# Patent

## Title
Method of generating random access preambles in wireless communication system

## Abstract

A method of generating random access preambles includes receiving information on a source logical index and generating random access preambles in the order of increasing cyclic shift from root ZC sequences with the consecutive logical indexes from the beginning of the source logical index until a predetermined number of the random access preambles are found, wherein the consecutive logical indexes are mapped to root indexes of the root ZC sequences.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of priority of Korean Patent Application No. 10-2007-0062371 filed on Jun. 25, 2007, Korean Patent Application No. 10-2007-0091198 filed on Sep. 7, 2007, Korean Patent Application No. 10-2007-0125290 filed on Dec. 5, 2007, U.S. Provisional application Ser. No. 60/895,412 filed on Mar. 16, 2007, U.S. Provisional application Ser. No. 60/895,703 filed on Mar. 19, 2007, U.S. Provisional application Ser. No. 60/896,237 filed on Mar. 21, 2007, U.S. Provisional application Ser. No. 60/955,830 filed on Aug. 14, 2007, U.S. Provisional application Ser. No. 60/972,257 filed on Sep. 14, 2007, U.S. Provisional application Ser. No. 60/976,125 filed on Sep. 28, 2007 and U.S. Provisional application Ser. No. 60/980,293 filed on Oct. 16, 2007, which are incorporated by reference in its entirety herein.


BACKGROUND
1. Technical Field
The present invention relates to wireless communication and, in particular, to a method of generating random access preambles in a wireless communication system.
2. Related Art
The 3GPP (3rd Generation Partnership Project) mobile communication system based on WCDMA (Wideband Code Division Multiple Access) radio access technologies is widely deployed all over the world. An HSDPA (High Speed Downlink Packet Access), which could be defined as the first evaluation phase of the WCDMA, provides radio access technologies that are highly competitive in the mid-term future. However, because radio access technologies are being constantly advanced to meet the increasing demands and expectations of users and providers, new technological evolution is required in the 3GPP to ensure competitiveness in the future.
One of the systems that are considered to follow the 3rd generation systems is an OFDM (Orthogonal Frequency Division Multiplexing) system that attenuates inter-symbol interference (ISI) with low complexity. In the OFDM, serially inputted data symbols are converted into the N number of parallel data symbols, transmitted on the N number of orthogonal subcarriers. The subcarriers maintain orthogonality in frequency domain. Respective orthogonal channels experience mutually independent frequency selective fading, and when the interval between symbols is long enough, ISI can be canceled. An OFDMA (Orthogonal Frequency Division Multiple Access) refers to a multiple access method using the OFDM as modulation scheme. In the OFDMA, the frequency resources, namely, the subcarriers, are provided to each user. In this case, because each frequency resource is independently provided to a plurality of users, the frequency resources do not overlap with each other. Namely, the frequency resources are allocated to the users exclusively.
In order to transmit or receive a data packet, control information needs to be transmitted. For example, uplink control information includes ACK (Acknowledgement)/NACK (Negative-Acknowledgement) signals indicating successful transmission of downlink data, a CQI (Channel Quality Indicator) indicating quality of a downlink channel, a PMI (Precoding Matrix Index), an RI (Rank Indicator), etc. In addition, a random access preamble needs to be transmitted to perform a random access procedure.
A sequence is commonly used to transmit the uplink control information or the random access preamble. The sequence is transmitted in the form of a spreading code, a user equipment identifier, or a signature via a control channel or a random access channel.
FIG. 1 is an exemplary view showing a method for performing a random access procedure in a WCDMA system. The random access procedure is performed to allow a user equipment to acquire uplink synchronization with a network or acquire uplink radio resources for transmitting uplink data.
Referring to FIG. 1, a user equipment transmits a preamble via a PRACH (Physical Random Access Channel) which is an uplink physical channel. The preamble is transmitted during the access slot of 1.33 ms. The preamble is randomly selected from sixteen preambles.
Upon receiving the preamble from the user equipment, a base station transmits a response via an AICH (Acquisition Indicator Channel) which is a downlink physical channel. The base station transmits an acknowledgement (ACK) or a negative acknowledgement (NACK) to the user equipment via the AICH. If the user equipment receives ACK, the user equipment transmits a message having a length of 10 ms or 20 ms by using an OVSF (Orthogonal Variable Spreading Factor) code corresponding to the preamble. If the user equipment receives NACK, the user equipment transmits the preamble again in a suitable time. If the user equipment fails to receive a response corresponding to the previously transmitted preamble, the user equipment transmits a new preamble with power level higher than that of the previous preamble after a determined access slot.
The user equipment acquire information on sixteen preambles (namely, sequences), and uses one selected from the sixteen preambles as a preamble in the random access procedure. If the base station informs the user equipment of information regarding every available sequence, signaling overhead may be increased. So, generally, the base station previously designates sets of sequences and transfers an index of the sets of sequences to the sixteen preambles. For this purpose, the user equipment and the base station should store the sets of sequences according to the index in their buffer, respectively. This may be burdensome if the number of sequences belonging to the sequence sets is increased or the number of sets of sequences is increased.
In order to enhance performance of data detection in a receiver and increase capability, correlation or CM (Cubic Metric) characteristics of the sequences should be guaranteed to a degree. This means that the sequences belonging to the sequence sets used for the random access procedure should have correlation or CM characteristics guaranteed by more than a certain level. In particular, a sequence used for a high speed environment in which the user equipment is moved by a speed of 30 km/h or faster and a sequence used for a low speed environment need to be separately used in order to guarantee sequence characteristics in consideration of Doppler effect.
A method is sought for guaranteeing the characteristics of sequences used for transmission of the uplink control information with smaller amount of signaling overhead.
SUMMARY
A method of generating logical indexes of root Zadoff-Chu (ZC) sequences to facilitate sequence generation is provided.
A method of performing a random access procedure in a wireless communication system using the logical indexes of root ZC sequences is provided.
A method of generating random access preambles using the logical indexes of root ZC sequences is provided.
In an aspect, a method of generating logical indexes of root Zadoff-Chu (ZC) sequences is provided. The method includes dividing a plurality of root indexes of root ZC sequences into one or more subgroups according to predetermined cyclic shift parameters, a subgroup including at least one root index of a root ZC sequence and mapping the root indexes of the root ZC sequences in the subgroup to consecutive logical indexes.
In another aspect, a method of performing random access procedure in a wireless communication system is provided. The method includes selecting a random access preamble from a plurality of random access preambles, the plurality of random access preambles being generated from available cyclic shifts of root ZC sequences with consecutive logical indexes, wherein the consecutive logical indexes are mapped to root indexes of the root ZC sequences, transmitting the selected random access preamble and receiving a random access response including the identifier of the selected random access preamble.
In still another aspect, a method of performing random access procedure in a wireless communication system is provided. The method includes transmitting a source logical index for generating a plurality of random access preambles and a predetermined cyclic shift parameter, receiving a random access preamble selected from the plurality of random access preambles, the plurality of random access preambles being generated from available cyclic shifts of root ZC sequences with the source logical index and at least one consecutive logical index of the source logical index and transmitting a random access response including the identifier of the random access preamble.
In still another aspect, a method of generating random access preambles is provided. The method includes generating random access preambles in the order of increasing cyclic shift from a first root ZC sequence with a first root index mapped to a first logical index and generating additional random access preambles in the order of increasing cyclic shift from a second root ZC sequence with a second root index mapped to a second logical index when a predetermined number of random access preambles cannot be generated from the first root ZC sequence, the second logical index being consecutive to the first logical index.
In still another aspect, a method of generating random access preambles includes receiving information on a source logical index and generating random access preambles in the order of increasing cyclic shift from root ZC sequences with the consecutive logical indexes from the beginning of the source logical index until a predetermined number of the random access preambles are found, wherein the consecutive logical indexes are mapped to root indexes of the root ZC sequences.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is an exemplary view showing a method of performing a random access procedure in a WCDMA system.
FIG. 2 is a view showing a wireless communication system.
FIG. 3 is a flow chart illustrating the process of a method of generating sequences according to one exemplary embodiment of the present invention.
FIG. 4 is a graph showing CM (Cubic Metric) characteristics and maximum supportable cell radius characteristics according to physical root indexes according to one exemplary embodiment of the present invention.
FIG. 5 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to one exemplary embodiment of the present invention.
FIG. 6 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention.
FIGS. 7 to 14 are graphs showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to still another exemplary embodiment of the present invention.
FIG. 15 is a graph showing the number of restricted cyclic shifts that can be used per logical root index according to Ncs with respect to CM mapping according to one exemplary embodiment of the present invention.
FIG. 16 is a graph showing the number of restricted cyclic shifts that can be used per logical root index according to Ncs with respect to maximum supportable cell size mapping according to one exemplary embodiment of the present invention.
FIG. 17 is a graph showing the number of restricted cyclic shifts that can be used per logical root index according to Ncs with respect to hybrid mapping according to one exemplary embodiment of the present invention.
FIG. 18 is a graph showing examples of logical root indexes allocated to cells with respect to CM mapping according to one exemplary embodiment of the present invention.
FIG. 19 is a graph showing examples of logical root indexes allocated to cells with respect to maximum supportable cell size mapping according to one exemplary embodiment of the present invention.
FIG. 20 is a graph showing examples of logical root indexes allocated to cells with respect to maximum supportable cell size mapping according to one exemplary embodiment of the present invention.
FIG. 21 is a view illustrating a method of searching logical root indexes according to CM characteristics according to one exemplary embodiment of the present invention.
FIG. 22 is a view illustrating a method of searching logical root indexes according to CM characteristics according to another exemplary embodiment of the present invention.
FIG. 23 is a view illustrating a method of searching logical root indexes according to CM characteristics according to still another exemplary embodiment of the present invention.
FIG. 24 is a graph showing CM characteristics according to physical root indexes according to one exemplary embodiment of the present invention.
FIG. 25 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention.
FIG. 26 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention.
FIG. 27 is a graph showing a process of grouping CM ordering into two groups.
FIG. 28 is a graph showing a process of grouping indexes ordered according to maximum supportable Ncs characteristics into Ncs groups in each group.
FIG. 29 is a graph showing a process of ordering indexes according to the CM characteristics in each Ncs group.
FIG. 30 is a flow chart illustrating the random access procedure according to one exemplary embodiment of the present invention.
FIG. 31 is a schematic block diagram of elements of a user equipment to which the exemplary embodiments are applied.



DESCRIPTION OF EXEMPLARY EMBODIMENTS
FIG. 2 illustrates a wireless communication system. The wireless communication system can widely be deployed to provide various communication services such as voice and packet data, etc.
Referring to FIG. 2, a wireless communication system includes a user equipment (UE) 10 and a base station (BS) 20. The UE 10, which may be fixed or mobile, may be called other terms such as an MS (Mobile Station), a UT (User Terminal), an SS (Subscriber Station), a wireless device, and so on. The BS 20 refers to a fixed station that communicates with the UE 10, and may be also called a Node-B, a BTS (Base Transceiver System), an AP (Access Point), and so on. One or more cells may exist in a BS 20.
Hereinafter, downlink refers to communication from the BS 20 to the UE 10, and uplink refers to communication from the UE 10 to the BS 20. In the downlink, a transmitter may be a part of the BS 20, and a receiver may be a part of the UE 10. In the uplink, a transmitter may be a part of the UE 10 and a receiver may be a part of the BS 20.
There is no limitation in multiple access techniques applied to the wireless communication system. For example, various multiple access techniques such as CDMA (Code Division Multiple Access), TDMA (Time Division Multiple Access), FDMA (Frequency Division Multiple Access), SC-FDMA (Single Carrier-FDMA), and OFDMA (Orthogonal Frequency Division Multiple Access) can be used. For clarification, the OFDMA-based wireless communication system will now be described hereinafter.
The OFDM uses a plurality of orthogonal subcarriers. The OFDM uses orthogonality between IFFT (Inverse Fast Fourier Transform) and FFT (Fast Fourier Transform). A transmitter performs IFFT on data and transmits the same. A receiver performs FFT on a received signal to restore the original data. The transmitter uses IFFT to combine multiple subcarriers and the receiver uses corresponding FFT to split the combined multiple subcarriers. According to the OFDM, the complexity of the receiver in a frequency selective fading environment of a broadband channel can be reduced and a spectral efficiency can be improved through selective scheduling in a frequency domain by utilizing different channel characteristics of subcarriers. The OFDMA is a multiple access scheme based on the OFDM. According to the OFDMA, different subcarriers can be allocated to a plurality of users, thereby improving the efficiency of radio resources.
There may be various types of control information such as an ACK (Acknowledgement)/NACK (Negative Acknowledgement) signal indicating whether or not re-transmission should be performed, a CQI (Channel Quality Indicator) indicating quality of a downlink channel, a random access preamble for a random access procedure, and MIMO control information such as a PMI (Precoding Matrix Index), an RI (Rank Indicator), etc.
An orthogonal sequence may be used to transmit control information. The orthogonal sequence refers to a sequence having good correlation characteristics. The orthogonal sequence may include, for example, a CAZAC (Constant Amplitude Zero Auto-Correction) sequence.
Regarding a ZC (Zadoff-Chu) sequence, one of the CAZAC sequences, the k-th element c(k) of a root ZC sequence which corresponds to a root index M may be expressed as shown:




  
    
      
        
          
            
              c
              ⁡
              
                (
                k
                )
              
            
            =
            
              exp
              ⁢
              
                {
                
                  -
                  
                    
                      jπ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        Mk
                        ⁡
                        
                          (
                          
                            k
                            +
                            1
                          
                          )
                        
                      
                    
                    N
                  
                
                }
              
            
          
          ,
          
            for
            ⁢
            
              
            
            ⁢
            N
            ⁢
            
              
            
            ⁢
            odd
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              c
              ⁡
              
                (
                k
                )
              
            
            =
            
              exp
              ⁢
              
                {
                
                  -
                  
                    
                      jπ
                      ⁢
                      
                        
                      
                      ⁢
                      
                        Mk
                        2
                      
                    
                    N
                  
                
                }
              
            
          
          ,
          
            for
            ⁢
            
              
            
            ⁢
            N
            ⁢
            
              
            
            ⁢
            even
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          1
        
        ]
      
    
  




where N is the length of the root ZC sequence, the root index M is relatively prime to N. If N is a prime number, the number of root indexes of the ZC sequence would be N−1.
The ZC sequence c(k) has the following three characteristics.

|c(k)|=1 for all k,N,M,  [Equation 2]





  
    
      
        
          
            R
            
              M
              ;
              N
            
          
          ⁡
          
            (
            d
            )
          
        
        =
        
          {
          
            
              
                
                  1
                  ,
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    d
                  
                  =
                  0
                
              
            
            
              
                
                  0
                  ,
                
              
              
                
                  
                    for
                    ⁢
                    
                      
                    
                    ⁢
                    d
                  
                  ≠
                  0
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          3
        
        ]
      
    
  




RM1,M2;N(d)=const for all M1,M2  [Equation 4]

Equation 2 means that the size of the ZC sequence is always 1, and Equation 3 means that auto-correlation of the ZC sequence is expressed as a Dirac-delta function. Here, the auto-correlation is based on circular correlation. Equation 4 means that cross correlation is always a constant.
In the wireless communication system, if it is assumed that cells are discriminated by the root indexes of the ZC sequence, the user equipment would need to know a root index or a group of root indexes that can be used within a cell and the base station should broadcast an available root index or an available group of root indexes to the user equipment.
If the length of the ZC sequence is N, the number of root indexes would be to the number of relative prime numbers to N among the natural numbers smaller than N. If N is a prime number, the number of root indexes would be N−1. In this case, in order for the base station to inform the user equipment about one of the N−1 number of root indexes, ceil(log2(N−1)) bits are required. Ceil(x) indicates the smallest integer greater than x.
Each cell may use various number of root indexes according to a cell radius. If the cell radius increases, the number of ZC sequences that can maintain orthogonality through cyclic shift may be reduced due to an influence of propagation delay or a round trip delay and/or a delay spread. Namely, if the cell radius increases, although the length of the ZC sequence is fixed (regular, uniform), the number of available cyclic shifts in a corresponding root index may be reduced. Because the sequences created by the cyclic shifts in the root index have orthogonality to each other, so they are also called ZCZ (Zero Correlation Zone) sequences. The minimum number of ZC sequences allocated to user equipments in each cell should be guaranteed. Thus, if the cell radius increases, the number of root indexes used in each cell is increased to secure the minimum number of ZC sequences.
It is assumed that a group of available root ZC indexes in each cell is Ri, and the M number of groups of root ZC indexes in all is set. This can be expressed as R1, R2, . . . , RM. If Ri=10, it can be said that cells in which Riis set use 10 root ZC indexes. It is assumed that N=839, M=7, R1=1, R2=2, R3=4, R4=8, R5=16, R6=32, and R7=64 according to each cell radius. Then, if the cell radius is large, minimum 7 bits (ceil(log2(7))+ceil(log2(838/64))=7 bits) is required to transmit control information, and if the cell radius is small, maximum 13 bits (ceil(log2(7))+ceil(log2(838/1))=13 bits) are required to transmit control information.
As wireless communication systems are advanced, demands for a higher transfer rate are increasing and cells having a smaller radius are increasing. Because such cells having a small radius use only a single root ZC index, more bits are required to transmit control information, possibly causing a signal overhead. Thus, a technique for reducing the number of bits required for signaling is necessary in each cell. In particular, it is important to reduce the number of signaling bits in the cells having the small cell radius.
FIG. 3 is a flow chart illustrating the process of a method of generating sequences according to one exemplary embodiment of the present invention.
Referring to FIG. 3, a plurality of root ZC sequences is divided into one or more subgroups according to a predetermined cyclic shift parameter (S110). The subgroups include at least one root ZC sequence. If the cyclic shift parameter is Ncs, a root ZC sequence has zero correlation zones of length of Ncs−1. The cyclic shift parameter is a parameter for obtaining a cyclic shift unit of the root ZC sequence, and the subgroups may be ordered according to the cyclic shift parameter. Because the Doppler effect is strong in high speed environment, the cyclic shift unit is obtained by using the cyclic shift parameter according to each maximum supportable cell radius and a Doppler shift of detection stage. The cyclic shift unit is a unit for cyclic-shifting the root ZC sequence. The cyclic shift parameter of the root ZC sequence is smaller than or equal to the predetermined cyclic shift parameter of the subgroup of the root ZC sequence. The value of cyclic shift of the root ZC sequence is greater than the cyclic shift parameter of the root ZC sequence.
The root ZC sequences are ordered according to CM (Cubic Metric) in a subgroup (S120). The ordering of the root ZC sequences according to the CM characteristics refers to ordering the root ZC sequences according to the CM characteristics of the ZC sequences according to combination of the root ZC indexes. As the metric of ordering the root ZC sequences in a subgroup, cross-correlation, PAPR (Peak-to-Average Power Ratio), a Doppler frequency, etc, as well as the CM, may be used. The ordering according to the cross-correlation characteristics refers to ordering the root ZC sequences according to cross-correlation of ZC sequences according to combinations of the root ZC indexes. The ordering according to the PAPR characteristics refers to ordering the root ZC sequences according to PAPR characteristics of the ZC sequences according to combinations of the root ZC indexes. The ordering according to the Doppler frequency characteristics refers to ordering the root ZC sequences according to a robust degree of the root indexes to the Doppler frequency.
A gain can be obtained by using root indexes having a robust Doppler frequency in a relatively high mobility cell or high speed cell. In case of using restricted cyclic shifts in a high mobility cell, the root indexes of root ZC sequences can be ordered (or grouped) according to a maximum supportable cell radius or a maximum supportable cyclic shift characteristics. The root indexes of root ZC sequences can be divided into subgroups by comparing maximum supportable cyclic shift parameters and predetermined cyclic shift parameters of the respective root ZC cyclic sequences, whereby root ZC sequences in each subgroup can have similar characteristics.
Physical root indexes of root ZC sequences belonging to one subgroup are mapped to consecutive logical indexes (S130). The physical root indexes refer to root indexes of ZC sequences which are actually used for the base station and/or the user equipment to transmit control information or a random access preamble. The logical indexes refer to logical root indexes to which the physical root indexes are mapped.
In case that the root ZC sequences are divided into subgroups according to the predetermined cyclic shift parameters and the consecutive logical indexes are allocated in the subgroups as described above, the base station may inform the user equipment about only at least one logical index to provide information about a plurality of ZC sequences having similar characteristics. For example, it is assumed that the root ZC sequences are ordered in a subgroup according to the CM and a single logical index is informed to the user equipment. Then, the user equipment generates root ZC sequences from the physical root indexes to which the received single logical index is mapped. If the number of ZC sequences (e.g., the number of available cyclic shifts of the ZC sequences) generated from the single logical index is insufficient, the user equipment would generates new root ZC sequences from physical root indexes mapped to a logical index adjacent to the received logical index. Because the adjacent (consecutive) logical indexes have the similar CM characteristics, even if only one logical index is given, the user equipment can generate a plurality of ZC sequences having the similar CM characteristics.
Example of Ordering According to CM Characteristics
FIG. 4 is a graph showing CM (Cubic Metric) characteristics and maximum supportable cell radius characteristics according to physical root indexes according to one exemplary embodiment of the present invention. FIG. 5 is a graph showing the CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to one exemplary embodiment of the present invention. FIG. 6 is a graph showing the CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention.
If ‘N’ is the length of a ZC sequence, the physical root indexes in FIG. 4 may be expressed as UP=1, 2, 3, N−3, N−2, N−1. FIG. 5 shows the results obtained by alternately picking up the physical root indexes from the start and from the end, one by one, and re-ordering them as UL=1, N−1, 2, N−2, 3, N−3, 4 . . . . FIG. 6 shows the results obtained by ordering the physical indexes in FIG. 4 as CM values corresponding to the logical indexes.
Table 1 shows an example of CM-based ordering of the physical root indexes and logical indexes.








TABLE 1





Logical



index
Physical root index

































 1~50
1
838
2
837
836
3
4
835
834
5
833
6
832
7
8
831
9
830



10
829
828
11
12
827
826
13
14
825
15
824
823
16
822
17
19
820



18
821
818
189
21
20
23
817
816
22
815
26
813
24






 51~100
25
814
29
812
810
809
27
811
30
28
808
31
804
33
805
32
34
35



807
806
799
36
40
803
797
42
798
38
801
41
37
39
802
800
796
790



43
44
49
789
795
52
50
788
787
51
793
47
791
46






101~150
48
792
794
786
53
45
64
774
55
775
785
54
65
784
64
776
69
783



773
56
779
772
769
770
771
70
60
67
61
66
59
780
777
68
778
57



62
782
781
71
58
768
93
746
72
767
764
75
104
763






151~200
94
76
735
745
105
734
92
73
766
103
747
765
736
74
95
737
744
101



102
748
738
91
99
740
90
749
762
77
98
741
100
755
743
84
96
739



757
82
78
761
83
756
106
733
168
671
754
85
97
753






201~250
86
742
89
750
758
81
732
107
88
751
79
80
759
760
670
167
672
169



87
752
731
108
669
170
673
109
166
730
171
674
165
668
172
667
728
111



665
174
186
729
675
110
653
164
175
187
666
664
173
652






251~300
163
676
209
679
116
630
185
727
112
160
631
723
208
639
655
654
200
207



206
721
635
118
722
632
204
117
633
184
651
680
188
201
638
205
681
159



663
634
119
720
158
114
725
176
161
650
641
113
678
115






301~350
189
193
677
198
202
724
637
726
656
636
194
640
645
203
162
646
199
183



629
210
642
197
195
192
180
120
657
644
719
179
190
647
191
662
649
659



157
177
648
182
660
181
682
196
643
658
178
661
718
121






351~400
156
717
683
211
122
628
685
154
124
715
716
694
140
123
155
699
684
145



137
700
704
686
141
627
135
701
212
139
134
698
702
138
153
705
714
695



125
144
142
143
697
696
146
213
693
626
136
133
703
706






401~450
152
687
151
688
214
713
625
126
128
711
132
692
147
712
624
215
707
150



689
127
709
690
691
130
148
129
149
710
623
708
216
131
622
217
621
218



219
620
220
619
223
616
221
618
617
222
615
224
613
226






451~500
227
612
225
614
611
228
229
610
230
609
231
608
236
603
607
232
235
604



606
233
234
602
605
237
601
238
262
261
239
577
578
580
260
579
600
259



581
258
263
576
582
599
257
240
269
570
256
583
571
575






501~550
270
598
241
268
569
264
242
272
567
274
244
597
565
595
265
566
573
596



243
267
564
276
574
271
275
563
572
568
584
562
255
561
277
278
253
266



420
419
560
279
254
573
586
585
587
252
245
594
588
421






551~600
589
249
250
418
590
251
246
417
593
422
416
423
248
280
559
591
247
424



415
373
466
592
426
413
414
425
412
427
411
428
281
430
374
558
465
376



407
463
409
432
410
372
467
462
557
429
282
436
403
395






601~650
464
377
433
375
406
431
444
402
283
371
404
556
408
437
443
468
435
396



369
471
445
394
470
446
461
442
378
368
434
284
405
397
555
469
370
393



401
447
398
554
392
438
367
472
459
285
380
441
400
287






651~700
552
439
440
286
553
460
379
381
399
458
551
291
288
448
548
290
537
391



549
366
302
473
547
289
457
292
550
536
382
383
456
303
449
365
390
304



300
474
363
476
535
539
538
546
534
540
293
305
301
299






701~750
450
477
364
388
389
541
455
362
384
475
451
453
298
386
478
387
361
454



452
545
294
385
479
544
542
360
543
297
295
306
296
533
307
532
308
531



530
359
309
480
358
481
310
357
482
529
527
355
312
311






751~800
484
485
528
356
483
354
313
526
525
353
314
486
487
343
495
496
352
344



351
497
488
342
511
328
345
329
510
327
494
315
350
524
512
340
489
498



499
316
318
500
513
521
341
339
523
493
501
508
319
326






801~838
317
346
338
506
522
331
337
332
325
507
490
492
348
502
491
520
333
330



349
334
347
514
509
505
336
504
503
335
321
519
324
515
320
322
518
516



517
323









Because the physical root indexes are ordered according to the CM characteristics and then mapped to the logical indexes, the CM characteristics of the ZC sequences corresponding to the consecutive logical indexes can be similarly maintained and a CM-based cell planning can be possibly performed. The base station may plan the CM-based cell in a power-limited environment such as in a cell where a channel environment is not good or in a cell having a large cell radius, etc. In addition, the base station may use indexes having good CM characteristics as dedicated preambles for handover or the like. A user equipment in a bad channel environment already uses its maximum power, so it can hardly obtain a power ramping effect. Then, the base station can allocate an index with good CM characteristics to the user equipment to increase a detection probability.
Example of Ordering According to Maximum Supportable Cell Radius Characteristics
FIG. 7 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to physical root indexes according to another exemplary embodiment of the present invention. FIG. 8 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention. FIG. 9 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to still another exemplary embodiment of the present invention.
Referring to FIGS. 7 to 9, FIG. 7 shows the ordering of ZC sequences used in FIG. 4 according to the maximum supportable cell radius. If ‘N’ is the length of the ZC sequence, the physical root indexes UP=1, 2, 3, . . . , N−3, N−2, N−1 in FIG. 7 are re-ordered by (1/UP) mod N. In this case, performing (1/UP) mod N on the ZC sequence indexes generated in time domain refers to mapping the ZC sequence indexes generated in the time domain to ZC sequence indexes generated in a frequency domain. In other words, such conversion refers to reordering the characteristics of ZC sequence indexes generated in a time domain as the ZC sequence indexes generated in a frequency domain. FIG. 8 shows the results obtained by alternately picking up the indexes, which have been converted from the physical indexes UP into (1/UP) mod N, from the start and from the end, one by one, and re-ordering them as 1, N−1, 2, N−2, 3, N−3, 4, . . . . FIG. 9 shows the results obtained by accurately re-ordering according to the maximum supportable cell radius corresponding to the physical indexes.
Table 2 shows an example of the maximum supportable cell radius-based ordering.








TABLE 2





Logical



index
Physical root index

































 1~50
1
2
837
838
419
429
279
280
559
560
210
629
168
336
503
671
140
699



120
240
599
719
105
734
93
373
466
746
84
755
229
305
534
610
70
769



129
258
581
710
60
779
56
112
727
783
367
472
148
296






 51~100
543
691
233
606
265
309
530
574
42
797
40
80
759
799
267
572
73
146



693
766
35
804
235
302
537
604
355
484
31
404
435
808
30
809
29
405



434
810
28
811
27
406
433
812
236
603
178
356
483
661






101~150
74
765
24
48
791
815
303
536
68
136
703
771
287
552
43
86
753
796



21
818
266
307
532
573
20
819
39
78
761
800
286
553
261
317
522
578



383
456
125
357
482
714
402
437
137
274
565
702
151
688






151~200
181
329
510
658
242
597
95
190
649
744
202
637
61
122
717
778
15
824



103
368
471
736
217
622
128
256
583
711
14
825
55
110
729
784
203
636



253
293
546
586
118
721
142
284
555
697
89
750
263
288






201~250
551
576
37
802
231
304
535
608
12
827
130
260
579
709
268
571
23
46



793
816
34
805
179
358
481
660
276
563
207
316
523
632
398
441
223
308



531
616
409
430
145
290
549
694
133
706
91
374
465
748






251~300
10
829
227
306
533
612
400
439
135
270
569
704
143
696
66
132
707
773



289
550
83
378
461
756
228
611
9
415
424
830
241
598
53
106
733
786



201
638
173
346
493
666
351
488
161
339
500
678
344
495






301~350
108
216
623
731
255
584
57
391
448
782
121
718
8
16
823
831
372
467



149
345
494
690
101
738
254
331
508
585
389
450
257
325
514
582
412
427



245
297
542
594
184
655
197
321
518
642
311
528
251
294






351~400
545
588
64
775
141
282
557
698
7
832
104
208
631
735
392
447
191
382



457
648
318
521
47
396
443
792
273
566
218
403
436
621
59
780
13
26



813
826
71
768
269
301
538
570
375
464
82
164
675
757






401~450
144
695
87
174
665
752
401
438
49
98
741
790
152
687
169
338
501
670



6
833
119
238
601
720
65
774
88
176
663
751
134
705
81
162
677
758



408
431
234
371
468
605
17
822
107
366
473
732
330
509






451~500
50
100
739
789
138
701
170
340
499
669
158
681
249
341
498
590
199
640



171
342
497
668
154
685
248
343
496
591
215
624
99
370
469
740
347
492



175
350
489
664
353
486
239
300
539
600
187
652
211
417






501~550
422
628
5
834
139
278
561
700
153
686
157
314
525
682
200
639
97
194



645
742
352
487
163
326
513
676
348
491
237
365
474
602
33
806
75
150



689
764
275
564
51
394
445
788
189
650
243
298
541
596






551~600
114
725
195
322
517
644
212
627
166
332
507
673
299
540
182
364
475
657



393
446
123
246
593
716
319
520
213
313
526
626
333
506
185
327
512
654



244
595
115
362
477
724
250
589
156
312
527
683
172
667






601~650
96
192
647
743
54
785
62
124
715
777
292
547
221
397
442
618
224
615



77
381
458
762
359
480
277
281
558
562
4
835
167
334
505
672
186
653



193
323
516
646
247
592
160
320
519
679
369
470
58
116






651~700
723
781
127
712
272
295
544
567
225
614
205
410
429
634
291
548
79
380



459
760
206
633
220
399
440
619
271
568
85
377
462
754
92
747
11
414



425
828
259
580
69
385
454
770
264
575
18
36
803
821






701~750
147
692
25
407
432
814
32
807
177
354
485
662
349
490
165
337
502
674



416
423
94
188
651
745
52
787
183
328
511
656
196
643
113
363
476
726



324
515
214
411
428
625
159
684
198
641










751~800
117
361
478
722
283
556
63
388
451
776
109
730
102
204
635
737
390
449



111
222
617
728
413
426
230
379
460
609
384
455
45
90
749
794
285
554



67
386
453
772
607
19
38
801
820
41
798
22
44







801~838
795
817
72
767
131
262
577
708
376
463
226
387
452
613
219
620
126
525



587
713
395
444
180
360
479
659
76
763
209
315
524
630
335
504
3
418



421
836









The method of reordering according to the maximum supportable cell radius can be applicable in case of using restricted cyclic shifts in a high speed cell environment. In using the restricted cyclic shifts, a value of a supportable cyclic shift parameter Ncs may vary according to indexes. If the physical root indexes as shown in FIG. 4 are used as it is, it may be difficult to use the consecutive physical indexes in a single cell. Thus, indexes that are not repeated for each cell should be allocated in an overall network, but this may cause a problem: Reuse factors of a sequence are reduced to make cell planning difficult. This problem can be solved by using logical indexes ordered according to the maximum supportable cell radius characteristics, but such ordering according to the maximum supportable cell radius characteristics may fail to obtain a gain in the CM characteristics.
Example of Ordering According to CM Characteristics and Maximum Supportable Cell Radius Characteristics
The ordering according to the CM characteristics and the ordering according to the maximum supportable cell radius characteristics may have the opposite characteristics. A method for achieving both gains of the CM characteristics and the maximum supportable cell radius characteristics will now be described.
The method of ordering by combining various characteristics follows the following procedures.
Step 1. The entire indexes are ordered according to specific (particular) characteristics.
Step 2. The entire indexes are divided into sections (or groups) based on relevant values (grouping).
Step 3. The indexes of the sections are ordered according to respective different characteristics in each section (or group).
Step 4. The steps 2 and 3 are repeated. In this case, in dividing the indexes into sections, a subsequent section may be associated with a preceding section, or the subsequent section may not have any relation with the preceding section and a new rule may be applied to the subsequent section.
FIG. 10 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to still another exemplary embodiment of the present invention. Namely, FIG. 10 shows ordering according to the maximum supportable cell radius characteristics and sections of the maximum supportable cell radius set according to particular values Ncs (predetermined cyclic shift parameters). FIG. 11 is a graph showing ordering according to CM characteristics within set sections in FIG. 10.
Referring to FIGS. 10 and 11, first, the entire indexes are ordered according to the maximum supportable cell radius and divided into sections according to the cyclic shift parameters Ncs or the maximum supportable cell radio values. The cyclic shift parameters Ncs are to obtain a cyclic shift unit supported per ZC sequence.
Table 3 shows examples of cyclic shift parameters Ncs.











TABLE 3








No. of ZC
No. of cyclic shift 

Max. supportable



sequence per cell
per ZC sequence
Cyclic 
cell radius [km]












Configuration
(no cyclic shift
(no cyclic shift
shift
No guard
2 guard


No.
restrictions)
restrictions)
[samples]
sample
samples















1
1
64
13
1.1
0.8


2
2
32
26
2.9
2.6


3
3
22
38
4.5
4.2


4
4
16
52
6.5
6.2


5
5
13
64
8.1
7.8


6
6
11
76
9.8
9.5


7
7
10
83
10.8
10.5


8
8
8
104
13.7
13.4


9
10
7
119
15.8
15.5


10
11
6
139
18.6
18.3


11
13
5
167
22.4
22.1


12
16
4
209
28.3
28.0


13
22
3
279
38.0
37.7


14
32
2
419
57.4
57.1


15
64
1
0
115.8
115.5


16
reserved
reserved
reserved
reserved
Reserved









If the physical indexes have such characteristics as shown in FIG. 4, the entire indexes can be ordered according to the maximum supportable cell radius as shown in FIG. 9. When the sections are divided by the maximum supportable cell radius value with respect to the cyclic shift parameters Ncs, results as shown in FIG. 10 are obtained. Here, the values ‘No guard sample’ were used.
When the root indexes are ordered according to the CM characteristics in each divided section, results as shown in FIG. 11 are obtained. In this case, hybrid ordering that considers both the CM and the maximum supportable cell radius is applied to the mapping from the physical indexes to the logical indexes as shown in Table 4.








TABLE 4





Logical



index
Physical root index

































 1~50
1
838
2
837
769
70
93
746
105
734
755
84
168
671
629
210
120
719



140
699
129
229
610
599
240
420
419
560
279
280
559
373
466
534
305
336



503
804
35
799
40
797
42
783
56
779
60
73
766
80






 51~100
759
727
112
146
693
691
148
710
235
604
606
233
581
258
265
267
574
572



367
472
537
302
543
296
530
309
355
815
24
29
812
810
809
27
811
30



28
808
31
791
48
771
68
765
74
178
661
136
703
236






101~150
603
433
406
404
435
434
405
287
536
303
484
356
483
818
819
21
20
39



800
796
43
78
761
753
86
181
658
137
702
714
125
151
688
261
578
242



274
565
266
573
402
437
552
286
553
383
456
307
532
357






151~200
482
329
510
317
522
14
825
15
824
55
784
61
778
103
736
95
744
729



110
202
637
636
203
190
649
717
122
128
711
622
217
256
583
597
253
471



368
12
827
23
816
805
34
37
802
793
46
89
750
721






201~250
118
179
660
142
697
709
130
231
608
260
579
263
576
571
268
276
586
284



555
551
288
304
535
546
293
358
481
91
207
632
694
145
133
706
223
616



563
430
409
398
441
290
549
308
531
316
523
9
830
10






251~300
829
786
53
773
66
57
782
748
83
756
106
733
731
108
666
173
201
638



161
678
121
704
135
143
696
132
707
623
216
227
612
611
228
270
598
241



569
584
255
424
415
374
465
461
378
400
439
448
391
289






301~350
550
306
533
495
344
351
488
500
339
493
346
8
831
823
16
64
775
101



738
655
184
642
197
718
141
690
149
582
257
254
585
245
594
588
251
412



427
372
467
450
389
545
294
542
297
311
528
345
494
508






351~400
331
325
514
321
518
832
7
826
13
26
813
790
49
47
792
59
780
71



768
104
735
98
741
757
82
169
87
752
665
174
675
164
631
208
191
648



698
695
144
152
687
621
218
269
570
566
273
557
282
436






401~450
403
464
375
443
396
401
447
392
438
457
382
538
301
318
521
833
6
822



17
789
50
774
65
99
740
100
739
758
81
732
107
88
751
670
669
170



171
668
175
187
664
652
681
663
119
720
158
176
677
640






451~500
162
199
211
685
154
701
134
138
705
624
215
234
605
601
238
239
600
249



590
248
591
431
371
408
468
469
370
366
473
300
539
353
486
343
496
497



342
350
340
489
498
499
341
501
338
492
330
347
509
834






501~550
5
33
806
788
51
785
54
777
62
764
75
762
77
743
96
97
742
673



166
172
667
163
676
185
639
654
200
114
725
650
115
189
724
194
645
195



192
657
644
647
157
182
682
156
683
628
124
715
716
123






551~600
700
686
627
212
139
153
213
626
150
689
221
618
615
224
602
237
244
595



596
243
564
275
561
277
278
589
250
246
417
593
422
445
394
446
442
445



394
446
442
397
393
381
458
547
292
365
474
540
299
477
364
541
362
475


601~650
298
359
480
527
312
313
526
525
314
487
352
327
512
513
319
326
506
332



507
348
491
520
333
322
517
836
3
4
835
828
11
19
820
18
821
817



22
25
814
32
807
36
803
798
38
801
41
44
795
52






651~700
787
794
45
63
776
69
772
770
67
781
58
72
767
763
94
76
745
92



747
737
102
90
749
754
85
79
760
167
672
109
730
674
165
728
111
186



653
209
679
116
630
160
723
206
635
722
204
117
633
651






701~750
680
188
205
159
634
641
113
193
198
726
656
646
183
180
662
659
177
196



643
155
684
214
713
625
126
692
147
712
127
708
131
219
620
220
619
617



222
613
226
225
614
230
609
607
232
262
577
580
259
575






751~800
264
272
567
271
568
562
587
252
421
418
416
423
247
592
426
413
414
425



411
428
281
558
376
407
463
432
410
462
429
395
377
444
283
556
369
470



554
459
285
380
440
460
379
399
291
548
449
390
363
476






801~838
388
455
384
451
453
386
478
387
361
454
452
385
479
544
360
295
310
529



485
354
511
328
315
524
337
490
502
349
334
505
504
335
519
324
515
320



516
323









A plurality of sequences are divided into a plurality of sub-groups according to predetermined cyclic shift parameters Ncs, and ordered according to CM characteristics in each sub-group. The plurality of sub-groups may be ordered according to each corresponding cyclic shift parameter. The biggest peaks (or the smallest peaks) appearing at upper portions in the graph as shown in FIG. 11 indicate root indexes having a maximum CM (or a minimum CM) in each sub-group.
Each cell may use the consecutive logical indexes through the hybrid ordering according to the cyclic shift parameters and the CM characteristics regardless of a cell size, and CM-based cell planning can be possible according to characteristics of each cell. The base station may use the smallest logical index allocated to the base station itself for the user equipment in a particular power restricted environment in each cell. For example, the base station may use the smallest logical index as a dedicated preamble for a user equipment that performs handover. In the smallest cell size interval, a supportable cell size is very small and an index having a value smaller than 0 km may exist. Such index indicates an index that cannot use the restricted cyclic shift. In addition, the sections may be further divided for a simply index allocation. In FIG. 11, the first section is divided by 0 ̃1.1 km, but the section may be divided into smaller parts and ordered on the basis of the CM. For example, the first section may be divided into two parts of 0 ̃500 m and 500 m ̃1.1 km and can be ordered on the basis of the CM.
Table 5 shows physical indexes according to Ncs-configured sections.










TABLE 5







Logical



No
NCS
index
Physical root index


































0
13
 1~37
1
838
2
837
769
70
93
746
105
734
755
84
168
671
629
210
120





719
140
699
129
229
610
599
240
420
419
560
279
280
559
373
466
534





305
336
503
















1
26
38~77
804
35
799
40
797
42
783
56
779
60
73
766
80
759
727
112
146





693
691
148
710
235
604
606
233
581
258
265
267
574
572
367
472
537





302
543
296
530
309
355













2
38
 78~113
815
24
29
812
810
809
27
811
30
28
808
31
791
48
771
68
765





74
178
661
136
703
236
603
433
406
404
435
434
405
287
536
303
484





356
483

















3
52
114~155
818
819
21
20
39
800
796
43
78
761
753
86
181
658
137
702
714





125
151
688
261
578
242
274
565
266
573
402
437
552
286
553
383
456





307
532
357
482
329
510
317
522











4
64
156~187
14
825
15
824
55
784
61
778
103
736
95
744
729
110
202
637
636





203
190
649
717
122
128
711
622
217
256
583
597
253
471
368




5
76
188~227
12
827
23
816
805
34
37
802
793
46
89
750
721
118
179
660
142





697
709
130
231
608
260
579
263
576
571
268
276
586
284
555
551
288





304
535
546
293
358
481













6
83
228~247
91
207
632
694
145
133
706
223
616
563
430
409
398
441
290
549
308





531
316
523
















7
104
248~311
9
830
10
829
786
53
773
66
57
782
748
83
756
106
733
731
108





666
173
201
638
161
678
121
704
135
143
696
132
707
623
216
227
612





611
228
270
598
241
569
584
255
424
415
374
465
461
378
400
439
448





391
289
550
306
533
495
344
351
488
500
339
493
346






8
119
312~355
8
831
823
16
64
775
101
738
655
184
642
197
718
141
690
149
582





257
254
585
245
594
588
251
412
427
372
467
450
389
545
294
542
297





311
528
345
494
508
331
325
514
321
518









9
139
356~415
832
7
826
13
26
813
790
49
47
792
59
780
71
768
104
735
98





741
757
82
169
87
752
665
174
675
164
631
208
191
648
698
695
144





152
687
621
218
269
570
566
273
557
282
436
403
464
375
443
396
401





447
392
438
457
382
538
301
318
521










10
167
416~501
833
6
822
17
789
50
774
65
99
740
100
739
758
81
732
107
88





751
670
669
170
171
668
175
187
664
652
681
663
119
720
158
176
677





640
162
199
211
685
154
701
134
138
705
624
215
234
605
601
238
239





600
249
590
248
591
431
371
408
468
469
370
366
473
300
539
353
486





343
496
497
342
350
340
489
498
499
341
501
338
492
330
347
509



11
209
500~625
834
5
33
806
788
51
785
54
777
62
764
75
762
77
743
96
97





742
673
166
172
667
163
676
185
639
654
200
114
725
650
115
189
724





194
645
195
192
657
644
647
157
182
682
156
683
628
124
715
716
123





700
686
627
212
139
153
213
626
150
689
221
618
615
224
602
237
244





595
596
243
564
275
561
277
278
589
250
246
417
593
422
445
394
446





442
397
393
381
458
547
292
365
474
540
299
477
364
541
362
475
298





359
480
527
312
313
526
525
314
487
352
327
512
513
319
326
506
332





507
348
491
520
333
322
517












12
279
626~838
836
3
4
835
828
11
19
820
18
821
817
22
25
814
32
807
36





803
798
38
801
41
44
795
52
787
794
45
63
776
69
772
770
67





781
58
72
767
763
94
76
745
92
747
737
102
90
749
754
85
79





760
167
672
109
730
674
165
728
111
186
653
209
679
116
630
160
723





206
635
722
204
117
633
651
680
188
205
159
634
641
113
193
198
726





656
646
183
180
662
659
177
196
643
155
684
214
713
625
126
692
147





712
127
708
131
219
620
220
619
617
222
613
226
225
614
230
609
607





232
262
577
580
259
575
264
272
567
271
568
562
587
252
421
418
416





423
247
592
426
413
414
425
411
428
281
558
376
407
463
432
410
462





429
395
377
444
283
556
369
470
554
459
285
380
440
460
379
399
291





548
449
390
363
476
388
455
384
451
453
386
478
387
361
454
452
385





479
544
360
295
310
529
485
354
511
328
315
524
337
490
502
349
334





505
504
335
519
324
515
320
516
323









Table 5 shows that a plurality of physical root indexes are divided into a plurality of sub-groups according to predetermined cyclic shift parameters Ncs and consecutive logical indexes are allocated in each sub-group.
With such logical indexes set, a sequence can be easily selected according to a cell size in a high mobility cell. In addition, if a cell requires low CM characteristics, it may simply select front indexes among indexes that may be used in its cell size to thus use indexes having low CM characteristics. Table 5 does not mean that only the index values (physical indexes or logical indexes) related to the Ncs are used. An index, which may be suitable for the CM characteristics of a cell, may be selectively used regardless of a cell size in a low/middle mobility cell. In addition, An Ncs section table that can be used in the low/middle mobility cell may be separately set. In this case, a table to be applied by using a discrimination signal of a cell having the low/middle mobility cell and a cell having the high mobility cell may be selected.
FIG. 12 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to yet another exemplary embodiment of the present invention. Namely, FIG. 12 shows ordering based on the plurality of characteristics and pair allocation.
Referring to FIG. 12, ZC sequences have complex 0conjugate symmetry characteristics, based on which indexes having the complex conjugate symmetry can be pair-allocated consecutively.
The complex conjugate symmetry of the ZC sequences can be expressed as shown

xu=a(k)=x*u=N-a(k)  [Equation 5]

where (.)* indicates complex conjugate. The sum of two root indexes of two ZC sequences having complex conjugate symmetry is equal to the length of a ZC sequence. If only a single root index is used in a cell, such characteristics cannot be obtained, but in case of using a plurality of root indexes having complex conjugate symmetry characteristics, complexity of a detector of a receiver can be reduced to a half. The root indexes having complex conjugate symmetry characteristics can be consecutively allocated while applying the CM-based ordering, the maximum supportable cell radius-based ordering and the hybrid ordering, etc. thereto. When the indexes are pair-allocated, the base station signals only a single logical index and the user equipment naturally uses pair indexes while increasing the logical indexes as necessary.
In the above Table 5, each group includes the odd number of indexes, and in order to constitute the complex conjugate symmetry characteristics, one index of a higher group may be used by a lower group. This can be expressed as shown in Table 6.










TABLE 6







Logical



No
NCS
index
Physical root index


































0
13
 1~37
1
838
2
837
769
70
93
746
105
734
755
84
168
671
629
210
120





719
140
699
129
710
229
610
599
240
420
419
560
279
280
559
373
466





534
305
336
503















1
26
38~77
804
35
799
40
797
42
783
56
779
60
73
766
80
759
727
112
146





693
691
148
235
604
606
233
581
258
265
574
267
572
367
472
537
302





543
296
530
309
355
484













2
38
 78~113
815
24
29
810
812
27
809
30
811
28
808
31
791
48
771
68
765





74
178
661
136
703
236
603
433
406
404
435
434
405
287
552
536
303





356
483

















3
52
114~155
818
21
819
20
39
800
796
43
78
761
753
86
181
658
137
702
714





125
151
688
261
578
242
597
274
565
266
573
402
437
286
553
383
456





307
532
357
482
329
510
317
522











4
64
156~187
14
825
15
824
55
784
61
778
103
736
95
744
729
110
202
637
636





203
190
649
717
122
128
711
622
217
256
583
253
586
471
368




5
76
188~227
12
827
23
816
805
34
37
802
793
46
89
750
721
118
179
660
142





697
709
130
231
608
260
579
263
576
571
268
276
563
284
555
551
288





304
535
546
293
358
481













6
83
228~247
748
91
207
632
694
145
133
706
223
616
430
409
398
441
290
549
308





531
316
523
















7
104
248~311
9
830
10
829
786
53
773
66
57
782
83
756
106
733
731
108
666





173
201
638
161
678
718
121
704
135
143
696
132
707
623
216
227
612





611
228
270
569
241
598
584
255
424
415
374
465
461
378
400
439
448





391
289
550
306
533
495
344
351
488
500
339
493
346






8
119
312~355
8
831
823
16
64
775
101
738
655
184
642
197
141
698
690
149
582





257
254
585
245
594
588
251
412
427
372
467
450
389
545
294
542
297





311
528
345
494
508
331
325
514
321
518









9
139
356~415
832
7
826
13
26
813
790
49
47
792
59
780
71
768
104
735
98





741
757
82
670
169
87
752
665
174
675
164
631
208
191
648
695
144





152
687
621
218
269
570
566
273
557
282
436
403
464
375
443
396
401





438
392
447
457
382
538
301
318
521










10
167
416~501
833
6
822
17
789
50
774
65
99
740
100
739
758
81
732
107
88





751
669
170
171
668
175
664
187
652
681
158
119
720
663
176
677
162





640
199
211
628
685
154
701
138
134
705
624
215
234
605
601
238
239





600
249
590
248
591
431
408
371
468
469
370
366
473
300
539
353
486





343
496
497
342
350
489
340
499
498
341
501
338
492
347
330
509



11
209
500~625
834
5
33
806
788
51
785
54
777
62
764
75
762
77
743
96
97





742
673
166
172
667
163
676
185
654
639
200
114
725
650
189
115
724





194
645
195
644
647
192
657
182
157
682
156
683
124
715
716
123
700





139
627
212
686
153
213
626
150
689
221
618
615
224
602
237
244
595





596
243
564
275
562
277
561
278
589
250
246
593
417
422
445
394
446





393
397
442
381
458
547
292
365
474
540
299
477
362
475
364
541
298





359
480
527
312
313
526
525
314
487
352
327
512
513
326
319
520
332





507
348
491
506
333
322
517












12
279
626~838
836
3
4
835
828
11
19
820
18
821
817
22
25
814
32
807
36





803
798
41
801
38
44
795
52
787
794
45
63
776
69
770
772
67





781
58
72
767
763
76
94
745
92
747
737
102
90
749
754
85
79





760
167
672
109
730
674
165
728
111
186
653
209
630
160
679
116
723





206
633
722
117
204
635
651
188
680
159
205
634
641
198
726
113
193





646
656
183
180
659
662
177
196
643
155
684
214
625
713
126
692
147





712
127
708
131
219
620
220
619
617
222
613
226
225
614
230
609
607





232
262
577
580
259
575
264
272
567
271
568
587
252
421
418
416
423





247
592
426
413
414
425
411
428
281
558
376
463
407
432
410
429
462





377
395
444
283
556
369
470
554
285
459
380
440
399
379
460
291
548





449
390
363
476
388
451
384
455
453
386
478
361
387
452
454
385
479





360
544
295
310
529
485
354
511
328
315
524
337
502
490
349
334
505





504
335
519
320
515
324
516
323









The results of constituting the complex conjugate symmetry characteristics appear to be similar to those of hybrid ordering in FIG. 11. Namely, the indexes can be ordered such that they can be pair-allocated without degrading particular characteristics of them.
FIG. 13 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention. Namely, FIG. 13 shows ordering based on the plurality of characteristics and pair allocation.
Referring to FIG. 13, the sections divided in FIG. 12 can be more minutely divided. For example, the sections of the configuration numbers 11 and 12 in Table 3 can be halved to use a wider maximum cell radius.
Table 7 is a mapping table showing physical indexes of respective sections when the 11-th and 12-th sections are halved.










TABLE 7







Logical



No
NCS
index
Physical root index


































0
13
 1~37
1
838
2
837
769
70
93
746
105
734
755
84
168
671
629
210
120





719
140
699
129
710
229
610
599
240
420
419
560
279
280
559
373
466





534
305
336
503















1
26
38~77
804
35
799
40
797
42
783
56
779
60
73
766
80
759
727
112
146





693
691
148
235
604
606
233
581
258
265
574
267
572
367
472
537
302





543
296
530
309
355
484













2
38
 78~113
815
24
29
810
812
27
809
30
811
28
808
31
791
48
771
68
765





74
178
661
136
703
236
603
433
406
404
435
434
405
287
552
536
303





356
483

















3
52
114~155
818
21
819
20
39
800
796
43
78
761
753
86
181
658
137
702
714





125
151
688
261
578
242
597
274
565
266
573
402
437
286
553
383
456





307
532
357
482
329
510
317
522











4
64
156~187
14
825
15
824
55
784
61
778
103
736
95
744
729
110
202
637
636





203
190
649
717
122
128
711
622
217
256
583
253
586
471
368




5
76
188~227
12
827
23
816
805
34
37
802
793
46
89
750
721
118
179
660
142





697
709
130
231
608
260
579
263
576
571
268
276
563
284
555
551
288





304
535
546
293
358
481













6
83
228~247
748
91
207
632
694
145
133
706
223
616
430
409
398
441
290
549
308





531
316
523
















7
104
248~311
9
830
10
829
786
53
773
66
57
782
83
756
106
733
731
108
666





173
201
638
161
678
718
121
704
135
143
696
132
707
623
216
227
612





611
228
270
569
241
598
584
255
424
415
374
465
461
378
400
439
448





391
289
550
306
533
495
344
351
488
500
339
493
346






8
119
312~355
8
831
823
16
64
775
101
738
655
184
642
197
141
698
690
149
582





257
254
585
245
594
588
251
412
427
372
467
450
389
545
294
542
297





311
528
345
494
508
331
325
514
321
518









9
139
356~415
832
7
826
13
26
813
790
49
47
792
59
780
71
768
104
735
98





741
757
82
670
169
87
752
665
174
675
164
631
208
191
648
695
144





152
687
621
218
269
570
566
273
557
282
436
403
464
375
443
396
401





438
392
447
457
382
538
301
318
521










10
167
416~501
833
6
822
17
789
50
774
65
99
740
100
739
758
81
732
107
88





751
669
170
171
668
175
664
187
652
681
158
119
720
663
176
677
162





640
199
211
628
685
154
701
138
134
705
624
215
234
605
601
238
239





600
249
590
248
591
431
408
371
468
469
370
366
473
300
539
353
486





343
496
497
342
350
489
340
499
498
341
501
338
492
347
330
509



11
209
500~563
834
5
33
806
788
51
764
75
97
742
673
166
163
676
639
200
114





725
650
189
194
645
195
644
157
682
700
139
627
212
686
153
150
689





602
237
596
243
564
275
561
278
417
422
445
394
365
474
540
299
541





298
525
314
487
352
513
326
332
507
348
491
322
517








564-625
785
54
777
62
762
77
743
96
172
667
185
654
115
724
192
647
657





182
156
683
124
715
716
123
213
626
221
618
615
224
244
595
562
277





589
250
246
593
446
393
397
442
381
458
547
292
477
362
364
475
359





480
527
312
313
526
327
512
319
520
506
333








12
279
626~731
4
835
828
11
18
821
25
814
32
807
36
803
52
787
69
770
781





58
94
745
92
747
754
85
79
760
167
672
674
165
186
653
679
160





116
723
206
633
651
188
205
634
193
646
656
183
662
177
196
643
692





147
712
127
220
619
225
614
580
259
575
264
272
567
271
568
416
423





247
592
414
425
281
558
407
432
410
429
462
377
369
470
459
380
440





399
291
548
454
385
544
295
485
354
511
328
337
502
490
349
334
505





519
320
516
323

















732-838
836
3
19
820
817
22
798
41
801
38
44
795
794
45
63
776
772





67
72
767
763
76
737
102
90
749
109
730
728
111
209
630
635
204





722
117
680
159
641
198
113
726
180
659
155
684
214
625
713
126
708





131
219
620
617
222
613
226
230
609
607
232
262
577
587
252
421
418





426
413
411
428
376
463
395
444
283
556
554
285
460
379
449
390
363





476
388
451
384
455
453
386
478
361
387
452
479
360
310
529
315
524





504
335
324
515









The maximum cell radius can be increased from 29.14 km to 34.15 km so as to be used by applying Table 7. Here, particular sections are halved and re-ordered, but it is merely an example. That is, the size of particular sections can be divided in various manners. For example, in order to support a particular maximum cell radius, sections may be divided based on the particular maximum cell radius. Alternatively, sections may be divided such that the number of indexes used in a particular section is doubled. Sections having a small number of indexes can be grouped into one section, to which the second ordering may be applied. In addition, a section having a large number of indexes can be divided into two (or more) sections, to which the second ordering may be applied.
FIG. 14 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention. Namely, FIG. 13 shows that indexes are divided into groups based on the CM characteristics and are ordered according to a maximum supportable cell size in each group.
Referring to FIG. 14, first, the indexes may be ordered according to the CM characteristics, divided into a group having a CM higher than 1.2 dB, namely, a QPSK CM, and a group having a lower CM, and then ordered according to the maximum supportable cell radius in each group. The indexes in the group having the CM lower than QPSK may be ordered according to the order that the maximum supportable cell size is reduced, and the indexes in the group having the CM higher than QPSK may be ordered in the order that the maximum supportable cell size is increased.
Table 8 is a mapping table of physical indexes by section in case where the indexes are ordered according to the CM characteristics, divided into groups based on 1.2 dB, a single CM value, and then ordered according to the maximum supportable cell size in each group.









TABLE 8






Logical



No
index
Physical root index


































0
 1~50
3
836
209
630
76
763
180
659
126
713
219
620
226
613
131
708
262
577




72
767
22
817
44
795
41
798
19
820
38
801
232
607
67
772
45
794




90
749
230
609
111
728
222
617
102
737
204
635
109
730






1
 51~100
63
776
117
722
198
641
155
684
159
680
214
625
113
726
196
643
183
656




52
787
94
745
188
651
165
674
177
662
32
807
25
814
147
692
18
821




36
803
69
770
259
580
11
828
92
747
85
754
220
619






2
101~150
206
633
79
760
205
634
225
614
127
712
58
781
116
723
160
679
193
646




186
653
167
672
4
835
77
762
224
615
221
618
62
777
124
715
54
785




96
743
192
647
172
667
156
683
115
724
185
654
213
626






3
151~200
123
716
182
657
166
673
212
627
195
644
114
725
189
650
51
788
75
764




150
689
33
806
237
602
163
676
97
742
194
645
200
639
157
682
153
686




139
700
5
834
211
628
187
652
239
600
175
664
99
740






4
201~250
215
624
154
685
171
668
199
640
158
681
170
669
138
701
50
789
100
739




107
732
17
822
234
605
81
758
162
677
134
705
88
751
176
663
65
774




119
720
238
601
6
833
169
670
152
687
49
790
98
741






5
251~300
87
752
174
665
144
695
82
757
164
675
71
768
13
826
26
813
59
780




218
621
47
792
191
648
104
735
208
631
7
832
141
698
64
775
197
642




184
655
101
738
149
690
8
831
16
823
121
718
57
782






6
301~350
108
731
216
623
161
678
173
666
201
638
53
786
106
733
9
830
228
611




83
756
66
773
132
707
143
696
135
704
227
612
10
829
91
748
133
706




145
694
223
616
207
632
179
660
34
805
23
816
46
793






7
351~400
130
709
260
579
12
827
231
608
37
802
263
576
89
750
142
697
118
721




203
636
55
784
110
729
14
825
128
711
217
622
103
736
15
824
61
778




122
717
202
637
95
744
190
649
181
658
151
688
137
702






8
401~450
125
714
261
578
39
800
78
761
20
819
21
818
43
796
86
753
68
771




136
703
24
815
48
791
74
765
178
661
236
603
27
812
28
811
29
810




30
809
31
808
235
604
35
804
73
766
146
693
40
799






9
451~500
80
759
42
797
233
606
148
691
56
783
112
727
60
779
129
710
258
581




70
769
229
610
84
755
93
746
105
734
120
719
140
699
168
671
210
629




1
838
2
837
419
420
279
560
280
559
336
503
240
599






10
501~550
373
466
305
534
367
472
296
543
265
574
309
530
267
572
302
537
355
484




404
435
405
434
406
433
356
483
303
536
287
552
266
573
307
532
286
553




317
522
383
456
357
482
402
437
274
565
329
510
242
597






11
551~600
368
471
256
583
253
586
293
546
284
555
288
551
304
535
268
571
358
481




276
563
316
523
398
441
308
531
409
430
290
549
374
465
306
533
400
439




270
569
289
550
378
461
415
424
241
598
346
493
351
488






12
601~650
339
500
344
495
255
584
391
448
372
467
345
494
254
585
331
508
389
450




257
582
325
514
412
427
245
594
297
542
321
518
311
528
251
588
294
545




282
557
392
447
382
457
318
521
396
443
273
566
403
436






13
651~700
269
570
301
538
375
464
401
438
338
501
408
431
371
468
366
473
330
509




340
499
249
590
341
498
342
497
248
591
343
496
370
469
347
492
350
489




353
486
300
539
417
422
278
561
314
525
352
487
326
513






14
701~750
348
491
365
474
275
564
394
445
243
596
298
541
322
517
332
507
299
540




364
475
393
446
246
593
319
520
313
526
333
506
327
512
244
595
362
477




250
589
312
527
292
547
397
442
381
458
359
480
277
562






15
751~800
281
558
334
505
323
516
247
592
320
519
369
470
272
567
295
544
410
429




291
548
380
459
399
440
271
568
377
462
414
425
385
454
264
575
407
432




354
485
349
490
337
502
416
423
328
511
363
476
324
515






16
801~838
411
428
310
529
361
478
283
556
388
451
390
449
413
426
379
460
384
455




285
554
386
453
376
463
387
452
252
587
395
444
360
479
315
524
335
504




418
421









<Comparison with a Reuse Factor in a Large Cell>
FIG. 15 is a graph showing the number of restricted cyclic shifts available per logical index according to an Ncs with respect to CM mapping according to one exemplary embodiment of the present invention. FIG. 16 is a graph showing the number of restricted cyclic shifts available per logical index according to the Ncs with respect to maximum supportable cell size mapping according to one exemplary embodiment of the present invention. FIG. 17 is a graph showing the number of restricted cyclic shifts available per logical index according to the Ncs with respect to hybrid mapping according to one exemplary embodiment of the present invention.
Referring to FIGS. 15 to 17, compared with the CM mapping, the maximum supportable cell size mapping and the hybrid mapping may use consecutive indexes in a high speed cell. For example, it is assumed that there are twenty cells, the cyclic shift parameter Ncs of a first cell is 13, the Ncs of the subsequent two cells (i.e., second and third cells) are 26, those of the subsequent three cells are 38, those of the subsequent four cells are 38, those of the subsequent four cells are 52, and those of the subsequent four cells are 64. In this case, pair index allocation is applied to each mapping. The Ncs indicates the number of cyclic shifts according to cell sizes. Referring to FIG. 13, it is noted that a middle portion is 0 and any available restricted cyclic shift does not appear. On the contrary, Referring to FIGS. 15 and 16, any available restricted cyclic shift does not appear. Namely, the consecutive indexes cannot be used in the CM mapping but can be used in the maximum supportable cell size mapping and hybrid mapping.
FIG. 18 is a graph showing examples of logical root indexes allocated to cells with respect to the CM mapping according to one exemplary embodiment of the present invention. FIG. 19 is a graph showing examples of logical root indexes allocated to cells with respect to the maximum supportable cell size mapping according to one exemplary embodiment of the present invention. FIG. 20 is a graph showing examples of logical root indexes allocated to cells with respect to the maximum supportable cell size mapping according to one exemplary embodiment of the present invention. Namely, FIGS. 18 to 20 show which indexes are allocated to cells based on the assumption in FIGS. 15 to 17.
Referring to FIGS. 18 to 20, it is assumed that every cell has high speed mobility. Referring to FIG. 18, it is noted that consecutive indexes are not used in a large cell. In comparison, Referring to FIGS. 19 and 20, it is noted that consecutive indexes can be used in a large cell. In FIGS. 19 and 20, if a cell has the Ncs of 209 (Ncs=209), four cells having the Ncs of 167 (Ncs=167) can be constructed. The reason is because, in FIG. 18, consecutive indexes cannot be used. More importantly, in FIG. 18, it is noted that, if a cell has the Ncs of 209 and three cells have the Ncs of 167, any of cells having NCS=139, Ncs=104, Ncs=83, and Ncs=76 cannot be constructed. In comparison, in FIGS. 19 and 20, cells of various sizes can be constructed. Also, in FIG. 18, it is noted that a plurality of indexes has a value 0 at the y axis and are not used in a high mobility cell. If those indexes can be used when the high mobility cell is mixed with only a low mobility cell, but such indexes drastically degrade the cell construction capabilities. Thus, failing to use the consecutive indexes much degrades the re-use factor when a plurality of large cells exists. That is, by using the consecutive indexes, a different cell may use an extra space. The use of the consecutive indexes may not make much difference in a network including only small cells, but as far as a network including a plurality of large cells concerned, the support of the use of the consecutive indexes can increase the re-use factor. FIGS. 18 to 20 consider the case where every cell has high speed mobility, but even in a case where cells having low speed mobility or middle speed mobility exist, the re-use factor is restricted if the consecutive indexes are not used for the same reasons. Also, if the consecutive indexes are used in a cell having low speed mobility or middle speed mobility, the re-use factor of the cell having high speed mobility is further restricted.
The accurate indexes of each mapping as used are as shown in Table 9, Table 10, and Table 11. Table 9 shows the indexes used for the CM mapping, Table 10 shows indexes used for the maximum support cell size mapping, and Table 11 shows the indexes used for the hybrid mapping. In Table 9 and Table 10, physical root indexes with respect to logical indexes 1 to 838 are arranged in sequence.








TABLE 9





Logical



index
Physical root index

































1~838
1
838
2
837
3
836
4
835
5
834
6
833
7
832
8
831
9
830



10
829
11
828
12
827
13
826
14
825
15
824
16
823
17
822
19
820



18
821
21
818
20
819
23
816
22
817
26
813
24
815
25
814
29
810



27
812
30
809
28
811
31
808
34
805
35
804
32
807
33
806
40
799



36
803
42
797
41
798
38
801
37
802
39
800
43
796
49
790
44
795



50
789
52
787
51
788
46
793
48
791
47
792
53
786
45
794
64
775



65
774
54
785
55
784
63
776
56
783
69
770
70
769
60
779
67
772



66
773
68
771
59
780
61
778
62
777
57
782
58
781
71
768
93
746



72
767
75
764
104
735
76
763
94
745
105
734
73
766
92
747
103
736



74
765
95
744
102
737
101
738
91
748
99
740
90
749
77
762
98
741



84
755
96
743
100
739
82
757
78
761
83
756
106
733
168
671
85
754



86
753
97
742
89
750
81
758
107
732
88
751
80
759
79
760
167
672



169
670
87
752
108
731
170
669
166
673
109
730
171
668
165
674
172
667



111
728
174
665
186
653
110
729
164
675
175
664
187
652
173
666
163
676



209
630
160
679
112
727
116
723
185
654
208
631
200
639
184
655
207
632



118
721
206
633
204
635
117
722
188
651
201
638
159
680
205
634
158
681



119
720
176
663
114
725
161
678
189
650
198
641
113
726
115
724
202
637



193
646
162
677
194
645
203
636
199
640
183
656
210
629
197
642
195
644



120
719
192
647
180
659
190
649
182
657
179
660
177
662
191
648
157
682



196
643
181
658
178
661
121
718
156
683
122
717
211
628
154
685
124
715



123
716
140
699
155
684
145
694
135
704
139
700
137
702
212
627
153
686



141
698
138
701
134
705
125
714
144
695
142
697
143
696
146
693
213
626



136
703
133
706
152
687
151
688
214
625
126
713
128
11
147
692
132
707



215
624
127
712
150
689
130
709
148
691
149
690
129
710
216
623
131
708



217
622
218
621
219
620
220
619
223
616
221
618
222
617
224
615
226
613



227
612
225
614
228
611
229
610
230
609
231
608
236
603
232
607
235
604



233
606
234
605
237
602
238
601
262
577
261
578
239
600
260
579
259
580



258
581
263
576
257
582
240
599
269
570
256
583
268
571
241
598
264
575



270
569
272
567
242
597
274
565
244
595
273
566
243
596
265
574
275
564



267
572
276
563
271
568
255
584
277
562
278
561
419
420
266
573
253
586



279
560
254
585
252
587
245
594
418
421
250
589
251
588
249
590
246
593



417
422
416
423
280
559
248
591
415
424
247
592
373
466
413
426
414
425



412
427
411
428
281
558
374
465
376
463
409
430
407
432
372
467
410
429



282
557
377
462
403
436
375
464
406
433
395
444
408
431
283
556
402
437



371
468
404
435
396
443
369
470
394
445
368
471
378
461
397
442
405
434



393
446
284
555
370
469
401
438
392
447
285
554
398
441
367
472
380
459



400
439
287
552
286
553
399
440
379
460
381
458
288
551
291
548
391
448



290
549
302
537
366
473
292
547
289
550
382
457
303
536
383
456
390
449



365
474
304
535
363
476
300
539
293
546
305
534
301
538
299
540
389
450



362
477
364
475
384
455
388
451
298
541
386
453
361
478
387
452
385
454



294
545
360
479
297
542
295
544
296
543
306
533
307
532
308
531
309
530



359
480
358
481
310
529
357
482
312
527
355
484
311
528
354
485
356
483



313
526
314
525
353
486
352
487
343
496
344
495
351
488
342
497
328
511



345
494
329
510
327
512
315
524
350
489
340
499
341
498
318
521
339
500



316
523
326
513
346
493
338
501
331
508
317
522
319
520
332
507
337
502



333
506
348
491
349
490
325
514
347
492
330
509
334
505
336
503
335
504



321
518
324
515
320
519
322
517
323
516

















TABLE 10





Logical



index
Physical root index


































1~838
1
838
2
837
419
420
279
560
280
559
210
629
168
671
336
503
140
699
120



719
240
599
105
734
93
746
373
466
84
755
229
610
305
534
70
769
129
710



258
581
60
779
56
783
112
727
367
472
148
691
296
543
233
606
265
574
309



530
42
797
40
799
80
759
267
572
73
766
146
693
35
804
235
604
302
537



355
484
31
808
404
435
30
809
29
810
405
434
28
811
27
812
406
433
236



603
178
661
356
483
74
765
24
815
48
791
303
536
68
771
136
703
287
552



43
796
86
753
21
818
266
573
307
532
20
819
39
800
78
761
286
553
261



578
317
522
383
456
125
714
357
482
402
437
137
702
274
565
151
688
181
658



329
510
242
597
95
744
190
649
202
637
61
778
122
717
15
824
103
736
368



471
217
622
128
711
256
583
14
825
55
784
110
729
203
636
253
586
293
546



118
721
142
697
284
555
89
750
263
576
288
551
37
802
231
608
304
535
12



827
130
709
260
579
268
571
23
816
46
793
34
805
179
660
358
481
276
563



207
632
316
523
398
441
223
616
308
531
409
430
145
694
290
549
133
706
91



748
374
465
10
829
227
612
306
533
400
439
135
704
270
569
143
696
66
773



132
707
289
550
83
756
378
461
228
611
9
830
415
424
241
598
53
786
106



733
201
638
173
666
346
493
351
488
161
678
339
500
344
495
108
731
216
623



255
584
57
782
391
448
121
718
8
831
16
823
372
467
149
690
345
494
101



738
254
585
331
508
389
450
257
582
325
514
412
427
245
594
297
542
184
655



197
642
321
518
311
528
251
588
294
545
64
775
141
698
282
557
7
832
104



735
208
631
392
447
191
648
382
457
318
521
47
792
396
443
273
566
218
621



403
436
59
780
13
826
26
813
71
768
269
570
301
538
375
464
82
757
164



675
144
695
87
752
174
665
401
438
49
790
98
741
152
687
169
670
338
501



6
833
119
720
238
601
65
774
88
751
176
663
134
705
81
758
162
677
408



431
234
605
371
468
17
822
107
732
366
473
330
509
50
789
100
739
138
701



170
669
340
499
158
681
249
590
341
498
199
640
171
668
342
497
154
685
248



591
343
496
215
624
99
740
370
469
347
492
175
664
350
489
353
486
239
600



300
539
187
652
211
628
417
422
5
834
139
700
278
561
153
686
157
682
314



525
200
639
97
742
194
645
352
487
163
676
326
513
348
491
237
602
365
474



33
806
75
764
150
689
275
564
51
788
394
445
189
650
243
596
298
541
114



725
195
644
322
517
212
627
166
673
332
507
299
540
182
657
364
475
393
446



123
716
246
593
319
520
213
626
313
526
333
506
185
654
327
512
244
595
115



724
362
477
250
589
156
683
312
527
172
667
96
743
192
647
54
785
62
777



124
715
292
547
221
618
397
442
224
615
77
762
381
458
359
480
277
562
281



558
4
835
167
672
334
505
186
653
193
646
323
516
247
592
160
679
320
519



369
470
58
781
116
723
127
712
272
567
295
544
225
614
205
634
410
429
291



548
79
760
380
459
206
633
220
619
399
440
271
568
85
754
377
462
92
747



11
828
414
425
259
580
69
770
385
454
264
575
18
821
36
803
147
692
25



814
407
432
32
807
177
662
354
485
349
490
165
674
337
502
416
423
94
745



188
651
52
787
183
656
328
511
196
643
113
726
363
476
324
515
214
625
411



428
159
680
155
684
310
529
198
641
117
722
361
478
283
556
63
776
388
451



109
730
102
737
204
635
390
449
111
728
222
617
413
426
230
609
379
460
384



455
45
794
90
749
285
554
67
772
386
453
232
607
19
820
38
801
41
798



22
817
44
795
72
767
131
708
262
577
376
463
226
613
387
452
219
620
126



713
252
587
395
444
180
659
360
479
76
763
209
630
315
524
335
504
3
836



418
421



















TABLE 11







Logical



No
NCS
index
Physical root index


































0
13
 1~36
1
838
2
837
70
769
93
746
105
734
84
755
168
671
210
629
120





719
140
699
229
610
240
599
419
420
279
560
280
559
373
466
305
534





336
503

















1
26
37~76
35
804
40
799
42
797
56
783
60
779
73
766
80
759
112
727
146





693
148
691
129
710
235
604
233
606
258
581
265
574
267
572
367
472





302
537
296
543
309
530













2
38
 77~112
24
815
29
810
27
812
30
809
28
811
31
808
48
791
68
771
74





765
178
661
136
703
236
603
406
433
404
435
405
434
303
536
355
484





356
483

















3
52
113~154
21
818
20
819
39
800
43
796
78
761
86
753
181
658
137
702
125





714
151
688
261
578
274
565
266
573
402
437
287
552
286
553
383






456
307
532
357
482
329
510
317
522










4
64
155~190
14
825
15
824
55
784
61
778
103
736
95
744
110
729
202
637
203





636
190
649
122
717
128
711
217
622
256
583
242
597
253
586
368






471
293
546
















5
76
191~226
12
827
23
816
34
805
37
802
46
793
89
750
118
721
179
660
142





697
130
709
231
608
260
579
263
576
268
571
284
555
288
551
304






535
358
481
















6
83
227~246
207
632
145
694
133
706
223
616
276
563
409
430
398
441
290
549






308
531
316
523















7
104
247~310
9
830
10
829
53
786
66
773
57
782
91
748
83
756
106
733
108





731
173
666
201
638
161
678
135
704
143
696
132
707
216
623
227
612





228
611
241
598
270
569
255
584
415
424
374
465
378
461
400
439






391
448
289
550
306
533
344
495
351
488
339
500
346
493





8
119
311~354
8
831
16
823
64
775
101
738
184
655
197
642
121
718
149
690
257





582
254
585
245
594
251
588
412
427
372
467
389
450
294
545
297






542
311
528
345
494
331
508
325
514
321
518








9
139
355~414
7
832
13
826
26
813
49
790
47
792
59
780
71
768
104
735
98





741
82
757
87
752
174
665
164
675
208
631
191
648
141
698
144
695





152
687
218
621
269
570
273
566
282
557
403
436
375
464
396
443
401





438
392
447
382
457
301
538
318
521










10
167
415~498
6
833
17
822
50
789
65
774
99
740
100
739
81
758
107
732
88





751
169
670
170
669
171
668
175
664
187
652
158
681
119
720
176
663





162
677
199
640
154
685
138
701
134
705
215
624
234
605
238
601






239
600
249
590
248
591
408
431
371
468
370
469
366
473
300
539






353
486
343
496
342
497
350
489
340
499
341
498
338
501
347
492






330
509

















11
209
499~624
5
834
33
806
51
788
54
785
62
777
75
764
77
762
96
743
97





742
166
673
172
667
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
124
715






123
716
139
700
212
627
153
686
213
626
150
689
221
618
224
615






237
602
244
595
243
596
275
564
278
561
250
589
246
593
417
422






394
445
397
442
393
446
381
458
292
547
365
474
299
540
362
477






364
475
298
541
359
480
312
527
313
526
314
525
352
487
327
512






326
513
319
520
332
507
333
506
348
491
322
517







12
279
625~838
3
836
4
835
11
828
19
820
18
821
22
817
25
814
32
807
36





803
41
798
38
801
44
795
52
787
45
794
63
776
69
770
67
772





58
781
72
767
76
763
94
745
92
747
102
737
90
749
85
754
79





760
167
672
109
730
165
674
111
728
186
653
209
630
160
679
116
723





206
633
204
635
117
722
188
651
159
680
205
634
198
641
113
726
193





646
183
656
180
659
177
662
196
643
155
684
214
625
126
713
147
692





127
712
131
708
219
620
220
619
222
617
226
613
225
614
230
609






232
607
262
577
259
580
264
575
272
567
271
568
277
562
252
587






418
421
416
423
247
592
413
426
414
425
411
428
281
558
376
463






407
432
410
429
377
462
395
444
283
556
369
470
285
554
380
459






399
440
379
460
291
548
390
449
363
476
384
455
388
451
386
453






361
478
387
452
385
454
360
479
295
544
310
529
354
485
328
511






315
524
337
502
349
490
334
505
335
504
324
515
320
519
323
516









<Supportable Cell Size Ordering and CM Classification>
FIG. 21 is a view illustrating a method of searching logical root indexes according to the CM characteristics according to one exemplary embodiment of the present invention. FIG. 22 is a view illustrating a method of searching logical root indexes according to the CM characteristics according to another exemplary embodiment of the present invention. FIG. 23 is a view illustrating a method of searching logical root indexes according to the CM characteristics according to still another exemplary embodiment of the present invention.
Referring to FIGS. 21 to 23, the physical indexes are first ordered according to a supportable cell size. Thereafter, a method of using available indexes in each cell vary according to characteristics of a single transmitted index. Allocation of logical indexes may be formed according to one logical index+Ncs. It can be performed by the following two methods.
In one method, each cell uses only a single sequence class (See FIG. 20). It is divided into a low CM index and a high CM index.
If a transmitted logical index has CM characteristics which are lower than or the same as the QPSK CM (1.2 dB) of the SC-FDMA, the closest adjacent logical indexes having the CM characteristics which are lower than or the same as the QPSK CM of the SC-FDMA are searched and used in sequence. If a transmitted logical index has CM characteristics which are higher than the QPSK CM of the SC-FDMA, the closest adjacent logical indexes having the CM characteristics which are higher than the QPSK CM of the SC-FDMA are searched and used in sequence.
In another method, a single cell may use either sequence class (lower CM or higher CM) (See FIGS. 20 and 21). It is divided into a lower CM index, a higher CM index and a mixed CM index.
If a transmitted logical index has CM characteristics which are lower than or the same as the QPSK CM (1.2 dB) of the SC-FDMA, the closest adjacent logical indexes having the CM characteristics which are lower than or the same as the QPSK CM of the SC-FDMA are searched and used in sequence. In this case, when it reaches the end of an Ncs segment, the index is reset as an index having a first higher CM of a next Ncs segment. If a transmitted logical index has CM characteristics which are higher than the QPSK CM (1.2 dB) of the SC-FDMA, the closest adjacent logical indexes having the CM characteristics which are higher than the QPSK CM of the SC-FDMA are searched and used in sequence. In this case, if it reaches the end of an Ncs segment, the index is reset as an index having a first lower CM of a next Ncs segment.
The directions (+/−, direction in which indexes are increased/decreased) for searching indexes having the same characteristics may be the same or different. The direction for searching indexes does not affect the proposed technique, like the ordering direction (ascent/descent) of indexes as mentioned above.
FIG. 24 is a graph showing CM characteristics according to physical root indexes according to one exemplary embodiment of the present invention.
Referring to FIG. 24, the sequence class may be defined according to physical indexes. The physical root indexes may be classified by setting a CM classification threshold value. The classification of the physical root indexes may be simply performed by checking whether or not a selected physical index belongs to a high CM region or a low CM region. For example, it can be noted that, if a CM classification threshold value is 1.2 dB, a high CM region may be determined as [238, NZC−238]. The use of such method allows generation of indexes through a simple numerical formula to order the indexes (or index mapping) without the necessity of a complicated table.
Mapping to a physical index uphy(ulog) in response to a logical index ulog based on the maximum supportable cell size (or Ncs) can be expressed as shown




  
    
      
        
          
            u
            phy
          
          ⁡
          
            (
            
              
                6
                ·
                
                  (
                  
                    i
                    -
                    1
                  
                  )
                
              
              +
              
                2
                ·
                j
              
              -
              1
            
            )
          
        
        =
        
          {
          
            
              
                
                  
                    
                      
                        
                          
                            u
                            ′
                          
                          ⁡
                          
                            (
                            
                              α
                              
                                i
                                ,
                                j
                              
                            
                            )
                          
                        
                        ,
                      
                    
                    
                      
                        
                          j
                          =
                          
                            1
                            ,
                            2
                            ,
                            3
                          
                        
                        ,
                      
                    
                    
                      
                        
                          i
                          =
                          
                            1
                            ,
                            2
                          
                        
                        ,
                        ...
                        ⁢
                        
                          
                        
                        ,
                        139
                      
                    
                  
                  
                    
                      
                        
                          
                            u
                            ′
                          
                          ⁡
                          
                            (
                            
                              α
                              
                                i
                                ,
                                
                                  j
                                  +
                                  1
                                
                              
                            
                            )
                          
                        
                        ,
                      
                    
                    
                      
                        
                          j
                          =
                          
                            1
                            ,
                            2
                          
                        
                        ,
                      
                    
                    
                      
                        i
                        =
                        140
                      
                    
                  
                
                ⁢
                
                  

                
                ⁢
                
                  
                    u
                    phy
                  
                  ⁡
                  
                    (
                    
                      2
                      ·
                      i
                    
                    )
                  
                
              
              =
              
                
                  N
                  ZC
                
                -
                
                  
                    u
                    phy
                  
                  ⁡
                  
                    (
                    
                      
                        2
                        ·
                        i
                      
                      -
                      1
                    
                    )
                  
                
              
            
            ,
            
              i
              =
              
                1
                ,
                2
              
            
            ,
            ...
            ⁢
            
              
            
            ,
            
              
                (
                
                  
                    N
                    ZC
                  
                  -
                  1
                
                )
              
              /
              2
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          6
        
        ]
      
    
  




where αi,1=(NZC+1), αi,2=2i−1, αi,3=2i and u′(r)=(−1/r) mod NZC.
One example of selecting an adjacent available index when a plurality of indexes are used in a cell can be expressed as shown




  
    
      
        u
        =
        
          {
          
            
              
                
                  
                    
                      u
                      phy
                    
                    ⁡
                    
                      (
                      
                        
                          u
                          log
                        
                        ++
                      
                      )
                    
                  
                  ,
                
              
              
                
                  
                    
                      
                        
                          
                            if
                            ⁢
                            
                              
                            
                            ⁢
                            
                              I
                              t
                            
                          
                          <
                          
                            
                              u
                              phy
                            
                            ⁡
                            
                              (
                              
                                
                                  u
                                  log
                                
                                ++
                              
                              )
                            
                          
                          <
                          
                            N
                            -
                            
                              I
                              t
                            
                          
                        
                        ⁢
                        
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                        
                        ⁢
                        
                          
                            and
                            ⁢
                            
                              
                            
                            ⁢
                            
                              I
                              t
                            
                          
                          <
                          
                            
                              u
                              phy
                            
                            ⁡
                            
                              (
                              
                                u
                                log
                              
                              )
                            
                          
                          <
                          
                            N
                            -
                            
                              I
                              t
                            
                          
                        
                      
                    
                  
                
              
            
            
              
                
                  
                    
                      u
                      phy
                    
                    ⁡
                    
                      (
                      
                        
                          u
                          log
                        
                        ++
                      
                      )
                    
                  
                  ,
                
              
              
                
                  
                    
                      
                        if
                        ⁢
                        
                          
                        
                        [
                        
                          
                            
                              
                                
                                  
                                    u
                                    phy
                                  
                                  ⁡
                                  
                                    (
                                    
                                      
                                        u
                                        log
                                      
                                      ++
                                    
                                    )
                                  
                                
                                ≤
                                
                                  
                                    I
                                    t
                                  
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  or
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    u
                                    phy
                                  
                                  ⁡
                                  
                                    (
                                    
                                      
                                        u
                                        log
                                      
                                      ++
                                    
                                    )
                                  
                                
                                ≥
                                
                                  N
                                  -
                                  
                                    I
                                    t
                                  
                                
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      
                        and
                        ⁢
                        
                          
                        
                        [
                        
                          
                            
                              u
                              phy
                            
                            ⁡
                            
                              (
                              
                                u
                                log
                              
                              )
                            
                          
                          ≤
                          
                            
                              I
                              t
                            
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                
                                  or
                                  ⁢
                                  u
                                
                                phy
                              
                              ⁡
                              
                                (
                                
                                  u
                                  log
                                
                                )
                              
                            
                          
                          ≥
                          
                            I
                            t
                          
                        
                        ]
                      
                    
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
  




where, ulog++ indicates the next logical indexes (e.g., ulog+1, ulog+2, ulog+3, . . . ) associated with ulog and It=238. In this case, all the indexes are searched in a positive (+) direction (namely, in a direction that indexes increase). If a mixed CM index is not allowed, a searching procedure is simple. When a low CM sequence reaches a boundary of NZC−1 through the ulog++ procedure, it is set with a first logical index of ulog++. If, however, the mixed CM index is allowed, some conditions are necessary. If ulog++ reaches a boundary of an Ncs sequence, it is reset with a first logical index in a ulog++ Ncs segment. If ulog++ reaches a boundary of the Ncs segment in the ulog++ process for a higher CM, ulog++ is reset with a first logical index of a next Ncs segment. In this case, as for the CM characteristics when ulog++ is reset, if the mixed CM index is not allowed, ulog++ can be reset with a first index having the same characteristics as those of a transmitted index, and if the mixed CM index is allowed, ulog++ can be reset with a higher CM or a lower CM which has been previously determined according to the characteristics of a transmitted index.

Another example of selecting an adjacent available index when a plurality of indexes are used in a cell can be expressed as shown




  
    
      
        u
        =
        
          {
          
            
              
                
                  
                    
                      u
                      phy
                    
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                  ,
                
              
              
                
                  
                    
                      
                        
                          
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                            ⁢
                            
                              
                            
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                            N
                            -
                            
                              I
                              t
                            
                          
                        
                        ⁢
                        
                          
                        
                      
                    
                  
                  
                    
                      
                        
                          
                        
                        ⁢
                        
                          
                            and
                            ⁢
                            
                              
                            
                            ⁢
                            
                              I
                              t
                            
                          
                          <
                          
                            
                              u
                              phy
                            
                            ⁡
                            
                              (
                              
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                              )
                            
                          
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                            -
                            
                              I
                              t
                            
                          
                        
                      
                    
                  
                
              
            
            
              
                
                  
                    
                      u
                      phy
                    
                    ⁡
                    
                      (
                      
                        
                          u
                          log
                        
                        ++
                      
                      )
                    
                  
                  ,
                
              
              
                
                  
                    
                      
                        if
                        ⁢
                        
                          
                        
                        [
                        
                          
                            
                              
                                
                                  
                                    u
                                    phy
                                  
                                  ⁡
                                  
                                    (
                                    
                                      
                                        u
                                        log
                                      
                                      ++
                                    
                                    )
                                  
                                
                                ≤
                                
                                  
                                    I
                                    t
                                  
                                  ⁢
                                  
                                    
                                  
                                  ⁢
                                  or
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    u
                                    phy
                                  
                                  ⁡
                                  
                                    (
                                    
                                      
                                        u
                                        log
                                      
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                                    )
                                  
                                
                                ≥
                                
                                  N
                                  -
                                  
                                    I
                                    t
                                  
                                
                              
                            
                          
                        
                        ]
                      
                    
                  
                  
                    
                      
                        and
                        ⁢
                        
                          
                        
                        [
                        
                          
                            
                              u
                              phy
                            
                            ⁡
                            
                              (
                              
                                u
                                log
                              
                              )
                            
                          
                          ≤
                          
                            
                              I
                              t
                            
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                
                                  or
                                  ⁢
                                  u
                                
                                phy
                              
                              ⁡
                              
                                (
                                
                                  u
                                  log
                                
                                )
                              
                            
                          
                          ≥
                          
                            I
                            t
                          
                        
                        ]
                      
                    
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
  




where, ulog++ indicates the next logical indexes (e.g., ulog+1, ulog+2, ulog+3, . . . ) associated with ulog and It=238. In this case, indexes are searched in positive (+) and negative (−) directions (namely, in a direction that indexes increase or decrease).
If it is difficult to express the ordering of indexes in numerical formula, each base station and each user equipment should have a large ordering table of 838*10 bits (1 ̃838)=8,380 bits. However, if Equation 6 is given, each base station and each user equipment can use the maximum supportable cell size ordering without such an ordering table. Table 12 shows mapping from physical indexes to logical indexes based on the maximum supportable cell size using Equation 6.









TABLE 12






Logical



No
index
Physical root index


































0
 1~50
2
837
838
1
419
420
560
279
559
280
269
210
336
503
671
168
699
140




240
599
719
120
734
105
746
93
466
373
755
84
229
610
305
534
769
70




581
258
129
710
779
60
112
727
783
56
367
472
543
296






1
 51~100
148
691
233
606
530
309
574
265
797
42
80
759
799
40
572
267
146
693




766
73
804
35
235
604
302
537
484
355
808
31
435
404
809
30
29
810




405
434
811
28
812
27
433
406
603
236
356
483
661
178






2
101~150
74
765
48
791
815
24
536
303
703
136
68
771
287
552
753
86
43
796




818
21
307
532
266
573
819
20
761
78
39
800
286
553
317
522
261
578




383
456
125
714
357
482
402
437
274
565
702
137
151
688






3
151~200
181
658
329
510
242
597
190
649
744
95
637
202
717
122
61
778
824
15




736
103
471
368
622
217
256
583
711
128
825
14
729
110
55
784
636
203




586
253
546
293
721
118
284
555
697
142
750
89
263
576






4
201~250
288
551
37
802
608
231
535
304
827
12
260
579
709
130
268
571
46
793




816
23
34
805
358
481
660
179
563
276
632
207
523
316
441
398
616
223




531
308
409
430
549
290
145
694
133
706
91
748
374
465






5
251~300
829
10
612
227
533
306
439
400
569
270
135
704
143
696
132
707
773
66




550
289
83
756
378
461
611
228
830
9
424
415
598
241
106
733
786
53




201
638
346
493
666
173
351
488
678
161
500
339
495
344






6
301~350
216
623
731
108
584
255
782
57
448
391
121
718
16
823
831
8
372
467




149
690
345
494
738
101
331
508
254
585
450
389
514
325
582
257
412
427




594
245
542
297
655
184
197
642
321
518
311
528
251
588






7
351~400
294
545
775
64
557
282
141
698
832
7
631
208
104
735
447
392
382
457




648
191
318
521
47
792
396
443
273
566
403
436
218
621
780
59
813
26




13
826
768
71
538
301
570
269
375
464
675
164
82
757






8
401~450
144
695
665
174
87
752
438
401
98
741
790
49
687
152
501
338
169
670




833
6
601
238
119
720
774
65
663
176
88
751
134
705
677
162
81
758




408
431
371
468
234
605
17
822
107
732
366
473
330
509






9
451~500
739
100
50
789
701
138
340
499
669
170
681
158
498
341
590
249
640
199




497
342
171
668
685
154
343
496
248
591
624
215
740
99
469
370
492
347




489
350
175
664
486
353
239
600
300
539
187
652
417
422






10
501~550
211
628
834
5
561
278
139
700
686
153
525
314
157
682
639
200
194
645




742
97
487
352
513
326
163
676
491
348
365
474
237
602
806
33
150
689




764
75
275
564
51
788
394
445
189
650
243
596
298
541






11
551~600
725
114
644
195
517
322
212
627
507
332
166
673
299
540
475
364
182
657




393
446
246
593
716
123
520
319
626
213
526
313
333
506
654
185
512
327




595
244
115
724
362
477
250
589
312
527
683
156
667
172






12
601~650
647
192
96
743
785
54
124
715
777
62
292
547
397
442
221
618
224
615




762
77
458
381
480
359
277
562
281
558
835
4
505
334
167
672
186
653




646
193
516
323
592
247
320
519
679
160
369
470
116
723






13
651~700
781
58
127
712
295
544
272
567
225
614
429
410
205
634
291
548
760
79




459
380
206
633
399
440
220
619
271
568
754
85
462
377
747
92
11
828




414
425
580
259
770
69
454
385
575
264
803
36
18
821






14
701~750
147
692
25
814
407
432
807
32
485
354
177
662
490
349
165
674
337
502




416
423
188
651
745
94
52
787
183
656
328
511
643
196
726
113
476
363




324
515
428
411
625
214
159
680
310
529
684
155
198
641






15
751~800
117
722
361
478
556
283
776
63
451
388
109
730
204
635
737
102
390
449




222
617
728
111
426
413
460
379
609
230
384
455
749
90
45
794
285
554




67
772
386
453
607
232
38
801
820
19
41
798
44
795






16
801~838
817
22
72
767
262
577
708
131
463
376
387
452
226
613
219
620
587
252




126
713
395
444
479
360
180
659
763
76
209
630
315
524
504
335
421
418




836
3









In all the exemplary embodiments as described above, when indexes are ordered based on certain characteristics, the order of values having the same characteristics does not affect the order of ordering. Also, the order of pair indexes does not affect the order of ordering. In the ordering (mapping) method according to all the exemplary embodiments, as the indexes increase, they are ordered in an ascending order that the CM or the maximum supportable cell size increases, but it is merely an example. That is, as the indexes increase, they may be ordered in the ascending order that the CM or the maximum supportable cell size is increased or in a descending order that the CM or the maximum supportable cell size is decreased in each group. In addition, the indexes may be ordered in the shape of a mountaintop (^) or in the shape of a mountain valley (v). And, the directionality of the CM or the maximum supportable cell size can be determined to be different in each group.
FIG. 25 is a graph showing CM characteristics and maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention. As the logical indexes increase, they may be ordered in the ascending order that the maximum supportable cell size increases and in the descending order that the CM decreases. FIG. 26 is a graph showing the CM characteristics and the maximum supportable cell radius characteristics according to logical root indexes according to another exemplary embodiment of the present invention. Respective CM groups have been grouped based on the cyclic shift parameter Ncs. As the logical indexes increase, they are ordered in the ascending order that the maximum supportable cell radius size increases, in the descending order that the odd number groups of the CM decrease, and in the ascending order that the even number groups of the CM increase.
Referring to FIGS. 25 and 26, the directionality of the CM or the maximum supportable cell size may be determined to be different in each group. After the indexes are ordered in the ascending order that the maximum supportable cell size increases, when the indexes are ordered in the descending order that the CM decreases, the results appear as shown in FIG. 25. When the odd number groups are ordered in the descending order that the CM decreases and the even number groups are ordered in the ascending order that the CM increases, the results appear as shown in FIG. 26. By making the ordering in adjacent (consecutive) groups different, a larger number of adjacent (consecutive) indexes having low CM can be used in a low mobility cell regardless of the maximum supportable cell radius.
In all the exemplary embodiments as described above, if a single index is allocated in each cell in the ordering (mapping) method, each user equipment may use indexes by adding 1 to or subtracting 1 from a transmitted index, namely, by increasing or decreasing 1 at a time as necessary in order to meet the required number of random access preambles per cell. In case of using indexes by adding 1 at a time, when the largest index 838 is used, it may return to the smallest index 1 to use it. In case of using indexes by subtracting 1 at a time, when the smallest index 1 is used, it may return to the largest index 838 to use it. In addition, the ascending direction (+/−) may be used differently according to each characteristics (e.g., a lower CM/a higher CM). When the indexes are ordered in the ascending direction that the maximum supportable cell size increases as the indexes increase, because available indexes are limited in a large cell, it would be preferred to allocate indexes starting from a large cell. In this case, the simplest method of cell planning is to allocate the largest index to the largest cell and then use indexes by stages by subtracting 1 at a time.
Embodiment of Hybrid Ordering
FIG. 27 is a graph showing a process of grouping CM ordering into two groups. FIG. 28 is a graph showing a process of grouping indexes ordered according to maximum supportable Ncs characteristics into Ncs groups in each group. FIG. 29 is a graph showing a process of ordering indexes according to the CM characteristics in each Ncs group.
Referring to FIGS. 27 to 29, (1) the indexes are ordered according to the CM characteristics. The indexes are divided into a group higher than 1.2 dB, the QPSK CM of the SC-FDMA, and a group lower than 1.2 dB as shown in FIG. 27.
(2) After the entire indexes are ordered according to the maximum cell radius, they are divided into sections according to the Ncs value (or the maximum supportable cell radius value). After the respective groups are ordered according to the maximum supportable cell radius, they are divided into sections with a maximum supportable cell radius value with respect to the Ncs. In this case, the groups may be all divided into different groups according to the Ncs value, several particular Ncs values can be divisionally grouped, or a particular Ncs value can be further divided. Here, the case of using the groups corresponding to every Ncs value is used, and the divided sections are as shown in FIG. 28.
(3) The indexes are ordered according to the CM characteristics in each divided section as shown in FIG. 29. Here, as the Ncs sample values, 13, 15, 18, 22, 26, 32, 38, 46, 59, 76, 119, 167, 237, 279, and 419 were used. Table 13 shows the relationship between the physical indexes and the logical indexes according to the results of FIG. 29.









TABLE 13






Logical



No
index
Physical index



































0
1~24
1
838
2
837
70
769
93
746
105
734
84
755
168
671
210
629
120
719
140




699
129
710
229
610
















1
~28
60
779
56
783

















2
~34
112
727
148
691
233
606















3
~42
80
759
73
766
42
797
40
799













4
~50
31
808
35
804
146
693
235
604













5
~60
236
603
28
811
30
809
27
812
29
810











6
~74
24
815
43
796
48
791
68
771
74
765
178
661
136
703







7
~86
125
714
86
753
78
761
39
800
20
819
21
818









8
~110
15
824
61
778
103
736
95
744
202
637
190
649
181
658
122
717
137
702
151




688
128
711
217
622
















9
~142
231
608
130
709
142
697
179
660
203
636
118
721
207
632
110
729
89
750
55




784
46
793
37
802
34
805
23
816
14
825
12
827








10
~168
9
830
10
829
66
773
91
748
83
756
145
694
135
704
143
696
133
706
132




707
223
616
227
612
228
611














11
~202
216
623
149
690
141
698
121
718
197
642
161
678
201
638
184
655
173
666





108
731
106
733
101
738
57
782
64
775
53
786
16
823
8
831





12
~288
6
833
7
832
13
826
17
822
26
813
49
790
50
789
47
792
65
774
59




780
71
768
104
735
99
740
98
741
100
739
82
757
81
758
107
732
88
751




169
670
87
752
170
669
171
668
174
665
164
675
175
664
187
652
208
631
158




681
119
720
176
663
162
677
199
640
191
648
211
628
154
685
138
701
134
705




144
695
152
687
215
624
218
621
234
605











13
~400
237
602
225
614
224
615
221
618
220
619
150
689
127
712
147
692
213
626





153
686
212
627
139
700
123
716
124
715
156
683
157
682
177
662
182
657





192
647
195
644
194
645
193
646
115
724
189
650
114
725
205
634
206
633





200
639
185
654
116
723
160
679
163
676
186
653
172
667
166
673
167
672





79
760
97
742
85
754
96
743
77
762
92
747
75
764
58
781
62
777
69




770
54
785
51
788
36
803
33
806
32
807
25
814
18
821
11
828
5
834




4
835



















14
~474
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
196
643
155




684
214
625
126
713
131
708
219
620
222
617
226
613
230
609
232
607




15
~528
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



16
~626
323
516
322
517
320
519
334
505
348
491
333
506
332
507
319
520
326
513





327
512
352
487
314
525
313
526
312
527
359
480
295
544
385
454
298
541





364
475
362
477
299
540
365
474
292
547
291
548
381
458
399
440
380
459





393
446
397
442
394
445
369
470
377
462
410
429
407
432
281
558
414
425





247
592
417
422
246
593
250
589
278
561
277
562
271
568
275
564
243
596





244
595
272
567
264
575
259
580













17
~684
238
601
239
600
269
570
273
566
249
590
248
591
282
557
403
436
375
464





408
431
371
468
396
443
370
469
401
438
392
447
366
473
382
457
300
539





301
538
353
486
343
496
342
497
350
489
340
499
341
498
318
521
338
501





347
492
330
509

















18
~728
321
518
325
514
331
508
346
493
339
500
345
494
351
488
344
495
311
528





297
542
294
545
389
450
391
448
372
467
412
427
415
424
251
588
245
594





254
585
255
584
241
598
257
582













19
~752
270
569
276
563
374
465
409
430
378
461
398
441
400
439
290
549
289
550





306
533
308
531
316
523















20
~772
358
481
293
546
304
535
288
551
284
555
253
586
268
571
256
583
263
576





260
579



















21
~786
242
597
274
565
402
437
368
471
383
456
357
482
329
510







22
~798
317
522
307
532
286
553
287
552
266
573
261
578









23
~802
303
536
356
483

















24
~810
355
484
405
434
404
435
406
433













25
~814
267
572
302
537

















26
~816
265
574



















27
~822
367
472
296
543
309
530















28
~824
258
581



















29
~838
240
599
419
420
279
560
280
559
373
466
305
534
336
503









In Table 13, there are groups having only a smaller number of indexes. Such groups having only a smaller number of indexes may be united with an adjacent group to constitute a single group.
In all the exemplary embodiments as described above, in case of pair allocation, relative positions of two adjacent pair indexes do not affect the proposed technique. In addition, when the indexes are ordered according to certain characteristics (e.g., the CM, the maximum supportable cell size (or Ncs, etc.)), the order of indexes having similar characteristics does not affect the proposed technique.
In use the above-described method, the user equipment and the base station should have a mapping table showing the relationship between the physical indexes and the logical indexes in each memory. In this case, the entire 838 indexes may be stored in each memory or only a half of them may be stored according to pair allocation. If only the half is stored, it may be assumed that (N−i)-th index is present after the i-th index, for processing.
When the indexes are ordered by using the above-described method and indexes available in a cell are informed to the base station, a method of informing about the number of Ncs configurations and a single logical index may be used. In this case, a single logical index can be informed by logical indexes 1 to 838 by using 10 bits. Alternatively, indexes 1 to 419 may be informed by using only one value of pair allocation with 9 bits. In this case, for the separate use of the pair allocation, an additional 1 bit may be used to indicate whether the used indexes are the front indexes 1 to 419 or the rear indexes 420 to 838 in the pair allocation. When indexes are informed with only 9 bits, they can be processed on the assumption that the (N−i)-th index follows the i-th index.
FIG. 30 is a flow chart illustrating the random access procedure according to one exemplary embodiment of the present invention.
Referring to FIG. 30, a user equipment (UE) receives random access information from the base station (BS) (S310). The random access information includes information about a cyclic shift parameter Ncs and information about generation of a plurality of random access preambles. The cyclic shift parameter Ncs is used to obtain the value of cyclic shift of a root ZC sequence. The information about generation of a random access preamble is information regarding a logical index. The logical index is an index to which a physical root index of a root ZC sequence is mapped. The logical index becomes a source index for generating a set of random access preambles.
The information about the cyclic shift parameter Ncs and the logical index may be broadcasted as part of system information or transmitted on a downlink control channel. The method or format of transmitting the cyclic shift parameter Ncs or the logical index is not limited.
The user equipment acquires mapped physical root indexes from the logical index (S320). There are 64 preambles available in each cell. The set of 64 preamble sequences in a cell is found by including first, in the order of increasing cyclic shift, all the available cyclic shifts of a root Zadoff-Chu sequence with the logical index. Additional preamble sequences, in case 64 random access preambles cannot be generated from a single root Zadoff-Chu sequence, are obtained from the root sequences with the consecutive logical indexes until all the 64 sequences are found. The logical root sequence order is cyclic: the logical index 0 is consecutive to 837 when Nzc=838. Thus, the user equipment can find every available random access preamble through the single logical index.
Even if the base station informs the user equipment about only a single logical index, the user equipment can find the available 64 random access preambles. In addition, the root ZC sequences corresponding to the consecutive logical indexes have similar characteristics, all the generated sequences have substantially similar characteristics. Also, the root ZC sequences corresponding to the consecutive logical indexes may have complex conjugate symmetry which means the sum of two root index of the root ZC sequences corresponding to the two consecutive logical indexes is equal to the length of a root ZC sequence.
The logical indexes can be mapped to the physical root indexes of the root ZC sequence in sequence, after the physical root indexes are ordered according to the CM by subgroup. The subgroups have been obtained by grouping the ZC sequences by the predetermined cyclic shift parameter. Even if a consecutive logical index is selected, root ZC sequences having similar characteristics as those of the existing logical index can be obtained. Thus, only with a single logical index, the user equipment can acquire the 64 preamble sequences required for selecting the random access preamble.
As mentioned above, the logical index is the index to which the physical indexes are mapped in a state that the ZC sequences have been grouped into subgroups according to the predetermined cyclic shift parameter and ordered by the CM in each subgroup. Thus, the logical sequences belonging to a single subgroup have the same cyclic shift parameter. Although the base station allocates only the logical sequences in consideration of mobility of the user equipment, the user equipment can acquire the plurality of ZC sequences having the same cyclic shift parameter Ncs and similar CM characteristics.
The user equipment transmits a selected random access preamble to the base station on the RACH (Random Access Channel) (S330). That is, the user equipment randomly selects one of the 64 available random access preambles and transmits the selected random access preamble.
The base station transmits a random access response, a response to the random access preamble (S340). The random access response may be a MAC message configured in a MAC, a higher layer of a physical layer. The random access response is transmitted on a DL-SCH (Downlink Shared Channel). The random access response is addressed by an RA-RNTI (Random Access-Radio Network Temporary Identifier) transmitted on a PDCCH (Physical Downlink Control Channel). The RA-RNTI is a identifier to identify the used time/frequency resource for random access. The random access response may include timing alignment information, an initial uplink grant, and a temporary C-RNTI (Cell-Radio Network Temporary Identifier). The timing alignment information is timing correction information for uplink transmission. The initial uplink grant is ACK/NACK information with respect to the uplink transmission. The temporary C-RNTI refers to a user equipment's identifier that may not be permanent until collision is resolved.
The user equipment performs scheduled uplink transmission on a UL-SCH (S350). If there is data to be transmitted additionally as necessary, the user equipment performs uplink transmission to the base station and performs a collision settlement procedure.
If an error occurs in the transmission of the random access preamble, the random access procedure is delayed. Since the random access procedure is performed at an initial access to the base station or in a handover process to the base station, the delay of the random access procedure may cause an access delay or a service delay. A user equipment can obtain 64 preamble sequences suitable for the high speed environment, whereby the user equipment can reliably transmit the random access preamble in the high speed environment.
By using consecutive logical indexes, a set of random access preambles having similar physical characteristics can be generated. Control signaling to generate random access preambles can be minimized. Random access failure can be reduced under high speed environment and efficient cell planning can be performed.
FIG. 31 is a schematic block diagram of elements of a user equipment to which the exemplary embodiments are applied.
A user equipment 50 may include a processor 51, a memory 52, an RF unit 53, a display unit 54, and a user interface unit 55. The processor 51 may handle generation and mapping of sequences and implement functions regarding the various exemplary embodiments as described above. The memory 52 may be connected to the processor 51 and store an operating system, applications and files. The display unit 54 may display various information and use the known elements such as an LCD (Liquid Crystal Display), OLEDs (Organic Light Emitting Diodes), etc. The user interface unit 55 may be formed by combining user interfaces such as a keypad, a touch screen, or the like. The RF unit 53 is coupled to the processor 51 and transmits or receives radio signals.
Every function as described above can be performed by a processor such as a microprocessor based on software coded to perform such function, a program code, etc., a controller, a micro-controller, an ASIC (Application Specific Integrated Circuit), or the like. Planning, developing and implementing such codes may be obvious for the skilled person in the art based on the description of the present invention.
Although the embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope of the invention. Accordingly, the embodiments of the present invention are not limited to the above-described embodiments but are defined by the claims which follow, along with their full scope of equivalents.

## Claims

1. A method of transmitting a signal for a random access procedure, the method comprising:
receiving, by a radio frequency (RF) unit of a user equipment (UE), a first logical index from a base station, wherein the first logical index is one of consecutive logical indexes which are mapped to physical root indexes of a root Zadoff-Chu (ZC) sequence, the physical root indexes of the root ZC sequence are divided into subgroups according to cyclic shift parameters, and each of the subgroups includes at least one physical root index;
receiving, by the RF unit of the UE, information regarding a cyclic shift parameter from the base station; and
transmitting, by the RF unit of the UE, a random access preamble of a predetermined number of random access preambles,
wherein the predetermined number of random access preambles are obtained, at a processor of the UE, by generating random access preambles in the order of increasing cyclic shift from a first root ZC sequence with a first physical root index mapped to the first logical index in a memory of the UE and by generating additional random access preambles in an order of increasing cyclic shift from a second root ZC sequence with a second physical root index mapped to a second logical index in the memory of the UE when the predetermined number of random access preambles cannot be generated from the first root ZC sequence, wherein the second logical index is consecutive to the first logical index, and
wherein a sum of the first physical root index and the second physical root index is equal to a length of the root ZC sequence, and
wherein a value of the cyclic shift is obtained from the cyclic shift parameter.

2. The method of claim 1, wherein the physical root indexes are ordered such that a sequence of the physical root indexes is different from a sequence of the logical indexes.

3. The method of claim 1, wherein the predetermined number of the random access preambles is 64.

4. The method of 1, wherein the first logical index is broadcast.

5. The method of 1,
wherein a k-th element c(k) of the root ZC sequence is defined by




  
    
      
        c
        ⁡
        
          (
          k
          )
        
      
      =
      
        exp
        ⁢
        
          {
          
            -
            
              
                jπ
                ⁢
                
                  
                
                ⁢
                
                  Mk
                  ⁡
                  
                    (
                    
                      k
                      +
                      1
                    
                    )
                  
                
              
              N
            
          
          }
        
      
    
    ,
    
      for
      ⁢
      
        
      
      ⁢
      N
      ⁢
      
        
      
      ⁢
      odd
    
  




  
    
      
        c
        ⁡
        
          (
          k
          )
        
      
      =
      
        exp
        ⁢
        
          {
          
            -
            
              
                jπ
                ⁢
                
                  
                
                ⁢
                
                  Mk
                  2
                
              
              N
            
          
          }
        
      
    
    ,
    
      for
      ⁢
      
        
      
      ⁢
      N
      ⁢
      
        
      
      ⁢
      even
    
  


wherein N is the length of the root ZC sequence, and
wherein M is a physical root index and relatively prime to N.

6. A user equipment (UE) for transmitting a signal for a random access procedure, the UE comprising:
a radio frequency (RF) unit for:
receiving a first logical index from a base station, wherein the first logical index is one of consecutive logical indexes which are mapped to physical root indexes of a root Zadoff-Chu (ZC) sequence, the physical root indexes of the root ZC sequence are divided into subgroups according to cyclic shift parameters, and each of the subgroups includes at least one physical root index;
receiving information regarding a cyclic shift parameter from the base station; and
transmitting a random access preamble of a predetermined number of random access preambles;

a memory for storing the first logical index; and
a processor for obtaining the predetermined number of random access preambles by generating random access preambles in an order of increasing cyclic shift from a first root ZC sequence with a first physical root index mapped to the first logical index in the memory and by generating additional random access preambles in the order of increasing cyclic shift from a second root ZC sequence with a second physical root index mapped to a second logical index in the memory when the predetermined number of random access preambles cannot be generated from the first root ZC sequence, wherein the second logical index is consecutive to the first logical index,
wherein a sum of the first physical root index and the second physical root index is equal to a length of the root ZC sequence, and
wherein a value of the cyclic shift is obtained from the cyclic shift parameter.