668, 170, 669, 87, 752, 169, 670, 88, 751, 107, 732, 81, 758, 82, 757, 100, 739, 98, 741, 71, 768, 59, 780, 65, 774, 50, 789, 49, 790, 26, 813, 17, 822, 13, 826, 6, 833, 5, 834, 33, 806, 51, 788, 75, 764, 99, 740, 96, 743, 97, 742, 166, 673, 172, 667, 175, 664, 187, 652, 163, 676, 185, 654, 200, 639, 114, 725, 189, 650, 115, 724, 194, 645, 195, 644, 192, 647, 182, 657, 157, 682, 156, 683, 211, 628, 154, 685, 123, 716, 139, 700, 212, 627, 153, 686, 213, 626, 215, 624, 150, 689, 225, 614, 224, 615, 221, 618, 220, 619, 127, 712, 147, 692, 124, 715, 193, 646, 205, 634, 206, 633, 116, 723, 160, 679, 186, 653, 167, 672, 79, 760, 85, 754, 77, 762, 92, 747, 58, 781, 62, 777, 69, 770, 54, 785, 36, 803, 32, 807, 25, 814, 18, 821, 11, 828, 4, 835, 3, 836, 19, 820, 22, 817, 41, 798, 38, 801, 44, 795, 52, 787, 45, 794, 63, 776, 67, 772, 72, 767, 76, 763, 94, 745, 102, 737, 90, 749, 109, 730, 165, 674, 111, 728, 209, 630, 204, 635, 117, 722, 188, 651, 159, 680, 198, 641, 113, 726, 183, 656, 180, 659, 177, 662, 196, 643, 155, 684, 214, 625, 126, 713, 131, 708, 219, 620, 222, 617, 226, 613, 230, 609, 232, 607, 262, 577, 252, 587, 418, 421, 416, 423, 413, 426, 411, 428, 376, 463, 395, 444, 283, 556, 285, 554, 379, 460, 390, 449, 363, 476, 384, 455, 388, 451, 386, 453, 361, 478, 387, 452, 360, 479, 310, 529, 354, 485, 328, 511, 315, 524, 337, 502, 349, 490, 335, 504, 324, 515, 323, 516, 320, 519, 334, 505, 359, 480, 295, 544, 385, 454, 292, 547, 291, 548, 381, 458, 399, 440, 380, 459, 397, 442, 369, 470, 377, 462, 410, 429, 407, 432, 281, 558, 414, 425, 247, 592, 277, 562, 271, 568, 272, 567, 264, 575, 259, 580, 237, 602, 239, 600, 244, 595, 243, 596, 275, 564, 278, 561, 250, 589, 246, 593, 417, 422, 248, 591, 394, 445, 393, 446, 370, 469, 365, 474, 300, 539, 299, 540, 364, 475, 362, 477, 298, 541, 312, 527, 313, 526, 314, 525, 353, 486, 352, 487, 343, 496, 327, 512, 350, 489, 326, 513, 319, 520, 332, 507, 333, 506, 348, 491, 347, 492, 322, 517, 330, 509, 338, 501, 341, 498, 340, 499, 342, 497, 301, 538, 366, 473, 401, 438, 371, 468, 408, 431, 375, 464, 249, 590, 269, 570, 238, 601, 234, 605, 257, 582, 273, 566, 255, 584, 254, 585, 245, 594, 251, 588, 412, 427, 372, 467, 282, 557, 403, 436, 396, 443, 392, 447, 391, 448, 382, 457, 389, 450, 294, 545, 297, 542, 311, 528, 344, 495, 345, 494, 318, 521, 331, 508, 325, 514, 321, 518, 346, 493, 339, 500, 351, 488, 306, 533, 289, 550, 400, 439, 378, 461, 374, 465, 415, 424, 270, 569, 241, 598, 231, 608, 260, 579, 268, 571, 276, 563, 409, 430, 398, 441, 290, 549, 304, 535, 308, 531, 358, 481, 316, 523, 293, 546, 288, 551, 284, 555, 368, 471, 253, 586, 256, 583, 263, 576, 242, 597, 274, 565, 402, 437, 383, 456, 357, 482, 329, 510, 317, 522, 307, 532, 286, 553, 287, 552, 266, 573, 261, 578, 236, 603, 303, 536, 356, 483, 355, 484, 405, 434, 404, 435, 406, 433, 235, 604, 267, 572, 302, 537, 367, 472, 296, 543, 336, 503, 305, 534, 373, 466, 280, 559, 279, 560, 419, 420, 240, 599, 258, 581, 229, 610; sequencing the ZC sequences of the RACH according to the created mapping relationship between the logical indices and the physical indices.
The present invention also provides a device for sequencing the ZC sequences of the RACH, the device for sequencing the ZC sequences of the RACH according to the present invention comprises, a first group dividing unit configured to divide ZC sequences of the RACH into a low CM group and a high CM group according to the CM of QPSK, to make the index of each ZC sequence within the low CM group smaller or larger than the index of each ZC sequence within the high CM group; a second group dividing unit configured to respectively divide the ZC sequences within the low CM group and within the high CM group into S sub-groups using S−1 maximum cyclic shift thresholds according to the maximum cell radius or maximum cyclic shift supported by the ZC sequences under high speed circumstance, wherein S is a positive integer; and a sequencing unit configured to sequence the sequences within each sub-group according to the CMs of the ZC sequences, to make the ZC sequences in adjacent sub-groups within the low CM group and within the high CM group have different sequencing, and the ZC sequences in adjacent sub-groups between the low CM group and the high CM group have the same sequencing, wherein the last sub-group within the low CM group and the first sub-group within the high CM group are adjacent with each other while the first sub-group within the low CM group and the last sub-group within the high CM group are adjacent with each other.
The method and device for sequencing the ZC sequences of the RACH provided by the present invention not only enables the assignment of the sequences according to the CMs, but also enables the collection of the sequence fragments for use, so that the generation of sequence fragments can be avoided.



BRIEF DESCRIPTION OF THE DRAWINGS
The drawings illustrated here provide a further understanding of the present invention and form a part of the present application. The exemplary embodiments and the description thereof are used to explain the present invention without unduly limiting the scope of the present invention, wherein:
FIG. 1 is a schematic diagram of the generation of the sequence fragments in the prior art;
FIG. 2 is a flowchart of the method for sequencing the ZC sequences of the random access channel according to an embodiment of the present invention;
FIG. 3 is a schematic diagram showing the grouping of the ZC sequences of the RACH according to an embodiment of the present invention;
FIG. 4a-4d are schematic diagrams showing the grouping and sequencing of the ZC sequences of the RACH according to an embodiment of the present invention; and
FIG. 5 is a schematic diagram showing the corresponding relation between the physical indices and the CM values of the ZC sequences according to an embodiment of the present invention.



DETAILED DESCRIPTION OF THE EMBODIMENTS
The embodiments of the present invention will be described hereinafter in detail in conjunction with the drawings thereof.
The present invention provides a method for sequencing the ZC sequences of the RACH.
FIG. 2 shows the method for sequencing the ZC sequences of the RACH according to an embodiment of the present invention. As shown in FIG. 2, the method comprises:
step S202, according to the CM of OPSK, ZC sequences of the RACH are divided into low CM group and high CM group, to make the index of each ZC sequence within the low CM group smaller or larger than the index of each ZC sequence within the high CM group.
step S204, according to the maximum cell radius or maximum cyclic shift supported by the ZC sequences under a high speed circumstance, the ZC sequences within the low CM group and within the high CM group are respectively divided into S sub-groups using S−1 maximum cyclic shift thresholds, wherein S is a positive integer.
step S206, according to the CMs of the ZC sequences, the sequences are sequenced within each sub-group, to make the ZC sequences in adjacent sub-groups within the low CM group and within the high CM group have different sequencing and the ZC sequences in adjacent sub-groups between the low CM group and the high CM group have the same sequencing, wherein the last sub-group within the low CM group and the first sub-group within the high CM group are adjacent with each other while the first sub-group within the low CM group and the last sub-group within the high CM group are adjacent with each other.
In the FDD mode of the LTE, the length of the ZC sequences used by the RACH is 839, and the number of usable sequences is 838.
All the ZC sequences of the RACH are divided, using the CM of QPSK as a threshold, into two groups, i.e., the low CM group and the high CM group. The CMs of the ZC sequences in the low CM group are smaller than or equal to the CM of QPSK, while the CMs of the ZC sequences in the high CM group are larger than the CM of QPSK, which is 1.2 dB.
After the final sequencing process, the indices of the sequences in the low CM group are smaller than the indices of the sequences in the high CM group, as shown in FIG. 3, or the indices of the sequences in the low CM group are larger than the indices of the sequences in the high CM group.
According to the maximum cell radius or maximum cyclic shift supported by the ZC sequences under a high speed circumstance, the ZC sequences within each group are divided into S sub-groups using S−1 maximum cyclic shift thresholds, these sub-groups are numbered with 1 to S, wherein S is a positive integer.
After the final sequencing process is completed, the indices of the sequences in sub-group i are all smaller than the indices of the sequences in sub-group i+1, 1≦i≦S−1, the ith maximum cyclic shift threshold is Th_Ncs(i), and Th_Ncs(i)<Th_Ncs(i+1), wherein, 1≦i≦S−2 and i is a positive integer.
Setting S=16, then 15 maximum cyclic shift thresholds Th_Ncs(1), Th_Ncs(2), . . . , Th_Ncs(15) are 15, 18, 22, 26, 32, 38, 46, 55, 68, 82, 100, 128, 158, 202, 237, respectively.
If the maximum value of the maximum cyclic shift supported by the ZC sequences in the jth sub-group under the high speed circumstance is made to be MaxNcs(i), 1≦i≦S, then each sub-group in each group shall satisfy the following property (Property a), as shown in FIG. 4a: for the low CM group, when 1<i<S, Th_Ncs(i−1)≦MaxNcs(i)<Th_Ncs(i), when i=1, MaxNcs(1)<Th_Ncs(1), when i=S, Th_Ncs(S−1)≦MaxNcs(S); for the high CM group, when 1<i<S, Th_Ncs(S−i)≦MaxNcs(i)<Th_Ncs(S−i+1), when i=1, Th_Ncs(S−1)≦MaxNcs(1), when i=S, MaxNcs(S)<Th_Ncs(1);
or the following property (Property b) shall be satisfied, as shown in FIG. 4b: for the low CM group, when 1<i<S, Th_Ncs(i−1)<MaxNcs(i)≦Th_Ncs(i), when i=1, MaxNcs(1)≦Th_Ncs(1), when i=S, Th_Ncs(S−1)<MaxNcs(S); for the high CM group, when 1<i<S, Th_Ncs(S−i)<MaxNcs(i)≦Th_Ncs(S−i+1), when i=1, Th_Ncs(S−1)<MaxNcs(1), when i=S, MaxNcs(S)≦Th_Ncs(1).
The following method can be used to realize the sequencing target in step S204.
step S2042, for the two groups of sequences obtained in step S202, i.e., the low CM group and the high CM group, the ZC sequences in each group are sequenced according to the maximum cell radius or the maximum cyclic shift supported by the ZC sequences under the high speed circumstance. The principles for the sequencing may be: the low CM group is sequenced in the increasing order, while the high CM group is sequenced in the decreasing order, the two groups use different sequencing principles.
step S2044, in each group, the sequencing result obtained in step S2042 is divided, according to S−1 maximum cyclic shift thresholds, into several segments, each of which is taken as a sub-group.
In each sub-group of each group, the sequencing is performed according to the CMs of the ZC sequences. In the low CM group, the sub-group with an odd sequence number is sequenced in the decreasing order, while the sub-group with an even sequence number is sequenced in the increasing order; in the high CM group, the sub-group with an odd sequence number is sequenced in the increasing order, while the sub-group with an even sequence number is sequenced in the decreasing order. Thus it is ensured that the sub-groups at the boundary of the two groups have the same sequencing order (the boundary of the groups shall be considered in a cyclic view). The sequencing results are shown in FIG. 4c and FIG. 4d, the indices are from 1 to N (N is the total number of the ZC sequences). In addition, the indices of the sequences are cyclic, that is, the index of the sequence which is next to the sequence with an index of N is 1.
The above mentioned maximum cyclic shift of the ZC sequence is NCS=min(du,NZC−2·du), wherein, du is the distance between the correlation peak alias and the correlation peak, NZC is the length of the ZC sequence, and the distance between the correlation peak alias and the correlation peak is




  du
  =
  
    {
    
      
        
          
            
              
                
                  
                    m
                    ·
                    
                      N
                      ZC
                    
                  
                  -
                  1
                
                u
              
              ,
            
          
          
            
              
                when
                ⁢
                
                  
                
                ⁢
                
                  
                    
                      m
                      ·
                      
                        N
                        ZC
                      
                    
                    -
                    1
                  
                  u
                
              
              ≤
              
                floor
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    N
                    ⁢
                    
                      /
                    
                    ⁢
                    2
                  
                  )
                
              
            
          
        
        
          
            
              
                
                  N
                  ZC
                
                -
                
                  
                    
                      m
                      ·
                      
                        N
                        ZC
                      
                    
                    -
                    1
                  
                  u
                
              
              ,
            
          
          
            
              
                when
                ⁢
                
                  
                
                ⁢
                
                  
                    
                      m
                      ·
                      
                        N
                        ZC
                      
                    
                    -
                    1
                  
                  u
                
              
              >
              
                
              
              ⁢
              
                floor
                ⁢
                
                  
                
                ⁢
                
                  (
                  
                    N
                    ⁢
                    
                      /
                    
                    ⁢
                    2
                  
                  )
                
              
            
          
        
      
      ,
    
  




wherein u is the serial number of the ZC sequence, m is the minimum positive integer which makes





  
    
      m
      ·
      
        N
        ZC
      
    
    -
    1
  
  u




a positive integer.

The most essential feature of the aforementioned sequencing result lie in that the sequences are divided into two groups according to the CM of QPSK; the sequences in each group are further divided into sub-groups according to the maximum cyclic shift thresholds; and the sequences in each sub-group are further sequenced according to the CM of the ZC sequences.
The sequencing results obtained from the above processes are shown in Table 1 to Table 4, wherein Table 1 and Table 2 show the elements of the low CM group and the high CM group, and Table 3 and Table 4 show the elements of each sub-group (SG) in the low CM group and the high CM group when Property a is satisfied.







TABLE 1





Low CM group


























838
21
798
63
745
83
171
655
202
643
701
689


1
818
41
776
94
756
668
184
637
196
138
150


837
20
38
56
734
106
165
207
677
658
705
709


2
819
801
783
105
733
674
632
162
181
134
130


3
816
37
770
766
671
172
118
646
661
125
148


836
23
802
69
73
168
667
721
193
178
714
691


4
817
800
60
747
85
728
206
194
718
695
149


835
22
39
779
92
754
111
633
645
121
144
690


5
24
43
769
103
753
174
204
636
156
142
710


834
815
796
70
736
86
665
635
203
683
697
129


833
26
790
772
74
97
653
117
199
717
696
623


6
813
49
67
765
742
186
722
640
122
143
216


832
814
44
773
744
750
110
651
656
211
693
708


7
25
795
66
95
89
729
188
183
628
146
131


831
810
50
771
737
81
675
638
210
154
213
622


8
29
789
68
102
758
164
201
629
685
626
217


830
27
52
780
101
732
664
680
197
715
703
218


9
812
787
59
738
107
175
159
642
124
136
621


829
809
788
778
91
88
652
634
195
716
133
219


10
30
51
61
748
751
187
205
644
123
706
620


11
28
793
777
740
759
173
158
120
699
152
619


828
811
46
62
99
80
666
681
719
140
687
220


12
31
791
57
90
79
676
720
659
155
151
223


827
808
48
782
749
760
163
119
180
684
688
616


13
34
792
58
762
672
209
663
647
694
625
221


826
805
47
781
77
167
630
176
192
145
214
618


14
35
786
71
741
169
160
114
649
135
126
617


825
804
53
768
98
670
679
725
190
704
713
222


15
806
45
93
755
752
112
678
177
702
711
224


824
33
794
746
84
87
727
161
662
137
128
615


823
32
64
72
743
108
116
189
660
700
692
613


16
807
775
767
96
731
723
650
179
139
147
226


17
799
774
764
739
669
185
198
648
212
707
612


822
40
65
75
100
170
654
641
191
627
132
227


820
36
785
735
757
166
631
113
182
686
215
614


19
803
54
104
82
673
208
726
657
153
624
225


18
797
55
76
78
109
639
724
682
141
712
611


821
42
784
763
761
730
200
115
157
698
127
228
















TABLE 2





High CM group



























229
258
574
421
558
437
398
292
362
531
344
346
321


610
576
265
589
281
371
441
289
477
309
495
501
518


609
263
275
250
374
468
367
550
455
530
488
338
515


230
257
564
588
465
404
472
457
384
480
351
331
324


608
582
572
251
463
435
459
382
451
359
342
508
519


231
599
267
590
376
396
380
383
388
358
497
522
320


603
240
563
249
430
443
400
456
541
481
511
317
517


236
570
276
246
409
369
439
303
298
529
328
319
322


232
269
271
593
432
470
287
536
386
310
512
520
516


607
256
568
417
407
445
552
449
453
482
327
332
323


604
583
584
422
467
394
286
390
478
357
345
507


235
268
255
416
372
368
553
365
361
527
494
337


606
571
277
423
410
471
440
474
452
312
510
502


233
241
562
559
429
378
399
535
387
355
329
506


234
598
561
280
557
461
379
304
385
484
524
333


605
575
278
248
282
397
460
363
454
528
315
491


237
264
420
591
377
442
458
476
294
311
350
348


602
270
419
424
462
393
381
300
545
485
489
349


601
569
266
415
436
446
551
539
360
354
340
490


238
567
573
247
403
405
288
293
479
356
499
514


577
272
586
592
375
434
548
546
542
483
341
325


262
242
253
373
464
555
291
538
297
313
498
492


261
597
279
466
406
284
448
301
295
526
318
347


578
274
560
426
433
370
391
305
544
525
521
330


600
565
254
413
444
469
549
534
296
314
316
509


239
244
585
414
395
438
290
299
543
353
523
505


260
595
587
425
431
401
302
540
533
486
339
334


579
566
252
412
408
447
537
389
306
487
500
336


259
273
245
427
283
392
473
450
532
352
326
503


580
243
594
428
556
285
366
475
307
343
513
504


581
596
418
411
402
554
547
364
308
496
493
335
















TABLE 3







Low CM group (Property a)































SG
SG
SG
SG
SG
SG
SG


SG 1
SG 2
SG 3
SG 4
SG 5
SG 6
SG 7
SG 8
SG 9
10
11
12
13
14
15
16

























129
56
80
35
808
24
86
744
217
12
228
832
687
5
225
3


710
783
759
804
31
815
753
95
622
827
611
7
152
834
614
836


140
112
42
766
811
791
761
202
128
816
227
831
144
806
615
820


699
727
797
73
28
48
78
637
711
23
612
8
695
33
224
19


719
148
40
693
30
771
796
649
697
34
132
823
134
788
618
817


120
691
799
146
809
68
43
190
142
805
707
16
705
51
221
22


629



812
74
39
658
122
37
706
792
138
764
220
798


210



27
765
800
181
717
802
133
47
701
75
619
41


168



29
661
819
702
203
793
143
64
640
740
127
38


671



810
178
20
137
636
46
696
775
199
99
712
801


84




703
818
125
721
207
704
57
162
743
147
44


755




136
21
714
118
632
135
782
677
96
692
795


105






151
729
660
161
735
176
97
124
52


734






688
110
179
678
104
663
742
715
787


746







89
694
201
101
119
166
193
45


93







750
145
638
738
720
673
646
794


70







736
709
666
108
681
172
205
63


769







103
130
173
731
158
667
634
776


779







61
223
733
631
164
664
633
772


60







778
616
106
208
675
175
206
67


2







784

756
655
665
652
723
72


837







55

83
184
174
187
116
767


1







824

748
197
668
676
679
76


838







15

91
642
171
163
160
763










825

66
648
170
185
186
745










14

773
191
669
654
653
94












53
718
87
639
167
737












786
121
752
200
672
102












10
141
670
114
760
90












829
698
169
725
79
749












9
149
751
189
754
109












830
690
88
650
85
730













623
107
724
77
165













216
732
115
762
674













218
758
194
92
728













621
81
645
747
111














82
195
781
209














757
644
58
630














100
647
62
204














739
192
777
635














98
182
69
117














741
657
770
722














768
682
54
651














71
157
785
188














59
156
803
680














780
683
36
159














65
211
807
198














774
628
32
641














789
154
25
113














50
685
814
726














49
716
821
656














790
123
18
183














813
700
828
659














26
139
11
180














822
212
835
177














17
627
4
662














826
686

643














13
153

196














6
213

155














833
626

684















215

625















624

214















689

126















150

713

















708

















131

















219

















620

















617

















222

















613

















226
















TABLE 4







High CM group (Property a)































SG
SG
SG
SG
SG
SG
SG


SG 1
SG 2
SG 3
SG 4
SG 5
SG 6
SG 7
SG 8
SG 9
10
11
12
13
14
15
16

























609
323
237
509
257
346
608
546
242
317
603
484
604
530
367
503


230
516
602
330
582
493
231
293
597
522
236
355
235
309
472
336


232
320
600
338
566
500
260
288
274
307
303
434
572
265
296
534


607
519
239
501
273
339
579
551
565
532
536
405
267
574
543
305


577
334
244
498
584
351
268
284
402
553
356
435
302
233

466


262
505
595
341
255
488
571
555
437
286
483
404
537
606

373


587
359
243
499
254
306
563
471
383
552

433



280


252
480
596
340
585
533
276
368
456
287

406



559


418
544
275
497
245
550
430
253
482
573





560


421
295
564
342
594
289
409
586
357
266





279


416
454
561
301
588
439
398
583
510
578





419


423
385
278
538
251
400
441
256
329
261





420


426
292
589
366
412
461
549
263







240


413
547
250
473
427
378
290
576







599


428
291
246
401
467
465
535








258


411
548
593
438
372
374
304








581


463
381
417
468
557
415
308








610


376
458
422
371
282
424
531








229


444
399
248
408
436
569
358


395
440
591
431
403
270
481


283
380
445
464
396
598
316


556
459
394
375
443
241
523


285
442
393
249
447


554
397
446
590
392


379
470
370
269
448


460
369
469
570
391


449
462
365
238
457


390
377
474
601
382


363
429
300
605
389


476
410
539
234
450


455
407
299

294


384
432
540

545


451
281
475

542


388
558
364

297


386
425
362

528


453
414
477

311


478
592
541

344


361
247
298

495


452
562
527

345


387
277
312

494


360
568
313

318


479
271
526

521


529
272
525

331


310
567
314

508


485
264
353

514


354
575
486

325


511
580
487

321


328
259
352

518


524

343


315

496


337

512


502

327


349

350


490

489


504

326


335

513


515

319


324

520




332




507




506




333




491




348




492




347




517




322









The present invention further provides a method for sequencing the ZC sequences of the RACH.
For the ZC sequences generated according to Equation 3, the sequence with a physical index u and the sequence with a physical index N-u have the same CM value, as shown in FIG. 5, which is a schematic diagram showing the corresponding relation between the physical indices and the CM values of the ZC sequences according to an embodiment of the present invention. According to the method for sequencing the ZC sequences of the above embodiments, the sequencing is performed (from high to low or from low to high) according to the CM values of the sequences in each sub-group, thus in each sub-group, sequence u and N-u (u is the physical index of the sequence, and 0<=N−1, N is the length of each ZC sequence) are exchangeable in order. At last, the mapping relationship between logical indices and physical indices shown in Table 5 can be obtained by combining Table 3 and Table 4.









TABLE 5





group
Sub-group (logical indices)
Physical indices







low CM group
SG1 (0-23)
129, 710, 140, 699, 120, 719, 210, 629, 168, 671, 84, 755, 105, 734, 93,




746, 70, 769, 60, 779, 2, 837, 1, 838



SG2 (24-29)
56, 783, 112, 727, 148, 691



SG3 (30-35)
80, 759, 42, 797, 40, 799



SG4 (36-41)
35, 804, 73, 766, 146, 693



SG5 (42-51)
31, 808, 28, 811, 30, 809, 27, 812, 29, 810



SG6 (52-63)
24, 815, 48, 791, 68, 771, 74, 765, 178, 661, 136, 703



SG7 (64-75)
86, 753, 78, 761, 43, 796, 39, 800, 20, 819, 21, 818



SG8 (76-89)
95, 744, 202, 637, 190, 649, 181, 658, 137, 702, 125, 714, 151, 688



SG9 (90-115)
217, 622, 128, 711, 142, 697, 122, 717, 203, 636, 118, 721, 110, 729, 89,




750, 103, 736, 61, 778, 55, 784, 15, 824, 14, 825



SG10 (116-135)
12, 827, 23, 816, 34, 805, 37, 802, 46, 793, 207, 632, 179, 660, 145, 694,




130, 709, 223, 616



SG11 (136-167)
228, 611, 227, 612, 132, 707, 133, 706, 143, 696, 135, 704, 161, 678, 201,




638, 173, 666, 106, 733, 83, 756, 91, 748, 66, 773, 53, 786, 10, 829, 9, 830



SG12 (168-203)
7, 832, 8, 831, 16, 823, 47, 792, 64, 775, 57, 782, 104, 735, 101, 738, 108,




731, 208, 631, 184, 655, 197, 642, 191, 648, 121, 718, 141, 698, 149, 690,




216, 623, 218, 621



SG13 (204-263)
152, 687, 144, 695, 134, 705, 138, 701, 199, 640, 162, 677, 176, 663, 119,




720, 158, 681, 164, 675, 174, 665, 171, 668, 170, 669, 87, 752, 169, 670,




88, 751, 107, 732, 81, 758, 82, 757, 100, 739, 98, 741, 71, 768, 59, 780, 65,




774, 50, 789, 49, 790, 26, 813, 17, 822, 13, 826, 6, 833



SG14 (264-327)
5, 834, 33, 806, 51, 788, 75, 764, 99, 740, 96, 743, 97, 742, 166, 673, 172,




667, 175, 664, 187, 652, 163, 676, 185, 654, 200, 639, 114, 725, 189, 650,




115, 724, 194, 645, 195, 644, 192, 647, 182, 657, 157, 682, 156, 683, 211,




628, 154, 685, 123, 716, 139, 700, 212, 627, 153, 686, 213, 626, 215, 624,




150, 689



SG15 (328-383)
225, 614, 224, 615, 221, 618, 220, 619, 127, 712, 147, 692, 124, 715, 193,




646, 205, 634, 206, 633, 116, 723, 160, 679, 186, 653, 167, 672, 79, 760,




85, 754, 77, 762, 92, 747, 58, 781, 62, 777, 69, 770, 54, 785, 36, 803, 32,




807, 25, 814, 18, 821, 11, 828, 4, 835



SG16 (384-455)
3, 836, 19, 820, 22, 817, 41, 798, 38, 801, 44, 795, 52, 787, 45, 794, 63,




776, 67, 772, 72




767, 76, 763, 94, 745, 102, 737, 90, 749, 109, 730, 165, 674, 111, 728, 209,




630, 204, 635, 117, 722, 188, 651, 159, 680, 198, 641, 113, 726, 183, 656,




180, 659, 177, 662, 196, 643, 155, 684, 214, 625, 126, 713, 131, 708, 219,




620, 222, 617, 226, 613


High CM group
SG1 (456-513)
230, 609, 232, 607, 262, 577, 252, 587, 418, 421, 416, 423, 413, 426, 411,




428, 376, 463, 395, 444, 283, 556, 285, 554, 379, 460, 390, 449, 363, 476,




384, 455, 388, 451, 386, 453, 361, 478, 387, 452, 360, 479, 310, 529, 354,




485, 328, 511, 315, 524, 337, 502, 349, 490, 335, 504, 324, 515



SG2 (514-561)
323, 516, 320, 519, 334, 505, 359, 480, 295, 544, 385, 454, 292, 547, 291,




548, 381, 458, 399, 440, 380, 459, 397, 442, 369, 470, 377, 462, 410, 429,




407, 432, 281, 558, 414, 425, 247, 592, 277, 562, 271, 568, 272, 567, 264,




575, 259, 580



SG3 (562-629)
237, 602, 239, 600, 244, 595, 243, 596, 275, 564, 278, 561, 250, 589, 246,




593, 417, 422, 248, 591, 394, 445, 393, 446, 370, 469, 365, 474, 300, 539,




299, 540, 364, 475, 362, 477, 298, 541, 312, 527, 313, 526, 314, 525, 353,




486, 352, 487, 343, 496, 327, 512, 350, 489, 326, 513, 319, 520, 332, 507,




333, 506, 348, 491, 347, 492, 322, 517



SG4 (630-659)
330, 509, 338, 501, 341, 498, 340, 499, 342, 497, 301, 538, 366, 473, 401,




438, 371, 468, 408, 431, 375, 464, 249, 590, 269, 570, 238, 601, 234, 605



SG5 (660-707)
257, 582, 273, 566, 255, 584, 254, 585, 245, 594, 251, 588, 412, 427, 372,




467, 282, 557, 403, 436, 396, 443, 392, 447, 391, 448, 382, 457, 389, 450,




294, 545, 297, 542, 311, 528, 344, 495, 345, 494, 318, 521, 331, 508, 325,




514, 321, 518



SG6 (708-729)
346, 493, 339, 500, 351, 488, 306, 533, 289, 550, 400, 439, 378, 461, 374,




465, 415, 424, 270, 569, 241, 598



SG7 (730-751)
231, 608, 260, 579, 268, 571, 276, 563, 409, 430, 398, 441, 290, 549, 304,




535, 308, 531, 358, 481, 316, 523



SG8 (752-765)
293, 546, 288, 551, 284, 555, 368, 471, 253, 586, 256, 583, 263, 576



SG9 (766-777)
242, 597, 274, 565, 402, 437, 383, 456, 357, 482, 329, 510



SG10 (778-789)
317, 522, 307, 532, 286, 553, 287, 552, 266, 573, 261, 578



SG11 (790-795)
236, 603, 303, 536, 356, 483



SG12 (796-803)
355, 484, 405, 434, 404, 435, 406, 433



SG13 (804-809)
235, 604, 267, 572, 302, 537



SG14 (810-815)
309, 530, 265, 574, 233, 606



SG15 (816-819)
367, 472, 296, 543



SG16 (820-837)
336, 503, 305, 534, 373, 466, 280, 559, 279, 560, 419, 420, 240, 599, 258,




581, 229, 610









In a practical system, according to the random access system parameters (comprising the logical index of the first usable ZC sequence, cyclic shift, and high speed indication, etc.), a base station and a mobile terminal use the following method, to generate a random access preamble sequence of the current cell (the base station transmits the system parameters to the mobile terminal via broadcast channel).
1. the logical index x of the first usable ZC sequence is obtained;
2. the physical index of the ZC sequence is determined according to Table 5 and x;
3. a physical root sequence is generated using the determined physical index according to Equation 3;
4. the preamble sequence of the RACH is generated according to the cyclic shift Ncs and cyclic shift limitation rule;
5. if the total number of the current preamble sequences is less than an upper limit Q (Q=64), the logical index x of the usable ZC sequences is incremented, and steps 2-5 are repeated until the total number of the preamble sequences reaches to Q.
The present invention further provides a device for sequencing the ZC sequences of the RACH, which comprises: a first group dividing unit configured to divide the ZC sequences of the RACH into a low CM group and a high CM group according to the CM of QPSK, to make the index of each ZC sequence within the low CM group smaller or larger than the index of each ZC sequence within the high CM group; a second group dividing unit configured to respectively divide the ZC sequences within the low CM group and within the high CM group into S sub-groups using S−1 maximum cyclic shift thresholds according to the maximum cell radius or maximum cyclic shift supported by the ZC sequences under the high speed circumstance, wherein S is a positive integer; and a sequencing unit configured to sequence the sequences within each sub-group according to the CMs of the ZC sequences, to make the ZC sequences in adjacent sub-groups within the low CM group and within the high CM group have different sequencing, and the ZC sequences in adjacent sub-groups between the low CM group and the high CM group have the same sequencing, wherein the last sub-group within the low CM group and the first sub-group within the high CM group are adjacent with each other while the first sub-group within the low CM group and the last sub-group within the high CM group are adjacent with each other.
The present invention not only enables the assignment of the sequences according to the CMs, but also enables the collection of the sequence fragments for use, so that the generation of sequence fragments can be avoided. Meanwhile, the present invention is fully compatible to the first and the second re-sequencing methods described in the Background of the Invention, without introducing any extra signaling cost.
The descriptions above are only preferable embodiments of the present invention, which are not used to restrict the present invention. For those skilled in the art, the present invention may have various changes and variations. Any amendments, equivalent substitutions, improvements etc. within the spirit and principle of the present invention are all included in the scope of the claims of the present invention.

## Claims

1. A method for sequencing the Zadoff-Chu (ZC) sequences of the Random Access Channel (RACH), comprising:
step 1: a mobile terminal acquiring a logical index from logical indices of each ZC sequence via a Broadcast Channel, BCH, channel;
step 2: the mobile terminal creating mapping relationship between the logical indices and physical indices and acquiring a physical index corresponding to the logical index, wherein creating mapping relationship between the logical indices and physical indices comprising the following steps:
setting the logical index of each ZC sequence as α, and the physical index of each ZC sequence as u, wherein 1≦u≦N−1,0≦α≦N−2, N is the length of each ZC sequence and N=839;
creating the physical indices u corresponding to the logical indices α=0, 1, . . . , 837, the physical indices u are:
129, 710, 140, 699, 120, 719, 210, 629, 168, 671, 84, 755, 105, 734, 93, 746, 70, 769, 60, 779, 2, 837, 1, 838, which correspond to logical indices 0-23 of a sub-group 1 of a low CM group;
56, 783, 112, 727, 148, 691, which correspond to logical indices 24-29 of a sub-group 2 of the low CM group;
80, 759, 42, 797, 40, 799, which correspond to logical indices 30-35 of a sub-group 3 of the low CM group;
35, 804, 73, 766, 146, 693, which correspond to logical indices 36-41 of a sub-group 4 of the low CM group;
31, 808, 28, 811, 30, 809, 27, 812, 29, 810, which correspond to logical indices 42-51 of a sub-group 5 of the low CM group;
24, 815, 48, 791, 68, 771, 74, 765, 178, 661, 136, 703, which correspond to logical indices 52-63 of a sub-group 6 of the low CM group;
86, 753, 78, 761, 43, 796, 39, 800, 20, 819, 21, 818, which correspond to logical indices 64-75 of a sub-group 7 of the low CM group;
95, 744, 202, 637, 190, 649, 181, 658, 137, 702, 125, 714, 151, 688, which correspond to logical indices 76-89 of a sub-group 8 of the low CM group;
217, 622, 128, 711, 142, 697, 122, 717, 203, 636, 118, 721, 110, 729, 89, 750, 103, 736, 61, 778, 55, 784, 15, 824, 14, 825, which correspond to logical indices 90-115 of a sub-group 9 of the low CM group;
12, 827, 23, 816, 34, 805, 37, 802, 46, 793, 207, 632, 179, 660, 145, 694, 130, 709, 223, 616, which correspond to logical indices 116-135 of a sub-group 10 of the low CM group;
228, 611, 227, 612, 132, 707, 133, 706, 143, 696, 135, 704, 161, 678, 201, 638, 173, 666, 106, 733, 83, 756, 91, 748, 66, 773, 53, 786, 10, 829, 9, 830, which correspond to logical indices 136-167 of a sub-group 11 of the low CM group;
7, 832, 8, 831, 16, 823, 47, 792, 64, 775, 57, 782, 104, 735, 101, 738, 108, 731, 208, 631, 184, 655, 197, 642, 191, 648, 121, 718, 141, 698, 149, 690, 216, 623, 218, 621, which correspond to logical indices 168-203 of a sub-group 12 of the low CM group;
152, 687, 144, 695, 134, 705, 138, 701, 199, 640, 162, 677, 176, 663, 119, 720, 158, 681, 164, 675, 174, 665, 171, 668, 170, 669, 87, 752, 169, 670, 88, 751, 107, 732, 81, 758, 82, 757, 100, 739, 98, 741, 71, 768, 59, 780, 65, 774, 50, 789, 49, 790, 26, 813, 17, 822, 13, 826, 6, 833, which correspond to logical indices 204-263 of a sub-group 13 of the low CM group;
5, 834, 33, 806, 51, 788, 75, 764, 99, 740, 96, 743, 97, 742, 166, 673, 172, 667, 175, 664, 187, 652, 163, 676, 185, 654, 200, 639, 114, 725, 189, 650, 115, 724, 194, 645, 195, 644, 192, 647, 182, 657, 157, 682, 156, 683, 211, 628, 154, 685, 123, 716, 139, 700, 212, 627, 153, 686, 213, 626, 215, 624, 150, 689, which correspond to logical indices 264-327 of a sub-group 14 of the low CM group;
225, 614, 224, 615, 221, 618, 220, 619, 127, 712, 147, 692, 124, 715, 193, 646, 205, 634, 206, 633, 116, 723, 160, 679, 186, 653, 167, 672, 79, 760, 85, 754, 77, 762, 92, 747, 58, 781, 62, 777, 69, 770, 54, 785, 36, 803, 32, 807, 25, 814, 18, 821, 11, 828, 4, 835, which correspond to logical indices 328-383 of a sub-group 15 of the low CM group;
3, 836, 19, 820, 22, 817, 41, 798, 38, 801, 44, 795, 52, 787, 45, 794, 63, 776, 67, 772, 72, 767, 76, 763, 94, 745, 102, 737, 90, 749, 109, 730, 165, 674, 111, 728, 209, 630, 204, 635, 117, 722, 188, 651, 159, 680, 198, 641, 113, 726, 183, 656, 180, 659, 177, 662, 196, 643, 155, 684, 214, 625, 126, 713, 131, 708, 219, 620, 222, 617, 226, 613, which correspond to logical indices 384-455 of a sub-group 16 of the low CM group;
230, 609, 232, 607, 262, 577, 252, 587, 418, 421, 416, 423, 413, 426, 411, 428, 376, 463, 395, 444, 283, 556, 285, 554, 379, 460, 390, 449, 363, 476, 384, 455, 388, 451, 386, 453, 361, 478, 387, 452, 360, 479, 310, 529, 354, 485, 328, 511, 315, 524, 337, 502, 349, 490, 335, 504, 324, 515, which correspond to logical indices 456-513 of a sub-group 1 of a high CM group;
323, 516, 320, 519, 334, 505, 359, 480, 295, 544, 385, 454, 292, 547, 291, 548, 381, 458, 399, 440, 380, 459, 397, 442, 369, 470, 377, 462, 410, 429, 407, 432, 281, 558, 414, 425, 247, 592, 277, 562, 271, 568, 272, 567, 264, 575, 259, 580, which correspond to logical indices 514-561 of a sub-group 2 of the high CM group;
237, 602, 239, 600, 244, 595, 243, 596, 275, 564, 278, 561, 250, 589, 246, 593, 417, 422, 248, 591, 394, 445, 393, 446, 370, 469, 365, 474, 300, 539, 299, 540, 364, 475, 362, 477, 298, 541, 312, 527, 313, 526, 314, 525, 353, 486, 352, 487, 343, 496, 327, 512, 350, 489, 326, 513, 319, 520, 332, 507, 333, 506, 348, 491, 347, 492, 322, 517, which correspond to logical indices 562-629 of a sub-group 3 of the high CM group;
330, 509, 338, 501, 341, 498, 340, 499, 342, 497, 301, 538, 366, 473, 401, 438, 371, 468, 408, 431, 375, 464, 249, 590, 269, 570, 238, 601, 234, 605, which correspond to logical indices 630-659 of a sub-group 4 of the high CM group;
257, 582, 273, 566, 255, 584, 254, 585, 245, 594, 251, 588, 412, 427, 372, 467, 282, 557, 403, 436, 396, 443, 392, 447, 391, 448, 382, 457, 389, 450, 294, 545, 297, 542, 311, 528, 344, 495, 345, 494, 318, 521, 331, 508, 325, 514, 321, 518, which correspond to logical indices 660-707 of a sub-group 5 of the high CM group;
346, 493, 339, 500, 351, 488, 306, 533, 289, 550, 400, 439, 378, 461, 374, 465, 415, 424, 270, 569, 241, 598, which correspond to logical indices 708-729 of a sub-group 6 of the high CM group;
231, 608, 260, 579, 268, 571, 276, 563, 409, 430, 398, 441, 290, 549, 304, 535, 308, 531, 358, 481, 316, 523, which correspond to logical indices 730-751 of a sub-group 7 of the high CM group;
293, 546, 288, 551, 284, 555, 368, 471, 253, 586, 256, 583, 263, 576, which correspond to logical indices 752-765 of a sub-group 8 of the high CM group;
242, 597, 274, 565, 402, 437, 383, 456, 357, 482, 329, 510, which correspond to logical indices 766-777 of a sub-group 9 of the high CM group;
317, 522, 307, 532, 286, 553, 287, 552, 266, 573, 261, 578, which correspond to logical indices 778-789 of a sub-group 10 of the high CM group;
236, 603, 303, 536, 356, 483, which correspond to logical indices 790-795 of a sub-group 11 of the high CM group;
355, 484, 405, 434, 404, 435, 406, 433, which correspond to logical indices 796-803 of a sub-group 12 of the high CM group;
235, 604, 267, 572, 302, 537, which correspond to logical indices 804-809 of a sub-group 13 of the high CM group;
309, 530, 265, 574, 233, 606, which correspond to logical indices 810-815 of a sub-group 14 of the high CM group;
367, 472, 296, 543, which correspond to logical indices 816-819 of a sub-group 15 of the high CM group;
336, 503, 305, 534, 373, 466, 280, 559, 279, 560, 419, 420, 240, 599, 258, 581, 229, 610, which correspond to logical indices 820-837 of a sub-group 16 of the high CM group;
wherein the ZC sequences of the RACH are divided into the high CM group and the low CM group according to a CM of QPSK, and sequences in each group are further divided into sub-groups according to maximum cyclic shift thresholds; and

sequencing the ZC sequences of the RACH according to the created mapping relationship between the logical indices and the physical indices; and

step 3: the mobile terminal determining a preamble according to the physical index.