# Patent

## Title
Sequence-generating method, and apparatus for same

## Abstract

The present invention relates to a wireless communication system. More particularly, the present invention relates to a method for enabling a transmitter to transmit a sequence in a wireless communication system, and to an apparatus for the same. A sequence-transmitting method comprises the steps of: performing at least one of a complex conjugate operation and a reverse operation on a first sequence to generate a second sequence; mapping the second sequence to a plurality of subcarriers in an Orthogonal Frequency Division Multiple Access (OFDMA) symbol; and transmitting the OFDMA symbol to a receiver. The invention also relates to an apparatus for the sequence-generating method.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application is a Continuation application of U.S. application Ser. No. 13/119,670, filed on Mar. 17, 2011, now U.S. Pat. No. 8,520,501, which is the National Phase of PCT/KR2010/000824 filed on Feb. 10, 2010, which claims priority under 35 USC 119(e) to U.S. Provisional Application Nos. 61/153,291 filed Feb. 17, 2009; 61/156,892 filed Mar. 3, 2009; 61/168,221 filed Apr. 10, 2009; 61/223,355 filed Jul. 6, 2009 and under 35 USC 119(a) to Patent Application No. 10-2009-0077562 filed in Republic of Korea on Aug. 21, 2009, all of which are hereby expressly incorporated by reference into the present application.


TECHNICAL FIELD
The present invention relates to a wireless communication system, and more particularly, to a method and apparatus for transmitting and receiving a sequence in a wireless communication system.
BACKGROUND ART
FIG. 1 illustrates an exemplary wireless communication system. Referring to FIG. 1, a wireless communication system 100 includes a plurality of Base Stations (BSs) 110a, 110b and 110c and a plurality of Mobile Stations (MSs) 120a to 120i. The wireless communication system 100 may include a homogeneous network or a heterogeneous network. A heterogeneous network refers to a network in which different network entities co-exist, such as macro cells, femto cells, pico cells, relays, etc. A BS is typically a fixed station that communicates with MSs and each BS 110a, 110b or 110c provides services to a specific geographical area 102a, 102b or 102c. To increase system performance, the specific area may be divided into a plurality of smaller areas 104a, 104b and 104c, which may be called cells, sectors, or segments. In an Institute of Electrical and Electronics Engineers (IEEE) 802.16 system, a cell Identifier (ID) (IDcell) is assigned from the perspective of the entire system, whereas a sector ID or segment ID is assigned from the perspective of the coverage area of each BS, ranging from 0 to 2. The MSs 120a to 120i are fixed or mobile terminals that are usually distributed over the wireless communication system 100. Each MS may communicate with one or more BSs at a given time instant on a downlink and uplink. The communication between an MS and a BS may be carried out in Frequency Division Multiple Access (FDMA), Time Division Multiple Access (TDMA), Code Division Multiple Access (CDMA), Single Carrier-FDMA (SC-FDMA), Multi Carrier-FDMA (MC-FDMA), Orthogonal Frequency Division Multiple Access (OFDMA), or a combination of two or more of them. Herein, the term “uplink” refers to a communication link directed from an MS to a BS, and the term “downlink” refers to a communication link directed from a BS to an MS.
FIG. 2 illustrates the structure of a downlink subframe in an IEEE 802.16e system. The downlink frame structure was designed for operation in Time Division Duplex (TDD) mode.
Referring to FIG. 2, the downlink subframe includes a plurality of Orthogonal Frequency Division Multiplexing (OFDM) symbols. The downlink subframe is divided in structure into a preamble, a Frame Control Header (FCH), a Downlink-MAP (DL-MAP), an Uplink-MAP (UL-MAP), and DL bursts. Each downlink subframe starts with a preamble that occupies the first OFDM symbol of the downlink subframe. The preamble is used for time synchronization acquisition, frequency synchronization acquisition, cell search, and channel estimation.
FIG. 3 illustrates subcarriers to which a preamble is mapped in 1024-Fast Fourier Transform (FFT) mode (a 10-MHz bandwidth) in the IEEE 802.16e system.
Referring to FIG. 3, some areas at both sides of a given bandwidth are used as guard bands. Therefore, the preamble is mapped to the rest except the guard bands. The remaining frequency area except the guard bands is divided into three segments for three sectors. A preamble is inserted at an interval of three subcarriers, with 0s filled at the other subcarriers. For example, a preamble for segment 0 is inserted at subcarriers 0, 3, 6, 9, . . . , 843, 846 and 849. A preamble for segment 1 is inserted at subcarriers 1, 4, 7, 10, . . . , 844, 847 and 850. A preamble for segment 2 is inserted at subcarriers 2, 5, 8, 11, . . . , 845, 848 and 851.
In the IEEE 802.16e system, a sequence used for the preamble is a binary code inserted in a frequency area, as proposed by Runcom. Among sequences that can be generated as binary codes, sequences that satisfy certain correlation properties and have low Peak-to-Average Power Ratios (PAPRs) in the time domain were found by computer-aided search. Table 1 below lists some preamble sequences.










TABLE 1





Index
IDcell
Segment
Series to modulate (in hexadecimal format)







0
0
0
0xA6F294537B285E1844677D133E4D53CCB1F182DE00489E53E6B6E





77065C7EE7D0ADBEAF


1
1
0
0x668321CBBE7F462E6C2A07E8BBDA2C7F7946D5F69E35ACEACF7





D64AB4A33C467001F3B2


2
2
0
0x1C75D30B2DF72CEC9117A0BD8EAF8E0502461FC07456AC906AD





E03E9B5AB5E1D3F98C6E


3
3
0
0x5F9A2E5CA7CC69A5227104FB1CC2262809F3B10D0542B9BDFDA





4A73A7046096DF0E8D3D









Referring to Table 1, a preamble sequence is determined according to a segment number and a parameter IDcell. Each preamble sequence is converted to a binary signal and modulated by Binary Phase Shift Keying (BPSK), prior to mapping to subcarriers. Specifically, a hexadecimal sequence is converted to a binary sequence Wk and modulated by BPSK in the order from the Most Significant Bit (MSB) to the Least Significant Bit (LSB) (0=>+1, 1=>−1). For example, hexadecimal sequence 0 is converted to Wk[110000010010 . . . ] and then modulated to [−1 −1 +1 +1 +1 +1 +1 −1 +1 +1−1 +1 . . . ].
FIGS. 2 and 3 are examples of using sequences for signal transmission. Besides the preamble, sequences are used for transmission of many other channels and signals in the wireless communication system. For example, sequences have a variety of usages including synchronization channels, a midamble, a reference signal, control channels, scrambling codes, and multiplexing in the wireless communication system. The sequences preferably satisfy the following characteristics:

    
    
        The sequences have good correlation properties to provide good detection performance;
        The sequences have Low Cubic Metrics (CMs) or PAPRs to maximize the efficiency of a power amplifier;
        Many sequences are available to facilitate transmission of a large amount of information or cell planning;
        The sequences reduce a memory size requirement for storing the sequences; and
        A receiver has a low complexity, when the receiver uses the sequences.
    
    


Especially the complexity of the receiver is a very significant factor that directly affects its battery lifetime. Accordingly, there exists a need for a method for generating a sequence so as to further decrease a memory size requirement, while reducing complexity.
DISCLOSURE
Technical Problem
Accordingly, the present invention is directed to a method for generating a sequence that substantially obviates one or more problems due to limitations and disadvantages of the related art.
An object of the present invention is to provide a method and apparatus for generating sequences in a wireless communication system.
Another object of the present invention is to provide a method and apparatus for generating sequences having excellent correlation properties and low Peak-to-Average Power Ratios (PAPRs) or Cubic Metrics (CMs).
Another object of the present invention is to provide a method and apparatus for generating sequences in such a manner that maximizes the number of available sequences.
A further object of the present invention is to provide a method and apparatus for generating sequences which have a low memory size requirement and which a receiver can detect or estimate with low complexity.
Technical Solution
To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a method for transmitting a sequence at a transmitter in a wireless communication system includes generating a second sequence by performing at least one of complex conjugation and a reverse operation on a first sequence, mapping the second sequence to a plurality of subcarriers in an Orthogonal Frequency Division Multiple Access (OFDMA) symbol, and transmitting the OFDMA symbol to a receiver.
The method may further include modulating the first sequence to a complex sequence according to a type of the first sequence.
The first sequence may be at least one of sequences included in a sequence set that is stored in the transmitter.
The type of the first sequence may be Quadrature Phase Shift Keying (QPSK).
The second sequence may be transmitted on a synchronization channel. Also, the second sequence may be transmitted on a ranging channel.
The first sequence may be at least one of sequences listed in Table 11, Table 12 and Table 13.
In another aspect of the present invention, a transmitter for transmitting a sequence in a wireless communication system includes a second sequence generator for generating a second sequence by performing at least one of complex conjugation and a reverse operation on a first sequence, a subcarrier mapper for mapping the second sequence to a plurality of subcarriers in an OFDMA symbol, and a transmission module for transmitting the OFDMA symbol to a receiver.
The transmitter may further include a constellation mapper for modulating the first sequence to a complex sequence according to a type of the first sequence.
In another aspect of the present invention, a method for transmitting a sequence at a transmitter in a wireless communication system includes modulating a first sequence to a complex sequence according to a type of the first sequence, mapping the complex sequence to a plurality of subcarriers in an OFDMA symbol, and transmitting the OFDMA symbol to a receiver. The first sequence is at least one of sequences included in Table 11, Table 12 and Table 13.
The type of the first sequence may be QPSK. Then, the first sequence Wi(p) may be modulated to QPSK symbols w2i(p) and w2i+1(p) by the following equation,



  
    
      w
      
        2
        ⁢
        
          
        
        ⁢
        i
      
      
        (
        p
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  a
                  
                    i
                    ,
                    0
                  
                  
                    (
                    p
                    )
                  
                
              
              +
              
                a
                
                  i
                  ,
                  1
                
                
                  (
                  p
                  )
                
              
            
            )
          
        
        )
      
    
  




  
    
      w
      
        
          2
          ⁢
          
            
          
          ⁢
          i
        
        +
        1
      
      
        (
        p
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  a
                  
                    i
                    ,
                    2
                  
                  
                    (
                    p
                    )
                  
                
              
              +
              
                a
                
                  i
                  ,
                  3
                
                
                  (
                  p
                  )
                
              
            
            )
          
        
        )
      
    
  



where Wi(p)=23·ai,0(p)+22·ai,1(p)+21·ai,2(p)+20·ai,3(p) and i is an integer from 0 to 107.

The first sequence may be cyclically extended according to a Fast Fourier Transform (FFT) size.
The first sequence may be a Secondary Advanced Preamble (SA-Preamble) used for downlink synchronization. The SA-Preamble may be mapped to subcarriers by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  




where n denotes an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP denotes a length of the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

The first sequence may indicate information about a cell ID, IDcell according to the following equation,

IDcell=256×n+Idx

where n is an index of an SA-Preamble carrier set, indicating a segment ID ranging from 0 to 2, and Idx is an integer ranging from 0 to 255.

The method may further include performing at least one of complex conjugation and a reverse operation on the first sequence.
One of block cover sequences listed in the following table may be applied to the first sequence on a subblock basis,
Block cover sequence (hexadecimal format)













(FFT, number of





antennas)\Segment ID
0
1
2







 (512,1)
00
00
00


 (512,2)
22
22
37


 (512,4)
09
01
07


 (512,8)
00
00
00


(1024,1)
0FFF
555A
000F


(1024,2)
7373
3030
0000


(1024,4)
3333
2D2D
2727


(1024,8)
0F0F
0404
0606


(2048,1)
0F0FFF00
00000FF0
0F000FFF


(2048,2)
7F55AA42
4438180C
3A5A26D9


(2048,4)
1A13813E
03284BF0
391A8D37


(2048,8)
0D0EF8FA
0C0BFC59
03000656









In the above table, a block cover sequence converted to a binary sequence {0, 1} is mapped to {+1, −1}.

Transmission power of the first sequence may be boosted using one of boosting levels listed in the following table,
Boosting Level
















Ant\FFT
512
1024
2048









1
1.87
1.75
1.69



2
2.51
2.33
2.42



4
4.38
3.56
3.50



8
8.67
6.25
4.95










The first sequence may be transmitted through a plurality of antennas. In this case, the first sequence may be interleaved across the plurality of antennas on a block basis.
In another aspect of the present invention, a transmitter for transmitting a sequence in a wireless communication system includes a memory for storing at least part of sequences included in Table 11, Table 12, and Table 13, a constellation mapper for modulating a first sequence selected from the memory to a complex sequence according to a type of the first sequence, a subcarrier mapper for mapping the complex sequence to a plurality of subcarriers in an OFDMA symbol, and an RF module for transmitting the OFDMA symbol to a receiver.
In another aspect of the present invention, a method for detecting a sequence at a receiver in a wireless communication system includes receiving from a transmitter a sequence mapped to a plurality of subcarriers in an OFDMA symbol, correlating a first sequence with the received sequence, and detecting the received sequence based on a correlation. The first sequence is at least one of sequences included in Table 11, Table 12 and Table 13.
For the correlation operation, preliminary computations may be performed on combinations between real and imaginary parts of the received sequence and real and imaginary parts of the at least one first sequence. Correlations between the received sequence and the at least one first sequence and between the received sequence and a complex conjugate sequence of the first sequence may be obtained by combining a plurality of preliminary correlations.
The first sequence may be an SA-Preamble used for downlink synchronization. The SA-Preamble may be mapped to subcarriers by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  




where n denotes an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP denotes a length of the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

The method may further include acquiring a cell ID from the received sequence.
In a further aspect of the present invention, a receiver for detecting a sequence in a wireless communication system includes an RF module for receiving from a transmitter a sequence mapped to a plurality of subcarriers in an OFDMA symbol, a memory for storing at least part of sequences included in Table 1, Table 2 and Table 3, and a processor for correlating at least one first sequence stored in the memory with the received sequence and detecting the received sequence based on a correlation.
The processor may acquire a cell ID from the received sequence.
The receiver may further include a buffer for temporarily storing a real part of a sequence and a buffer for temporarily storing an imaginary part of the sequence.
The receiver may further include a first buffer for temporarily storing a real part of the received sequence, a second buffer for temporarily storing an imaginary part of the received sequence, a third buffer for temporarily storing a real part of the at least one first sequence, and a fourth buffer for temporarily storing an imaginary part of the at least one first sequence.
It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed.
Advantageous Effects
As is apparent from the above description, the embodiments of the present invention have the following effects.
Sequences can be provided for use in channels, signals, etc.
In addition, sequences having excellent correlation properties and low PAPRs or CMs can be provided.
The number of available sequences can be maximized.
Further, a memory size requirement for storing sequences can be reduced and a receiver can detect or estimate sequences with low complexity.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.



DESCRIPTION OF DRAWINGS
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiments of the invention and together with the description serve to explain the principle of the invention. In the drawings:
FIG. 1 illustrates an exemplary wireless communication system.
FIG. 2 illustrates a downlink subframe structure in an Institute of Electrical and Electronics Engineers (IEEE) 802.16e system.
FIG. 3 illustrates subcarriers to which a preamble is mapped in 1024-Fast Fourier Transform (FFT) mode (a 10 MHz-bandwidth) in the IEEE 802.16e system.
FIG. 4 is a flowchart illustrating a method for generating sequences having Peak-to-Average Power Ratios (PAPRs) or Cubic Metrics (CMs) and excellent basic properties in terms of auto-correlation, cross-correlation, differential auto-correlation, and differential cross-correlation according to an embodiment of the present invention.
FIG. 5 is a block diagram of a transmitter for extending sequences by complex conjugation according to an embodiment of the present invention.
FIG. 6 is a block diagram of a receiver for detecting sequences according to an embodiment of the present invention.
FIGS. 7A to 7E are graphs illustrating properties of sequences generated according to an embodiment of the present invention.
FIG. 8 illustrates a radio frame structure in an IEEE 802.16m system.
FIG. 9 illustrates an exemplary transmission of synchronization channels in the IEEE 802.16m system.
FIG. 10 illustrates subcarriers to which a Primary Advanced Preamble (PA-Preamble) is mapped.
FIG. 11 illustrates an exemplary mapping of Secondary Advanced Preambles (SA-Preambles) to frequency areas.
FIG. 12 illustrates an exemplary SA-Preamble structure for 512-FFT.
FIGS. 13, 14 and 15 illustrate exemplary SA-preamble structures in multi-antenna systems.
FIG. 16 illustrates exemplary ranging channel structures in the IEEE 802.16m system.
FIG. 17 is a block diagram of a transmitter and a receiver according to an embodiment of the present invention.



MODE FOR INVENTION
The above and other objects, features and other advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings. Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. Embodiments of the present invention are examples to which the technical features of the present invention are applied. While the present invention is described in the context of an Institute of Electrical and Electronics Engineers (IEEE) 802.16 system by way of example, it is also applicable to a variety of wireless communication systems including a 3rd Generation Partnership Project (3GPP) system.
In wireless communication systems, sequences are used as follows. The followings are mere examples and thus sequences are available to many other channels and signals.
Downlink (DL) Sync Channel
The DL sync channel is used for acquisition of downlink time synchronization and frequency synchronization and for cell search. Specifically, synchronization is acquired and a physical cell Identifier (ID) is detected, by correlating sequences with a sequence received on the DL sync channel. For the purpose of cell ID detection, the existence of as many sequences as possible is favorable in terms of cell planning.
According to systems, the DL sync channel is called different names. For example, the DL sync channel is called a Synchronization Signal (SS) in 3GPP Long Term Evolution (LTE), a preamble in IEEE 802.16e, and an advanced preamble in IEEE 802.16m.
Since a Mobile Station (MS) serves as a receiver, the complexity of the receiver is a very significant issue.
Uplink (UL) Sync Channel
The UL sync channel is used for acquisition of uplink time synchronization and frequency synchronization, access for network registration, a scheduling request, a bandwidth request, etc. A sequence transmitted on the UL sync channel is regarded as an opportunity. A Base Station (BS) may identify an opportunity in which an MS has transmitted a signal by detecting the sequence. The BS may also track timing or estimate a residual frequency offset by use of the detected sequence. Since less collision occurs with more opportunities, the existence of many sequences is favorable. In terms of cell planning, it is also preferable to generate as many sequences as possible.
The UL sync channel is also called a Random Access CHannel (RACH) in 3GPP LTE, and a ranging channel in IEEE 802.16e/m.
In relation to the UL sync channel, the receiver complexity is a consideration.
DL/UL Reference Signal
If a transmitter transmits a signal after coherent modulation (e.g. Phase Shift Keying (PSK), Quadrature Amplitude Modulation (QAM), etc.), a receiver should estimate a fading channel that the signal has experienced and compensate for the fading channel, for signal demodulation. In general, to help the receiver with the fading channel estimation, the transmitter transmits a Reference Signal (RS) along with the signal. The RS is also used for the receiver to measure the channel quality of its serving cell or another cell. The RS may also serve the purpose of timing/frequency tracking. In addition, an MS may synchronize its timing using an RS, when it wakes up from sleep mode. In this manner, the RS may serve many purposes. The RS is generally transmitted using a sequence and as more sequences are available, it is better in terms of cell planning.
An RS is called as it is in 3GPP LTE and a pilot signal in IEEE 802.16e/m.
The receiver complexity is to be considered in relation to the DL/UL RS.
DL/UL Control Channel
Control information may be transmitted using a sequence on a control channel. For example, a Channel Quality Indicator (CQI) or an ACKnowledgement/Negative ACKnowledgement (ACK/NACK) may be transmitted as a sequence. More information can be transmitted with more sequences.
In relation to the DL/UL control channel, the receiver complexity needs to be considered.
Scrambling
Scrambling has many usages. For example, scrambling may be used for randomization or PAPR (or CM) reduction. A signal can be scrambled by multiplying it by a sequence, element by element. Also, a signal can be scrambled by adding the signal to a sequence, element by element and then modulo-operating the sum. Scrambling is not limited to a specific channel. In terms of cell planning, it is better to have many available sequences.
The receiver complexity needs to be considered in relation to scrambling.
User Multiplexing or Channel Multiplexing
Sequences may be used in multiplexing a plurality of users in one channel by Code Division Multiplexing (CDM). Sequences may also be used in multiplexing channels by CDM. A multiplexing capability is related to the number of available sequences.
In relation to user multiplexing or channel multiplexing, the receiver complexity is an issue to be considered.
Midamble
A midamble is an area allocated for a common pilot in a frame. A midamble sequence may be used for channel estimation, Multiple Input Multiple Output (MIMO) channel estimation, CQI estimation, etc.
In relation to the midamble, the receiver complexity is to be considered.
The following embodiments of the present invention are applicable simply to all of the above-described channels (e.g. pilot, control channel, UL sync channel, etc.). Accordingly, unless stated otherwise, the embodiments of the present invention will be described, centering on a DL sync channel (e.g. a preamble, a Synchronization CHannel (SCH), etc.), for the convenience' sake of description.
Embodiment 1
Sequence Generation
Preferably, sequences satisfy the following conditions for a DL sync channel:

    
    
        A. Low PAPR (or CM): for channel boosting to extend coverage;
        B. Low complexity: for saving battery power by reducing the computation volume of correlation at an MS;
        C. Small memory size: for reducing a memory size required for storing sequences; and
        D. Low correlation properties
        
            Low cross-correlation: for reducing false alarm during cell ID detection and for distinguishing an intended cell component from a neighbor cell component during channel estimation
            Low differential cross-correlation: a cross-correlation property regarding non-coherent detection on frequency-selective fading channels, when a sequence is transmitted in a wide band.
            Low auto-correlation side peak in frequency domain: for compensating for an integer frequency offset.
            Low differential auto-correlation side peak in frequency domain: for compensating for an integer frequency offset by differential auto-correlation, for frequency-domain implementation.
            Low cross-correlation in time domain: cross-correlation in the frequency domain is equivalent to cross-correlation in the time domain. Therefore, low cross-correlation in the time domain amounts to low cross-correlation in the frequency domain.
            Low auto-correlation side peak in time domain: important for detection of accurate symbol timing. When timing synchronization is acquired by cross-correlation with a known sequence, a non-periodic auto-correlation property is significant (e.g. a 3GPP family). On the other hand, if coarse timing synchronization based on waveform characteristics (e.g. a repetition structure) is followed by fine timing synchronization during a Cyclic Prefix (CP) duration after cell ID detection, a periodic auto-correlation property in the time domain is significant (e.g. IEEE 802.16e/m, IEEE 802.20, etc.). For a sequence having a flat spectrum in the frequency domain, a periodic auto-correlation side peak in the time domain is zero (i.e. a delta function). Hence, this property may not be examined for a sequence having a frequency flat amplitude.
        
        
    
    


FIG. 4 is a flowchart illustrating a method for generating sequences having low PAPRs or CMs and excellent basic properties in terms of auto-correlation, cross-correlation, differential auto-correlation, and differential cross-correlation according to an embodiment of the present invention. The sequence generation largely involves three steps.
Step 1: sequences with low PAPRs are selected from among randomly generated sequences. First, a sequence generation criterion is set according to an intended purpose in step 402. In steps 404 and 406, a sequence of length N is generated in such a manner that each element of the sequence has a constant amplitude and a random phase. The random phase may be created using a random variable having a uniform or Gaussian distribution, as is known in the art. Considering a channel that will carry the sequence, the sequence of length N is mapped to subcarriers in the frequency domain in step 408. For example, the sequence may be mapped to consecutive or distributed subcarriers. Specifically, the sequence is inserted at an interval of two subcarriers (2× mapping) or three subcarriers (3× mapping). Besides, the sequence may be mapped to subcarriers on a small block basis. Or the sequence may be mapped to subcarriers in a random-like manner. Then null subcarriers are inserted into the sequence, taking into account of oversampling or guard subcarriers, so that the sequence is of length Ndft in step 410. The sequence mapped to the subcarriers is converted to a time signal by Ndft-point Inverse Discrete Fourier Transform (IDFT) in step 412 and the PAPR (or CM) of the time signal is calculated in step 414. If the PAPR is smaller than the PAPR of a previous iteration, the iteration continues by Discrete Fourier Transform (DFT) in steps 416, 418a, 418b, 422, 424 and 426. On the contrary, if the PAPR is larger than the PAPR of the previous iteration, the loop (steps 416, 418a, 418b, 422, 424 and 426) is terminated. Then the sequence resulting from the DFT is quantized according to its type (e.g. a BPSK type, a QPSK type, an 8PSK type, a poly-phase type, etc.) and thus a final sequence is acquired in steps 428 and 430. For example, the sequence resulting from the DFT may be quantized according to its type as follows.

    
    
        BPSK type sequence: +1, −1
        QPSK type sequence: +1, −1, +j, −j
        Poly-phase type sequence:
    
    






  
    e
    jφ
  
  =
  
    
      
        a
        I
      
      +
      
        j
        ⁢
        
          
        
        ⁢
        
          a
          Q
        
      
    
    
      
        
          a
          I
          2
        
        +
        
          a
          Q
          2
        
      
    
  




While the BPSK-type sequence and the QPSK-type sequence require the same volume of computation, the QPSK-type sequence (2 bits per element) requires twice as large a memory size as the BPSK-type sequence (1 bit per element).
Step 2: A sequence set satisfying PAPR<PAPR_THRESHOLD (or CM<CM_THRESHOLD) is selected from sequences generated in Step 1. PAPR_THRESHOLD or CM_THRESHOLD is a maximum allowed value for a channel that will deliver the sequences.
Step 3: A sequence set is finally selected from the sequence set selected in Step 2, which satisfies CORR<CORR_THRESHOLD. CORR_THRESHOLD may be an auto-/cross-correlation value and/or a differential auto-/cross-correlation value optimized for the channel. Steps 2 and 3 may be reversed in order. A sequence set may be additionally selected by applying a criterion different from the criteria used in Steps 2 and 3.
Embodiment 2
Sequence Extension by Reverse Operation
While this embodiment is applicable irrespective of time-domain or frequency-domain sequences, the following description is made in the context of frequency-domain sequences, for the convenience' sake. Given M sequences of length N, an nth element of an mth sequence (m=0, 1, . . . , M−1) is denoted by am(n). M sequences described in [Equation 1] may be extended to 2×M sequences described in [Equation 2] by a reverse operation.

{am(n)}

m=0,1, . . . ,M−1

n=0,1, . . . ,N−1  [Equation 1]

{aext —revm(n)}={am(n); rev(am(n))}

m=0,1, . . . ,M−1

n=0,1, . . . ,N−1  [Equation 2]

where the reverse operation rev(.) may be defined as





  
    
      
        
          
            
              a
              
                m
                1
              
            
            ⁡
            
              (
              n
              )
            
          
          =
          
            
              rev
              ⁡
              
                (
                
                  
                    a
                    
                      m
                      0
                    
                  
                  ⁡
                  
                    (
                    n
                    )
                  
                
                )
              
            
            =
            
              
                a
                
                  m
                  0
                
              
              ⁡
              
                (
                
                  N
                  -
                  1
                  -
                  n
                
                )
              
            
          
        
        ,
        
          

        
        ⁢
        
          n
          =
          0
        
        ,
        1
        ,
        ...
        ⁢
        
          
        
        ,
        
          N
          -
          1
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          3
        
        ]
      
    
  




The reverse operation-based sequence extension offers the following benefits.
If original complex sequences are random enough, sequences reverse to the original complex sequences and sets of the reverse sequences are also random enough. Optimization may be further performed by selecting reverse complex sequences having good characteristics.
The original complex sequences and their reverse complex sequences are identical in PAPR (or CM) properties. That is, if the original complex sequences have good PAPR (or CM) properties, their reverse complex sequences have also the same level of PAPR (or CM) properties.
There is no need for securing a memory size for storing the reverse complex sequences. This means that the memory size requirement can be reduced to a half.
Embodiment 3
Sequence Extension by Complex Conjugation
While this embodiment is applicable irrespective of time-domain or frequency-domain sequences, the following description is made in the context of frequency-domain sequences, for convenience' sake. Given M sequences of length N, an nth element of an mth sequence (m=0, 1, . . . , M−1) is denoted by am(n). M sequences described in [Equation 4] may be extended to 2×M sequences described in [Equation 5] by complex conjugation.

{am(n)}

m=0,1, . . . ,M−1

n=0,1, . . . ,N−1  [Equation 4]

{aext—conjm(n)}={am(n); (am(n))*}

m=0,1, . . . ,M−1

n=0,1, . . . ,N−1  [Equation 5]

where the complex conjugation (.)* may be defined as conversion from a complex signal (a+jb) to a complex signal (a−jb) and conversion from the complex signal (a−jb) to the complex signal (a+jb).

The complex conjugation-based sequence extension offers the following benefits.
If original complex sequences are random enough, their complex conjugates and sets of the complex conjugates are also random enough. Optimization may be further performed by selecting complex conjugates having good characteristics.
The original complex sequences and their complex conjugates are identical in PAPR (or CM) properties. That is, if the original complex sequences have good PAPR (or CM) properties, their complex conjugates have also the same level of PAPR (or CM) properties.
The cross-correlations of an original sequence and its complex conjugate with respect to a received signal can be calculated by one computation. In general, there are M hypotheses for M sequences, thus requiring M cross-correlation computations. Specifically, M×N complex additions are required to calculate cross-correlations for M hypotheses of M QPSK-type sequences. However, in the case where M sequences are extended to 2×M sequences by complex conjugation, the amount of information is doubled but M×N complex additions are needed, that is, the required computation volume is the same, which will be described later in more detail with reference to FIG. 6.
The complex conjugates do not need an additional memory size. That is, the required memory size may be reduced to a half.
Table 2 below compares conventional sequences with extended sequences according to an embodiment of the present invention, in terms of computation complexity and memory size requirement. It is assumed herein that a total of M sequences are available to a transmitter and a receiver and each of the M sequences is of length N.










TABLE 2








Proposed QPSK





type





(conjugate and



BPSK type
QPSK type
reverse)







Number of real-
0
0
0


value





multiplications





Number of real-
M(2N − 2)
M(2N − 2)
M(2N − 2)/2


value additions





Normalized
100%
100%
50%


complexity to





BPSK type (%)





 


Required memory size for M-set [in Bytes]




  ⌈
  
    
      M
      ·
      N
    
    8
  
  ⌉








  ⌈
  
    
      2
      ·
      M
      ·
      N
    
    8
  
  ⌉








  
    ⌈
    
      
        2
        ·
        M
        ·
        N
      
      8
    
    ⌉
  
  ⁢
  
    /
  
  ⁢
  4






 


Normalized
100%
200%
50%


memory size to





BPSK type (%)









FIG. 5 is a block diagram of a transmitter for extending sequences by complex conjugation according to an embodiment of the present invention. For uplink transmission, a transmitter may be part of an MS and a receiver may be part of a BS.
Referring to FIG. 5, a first sequence provider 502 outputs a first sequence (hereinafter, referred to as a base sequence) to a constellation mapper 504 according to an inner setting. Depending on implementation, the base sequence may be selected from a set of pre-stored sequences in a memory, or generated from a sequence generator using a predetermined parameter. The constellation mapper 504 sequentially maps the received bit stream to complex values according to the type of the sequence. The sequence type may be an n-PSK type, an n-QAM type, a poly-phase type, etc. Here, n is an integer equal to or larger than 0. More specifically, the sequence type may be a QPSK type, an 8-PSK type, a 16-QAM type, a 64-QAM type, a poly-phase type, or the like. Especially, the QPSK type is preferable because it requires the same volume of computation as the BPSK type. For example, if the base sequence is a QPSK-type hexadecimal sequence, the constellation mapper 504 may sequentially map a hexadecimal sequence Wi(p) to two QPSK symbols w2i(p) and w2i+1(p), as expressed in [Equation 16].




  
    
      
        
          
            w
            
              2
              ⁢
              
                
              
              ⁢
              i
            
            
              (
              p
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        a
                        
                          i
                          ,
                          0
                        
                        
                          (
                          p
                          )
                        
                      
                    
                    +
                    
                      a
                      
                        i
                        ,
                        1
                      
                      
                        (
                        p
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            w
            
              
                2
                ⁢
                
                  
                
                ⁢
                i
              
              +
              1
            
            
              (
              p
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        a
                        
                          i
                          ,
                          2
                        
                        
                          (
                          p
                          )
                        
                      
                    
                    +
                    
                      a
                      
                        i
                        ,
                        3
                      
                      
                        (
                        p
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          16
        
        ]
      
    
  




where Wi(p)=23·ai,0(p)+22·ai,1(p)+21·ai,2(p)+20·ai,3(p). According to [Equation 16], binary numbers 00, 01, 10 and 11 are converted to 1, j, −1 and −j, respectively.

The constellation mapper 504 outputs the modulated complex values of the base sequence to a second sequence generator 506 and/or a subcarrier mapper 508. When the base sequence is to be transmitted, the constellation mapper 504 may output the complex values of the base sequence to the subcarrier mapper 508. On the other hand, if a second sequence (hereinafter, referred to as an extended sequence) extended from the base sequence is to be transmitted, the constellation mapper 504 may output the complex values of the base sequence to the second sequence generator 506. Also, the constellation mapper 504 may output the QPSK symbols of the base sequence to the second sequence generator 506 irrespective of whether the base sequence is to be transmitted or not. That is, both the base sequence and the extended sequence may be generated and then one of the sequences is selected for transmission to a receiver.
The second sequence generator 504 may generate an extended sequence by subjecting the complex values of the base sequence to complex conjugation and/or a reverse operation. If there is no need for generating an extended sequence, the transmitter may not be provided with the second sequence generator 504. If M base sequences are available to the transmitter, the number of available sequences is increased up to 4×M by complex conjugation and the reverse operation. Let an nth element of an Mth sequence (m=0, 1, . . . , M−1) be denoted by am(n). With the use of complex conjugation and the reverse operation, M base sequences expressed as [Equation 7] may be extended to 4×M sequences as described in [Equation 8].




  
    
      
        
          
        
        ⁢
        
          
            {
            
              
                a
                m
              
              ⁡
              
                (
                n
                )
              
            
            }
          
          ⁢
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              m
              =
              0
            
            ,
            1
            ,
            ...
            ⁢
            
              
            
            ,
            
              M
              -
              1
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          ⁢
          
            
              n
              =
              0
            
            ,
            1
            ,
            ...
            ⁢
            
              
            
            ,
            
              N
              -
              1
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          7
        
        ]
      
    
  
  
    
      
        
          
            {
            
              
                a
                ext_hybrid
              
              ⁡
              
                (
                n
                )
              
            
            }
          
          =
          
            
              {
              
                
                  
                    a
                    m
                  
                  ⁡
                  
                    (
                    n
                    )
                  
                
                ;
                
                  
                    (
                    
                      
                        a
                        m
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                    )
                  
                  *
                
                ;
                
                  rev
                  ⁡
                  
                    (
                    
                      
                        a
                        m
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                    )
                  
                
                ;
                
                  
                    (
                    
                      rev
                      ⁡
                      
                        (
                        
                          
                            a
                            m
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                    
                    )
                  
                  *
                
              
              }
            
            =
            
              {
              
                
                  
                    a
                    m
                  
                  ⁡
                  
                    (
                    n
                    )
                  
                
                ;
                
                  
                    (
                    
                      
                        a
                        m
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                    )
                  
                  *
                
                ;
                
                  rev
                  ⁡
                  
                    (
                    
                      
                        a
                        m
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                    )
                  
                
                ;
                
                  rev
                  ⁡
                  
                    (
                    
                      
                        (
                        
                          
                            a
                            m
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      *
                    
                    )
                  
                
              
              }
            
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          
            m
            =
            0
          
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            M
            -
            1
          
        
        ⁢
        
          

        
        ⁢
        
          
        
        ⁢
        
          
            n
            =
            0
          
          ,
          1
          ,
          ...
          ⁢
          
            
          
          ,
          
            N
            -
            1
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          8
        
        ]
      
    
  




where the complex conjugation (.)* and the reverse operation rev(.) have been defined before.

The subcarrier mapper 508 maps the complex values received from the constellation mapper 504 to subcarriers in the frequency domain. The complex values may be mapped to consecutive or distributed subcarriers, taking into account a channel that will carry the sequence. Then an Inverse Fast Fourier Transform (IFFT) module 510 converts the sequence mapped to the subcarriers to a time signal. The time signal is added with a CP and processed by digital-to-analog conversion, frequency upconversion, and power amplification, prior to transmission to the receiver.
FIG. 6 is a block diagram of a receiver for detecting a sequence according to an embodiment of the present invention. For uplink transmission, a receiver may be part of a BS, whereas for downlink transmission, a receiver may be part of an MS.
Referring to FIG. 6, an index mapper 602 distributes a received signal to first adders 604, 606, 608 and 610. The received signal may be expressed as

r(n)=rI(n)+jrQ(n)  [Equation 9]

where the subscript I represents an in-phase component, and the subscript Q represents a quadrature-phase component. Hereinbelow, the subscripts I and Q are used in the same meanings as above.

The first adders 604, 606, 608 and 610 perform preliminary computations required for calculating the correlation of each base sequence m0 selected from among total base sequences and the correlation of its extended sequence m1. The base sequence m0 and its extended sequence m1 may be expressed as

m0th sequence: am0(n)=aIm0(n)+jaQm0(n)

m1th sequence: am1(n)=aIm1(n)+jaQm1(n)

amj(n)=(am0(n))*  [Equation 10]

For example, the first adders 604, 606, 608 and 610 may carry out preliminary computations required for calculating correlations by [Equation 11].




  
    
      
        
          
            
              R
              II
            
            ⁡
            
              (
              d
              )
            
          
          =
          
            
              1
              N
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      r
                      I
                    
                    ⁡
                    
                      (
                      
                        n
                        +
                        d
                      
                      )
                    
                  
                  ⁢
                  
                    
                      a
                      I
                      
                        m
                        0
                      
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              R
              QQ
            
            ⁡
            
              (
              d
              )
            
          
          =
          
            
              1
              N
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      r
                      Q
                    
                    ⁡
                    
                      (
                      
                        n
                        +
                        d
                      
                      )
                    
                  
                  ⁢
                  
                    
                      a
                      Q
                      
                        m
                        0
                      
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              I
              QI
            
            ⁡
            
              (
              d
              )
            
          
          =
          
            
              1
              N
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      r
                      Q
                    
                    ⁡
                    
                      (
                      
                        n
                        +
                        d
                      
                      )
                    
                  
                  ⁢
                  
                    
                      a
                      I
                      
                        m
                        0
                      
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              I
              IQ
            
            ⁡
            
              (
              d
              )
            
          
          =
          
            
              1
              N
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  1
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      r
                      I
                    
                    ⁡
                    
                      (
                      
                        n
                        +
                        d
                      
                      )
                    
                  
                  ⁢
                  
                    
                      a
                      Q
                      
                        m
                        0
                      
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          11
        
        ]
      
    
  




where d represents a delay. Hereinbelow, d denotes the same.

Referring to [Equation 10], the preliminary computations required for calculating the correlations of the base sequence m0 and the extended sequence m1 may be performed using only the base sequence m0.
The first adders 604, 606, 608 and 610 output the preliminary computation values to second adders 612, 614, 616 and 618. The second adders 612, 614, 616 and 618 calculate final correlations by appropriately combining the preliminary computation values. Specifically, the two second adders 612 and 616 calculate the real and imaginary values of the correlation of the base sequence m0 and the other two second adders 614 and 618 calculate the real and imaginary values of the correlation of the extended sequence m1. The relationship between the first adders 604, 606, 608 and 610 and the second adders 612, 164, 616 and 618 may be described with reference to [Equation 12] and [Equation 13].
[Equation 12] describes the cross-correlation between the received signal and the base sequence m0.




  
    
      
        
          
            
              
                
                  R
                  
                    m
                    0
                  
                
                ⁡
                
                  (
                  d
                  )
                
              
              =
              
              ⁢
              
                
                  1
                  N
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      1
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      r
                      ⁡
                      
                        (
                        
                          n
                          +
                          d
                        
                        )
                      
                    
                    ·
                    
                      
                        (
                        
                          
                            a
                            
                              m
                              0
                            
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      *
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  1
                  N
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      1
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    [
                    
                      
                        (
                        
                          
                            
                              
                                r
                                I
                              
                              ⁡
                              
                                (
                                
                                  n
                                  +
                                  d
                                
                                )
                              
                            
                            ⁢
                            
                              
                                a
                                I
                                
                                  m
                                  0
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                          
                          +
                          
                            
                              
                                r
                                Q
                              
                              ⁡
                              
                                (
                                
                                  n
                                  +
                                  d
                                
                                )
                              
                            
                            ⁢
                            
                              
                                a
                                Q
                                
                                  m
                                  0
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                          
                        
                        )
                      
                      +
                    
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                j
                ⁡
                
                  (
                  
                    
                      
                        
                          r
                          Q
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      ⁢
                      
                        
                          a
                          I
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                    
                    -
                    
                      
                        
                          r
                          I
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      ⁢
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                    
                  
                  )
                
              
              ]
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        R
                        II
                      
                      ⁡
                      
                        (
                        d
                        )
                      
                    
                    +
                    
                      
                        R
                        QQ
                      
                      ⁡
                      
                        (
                        d
                        )
                      
                    
                  
                  )
                
                +
                
                  j
                  ⁡
                  
                    (
                    
                      
                        
                          I
                          QI
                        
                        ⁡
                        
                          (
                          d
                          )
                        
                      
                      -
                      
                        
                          I
                          IQ
                        
                        ⁡
                        
                          (
                          d
                          )
                        
                      
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          12
        
        ]
      
    
  




The components of the final expression of [Equation 12] are the outputs of the first adders 604, 606, 608 and 610 and the real and imaginary parts are the outputs of the second adders 612 and 616.
[Equation 13] describes the cross-correlation between the received signal and the extended sequence m1.




  
    
      
        
          
            
              
                
                  R
                  
                    m
                    1
                  
                
                ⁡
                
                  (
                  d
                  )
                
              
              =
              
              ⁢
              
                
                  1
                  N
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      1
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      r
                      ⁡
                      
                        (
                        
                          n
                          +
                          d
                        
                        )
                      
                    
                    ·
                    
                      
                        (
                        
                          
                            a
                            
                              m
                              1
                            
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      *
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  1
                  N
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      1
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      r
                      ⁡
                      
                        (
                        
                          n
                          +
                          d
                        
                        )
                      
                    
                    ·
                    
                      
                        a
                        
                          m
                          0
                        
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  1
                  N
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      1
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    (
                    
                      
                        (
                        
                          
                            
                              
                                r
                                I
                              
                              ⁡
                              
                                (
                                
                                  n
                                  +
                                  d
                                
                                )
                              
                            
                            ⁢
                            
                              
                                a
                                I
                                
                                  m
                                  0
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                          
                          -
                          
                            
                              
                                r
                                Q
                              
                              ⁡
                              
                                (
                                
                                  n
                                  +
                                  d
                                
                                )
                              
                            
                            ⁢
                            
                              
                                a
                                Q
                                
                                  m
                                  0
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                          
                        
                        )
                      
                      +
                    
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                j
                ⁡
                
                  (
                  
                    
                      
                        
                          r
                          Q
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      ⁢
                      
                        
                          a
                          I
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                    
                    +
                    
                      
                        
                          r
                          I
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      ⁢
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                    
                  
                  )
                
              
              )
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        R
                        II
                      
                      ⁡
                      
                        (
                        d
                        )
                      
                    
                    -
                    
                      
                        R
                        QQ
                      
                      ⁡
                      
                        (
                        d
                        )
                      
                    
                  
                  )
                
                +
                
                  j
                  ⁡
                  
                    (
                    
                      
                        
                          I
                          QI
                        
                        ⁡
                        
                          (
                          d
                          )
                        
                      
                      +
                      
                        
                          I
                          IQ
                        
                        ⁡
                        
                          (
                          d
                          )
                        
                      
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          13
        
        ]
      
    
  




The components of the final expression of [Equation 13] are the outputs of the first adders 604, 606, 608 and 610 and the real and imaginary parts are the outputs of the second adders 614 and 618.
The blocks illustrated in FIG. 6 may be used for calculating differential correlations with respect to a received signal. The function of each block has been described above in detail and thus the following description is made of calculation of differential correlations by equations.
A differential received signal may be expressed as

(r(n))′=(r1(n))′+j(rQ(n))′

(r(n))′=(r(n)*·r(n+1),n=0,1, . . . ,N−2  [Equation 14]

A differential base sequence m0 and a differential extended sequence m1 are expressed as

m0th sequence: (am0(n))′=(aIm0(n))′+j(aQm0(n))′

(am0(n))′=(am0(n))*·am0(n+1),n=0,1, . . . ,N−2

m1th sequence: (am1(n))′=(aIm0(n))′+j(aQm1(n))′

(am1(n))′=(am1(n))*·am1(n+1), i n=0, 1, . . . ,N−2  [Equation 15]

The first adders 604, 606, 608 and 610 may perform preliminary computations by [Equation 16], for calculation of correlations.




  
    
      
        
          
            
              (
              
                
                  R
                  II
                
                ⁡
                
                  (
                  d
                  )
                
              
              )
            
            ′
          
          =
          
            
              1
              
                N
                -
                1
              
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  2
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      (
                      
                        
                          r
                          I
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          I
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              (
              
                
                  R
                  QQ
                
                ⁡
                
                  (
                  d
                  )
                
              
              )
            
            ′
          
          =
          
            
              1
              
                N
                -
                1
              
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  2
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      (
                      
                        
                          r
                          Q
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              (
              
                
                  I
                  QI
                
                ⁡
                
                  (
                  d
                  )
                
              
              )
            
            ′
          
          =
          
            
              1
              
                N
                -
                1
              
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  2
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      (
                      
                        
                          r
                          Q
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          I
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            
              (
              
                
                  I
                  IQ
                
                ⁡
                
                  (
                  d
                  )
                
              
              )
            
            ′
          
          =
          
            
              1
              
                N
                -
                1
              
            
            ⁢
            
              
                ∑
                
                  n
                  =
                  0
                
                
                  N
                  -
                  2
                
              
              ⁢
              
                
              
              ⁢
              
                (
                
                  
                    
                      (
                      
                        
                          r
                          I
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          16
        
        ]
      
    
  




The first adders 604, 606, 608 and 610 output the preliminary computation values to the second adders 612, 614, 616 and 618. The relationship between the first adders 604, 606, 608 and 610 and the second adders 612, 164, 616 and 618 may be described with reference to [Equation 17] and [Equation 18].
[Equation 17] describes the differential correlation between the received signal and the base sequence m0.




  
    
      
        
          
            
              
                
                  (
                  
                    
                      R
                      
                        m
                        0
                      
                    
                    ⁡
                    
                      (
                      d
                      )
                    
                  
                  )
                
                ′
              
              =
              
              ⁢
              
                
                  1
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      2
                    
                  
                  ⁢
                  
                    
                      
                        (
                        
                          r
                          ⁡
                          
                            (
                            
                              n
                              +
                              d
                            
                            )
                          
                        
                        )
                      
                      ′
                    
                    ·
                    
                      
                        (
                        
                          
                            (
                            
                              
                                a
                                
                                  m
                                  0
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                            )
                          
                          ′
                        
                        )
                      
                      *
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  1
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      2
                    
                  
                  ⁢
                  
                    [
                    
                      (
                      
                        
                          
                            
                              (
                              
                                
                                  r
                                  I
                                
                                ⁡
                                
                                  (
                                  
                                    n
                                    +
                                    d
                                  
                                  )
                                
                              
                              )
                            
                            ′
                          
                          ⁢
                          
                            
                              (
                              
                                
                                  a
                                  I
                                  
                                    m
                                    0
                                  
                                
                                ⁡
                                
                                  (
                                  n
                                  )
                                
                              
                              )
                            
                            ′
                          
                        
                        +
                        
                          
                            (
                            
                              
                                r
                                Q
                              
                              ⁢
                              
                                (
                                
                                  n
                                  +
                                  d
                                
                                )
                              
                            
                            )
                          
                          ′
                        
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    (
                    
                      
                        a
                        Q
                        
                          m
                          0
                        
                      
                      ⁡
                      
                        (
                        n
                        )
                      
                    
                    )
                  
                  ′
                
                )
              
              +
              
                j
                (
                
                  
                    
                      
                        (
                        
                          
                            r
                            Q
                          
                          ⁡
                          
                            (
                            
                              n
                              +
                              d
                            
                            )
                          
                        
                        )
                      
                      ′
                    
                    ⁢
                    
                      
                        (
                        
                          
                            a
                            I
                            
                              m
                              0
                            
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      ′
                    
                  
                  -
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        
                          r
                          I
                        
                        ⁢
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
              ]
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        (
                        
                          
                            R
                            II
                          
                          ⁡
                          
                            (
                            d
                            )
                          
                        
                        )
                      
                      ′
                    
                    +
                    
                      
                        (
                        
                          
                            R
                            QQ
                          
                          ⁡
                          
                            (
                            d
                            )
                          
                        
                        )
                      
                      ′
                    
                  
                  )
                
                +
                
                  j
                  ⁡
                  
                    (
                    
                      
                        
                          (
                          
                            
                              I
                              QI
                            
                            ⁡
                            
                              (
                              d
                              )
                            
                          
                          )
                        
                        ′
                      
                      -
                      
                        
                          (
                          
                            
                              I
                              IQ
                            
                            ⁡
                            
                              (
                              d
                              )
                            
                          
                          )
                        
                        ′
                      
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          17
        
        ]
      
    
  




The components of the final expression of [Equation 17] are the outputs of the first adders 604, 606, 608 and 610 and the real and imaginary parts are the outputs of the second adders 612 and 616.
[Equation 18] describes the differential correlation between the received signal and the extended sequence m1.




  
    
      
        
          
            
              
                
                  (
                  
                    
                      R
                      
                        m
                        1
                      
                    
                    ⁡
                    
                      (
                      d
                      )
                    
                  
                  )
                
                ′
              
              =
              
              ⁢
              
                
                  1
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      2
                    
                  
                  ⁢
                  
                    
                      
                        (
                        
                          r
                          ⁡
                          
                            (
                            
                              n
                              +
                              d
                            
                            )
                          
                        
                        )
                      
                      ′
                    
                    ·
                    
                      
                        (
                        
                          
                            (
                            
                              
                                a
                                
                                  m
                                  1
                                
                              
                              ⁡
                              
                                (
                                n
                                )
                              
                            
                            )
                          
                          ′
                        
                        )
                      
                      *
                    
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  1
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      2
                    
                  
                  ⁢
                  
                    
                      
                        (
                        
                          r
                          ⁡
                          
                            (
                            
                              n
                              +
                              d
                            
                            )
                          
                        
                        )
                      
                      ′
                    
                    ·
                    
                      
                        (
                        
                          
                            a
                            
                              m
                              0
                            
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      ′
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  1
                  
                    N
                    -
                    1
                  
                
                ⁢
                
                  
                    ∑
                    
                      n
                      =
                      0
                    
                    
                      N
                      -
                      2
                    
                  
                  ⁢
                  
                    [
                    
                      (
                      
                        
                          
                            
                              (
                              
                                
                                  r
                                  I
                                
                                ⁡
                                
                                  (
                                  
                                    n
                                    +
                                    d
                                  
                                  )
                                
                              
                              )
                            
                            ′
                          
                          ⁢
                          
                            
                              (
                              
                                
                                  a
                                  I
                                  
                                    m
                                    0
                                  
                                
                                ⁡
                                
                                  (
                                  n
                                  )
                                
                              
                              )
                            
                            ′
                          
                        
                        -
                      
                    
                  
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        
                          r
                          Q
                        
                        ⁢
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
              +
              
                j
                (
                
                  
                    
                      
                        (
                        
                          
                            r
                            Q
                          
                          ⁡
                          
                            (
                            
                              n
                              +
                              d
                            
                            )
                          
                        
                        )
                      
                      ′
                    
                    ⁢
                    
                      
                        (
                        
                          
                            a
                            I
                            
                              m
                              0
                            
                          
                          ⁡
                          
                            (
                            n
                            )
                          
                        
                        )
                      
                      ′
                    
                  
                  +
                
              
            
          
        
        
          
            
              
                
                ⁢
                
                  
                    
                      (
                      
                        
                          r
                          I
                        
                        ⁡
                        
                          (
                          
                            n
                            +
                            d
                          
                          )
                        
                      
                      )
                    
                    ′
                  
                  ⁢
                  
                    
                      (
                      
                        
                          a
                          Q
                          
                            m
                            0
                          
                        
                        ⁡
                        
                          (
                          n
                          )
                        
                      
                      )
                    
                    ′
                  
                
                )
              
              ]
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        (
                        
                          
                            R
                            II
                          
                          ⁡
                          
                            (
                            d
                            )
                          
                        
                        )
                      
                      ′
                    
                    -
                    
                      
                        (
                        
                          
                            R
                            QQ
                          
                          ⁡
                          
                            (
                            d
                            )
                          
                        
                        )
                      
                      ′
                    
                  
                  )
                
                +
                
                  j
                  ⁡
                  
                    (
                    
                      
                        
                          (
                          
                            
                              I
                              QI
                            
                            ⁡
                            
                              (
                              d
                              )
                            
                          
                          )
                        
                        ′
                      
                      +
                      
                        
                          (
                          
                            
                              I
                              IQ
                            
                            ⁡
                            
                              (
                              d
                              )
                            
                          
                          )
                        
                        ′
                      
                    
                    )
                  
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          18
        
        ]
      
    
  




The components of the final expression of [Equation 18] are the outputs of the first adders 604, 606, 608 and 610 and the real and imaginary parts are the outputs of the second adders 614 and 618.
In accordance with the sequence detection method illustrated in FIG. 6, the correlations (or differential correlations) of the base sequence m0 and its extended sequence m1 can be calculated by one computation. While FIG. 6 has been described in the context of a sequence extended by complex conjugation, it is a mere exemplary application and the sequence detection method illustrated in FIG. 6 is readily applied to calculation of the correlation of an extended sequence created by a reverse operation. For example, the index mapper 602 may distribute a received signal on which the reverse operation has been performed to the first adders 604, 606, 608 and 610. In another example, the first adders 604, 606, 608 and 610 may perform preliminary computations using a base sequence on which the reverse operation has been performed.
Simulation: Analysis of Properties of Base Sequences and their Extended Sequences
Table 3 below lists six base sequences generated according to an embodiment of the present invention. The base sequences have indexed with 0 to 5 (p denotes an index) and are expressed in a hexadecimal format.
A modulated sequence mapped to subcarriers are obtained by converting a hexadecimal sequence Wi(p) to two QPSK symbols w2i(p) and w2i+1(p). Here, i is an integer ranging from 0 to 107. [Equation 19] describes an example of modulating the base sequence Wi(p) to two QPSK symbols.




  
    
      
        
          
            w
            
              2
              ⁢
              
                
              
              ⁢
              i
            
            
              (
              p
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        a
                        
                          i
                          ,
                          0
                        
                        
                          (
                          p
                          )
                        
                      
                    
                    +
                    
                      a
                      
                        i
                        ,
                        1
                      
                      
                        (
                        p
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            w
            
              
                2
                ⁢
                
                  
                
                ⁢
                i
              
              +
              1
            
            
              (
              p
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        a
                        
                          i
                          ,
                          2
                        
                        
                          (
                          p
                          )
                        
                      
                    
                    +
                    
                      a
                      
                        i
                        ,
                        3
                      
                      
                        (
                        p
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          19
        
        ]
      
    
  




where Wi(p)=23·ai,0(p)+22·ai,1(p)+21·ai,2(p)+20·ai,3(p). According to the above equation, binary values 00, 01, 10 and 11 are converted respectively to 1, j, −1 and −j. However, this is a mere exemplary application and thus the base sequence Wi(p) may be converted to QPSK symbols by any other similar equation.









TABLE 3





p
Sequence to modulate, Wi(p) (in hexadecimal format)







0
0CCF02E8216E980A50A62D0FCDC9A88BCF078AC6EAF8DD70A8D5E0EEE33E3



60458EAF42EA89C35271F8413615F74E50FFC6DB1084EF8


1
21C3C0B6A4A1653023111E274F8AFD4D88481B116B8D0B54673CE50D4E9AA



67BAC6DB6EA8E72180A204F5A7D6104A37E94CC35AD7007


2
0D684E2D0E360F81AEECE43EA204DA893D8B550C64667B58B7065F56C5BB8



D369211F38A992707E298C375451437FF32ABC9DB1C4878


3
3F89C5F1E37F6D634DCEB42D0374CE82D0C81C41382FE890B468B4EA816FC



63F322EAA367EB9063D478724756641EBF8114AFB4C1AA7


4
056320CC0B9AE2C5A4190BB1622B3A0F4FA23F41A2F2F79BC854CFCCC6534



3FE9739F7EB5E308A179349162E2502114259BE77CC312C


5
14422F9715FF0AD00C1F2FE0197BCA5E8B0944422D7382B5ABA3BF00DDCDF



6572C77E13F93462E31F4901374093A677561F4AFE4B9E4









The six base sequences listed in Table 3 may be extended to 24 sequences by complex conjugation and the reverse operation. 18 extended sequences except the base sequences are indicated by indexes (p) 6 to 23, expressed as




  
    
      
        
          w
          k
          
            (
            p
            )
          
        
        =
        
          {
          
            
              
                
                  
                    (
                    
                      w
                      k
                      
                        (
                        
                          p
                          -
                          6
                        
                        )
                      
                    
                    )
                  
                  *
                
              
              
                
                  
                    
                      for
                      ⁢
                      
                        
                      
                      ⁢
                      6
                    
                    ≤
                    p
                    <
                    12
                  
                  ,
                
              
            
            
              
                
                  
                    w
                    
                      215
                      -
                      k
                    
                    
                      (
                      
                        p
                        -
                        12
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                
              
              
                
                  
                    
                      for
                      ⁢
                      
                        
                      
                      ⁢
                      12
                    
                    ≤
                    p
                    <
                    18
                  
                  ,
                
              
            
            
              
                
                  
                    
                      (
                      
                        w
                        
                          215
                          -
                          k
                        
                        
                          (
                          
                            p
                            -
                            18
                          
                          )
                        
                      
                      )
                    
                    *
                  
                  ⁢
                  
                    
                  
                
              
              
                
                  
                    
                      for
                      ⁢
                      
                        
                      
                      ⁢
                      18
                    
                    ≤
                    p
                    <
                    24
                  
                  ,
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          20
        
        ]
      
    
  




where k is an integer ranging from 0 to 215.

The properties of the 24 sequences generated by use of Table 3 and [Equation 20] were measured in 512-FFT mode, and conventional 114 preamble sequences used in the IEEE 802.16e system were used as a comparison group (refer to IEEEStd 802.16E-2005, Table 309b).
To investigate the sequence properties, cross-correlations, differential cross-correlations, auto-correlations, differential auto-correlations, and CM values were measured (refer to [Equation 9] to [Equation 18]). The measurements are illustrated in FIGS. 7A to 7E, and Table 4, Table 5, and Table 6.










TABLE 4










Differential cross-










Cross-correlation
correlation












802.16e (114)
Examples (24)
802.16e (114)
Examples (24)





Min
0.000
0.000
0.000
0.005


Max
0.303
0.250
0.239
0.105


Mean
0.074
0.060
0.065
0.048


Median
0.070
0.056
0.056
0.043


std. dev.
0.039
0.032
0.049
0.023



















TABLE 5










Differential auto-










Auto-correlation
correlation












802.16e (114)
Examples (24)
802.16e (114)
Examples (24)





Min
0.091
0.083
0.127
0.144


Max
0.203
0.124
0.408
0.173


Mean
0.134
0.096
0.216
0.157


Median
0.133
0.091
0.211
0.153


std. dev.
0.020
0.015
0.044
0.011

















TABLE 6








Cubic Metric










802.16e (114)
Examples (24)





Min
0.790
0.994


Max
1.389
1.205


Mean
1.128
1.085


Median
1.139
1.077


std. dev.
0.131
0.063









Referring to FIGS. 7A to 7E, Table 4, Table 5 and Table 6, it is noted that both the base sequences and the extended sequences that are obtained by performing complex conjugation and the reverse operation on the base sequences have excellent properties, when they are evaluated according to the criteria described in Embodiment 1.
Application Example
Signal Transmission Using Base Sequence and its Extended Sequence
A description will be made of an example of applying sequences generated according to an embodiment of the present invention to a DL sync channel and a ranging channel, with the appreciation that the sequences are also applicable to transmission of many other channels and signals. For example, the sequences according to the embodiment of the present invention may be used for time/frequency synchronization, channel estimation (RS or pilot), control channels (e.g. CQI, ACK/NACK, etc.), scrambling, CDM, midamble, received signal measurement (e.g. Received Signal Strength Indication (RSSI), Signal to Noise ratio (SNR), Signal to Interference and Noise Ratio (SINR), etc.). While the application example is described in the context of IEEE 802.16m, it may be used for any other communication system using sequences (e.g. the 3GPP system).
FIG. 8 illustrates a radio frame structure in the IEEE 802.16m system. The radio frame structure is applicable to Frequency Division Duplex (FDD), Half-Frequency Division Duplex (H-FDD), Time Division Duplex (TDD), etc.
Referring to FIG. 8, the radio frame structure includes 20-ms superframes SU0 to SU3 supporting a 5-MHz, 8.75-MHz, 10-MHz or 20-MHz bandwidth. Each superframe is divided into four equally sized 5-ms frames F0 to F3, starting with a SuperFrame Header (SFH). Each frame includes eight subframes SF0 to SF7, each carrying a DL sync channel. Each subframe is allocated for downlink or uplink transmission. There are three types of subframes according to CPs. Specifically, a subframe may include 5, 6 or 7 OFDMA symbols. Each OFDMA symbol is divided into a CP and a useful symbol. The CP is generally a copy of the last part of the useful symbol, attached before the useful symbol. Therefore, the phase is continuous between the CP and the useful symbol. The length of the CP may be set but not limited to 1⁄8 or 1⁄6 of the length of the useful symbol. Table 7 illustrates some OFDMA parameters defined for the IEEE 802.16m system.












TABLE 7







Nomial Channel Bandwidth (MHz)
5
7
8.75
10
20


Over-sampling Factor
28/25
8/7
8/7
28/25
28/25


Sampling Frequency, Fs (MHz)
5.6
8
10
11.2
22.4


FFT Size, NFFT
512
1024
1024
1024
2048


Sub-Carrier Spacing, Δf (kHz)
10.937500
7.812500
9.765625
10.937500
10.937500


Useful Symbol Time, Tb (us)
91.429
128
102.4
91.429
91.429









FIG. 9 illustrates an exemplary transmission of a synchronization channel in the IEEE 802.16m system. This embodiment is based on the assumption of IEEE 802.16m only mode.
Referring to FIG. 9, one superframe SU1, SU2, SU3 or SU4 carries four Synchronization Channels (SCHs) in the IEEE 802.16m system. There are two types of DL SCHs, Primary SCH (P-SCH) and Secondary SCH (S-SCH) in the IEEE 802.16m system. The P-SCH and the S-SCH carry a Primary Advanced Preamble (PA-Preamble) and a Secondary Advanced Preamble (SA-Preamble), respectively. In both FDD mode and TDD mode, each DL SCH may be transmitted in the first OFDMA symbol of a frame. The PA-Preamble is usually used for acquisition of time/frequency synchronization, a partial cell ID, and some information such as system information, whereas the SA-Preamble is generally used for acquiring a final physical cell ID. The SA-Preamble may also be used for measuring an RSSI. The PA-Preamble is delivered in the first frame F0 and the SA-Preamble is delivered in the second, third and fourth frames F1, F2 and F03.
FIG. 10 illustrates subcarriers to which a PA-preamble is mapped.
Referring to FIG. 10, the PA-Preamble is of length 216 regardless of an FFT size. The PA-Preamble is inserted at an interval of two subcarriers, with 0s filled at the other subcarriers. For example, the PA-Preamble may be inserted at subcarriers 41, 43, . . . , 469 and 471. The PA-Preamble may carry information about a BS type, a system bandwidth, etc. If subcarrier 256 is reserved for Direct Current (DC), the allocation of subcarriers for the sequence may be determined by

PAPreambleCarrierSet=2×k+41  [Equation 21]

where k is an integer ranging from 0 to 215.

For example, a QPSK-type sequence of length 216 illustrated in Table 3 may be used for a PA-Preamble. For the convenience's sake, Table 8 lists the six base sequences again.








TABLE 8





p
Sequence to modulate,Wi(p) (in hexadecimal format)







0
0CCF02E8216E980A50A62D0FCDC9A88BCF078AC6EAF8DD70A8D5E0EEE33E360458E



AF42EA89C35271F8413615F74E50FFC6DB1084EF8


1
21C3C0B6A4A1653023111E274F8AFD4D88481B116B8D0B54673CE50D4E9AA67BAC6



DB6EA8E72180A204F5A7D6104A37E94CC35AD7007


2
0D684E2D0E360F81AEECE43EA204DA893D8B550C64667B58B7065F56C5BB8D36921



1F38A992707E298C375451437FF32ABC9DB1C4878


3
3F89C5F1E37F6D634DCEB42D0374CE82D0C81C41382FE890B468B4EA816FC63F322



EAA367EB9063D478724756641EBF8114AFB4C1AA7


4
056320CC0B9AE2C5A4190BB1622B3A0F4FA23F41A2F2F79BC854CFCCC65343FE973



9F7EB5E308A179349162E2502114259BE77CC312C


5
14422F9715FF0AD00C1F2FE0197BCA5E8B0944422D7382B5ABA3BF00DDCDF6572C7



7E13F93462E31F4901374093A677561F4AFE4B9E4









The description made with reference to FIG. 3 may be referred to for details of sequence conversion and extension of sequences by complex conjugation and/or a reverse operation. It can be concluded that a BS may transmit a total of 24 PA-Preambles based on the six base sequences listed in Table 8.
FIG. 11 illustrates an exemplary mapping of SA-Preambles to frequency areas.
Referring to FIG. 11, the length of the SA-Preamble may vary with an FFT size. For example, the lengths of the SA-Preamble may be 144, 288, and 576 for 512-FFT, 1024-FFT and 2048-FFT, respectively. If subcarrier 256, subcarrier 512 and subcarrier 1024 are reserved as DC components for the 512-FFT, 1024-FFT and 2048-FFT, respectively, allocation of subcarriers for an SA-Preamble may be determined by




  
    
      
        
          SAPreambleCarrierSet
          n
        
        =
        
          n
          +
          
            3
            ·
            k
          
          +
          
            40
            ·
            
              
                N
                SAP
              
              144
            
          
          +
          
            ⌊
            
              
                2
                ·
                k
              
              
                N
                SAP
              
            
            ⌋
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          22
        
        ]
      
    
  




where n represents the index of an SA-Preamble carrier set, ranging from 0 to 2, indicating a segment ID, NSAP represents the length of the SA-Preamble, and k is an integer ranging from 0 to NSAP-1.

Each cell has a cell ID (IDcell) ranging from 0 to 767. The cell ID is defined by a segment index and an index per segment. The cell ID may be determined by

IDcell=256×n+Idx  [Equation 23]

where n represents the index of the SA-Preamble carrier set, ranging form 0 to 2, indicating a segment ID, and Idx is an integer from 0 to 255.

For the 512-FFT, an SA-Preamble of length 144 is divided into eight subblocks, namely A, B, C, D, E, F, G and H. The length of each subblock is 18. For each segment ID, different sequence subblocks are defined. In the IEEE 802.16m system, known SA-Preambles are hexadecimal numbers of the BPSK type. 18 LSBs of a hexadecimal sequence for each subblock are used to represent binary sequences. A binary sequence {0, 1} is mapped to real values {+1, −1}, respectively. SA-Preambles defined for the IEEE 802.16m system will be described later in detail. In the 512-FFT, the subblocks A, B, C, D, E, F, G and H are sequentially modulated and mapped to an SA-Preamble subcarrier set corresponding to a segment ID. For a higher FFT size, the basic subblocks A, B, C, D, E, F, G and H are repeated in the same order. For example, for 1024-FFT, subblocks E, F, G, H, A, B, C, D, E, F, G, H, A, B, C and D are sequentially modulated and then mapped to an SA-Preamble subcarrier set corresponding to a segment ID.
A circular shift may be applied to three consecutive subcarriers after subcarrier mapping according to [Equation 22]. Each subblock has the same offset and the circular shift pattern [2, 1, 0, . . . , 2, 1, 0, . . . , 2, 1, 0, 2, 1, 0, DC, 1, 0, 2, 1, 0, 2, . . . , 1, 0, 2, . . . , 1, 0, 2] is used for each subblock. Herein, the circular shift includes a right circular shift. For a 512-FFT size, each of the subblocks A, B, C, D, E, F, G and H may experience the right circular shift (0, 2, 1, 0, 1, 0, 2, 1). FIG. 12 illustrates an exemplary SA-Preamble structure for 512-FFT.
FIGS. 13, 14 and 15 illustrate exemplary SA-Preamble structures in multi-antenna systems. The SA-Preamble structures are designed for 512-FFT, 1024-FFT and 2048-FFT, respectively.
Referring to FIGS. 13, 14 and 15, an SA-Preamble may be interleaved on a plurality of antennas. The SA-Preamble interleaving is not limited to any specific method. For example, when a multi-antenna system has 2n transmission antennas, the SA-Preamble may be interleaved as described in Table 9. For the convenience' sake, eight consecutive subblocks {E, F, G, H, A, B, C, D} are collectively referred to as a block and reference characters are defined as follows.

    
    
        Nt: the number of transmission antennas
        Nb: the total number of blocks
        Ns: the total number of subblocks (8×Nb)
        Nbt: the number of blocks per antenna (Nb/Nt)
        Nst: the number of subblocks per antenna (Ns/Nt)
    
    










TABLE 9







 
If (Nb t>= 1)



Distribute consecutive blocks across the Nt antennas



For a given antenna, a block is repeated with period Nt



Block position for antenna (t + 1) is t + pxNt, where t = 0, 1,



2, . . . , Nt − 1, p = 0, 1, 2, . . . , Nbt − 1



Else If (Nst = 4)



Interleave the 8 subblocks {E, F, G, H, A, B, C, D} across two



consecutive antennas



Block [E, 0, G, 0, A, 0, C, 0] is allocated to antenna i at



block position, floor (i/2)



Block [0, F, 0, H, 0, B, 0, D] is allocated to antenna i + 1 at



block position, floor (i + 1/2), where i = 0, 2, 4, . . . , Nt.



Else If (Nst = 2)



Interleave the 8 subblocks {E, F, G, H, A, B, C, D} across four



consecutive antennas



Block [E, 0, 0, 0, A, 0, 0, 0] is allocated to antenna i at



block position, floor (i/4)



Block [0, 0, G, 0, 0, 0, C, 0] is allocated to antenna i + 1 at



block position, floor ((i + 1)/4)



Block [0, F, 0, 0, 0, B, 0, 0] is allocated to antenna i + 2 at



block position, floor ((i + 2)/4)



Block [0, 0, 0, H, 0, 0, 0, D] is allocated to antenna i + 3 at



block position, floor ((i + 3)/4), where i = 0, 4, 8, . . . , Nt.



Else



Interleave the 8 subblocks {E, F, G, H, A, B, C, D} across four



consecutive antennas



Block [E, 0, 0, 0, 0, 0, 0, 0] is allocated to antenna i at



block position, floor (i/8)



Block [0, F, 0, 0, 0, 0, 0, 0] is allocated to antenna i + 1 at



block position, floor ((i + 1)/8)



Block [0, 0, G, 0, 0, 0, 0, 0] is allocated to antenna i + 2 at



block position, floor ((i + 2)/8)



Block [0, 0, 0, H, 0, 0, 0, 0] is allocated to antenna i + 3 at



block position, floor ((i + 3)/8),



Block [0, 0, 0, 0, 0, A, 0, 0] is allocated to antenna i + 4 at



block position, floor ((i + 4)/8)



Block [0, 0, 0, 0, 0, B, 0, 0] is allocated to antenna i + 5 at



block position, floor ((i + 5)/8)



Block [0, 0, 0, 0, 0, 0, C, 0] is allocated to antenna i + 6 at



block position, floor ((i + 6)/8)



Block [0, 0, 0, 0, 0, 0, 0, D] is allocated to antenna i + 7 at



block position, floor ((i + 7)/8),where i = 0, 8, . . . , Nt.









In each frame containing an SA-Preamble, the transmission structures may be rotated across the transmission antennas. For example, in a 512-FFT system with four transmission antennas, subblocks [A, 0, 0, 0, E, 0, 0, 0] are transmitted through a first antenna and subblocks [0, 0, 0, D, 0, 0, 0, H] are transmitted through a fourth antenna, in an fth frame containing an SA-Preamble. Then in an (f+1)th frame containing an SA-Preamble, subblocks [0, 0, 0, D, 0, 0, 0, H] may be transmitted through the first antenna and subblocks [A, 0, 0, 0, E, 0, 0, 0] may be transmitted through the fourth antenna.
Known BPSK-Type SA-Preambles
Table 10 tabulates known SA-Preambles for the IEEE 802.16m system. In Table 10, 256 BPSK-type sequences defined for segment 0 are illustrated. For sequences for segment 1 and segment 2, refer to Table 658 and Table 659 in IEEE 802.16m-09/0010r2. The 18 LSBs of each subblock are used to represent binary sequences. Binary values {0, 1} are mapped to real values {+1, −1}, respectively.







TABLE 10







Table 657 - SA Preamble for n = 0 (Segment 0)









blk















Idx
A
B
C
D
E
F
G
H


















0
2A1FA
3DE76
2CCA0
15722
2A509
0E904
0C5D5
10774


1
23836
378C2
3BFDA
1A401
27FBD
1FA0E
02DA2
03949


2
211B7
2855B
25BCD
17F09
32910
090FB
07C8C
0CC20


3
3836C
22AD2
349DB
183CA
3B2CA
09CE3
12C6C
12282


4
26F2D
3DFF6
315B1
1234E
2A0AF
1BEAD
0CE1A
03B36


5
3D1C3
23AFF
22B8B
1A9DE
3E5A3
08235
1B7AF
136AD


6
30709
2FA42
31CBD
0F424
3E570
1D9A8
008AA
0F9D3


7
38E39
33279
2FF20
08825
3EBCB
1DCCD
15D61
0DECF


8
21779
264CB
3230D
0AE06
35140
1CA03
0E570
059BE


9
270A8
2ADE1
3B6B7
1A629
29B35
0C99D
0AC04
03C08


10
30F40
3363F
361F3
00A13
36A99
1CC91
0F8CB
1EDD2


11
28A18
2F6B4
20AE4
0BA1C
25EA6
063B1
1C5F4
1B85B


12
26821
3A5B3
3EE12
08B45
3C594
016FD
02A94
054F7


13
3AC52
33B19
3H9C6
1609E
2EB43
065DC
08E91
0B952


14
32B67
298C0
20ED5
1A699
343F1
1D965
17927
07EF0


15
3AC4D
35BBC
29713
06420
28132
0B1D1
16A5B
176B1


16
28B79
22EA0
341E6
088EF
23052
1944A
1452F
0176D


17
3F8D6
20E09
3791E
1762C
3E8DA
13B94
0D4DB
15807


18
2080F
2E4D0
291F6
153B4
368A2
1AD5C
161AD
06C1E


19
27DC1
21FEA
2B540
1F1BF
3C773
05585
11644
1A59A


20
34CAB
2FE84
3E702
02C06
3AEEC
0F583
0CD57
04AD1


21
24991
3CF91
2AEE1
0D6EB
32F0D
07E07
1BB88
0D321


22
30822
398DC
2F478
04B4D
3361B
156BE
0D5AC
11E4F


23
3C355
36EEE
35068
085B0
2FCBB
0855E
1466C
050CB


24
3ECC3
2A52B
3DFCC
03ADF
2DF1D
05C43
05A8A
19D9F


25
2FF61
2B725
37F3E
14092
3E129
16F47
0E8CC
1E8B8


26
235C9
275AC
22420
175DB
2118A
06177
0FB7A
00DF4


27
299F2
3D5DF
34668
12631
20E22
1BC59
049E8
1209C


28
2F3F4
34251
36429
0B0CF
2CCE6
109F4
0BA71
1D846


29
32816
25786
259F6
0CD01
3BA6A
1FC99
1DB12
1FED3


30
3DF50
3EE78
2B708
19594
371DB
03C88
0794A
07B3C


31
3D053
3DF2C
273CC
165F6
2C436
09ED4
0C879
13571


32
3960E
26F45
33FBE
068B6
3C521
106C6
09C50
11A56


33
2B95B
385EE
3B804
03545
29D2E
01B2E
02F70
1C65A


34
3CC0F
201B2
28467
1D38A
258A4
0C37A
0F145
04C70


35
383EC
3A316
24A63
190FA
3AE63
0918B
1FE42
1DDD7


36
2C261
228F1
28B79
0D393
2DB97
1B131
105E9
1438A


37
2497F
292F3
2C371
12C8E
20A1D
14110
1A04F
0B028


38
372E6
304B6
2F16A
188E6
3688E
1D23F
0490A
1041F


39
34FFB
38DCD
25577
19DEF
251E4
00C71
01E27
15622


40
3D6FA
305DF
2AC73
1C8D6
3E5CA
00717
0851C
109B2


41
362C1
2723E
27046
134A2
3FCC3
0D635
0394C
02EE9


42
348E8
3972D
3D001
1315A
35EAE
1702C
11E63
0F600


43
2C7BB
2F28F
2015D
09325
24EE9
1F67B
1F377
1611E


44
2B3BE
27DA5
36FDF
0DD50
39C46
00D4E
1E49C
067C4


45
2614D
340BC
2B4F8
16369
31213
13F3F
0A130
1ECA1


46
26417
21306
33D64
130EF
39BC4
1751D
08580
13160


47
3F902
2A37D
361C8
19A54
3DB69
0C335
1171F
0F022


48
3AB24
3D551
3C977
1360A
3F0BC
021CF
14382
02E59


49
35E1E
26090
35738
158AF
3D8C2
1FAD3
01313
0868B


50
3AC9F
315BF
263B8
1C684
385D9
17DB0
0FDDD
1D8FF


51
2F482
3AC19
34498
0E65B
3D719
14DE7
17762
14F4D


52
2E248
348C5
35A9A
0D76F
3708E
1346E
1F653
1F281


53
2CFA2
28F3F
3A58F
15E30
3B0E7
1F67E
0187C
112E8


54
3DB3B
3D41B
3AC0A
0C7C3
2E71F
1946D
1C64B
06E3C


55
2C726
36DE4
252BF
1061D
25194
0FB2B
09B51
16744


56
229F2
32990
358C3
1BB30
2F008
0D0A2
051D3
17530


57
235C2
2EC63
2C3F8
16217
2183A
14406
0B8C8
10E19


58
25552
341AF
20810
073A1
2E1FB
1D58C
0F35C
0320E


59
39B09
209E8
35261
1D675
3A0DE
0A8A1
1EFF9
01F98


60
20A28
3792C
3F334
045D2
3D786
1A95C
08CB0
18DA1


61
29FE5
3E383
22DDB
14256
37B29
00FB1
10420
018A1


62
3F05B
30317
24779
1BB7B
269BC
0C785
04A86
118AA


63
3739A
373CC
2C605
138A5
22112
00ABC
134D5
0FABE


64
339EC
3DA7E
2256C
10CFF
2593D
0DE36
032EC
1E199


65
3B3AD
264C2
3BDE5
11FDE
38AA1
1D1EF
1821E
0EE3E


66
3D528
38958
23331
0E8B9
26FCE
127B8
0DA80
1DCF8


67
3DA17
2AB6D
26ECE
0401A
3FBD8
17692
1E7F2
05FF2


68
21ED1
2F966
316F9
071F2
3ACF4
025A9
047E4
01DDC


69
2904C
3C712
2C41E
06801
2F9F2
076BA
112C6
09E1C


70
2726A
2F4B0
25E3D
15DE6
308B1
0D7FB
1196C
0BD53


71
289FD
3495C
2C772
0D1C6
2D855
1BA59
01297
00B23


72
2E936
37553
31EE9
1E026
27D7F
134DE
146D7
1FBB6


73
37A24
36101
34473
07695
2D6C2
1C05F
06FFB
1443E


74
3D1AF
29853
36B2C
0C23D
2B5BF
0647F
12084
09C1D


75
2964F
30824
236A0
11F14
3EF38
0342E
1F876
16A2F


76
351F8
32CA8
33583
141DC
26533
06DA9
0BD59
000BA


77
22160
2FDEA
33446
17661
23FA3
0D7FE
16C48
052E6


78
36995
36A68
336BB
0CE56
3FE11
12FFA
0BB3F
1B8E3


79
318E2
3E532
2FDA4
09CAE
3C3EF
0B3A7
0E451
0CA29


80
207EB
36723
2F1F5
0CCC9
3984A
0C153
1D629
1745B


81
3FE13
2CF97
2CA31
1B457
2BD86
06B5D
04999
066EC


82
3F9A3
22F77
3AB11
057AD
3E5EF
13D13
1F378
03B3F


83
2510E
248A3
341C6
06A43
27BC8
0842E
0C4A2
1413C


84
33B40
3EE48
28FF9
11ADD
3D7BC
0DD6F
10961
15406


85
3459E
3FC42
38114
166CA
34C25
01779
107E5
008E9


86
36C4F
309D7
390A8
18A58
24FD3
047F0
00AAD
132EF


87
39717
25556
28121
1266C
3BCB4
0C94B
16BD4
17B46


88
39AE3
37836
3D134
0E4C2
2FF8F
15803
1B9B2
0E48E


89
20F58
30F56
37826
0DBE9
25172
01A01
09AF7
0CF5D


90
364B3
2B0CA
2BE32
1AAE4
29D7D
05D93
1B9D3
021FD


91
35084
3E213
32EDB
0F527
20813
09A6A
1878A
15683


92
379C8
288ED
36C85
18C8D
31498
1C7B3
1E2E4
06ADF


93
22008
2CA3B
2B613
1D1E8
23142
1D141
1F1E3
1C8D1


94
20DFD
36D64
337D3
15C09
29B5A
1C75C
1FB06
0E75B


95
31671
231B5
26127
0A0E4
35797
00D1A
12AB4
187B8


96
3EBB7
23D69
3D1F2
0EEFD
3AD47
1CC65
1C95B
03C78


97
25945
34B15
33E30
1127A
3B938
06A62
02D0D
1CB49


98
366BE
208F6
2DE7E
0713F
32D7A
1A0EC
06639
05F7F


99
31FF8
3A9D6
39DB2
1A1D9
3880C
011FE
1BE69
1F792


100
22535
3A2E2
298F0
0FE41
3E139
05858
101CA
1BC4D


101
3DDA5
23D87
32161
12156
2CA14
1F4E9
003D1
134CD


102
23F0D
231E8
316AD
147BF
21671
0AB19
141D3
130BA


103
3546F
251B4
33661
1B440
3827E
13FE7
0EAA5
1BCD6


104
39B3E
33A87
300B5
09DC0
2AC29
051E6
06706
179AA


105
372F2
3441D
34450
19F2C
22FF3
10C03
1A97E
16089


106
31287
394BD
329C7
0678B
2DE2E
0A8AF
1FD93
194E2


107
2AEC7
23388
293E7
0798F
27C06
0435B
1E169
11A0A


108
226E7
32E65
207B2
1DE2E
26B3D
178F7
15E56
16907


109
32A75
23B1C
35792
0FF8F
333D4
13399
0CD11
11C0D


110
21E53
3BF69
217F9
1E4CC
2FD44
0D3B4
08C04
17CFD


111
364A7
249A0
3273F
0B996
2FEBC
1ACEF
01EAB
0EDF3


112
34831
340E1
3C372
08432
253F5
1993C
0CA57
15BA3


113
3A7B8
2CFE0
31B37
0532D
2BD66
0B638
10C4F
02BA6


114
2CC36
33D15
354D3
0DCB9
34160
0E6A4
0A530
15AB7


115
36CD9
2B6B2
308A5
10C14
37DA2
14091
16635
09FC0


116
26390
3C089
20E90
198A0
3CF5A
0DA14
0B79E
00A81


117
35B16
2F4ED
329B7
0BABD
24957
071F8
1720B
00A51


118
21AEA
3CB09
3F850
1143F
26F6B
0B730
0A483
1C7B3


119
33300
2CDF0
23BE0
17190
33840
03912
1E470
07506


120
2CECA
2B8EE
227DA
1F9B9
3BE06
0F0C1
085D7
088DF


121
336A9
26C46
2A381
05AC3
3B3EF
1635F
02603
09A59


122
372BF
25ABE
3E1A1
02EBE
2797C
13647
14F10
056E9


123
2507B
269DD
393C9
14BC2
276FD
082A9
1E301
02204


124
2DAD4
233C2
24AE7
1A63E
3A4CD
19D27
00F38
1E632


125
3D94C
341EB
33B63
1E63F
20D60
0AA11
17730
040EC


126
314B1
21EEE
3A722
0D99D
2ADB6
1C749
0C11E
0300F


127
306CB
2D856
2B3E9
18998
3DCA7
00440
032D4
0AB14


128
2176F
2526A
2B8B8
03B7A
27F98
0C00A
15BC6
10BC4


129
3502C
3381D
30162
0A91C
3723C
0BA48
13991
10007


130
205A9
20E77
236F0
1208E
333DB
1FD1D
0F663
1A2CD


131
29EFE
3165B
391FC
18A82
24FA5
13B49
0EA6A
1E7C5


132
3BC8F
35058
2B040
03175
21D63
080FD
10564
1943B


133
33856
31A6D
37FA5
10D6A
2778B
13BA8
17FCD
07D78


134
2462C
3126A
3DE29
0EFCE
2CE17
1F670
00A16
09992


135
31358
3A006
3D6C9
09C3F
2E42D
0757F
07DE5
13F2A


136
26FDC
25BF0
22AC3
0D92D
2CB72
17AF7
1761B
13F44


137
39282
3E781
2807B
055FE
316E0
16070
125E6
1595E


138
237D2
2FB31
3DFD9
03B7C
28F55
09601
09A26
1210C


139
3A13B
330D3
2C606
033B0
293B9
1D684
173DD
18858


140
27825
3A0FF
288D0
16B7E
31A53
1358C
03259
07CA5


141
246FE
35C69
32A82
14D6A
3CAFC
03A11
19D90
037DC


142
37170
2C096
22EB9
088D9
3F0AC
116D0
0AA84
07AAC


143
31081
30C8F
38264
0AF24
24325
15FE1
026C7
04115


144
234A3
28DB6
3A4CD
0545C
35272
19CBD
07F1F
009B7


145
21F32
3677D
35CFB
1D63F
293B0
1244F
00CDF
0D3CB


146
30318
2EDED
2F09A
15C54
329CC
0B24E
0D93A
0BC81


147
201CB
2DBD1
3E4A5
0E7A3
2C50A
0A4BC
15412
182CC


148
26E83
3E68F
3D675
031A9
2EDD8
1AA4F
02443
16BD9


149
38C83
3892F
3E237
10FC3
26F2E
1FADD
19F56
191B2


150
2181D
26EFC
240B6
1224B
3BD01
0AB64
080DA
1BEAE


151
39273
26387
3BF09
1AF9D
37D3D
1A42A
09DE7
05D2C


152
3ECE9
380EB
2DD42
0F762
3D03E
1A53C
0687D
002A2


153
2ABB7
2FC33
234C2
1E30C
2DE4E
0DF46
1B022
0F06E


154
33D0E
2861C
2F481
0D8E2
3B345
18AFF
142B3
13ECD


155
2A691
39F50
3907C
18306
2999E
0826F
0F5C2
1C1E8


156
3F10D
2E86C
35EAF
0C23D
30BBF
1C939
142A2
1D1AE


157
30888
334D8
2F54E
095C0
22591
0A2A9
03575
07E27


158
2C05B
3A3A2
2B9E1
043FD
26767
0B509
152FC
05B3A


159
3F536
363C2
39C31
0A348
3EC9C
074E0
1E6C9
0A359


160
34212
2B602
25538
1D949
3110B
09D01
17649
030E5


161
27DA4
25283
33CB0
00F26
2F77A
0428B
19C1F
03A2B


162
29516
294A8
34D82
03B87
27025
03C98
13676
043DD


163
212A3
2BEB5
3A929
0EEB0
3C43E
18D49
013EE
07B2A


164
327A2
265B8
3E069
0615E
23B65
085AA
077FC
18161


165
26BC6
2D590
3213C
16691
20E7E
13460
1E439
079FB


166
353C0
26830
305A3
057BC
394DA
192E4
0F382
0867E


167
293AB
20EF0
22707
0816D
216A4
07B67
09B67
01B88


168
29915
2DEB9
3CE98
14D96
26F9B
15D4A
00853
1DE0C


169
36E40
3C7E1
3DE6B
0D335
39671
06EBA
18B85
07A81


170
36DBA
218AC
26D28
1BC51
37AF3
1635F
1B82C
0061A


171
33C22
3F96A
33645
05F3B
2AF82
16800
1630A
10F03


172
3EEEF
318D9
276E1
03FCD
34D35
05272
1B329
1D755


173
3D442
37142
3B3DC
1C93E
32C36
0DA72
05EE5
1D8BB


174
34B1B
2A7A5
2AA15
0CB44
3D239
08C8D
130BA
0BF9A


175
3E04B
3FF31
2B8B6
14832
2D5BA
01588
1F533
1FCF6


176
35613
2E44A
36AE7
186C8
2450D
00BAA
05F60
03973


177
2D44C
3C74B
21D8B
08900
21DB9
129AB
1C563
100D6


178
31176
2D23F
27D5C
11F23
23B1C
0803B
18D88
0EB94


179
3A4F7
3DC0C
3D797
0E67A
3281F
09BC7
03BF5
0F8B6


180
21F13
2DB72
2B9AD
10C4E
39523
1F841
07D9A
04F1B


181
26639
3613F
296F1
0B3F3
344F5
18059
175ED
0E5DE


182
3E770
2B61B
211C1
1AB8C
2BC76
1449F
09942
0F505


183
3548A
39519
3BC29
059E9
2AEDE
12581
0B2D0
0DC32


184
3177E
23D07
2440D
17B42
200DA
0C89E
16386
0B4D2


185
201A7
2797D
2A402
18C40
39516
042F6
1C339
0287C


186
37ED0
20BC2
20E2B
137F4
21262
19E9F
0A112
0C910


187
24EBC
2B01A
39C23
0A029
26819
02519
1694F
088A8


188
2EAED
3AFD0
364CB
1518B
2B3D2
1CA75
14337
1B365


189
2808C
3BAFC
2CDC2
0BFE2
20C06
193A3
1233B
14A7A


190
36EF7
37D4A
28F07
18BB0
2862F
09A95
0D154
1E3E6


191
33D1A
2C6B7
341BB
0CF28
2F438
154C3
0A2C7
15A5B


192
3F426
30FD5
2C7CE
07C50
2D1A0
06569
04B31
05FD0


193
303D5
27A8A
356D3
0FEF6
363EA
08562
0ED7A
175B4


194
3EC32
398EC
2CC89
0C404
3907C
1B759
1A587
03175


195
39F93
30E4C
35A26
07AF9
3797B
0EB5E
1AFF5
1A672


196
2BAD0
2EEA0
21BBA
1B7CA
32264
0F0B9
131FA
0E97E


197
38127
31582
36BBE
1FE4F
25DF2
07EA9
0565A
1698D


198
3DC73
25F38
33B0F
04B20
3B4BE
0F73D
1D9DB
1029C


199
33FB6
2F281
3EB2E
0D90A
37AB9
1579A
1994A
1EFC4


200
3C0F6
3566A
3DFD7
14834
22577
04383
034D3
1D63E


201
32C8E
39FE9
25309
0E783
22ED6
14413
182D0
1D94D


202
36BA4
278F4
3E3FB
049F4
34B51
10EB3
0AF98
1A3BE


203
23E59
3AC99
221F4
0BC4F
31DD7
07190
01735
0CF52


204
227C2
2BED6
30C21
1CC8D
317EF
16B4C
1629F
16DC8


205
300C3
28EAF
2A68F
0E941
2C3DD
163A5
09BD6
05CCA


206
21159
3D839
2365D
0856C
20C00
1AFEC
0674B
0AF29


207
2DF8E
36078
3C37B
1F5B8
32D1A
1D705
02B88
13BF3


208
3A2EB
3CA5E
277CB
19169
37018
1221E
17283
06BFE


209
3663E
38132
3DDC6
0620F
331D3
1AD84
0B417
0A02A


210
3883A
3448E
221A9
0EB88
3D9BD
0B119
1F0DD
18264


211
296BE
28C22
309D2
0E577
384E5
0F074
04077
06E5D


212
39B37
36C83
3E5D5
10C02
3E880
18FE2
03D7A
1E433


213
392BC
282EA
237CF
08F89
35EBE
04733
0F765
0A2F5


214
2D434
3254C
2E816
1F529
20AD8
111DD
0B23C
0CEF0


215
27A5B
3630B
2FAD9
1DB40
2B485
1D5F4
0D95E
0CFEC


216
30B51
39851
2A1E3
0A6DB
28299
18837
06E57
10018


217
31FBC
2E171
3DD23
18189
29A2A
1F5BE
1027B
05C6B


218
3B7EE
3B4AA
3A6D1
1063A
25E5F
17B00
01626
0FA77


219
2EB6B
27CA2
2A739
108DF
2BC9F
0DC9D
18257
0E2C3


220
305AC
221B1
37F7F
0777C
20BE4
12BB5
12E57
0794D


221
32ED1
2E012
3C456
08DCC
28693
17865
11892
1F6D4


222
33A3E
3EF38
29619
12828
2F785
0D1D9
02A7C
19C4B


223
277CA
2BAC3
20F0B
0E3CF
3E30B
17CF2
0C66F
0670D


224
38EB9
2027C
3D0AF
19FAD
2D3DE
0FEE5
1C843
08902


225
21C7F
2029B
3BED4
1E1DE
36F6C
0DD85
165A7
13637


226
2A986
3EEAF
2E182
164AE
26B0E
0FE0F
1A485
0EB33


227
38177
2A44F
2B222
0CD6D
32C15
06B95
14D30
00E7A


228
263A7
2F3E6
25C44
0D315
2C3AD
02353
13F61
16CB3


229
2A956
36F67
21791
14004
222FC
1C91B
02ACD
1DB09


230
2683E
3C516
290C7
18FFB
3AFE5
0C2F0
1CE5E
19B14


231
3FC36
39DA0
3AA4B
1243F
34FBB
09428
1BD4A
01927


232
23B36
3BA46
3D433
126CA
2F152
116C0
1E5B8
0424D


233
36725
3CD2B
24DD6
1AE63
321E3
1B63C
11D51
1F7D6


234
2D676
2F5D9
20324
11DD6
385F5
102D3
1D57A
0B0FE


235
3BAE9
36BC6
3E739
1BC41
31F1C
1FA27
12283
15721


236
25694
38D83
32268
14404
22C82
02B1F
14CB4
083D2


237
3E56B
23886
3EA38
0E52B
222A9
1B3E9
0F81E
1D9FD


238
30C8D
363DC
2AC53
12A7A
3AE50
11773
10491
05FE3


239
256BC
2DE49
20E69
10B0F
34A04
00655
12081
02A03


240
32289
33BC0
2553F
1DB8B
2C5C6
006BA
13963
0A787


241
2802D
336F6
2071B
1721B
23280
06D85
1C75C
18167


242
3AE04
212E6
29BF9
09B13
307AF
187AE
04EAF
00B52


243
22A6D
2BBB4
36270
12ACD
32C83
1CA49
0E821
0961A


244
228D5
2CF29
27DDF
12B25
3E57F
1172C
033D8
04713


245
23A41
354F3
30484
18145
3B17E
1EB32
0DBD5
0BF01


246
294CB
26FD8
3B034
1463D
3073F
01A3D
0AFCE
17661


247
319D3
2352A
2430D
099C7
3F840
07E20
138EC
0AA70


248
3DBE9
39A18
358A1
16567
3E3F4
0580C
051CD
0C072


249
2A925
314AF
205D4
02BE1
23C2D
0D41C
11E20
116C2


250
247D0
25515
2C6C9
14805
2BF9E
10CDB
1E2EB
130FE


251
390A5
2C3BC
3CE8E
04720
28D78
04B30
08FF7
01079


252
29329
3F13E
30A30
010EB
263A8
1A23A
0178B
1D231


253
3B888
37156
2C7D2
10C79
3FF07
0E112
06A42
08313


254
3D8F4
3F7F2
24F25
1651C
24A73
09BBA
064D3
0EAE1


255
2A685
3DFFB
22546
194CC
3DEE3
05C53
115B6
1A57E









QPSK-Type SA-Preambles According to Embodiment of the Present Invention
Table 11, Table 12 and Table 13 each illustrate 128 base sequences generated according to an embodiment of the present invention. Each base sequence is identified by index q and expressed in a hexadecimal format. The sequences listed in Table 11, Table 12 and Table 13 are for segment 0, segment 1 and segment 2, respectively. In Table 11, Table 12 and Table 13, blk denotes the subblocks of each sequence, (A, B, C, D, E, F, G, H).
A modulated sequence is obtained by converting a hexadecimal sequence Xi(q) (X=A, B, C, D, E, F, G, H) to two QPSK symbols, v2i(q) and v2i+1(q). Here, i is an integer from 0 to 8 and q is an integer from 0 to 127. [Equation 24] describes an example of converting the hexadecimal sequence Xi(q) to two QPSK symbols.




  
    
      
        
          
            v
            
              2
              ⁢
              i
            
            
              (
              q
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        b
                        
                          i
                          ,
                          0
                        
                        
                          (
                          q
                          )
                        
                      
                    
                    +
                    
                      b
                      
                        i
                        ,
                        1
                      
                      
                        (
                        q
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
        ⁢
        
          

        
        ⁢
        
          
            v
            
              
                2
                ⁢
                i
              
              +
              1
            
            
              (
              q
              )
            
          
          =
          
            exp
            ⁡
            
              (
              
                j
                ⁢
                
                  π
                  2
                
                ⁢
                
                  (
                  
                    
                      2
                      ·
                      
                        b
                        
                          i
                          ,
                          2
                        
                        
                          (
                          q
                          )
                        
                      
                    
                    +
                    
                      b
                      
                        i
                        ,
                        3
                      
                      
                        (
                        q
                        )
                      
                    
                  
                  )
                
              
              )
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          24
        
        ]
      
    
  




where Xi(q)=23·bi,0(q)+22·bi,1(q)+21·bi,2(q)+20·bi,3(q). According to the above equation, binary values 00, 01, 10 and 11 are converted respectively to 1, j, −1 and −j. However, this is a mere exemplary application and thus the hexadecimal sequence Xi(q) may be converted to QPSK symbols by any other similar equation.

For example, when q=0, the sequence of subblock A is given as 314C8648F and its modulated QPSK signal is [+1 −j +1 +j +j +1 −j +1 −1 +1 +j −1 +j +1 −1 +1 −j −j].
The 128 sequences illustrated in each of Table 12, Table 13 and Table 14 may be doubled in number by complex conjugation. That is, additional 128 sequences may be generated by complex conjugation of the 128 sequences. The additional sequences may be indexed with 128 to 255. [Equation 25] describes an extended sequence generated from a base sequence by complex conjugation.

vk(q)=(vk(q-128))* for 128≦q<256  [Equation 25]

where k is an integer from 0 to NSAP−1, NSAP denotes the length of an SA-Preamble, and the complex conjugation(.)* may be defined as conversion between complex signals (a−jb) and (a+jb).

In addition, the 128 sequences illustrated in each of Table 12, Table 13 and Table 14 may be doubled in number by a reverse operation. That is, additional 128 sequences may be generated by performing the reverse operation on the 128 sequences. The additional sequences may be indexed with 128 to 255. The use of both complex conjugation and the reverse operation may lead to production of 384 additional sequences which may be indexed with 128 to 511.







TABLE 11







n = 0: (Segment 0)









blk















q
A
B
C
D
E
F
G
H


















0
314C8648F
18BC23543
06361E654
27C552A2D
3A7C69A77
011B29374
277D31A46
14B032757


1
281E84559
1A0CDDF7E
2473A5D5B
2C6439AB8
1CA9304C1
0AC3BECD0
34122C7F5
25362F596


2
00538AC77
38F9CBBC6
04DBCCB40
33CDC6E42
181114BE4
0766079FA
2DD2F5450
13E0508B2


3
3BE4056D1
2C7953467
0E5F0DE66
03C9B2E7D
1857FD2E3
15A276D4F
210F282AF
27CE61310


4
3DBAAE31E
254AE8A85
168B63A64
05FDF74FB
3948B6856
33656C528
1799C9BA1
004E0B673


5
177CE8FBC
21CEE7F09
397CD6551
01D4A1A10
1730F9049
067D89EA9
3AC141077
3D7AD6888


6
3B78215A1
17F921D66
385006FDC
011432C9D
24ED16EA6
0A54922F1
02067E65D
0FEC2128D


7
01FF4E172
2A704C742
3A58705E1
3F3F66CD2
07CA4C462
1854C8AA3
03F576092
06A989824


8
1A5B7278E
1630D0D82
3001EF613
34CCF51A1
2120C250A
06893FA2D
156073692
07178CFA7


9
032E31906
2DD318EAA
1DE55B14D
0EF4B6FB3
27DED0610
1BC8440D3
0ED86BF8D
14FAFDE2C


10
174725FFD
0D2FB1732
124470F56
292D9912B
1571408A7
227197AE9
2430BC576
0B67304E0


11
1F1DCD669
293DD1701
0C34F1B84
28496EE51
3DC41327F
071C06523
28E1657B6
02588EFDA


12
22E4AA041
3810362F1
1955F1DE7
0D6D2F8BE
11F31358E
3EB27BB12
1F4E60111
119BDA927


13
14300B522
152E6D482
168DF6E43
0740B7AE0
14FE7DCDD
0FA092626
23697615A
1F1331EB8


14
12C65ED00
317643CD7
2C637A415
15E3E5185
0F5CBB9E0
23290B156
26F37EFE8
1AA174793


15
1DD6453F0
032C4BD39
082659BD5
320C5E691
224E555B2
3A9615A8D
1BED03424
28E6A9CED


16
068AE7EE9
16F724910
3803DD9BD
2A31A2FFB
010BF5237
33CB067E6
0280C28B7
184417B94


17
1D651280A
2C7BCF443
17324EFB0
236E5C411
381215183
2F076E64E
0A6F2EE74
3DA4196B7


18
27341650F
1B520099C
09AC91114
000A5F48B
30AB4B9B6
2D0DB0DE6
1CF57978A
2D424406B


19
3A01E2FB2
0DF5B257B
019D1C63A
0EA7DCDDB
242D96605
2DA675F15
1DEC54193
3B6341C16


20
2DDFAEB05
21D0A1700
0FA09BB78
17DA7F8BB
06E883B3F
02E6B929B
2C1C413B4
030E46DD1


21
1B625E3F9
0F708F756
00CD97B18
3F036B4DF
2CF08C3E5
213A5A681
14A298D91
3D2ED63BC


22
2DA48D5A9
0C085BD17
01903428A
3DF2A30D9
29061309A
16F7DC40E
2AF88A583
27C1DA5E9


23
30DBAC784
20C3B4C56
0F1538CB7
0DDE7E1BE
2C312903B
0FF21E6C2
032C15DE3
26C9A6BA4


24
3188E8100
385FEFE2D
3967B56C7
3F62D246B
1826A755E
2CDA895EA
2FAB77825
1B525FF88


25
339467175
2DE49506B
27B7282A9
0254470A3
3374310AF
2DF20FD64
3848A6806
11C183E49


26
02AFA38DC
0F2AFDDF4
1A05650E2
061439F88
11C275BE0
30C41DEC9
119E070E9
1E76542C1


27
1B364E155
086FF808C
29F1BA9DC
0A830C788
2E70D0B3A
34EA776B1
3D13615C0
15FC708D4


28
38ECFC198
07034E9B3
2340F86B3
07562464C
22823E455
1F68D29E9
257BB66C6
1083992F1


29
375C4F5AB
3C0F5A212
0EA21BC30
13E8A26F2
17C039773
283AD6662
1F63AB833
2DE933CAF


30
2B773E3C5
3849BBE6C
1CAD2E5AB
0405FA1DE
1B27B4269
3B3BF258F
300E77286
39599C4B1


31
1E878F0BE
0AE5267EC
376F42154
1CD517CC2
302781C47
123FEC7E0
16664D3D8
24B871A55


32
20E200C0A
1C94D2FF1
213F8F01B
369A536E0
161588399
29389C7FC
259855CAC
06025DCE2


33
28D2E001C
3C51C3727
106F37D0E
1FB0EFDD1
2CD9D33C3
1EA190527
0BB5A6F9E
074867D50


34
08EFC44B5
1B484EABE
05FEB2DE2
211AF91B5
0CF52B1E1
002B5C978
11D6E5138
0D402BDD2


35
337C618F4
0A4C31DDA
1D93003D6
006D7D088
348043A6D
325E05758
2C53EEEB8
15ED8E614


36
38375C2FF
18C78FD02
30C11EF53
3916581DD
1B75263FF
2D8DFD6A9
00C4E8482
1D201F96A


37
2E10B0D05
2EF203893
2491D95F1
34D995B51
32214BDF5
3E45674B1
3E74AC66E
1B813A999


38
153E7269D
2391C7BFC
1ADD3A595
0EFD3086E
00AD88A8E
0D8B007CA
0F22C5F9D
010E86385


39
3B58C7BFF
0BA76496E
3AD0B7BBF
1D6D10FB3
3A607BEFC
28F122A95
057950727
179449CB7


40
37AC5194A
390BD9C00
3A48C0461
12FBCE4C6
2A8DD4171
10E9F1E34
251F5D167
1124E96B1


41
0FEF20C67
31EC9EA3F
275B31143
22DA4F02B
352C0F648
21FF5B9F3
3E5BC2372
0A1AE08FE


42
080EDC49B
17AD7F7BA
390775B3C
1380B00DA
2477FF17C
2E6D9E5AF
05381F2DD
26143CC17


43
2DB485795
1B3252799
39AD0211C
3AAE31B76
30532A187
1C8EA5F5A
2EA6E4D6B
30570A2E4


44
11BB4F78A
12CCE1428
2C67EEF99
20E3F841A
20CFCD5F2
1618A7B94
111FF6092
2ED034E06


45
1C66335E5
0CA9B9BD2
3213028AE
15542DD28
290F7DAE2
2137F02D5
17DF9445D
24F162FFB


46
360FB966B
17D878955
1C1D67093
065B84F3A
1A1D955E3
24C73C11E
270EA9EB2
114DCA02C


47
002CE84DD
0616DD253
3EB188345
1FF852926
37E160F00
040DF51EC
1857A33BA
230FD8A0D


48
233C0A71F
22E428104
0325F8170
39566B188
32DA16A4A
039FDF1DC
27A3E946C
0D69F26D9


49
0583F9F73
378380CB6
059D8A960
3E3442C7F
026138ADB
25F370F1E
09D3EB2CC
2D37D50C0


50
08DF9CC66
2C2E7AA8F
3CB241ED2
03216B4D2
39736B451
25F6F113F
08FD2AC3C
1974574FD


51
3D1FF6041
2CE2AB97F
01A734F3B
1DCF9F3C5
268D595CA
1FBD2A8B8
0F1449F86
370C352FD


52
123218E40
3AA057589
20F73A16F
26E3BCA5F
3A7330DC6
12C659384
39D99FF1B
276DFC540


53
185AEDEA4
0418B3643
382F7700A
3FC35ED60
07BA2F838
1BC840C93
2469A41EC
0CE7B4CB0


54
2E194E2BF
3302A0B28
1836001EE
154A4738A
36A3BBD72
23CCD0EB1
044B3A13B
2B50C8057


55
0B76405D3
231AAA728
0EE05E9B6
0093A21F2
2065A01D0
1F2B810D4
1082F3A73
1DAFEA492


56
07AD23A3A
2091957F1
3B9D8CBF0
21E4160BE
1BFB25224
3D9085D16
03076DD39
1DBCF8D03


57
226D70EBF
3ED15246C
364130C46
22F6D4AA3
3FCC9A71B
3B9283111
0484F0E58
14574BD47


58
3F49B0987
305231FA6
0CF4F6788
3B9296AED
2346190C5
3365711F4
078900D4A
352686E95


59
1D62AC9A4
104EDD1F5
1B0E77300
1CED8E7F0
388E8002C
1FE6199F4
02239CB15
1FE5D49A2


60
21314C269
28600D12A
22E4F1BAA
044E211B1
0DECFE1B4
3E5B208CC
1CFC91293
21E7A906B


61
02C029E33
1BA88BE4D
3742AE82F
21EF0810F
17D23F465
240446FB5
17CCE51D9
2C0B0E252


62
16F9D2976
10185ECE6
2821673FD
02674271C
3A8A75B7C
226D4BF0F
2216004E5
0E8605674


63
06E4CB337
32A31755D
062BE7F99
1417A922D
2271C07E5
24D6111FA
3F2639C75
0CE2BB3A0


64
18D139446
2426B2EA8
352F18410
1133C535E
10CC1A28F
1A8B54749
22A54A6F4
2F1920F40


65
22443017D
2265A18F5
14E1DAE70
11AC6EA79
31A740502
3B14311E7
3AA31686D
26A3A961C


66
2018F4CA9
3A0129A26
39BDA332E
1941B7B49
03BBCE0D8
20E65BD62
2E4A6EE6C
3B095CCB3


67
0CC97E07D
11371E5FF
31DFF2F50
17D46E889
352B75BEA
1F1529893
21E6F4950
1BD034D98


68
275B00B72
125F0FE20
0FB6DE016
0C2E8C780
3026E5719
119910F5F
3B647515B
1D49FED6F


69
250616E04
0882F53BF
11518A028
3E9C4149D
09F72A7FB
0CC6F4F74
2838C3FD1
08E87689B


70
212957CC2
03DD3475B
044836A0B
2463B52C0
0342FB4B0
34AD95E9B
2936E2045
3B0592D99


71
2922BD856
22E06C30C
390070AED
09D6DC54F
3485FA515
064D60376
07E8288B3
3DD3141BF


72
29CB07995
007EE4B8B
16E787603
07C219E93
1031B93DD
23DEFF60B
30F1D7F67
0EFE02882


73
11F3A0A2F
38C598A57
3FE72D35B
1F655E0D1
0B3AC0D92
3430DDB1A
3BAADBF42
02D6124C0


74
05FC8085D
345A5C470
07DAAE1E9
0D7150B88
25D2A5B10
16F8E5021
3240EFC71
0F0F5922D


75
399F32F6E
2EEB17A8E
0D61665D0
2138EE96F
3F8119063
01B5048F7
27075153D
265DF8280


76
3962CC581
2337D2983
286FD7BBA
185126E0E
1F95AD927
0F7EBC374
1E3A4B6FF
20CA9B9BD


77
1C85C13AF
290C37167
1FDD26E8F
0C38736B8
0174DB972
0A921E3CC
097557C9D
09452C1E6


78
2D48D6C00
2D9BC8DFE
10FF1E128
25C96BA85
0FB071B8E
0F09B3C9C
1A3E11441
38EDDA03D


79
396B88B2F
0029F4BDB
30D098CAD
0D54D12CB
1D0823F55
2DC53B9AA
11BCF7438
33F6EC091


80
21E03CD65
1A2FE5B92
2851F8445
0251E386C
1468950D8
1A8B39748
001B42236
26CD82DA5


81
2CEA1E6BB
006C97E74
00C2B887D
23461AF95
0E9CB2BD2
0B0EA3022
1FB56A7A3
25A7FA625


82
208FC2A1F
381C5733A
03F11D7E3
07ED6A7B7
1FEC85E09
3D61E0440
356F4B1C3
3756E5042


83
2061E47F0
22EAA0AD3
24796BB65
03C59B4D8
32A75E105
22155381B
23E5F041C
155D2D7F9


84
381AFFB73
212B5E400
1F1FE108E
04BF2C90D
3C1A949D9
2854A9B45
001B09322
3A9372CC1


85
058B23433
0904C6684
158CADB9E
11BA4B978
1854368F4
1919ECEA7
147F1FD34
2E228AA3C


86
34857F3DB
2CB44F7BF
111A065D3
1BEAB392E
27F081ED8
3E67D1186
0F6265AC5
27716FAF9


87
38EBB8BF1
32ED6E78F
2B0BA4966
2188282AA
00D49B758
1765BA752
2B50AFDCC
068C82450


88
234F0B406
02FB239CD
15AD61139
2250A5A05
1CD8117E0
0D849163F
268C7A5A6
22A802020


89
2D0FE8D16
0C14E3771
07DE5320C
0640C2762
1CBD9FF4E
37A91986D
2024DA401
164D4A84C


90
3225B4D60
3013B75F2
2A77AE5C5
2C25377EE
03C8DF835
346E80FCB
116B79FA5
356D2B604


91
0D55231FD
247907F31
0CFA0B049
36D069A95
10D4CDE71
1A32544D7
38336885F
173ECC08D


92
207420EAC
26FCFE182
3FE7B31C6
15B320E13
187AA34A8
1B52253BF
1FA16669D
3725A81A5


93
3C9C7404A
092B77FEB
3B9865B46
349456F61
39B7C6A66
3075EC990
01BE637DF
330897B17


94
1CA4C048D
2B4D50621
2BF917627
3EA2CC5E1
33EC0A1E3
05FE0F747
349553D72
396077301


95
04CEC1C82
1F828DD00
30122C790
1AD8A7895
1CE0912C0
298382F37
2D4D33F06
001364B36


96
37F8BB035
2F0897994
333F5F096
0F28AB363
20036829F
338017E2D
3A5A05D76
0CC02E5E0


97
02FD351E6
03E316288
2FCAEB4F8
1C5A80CE3
3D3AC3FDD
3E456746D
119A5381F
1581C894E


98
1623B3D0F
103224DB0
0FB936BC8
2EED7F082
26C91513A
2F12E4C31
290F3AEF2
392CBFF67


99
02F75DE8F
2E61A834D
02A692866
1F21044A3
2D7881A95
18651EE05
11FE3D308
39EED56DA


100
3A858659E
2F7A87BE0
135FD561D
27B3B651A
05E131CB9
0D5865123
2CD6991E5
3EE6DF705


101
3F3B247E1
32D02B245
16B98A593
1E4CCFF18
0C4A9D285
06D519FE2
023A336CD
1B20E999E


102
3A9E8B49B
239656AD1
3396D1C51
06F4DCF40
15D819D3F
2A3061144
20BD2A33E
2FFB139CD


103
38622F3AF
24BF9BB7F
1D2729010
15877B93A
00376B0E7
0FF064887
3505CFD9B
354C366B6


104
2A0AB7033
1AFA65DE1
1198D0AD6
38E80C86A
27693D541
3BB26F3D4
39154881C
0E7DD6B6B


105
1B0DE4333
27FE0F6D1
0F00B2888
0BDA322FF
2759B5A4F
0543A2D27
0C36DD1E5
04E9A262D


106
1C7E636BF
000E9C271
2B44F4F30
28255BF77
1CC4D69CE
03F4C57B2
3E926D59B
00AA39BDB


107
1FDE98AE0
0CD076B07
171124FB5
33F098288
1E0B3043E
39731D117
3E7ABC2C8
19CC50279


108
28EE855ED
2A704C371
03288F4B0
3C83E26C2
0A905148B
18C66BB94
1BCC32537
10D71AB44


109
26238A065
0FBD7BCDD
02507CF76
059F69484
3FE0D6F77
2466A50DB
3C07A75B2
2DC0F099E


110
3CDCD6CBE
1446783DA
1626C83F9
2FD4C4DF3
13A59A2D1
2C903D2A3
0FD37F076
0B1039EDD


111
043B07DD7
28D9C2155
2CCEF57A8
34254C1B7
09B933B2F
1FA410127
10BD5E9E6
010EC6389


112
345E8FCAC
226BD7EFA
27341A51C
23854F031
04C297212
044DED8E8
319B3BFB8
37DBBBF57


113
16FBEFA72
1B5EF9484
2DEE7A5BF
097695C12
08AEAD5E8
3DA7C1327
2B81F3E2D
31AFBED32


114
3484086B1
2DFA56B9E
226E8AFE5
285F45484
3E69AC8E1
1CB33645F
2DE53BC30
2F6ED567E


115
1117B5E7D
122A4D471
1AC936544
267010D71
10428CA47
24B72A000
2E27FE185
1E62C1403


116
0B3161E37
038C3DC98
100793647
1A95D8D36
399668787
06C0D4922
25F48AA58
2DFFF1789


117
04FEF7231
381910B63
298783078
30CE5EC1C
29F6F299D
3C34CA770
37BAAB139
3D2069B65


118
18F644052
2051880EC
23ADBF949
04237280A
18304E663
287364EFF
314698D78
149A21E51


119
39E14BBCB
1DBDA9EF4
3ECCAD8D3
1BA3EF99D
26D85CEBF
270547292
0FB3C7826
0131E73D6


120
2DD6F3F93
0FC282088
14A143DDD
0AB840813
0B973037C
29535C9AB
0DF8DA2AC
271CBC095


121
1C1D063F9
3F4EF6DCC
00128D932
145E31F97
0B21590D1
38F1602D8
3AC2EBB74
2320957C5


122
3383C846F
12128F29B
19985CE7D
2834CBBF2
1E1513B3D
364DB5800
33EE3F46C
01A865277


123
0129D260B
238A85BA0
2D81AA924
3917048B6
36F857692
1D2F813C3
0505FB48B
3DC438BC5


124
05E0F8BDC
3D978C1F1
266F83FCA
0E89D715A
01821DEA4
12D9AE517
22F8EAC2C
3C098DA58


125
1575D1CE9
26F291851
3A7BB6D2C
12CC21A3A
2975589B0
39CF607FF
388ABF183
3D3BAAB0B


126
101E5EC7A
0B75BCF3B
13ED25A86
35FC032B6
2F6209FF0
13C7B2041
1F2791466
3A759A6C2


127
1EF89091A
11A653D2C
223FC1F42
2F7B97B31
2CA4EE011
00F68767D
10FE34682
018339212
















TABLE 12







n = 1 (Segment 1):









blk















q
A
B
C
D
E
F
G
H


















0
20A601017
10D0A84DE
0A8C74995
07B9C4C42
23DB99BF9
12114A3F5
25341EDB0
362D37C00


1
1364F32EC
0C4648173
08C12DA0C
19BD8D33A
3F5F0DDA6
24F99C596
026976120
3B40418C7


2
1C6548078
0A0D98F3C
0AC496588
38CBF2572
22D7DA300
1CCEAF135
356CA0CCF
093983370


3
03A8E3621
2D2042AF5
2AB5CC93B
05A0B2E2E
0B603C09E
117AC5C94
2D9DEA5A0
0BDFF0D89


4
07C4F8A63
3E6F78118
32CCD25F2
1792A7B61
0A8659788
1F9708C04
086AF6E64
040B9CD78


5
2D7EE485A
2C3347A25
3B98E86AF
242706DC3
1CEF639AF
2E1B0D6A9
3E9F78BC1
0FB31275F


6
0307936D0
21CE15F03
392655B2D
17BE2DE53
3718F9AB8
01A986D24
077BDA4EB
1D670A3A6


7
05A10F7B7
31900ACE0
28DCA8010
2D927ABE5
370B33E05
31E57BCBE
030DC5FE1
093FDB77B


8
092C4FED1
268BF6E42
24576811F
09F2DAA7F
24EFFC8B1
21C205A90
1E7A58A84
048C453EB


9
29F162A99
1F739A8BF
09F684599
1BEC37264
38ED51986
286325300
344FC460A
3907B1161


10
0E4616304
0FABDCD08
0F6D6BE23
1B0E7FEDD
0047DE6C2
36742C0C6
2D7ABB967
10D5481DF


11
32DD51790
237D6ACFA
2F691197A
16724EA58
149143636
3810C6EE1
3A78B3FC6
1B1259333


12
1BB0FD4D3
235F10A55
1C7302A27
1148B18E5
04F25FBC8
2A0A8830C
3646DBE59
2F25F8C30


13
0FB38C45B
069DF29E9
00F93771B
3AA35746D
2CAF48FD0
0A42CDD55
19A23CE8F
26318A30F


14
365FBEDAC
27710945F
2AA367D61
05A484318
2563F27D9
2D37D5C00
287D18FBB
3ADB44805


15
3038BC77D
2A45D29EC
156173792
03EC7679E
07577E1A4
1B6A94A74
1D26E5A94
0FD878D5A


16
1F22158E4
3F02A1D37
2767EC03F
1C8CD535A
23DA2E5AB
2D5F25A59
0971AA889
3E78C1846


17
16521E709
12C2DB8FE
3A596C221
1562D5C27
1D9E1F39A
345B96872
301C7894E
2797F032D


18
2EC951A24
1ED768F3F
11217930A
39DB44855
36E41B3FC
0F6E48C44
36254C517
14493C673


19
3EA159E72
24ADE96FE
3458C73A6
30674E1FB
242109AF2
24DAF32B6
24B1EDFFE
291CB9D15


20
2AD0E6696
04F4077D9
1BB279A53
38957605B
379B7A6A0
0BAD35616
1285EAE51
37425C7FF


21
083637980
34F2ED66F
282846A88
19D5E40A6
21205942C
27AC551E9
0F3F4C262
0505FB522


22
3E7D64856
1DB0E599E
159120A4B
1FC788139
235C454FB
3CE5B67C8
339EADB32
0F9F7DDC1


23
3956371B8
1D67BE6E5
1EFCF7D53
041A5C363
2E281EB3F
00AF8A1ED
2DE24A56F
1332C0793


24
0818C47A9
1F945634B
1C5ED3403
1043B5BF4
149702D22
024CBB687
34B01FA8B
1E9F5992F


25
3A6618167
3A0007886
3EDB5756B
2F2FA6FCD
21A5252B8
396FFAD9D
05347B60C
2E0ECA200


26
0D45F89A1
3F9C2C26E
1CBCF809E
3CBE5FCD0
3D2DCF245
14F351A1E
224F5B3FF
2AA6ED34B


27
3BA85ADF8
282005732
3AD7C0223
2E73D1800
23DEA3F46
2275280F6
1586270F9
0CEF4287B


28
07DFE662E
314B74F2F
397BDDC4C
223A8071F
1F5BE3BB4
093BB1F33
0FCA2D129
21B3526A9


29
39FEADC12
0ECE1CD67
206228FAA
38FCCA606
0C5EEE08F
1C1BBDD4E
1459E42ED
11FD64ADF


30
2735FFB20
2AE9B244A
1A5AED974
38FCFD5CB
20310DB81
1C5FC3E24
19FB3BA17
3785BE865


31
24FF6B7EC
01C682673
19CB14113
2C8CD3C2A
066725853
02CD0A23B
279B54315
0CD571063


32
015E28584
30B497250
127E9B2E1
2C675E959
05F442DEE
394AEF6E2
079E5C840
12703D619


33
3CE4B1266
35270B10F
03549C4B3
3B3E6C375
1DBEF270E
0042C9737
049522EC6
24961653E


34
34176CD90
2B5E9EAE1
1C95E3C2B
1EF541D4D
26D1450E6
3B9D895AB
1B0C84349
104B6B428


35
07A813421
2B39EAADC
33553571C
0F8046CDF
2CF6A7F23
0AE3BE8C8
308BFF531
2DBC0F9E3


36
168276972
2CF41744F
3CF2512E0
0F8B68ABC
2E609F6AF
04E03AC8C
0F9B66F49
3AFE28736


37
03456021F
1982574F3
0BB2B3F49
15A4A1CDE
15487D58E
2907C9ABB
15C0D2D73
28D8CFEC3


38
3D3FD677C
33AF2628F
3D217FDCF
30027E85F
0A463F23B
2F2AE8324
1D1E945E0
2EB355D28


39
3BCAF9076
3A7D2FF70
3C541F38B
249BD8A94
287BC4833
141391EB7
05B6443D0
2FEACC5E7


40
275F118FA
3A96B346D
0C713CDE5
02F394A28
3EBB1D18D
1BE7A9FDD
223C53CA1
2BF040F77


41
1161DE4F5
0544F9DB7
230847E45
322AF4E17
26944A0B4
3299F1420
1C9405B8E
2DBABD4CE


42
33165C531
268FE9B9B
081A914B4
39100772B
27DBF03E9
3E3A18AB0
13F2D2B83
2CEEE5FF4


43
275F97006
0A578F2EF
16CEE7EC8
38A5B0084
00DC9A1F5
1B88CFA3D
0D8B0B8EF
29FC4CCF2


44
04BBE4F2C
1546C3988
237105A43
339042B36
3A5DEBE2B
1BD09449D
38EFF588B
1CDD3A6C0


45
002E32D38
1E85D3125
3F51120D7
00420ED63
3384713AF
1D941BD34
2B39EA9CF
05B6D9E94


46
2B3100F7B
335EDB2E6
1AC8C8EE4
337FF7139
0672D7995
38A54856E
0124753F2
3A3560851


47
046207CE9
0FE1BC312
09BA5B289
39376EF2B
33F826C2C
2F6531496
3933B8616
23125B50F


48
3E5849C45
01EEDB390
141D9A024
2DE07E565
1813D12BB
36DB8D404
0E8A272AB
3A66B71AD


49
1A2A88A4C
3F0C9B4DB
266CFBDF9
163420CA5
281ABBE99
34771C295
3AC051848
3C53CB875


50
16F795184
3466F1FFA
1F433B456
1DDF13810
25F58CF69
1DD6CFE4E
10A236FDF
12AE697ED


51
1C8D17F4F
07C43B7D1
1C8DAD395
28F6C112E
3A336ADB3
0EB6889AB
2783A6A1F
2CDA40458


52
16044624E
252AA04B2
11484E85C
07F5024B7
286E3A67F
2EE6BACE4
277F1F864
22F3CF57D


53
2D1A3F4CF
0EEB6DEC1
30CD76F42
20403D1AC
3A72EF9D6
1DAAF2A39
03AB76CE0
0A2856267


54
0FA2A786B
38273EDF2
228A45016
0309DF52D
093BDAEDC
1B11E9300
1DA9C5324
03365EB1E


55
24DCFDC06
11CF909D6
2FF693F4C
366338F1F
22E641569
0ACA60D55
32D1B009E
035472E09


56
17F5D6662
062FCF913
35B211035
21ACE73FB
3B4148706
2D0CD106F
2CAB457A4
103E1E49B


57
21859E8DA
2F1E3B3D9
1F1014BE2
062A3DEB5
354C0C786
05A8982D4
35A758943
346EBA72A


58
00CB49E5F
211B1034A
3A5D2DAF1
21D3F3EB0
24B2D1150
1097C3685
2AA3671CE
0E5DC1308


59
24C8401BE
217B1F994
1FB9664A8
3D5057708
05A506088
1314842B9
3C8657064
14B1FA77F


60
2AD698E2E
3C129D1F6
2C744FF4E
1C1C052F8
18C38A9FE
252168A10
2EB68D098
3A001CBD2


61
2AF71324C
2BF41D408
0FC498E18
149A1A407
0FDC2C4A3
19D00C4A1
0F6B0DD29
268CF8E86


62
19F4D82A5
342C73FD5
0F5AEEDE7
21A2A8953
15ADB7A94
11DBE038D
0A5B6634A
0FA382B77


63
0A5985778
35AC3032D
35691C85D
2829D55EE
04A3FBD8C
2C85BFA8E
0F459B864
3E878F0BC


64
10C785EB0
054D4CE18
1BF657A8E
101DC64EF
0B4E3032A
24ECFD9C2
00C98BE0A
2A1F82444


65
300E8B09C
31A079FB3
0C41DEC5F
216CCFE4D
226C5A693
3C31A41DD
3A019974C
23B64EAFC


66
249BDC80F
0316ED79E
1E42B5567
0CFF04A4B
310678543
34D986980
1E3195429
280966E65


67
359A72B64
186A3999D
065825DDF
2D28E6000
10964C1E1
1468C970E
34C8B606A
33CC94DB1


68
370B29C05
12841A9E8
2147E7160
1835345EE
06DB43F37
33854A725
065E6614C
151E2D7B1


69
0EAADDB27
004EC6DDD
30AA39B8B
2AEB34AD4
2A13D6649
00EC67B83
1176417CE
0E3683151


70
0832BA87B
3B67515B9
0FD34BC87
1688F83CB
370B52AD5
3A2CD6F3F
3343BF461
37BD48546


71
16EA2751C
1799D9C42
24055CEC9
226A907D4
133C68F80
22CA03BF0
05F723395
2D35008AF


72
122A5C67D
3E46230BC
09F475BA9
15B4B6754
11DE75C50
28C17544F
1D85FAB8D
0D5AD9537


73
1C5497CD9
3D405F487
05535D737
06952087B
1C4744AF4
3E0EF881C
3CED3D1BB
1D91157CE


74
1D276153D
14604EA77
1661FB979
3BAC5E9FB
089F41406
283154122
2AFDCE892
1FD5E0810


75
2A620F4C2
0DE484180
2D05E6458
3E6D15A27
0A92FF0B7
2CBF7BF53
25A2F28FA
19A10CE02


76
3A77B1FBE
2B262F810
2BEEA0F46
39706BBA2
09257163F
1026D5D74
2E2483EBF
1D6527C1E


77
0DC1EBA02
383C59C77
28C7ED115
06FED31D4
16F610DC3
000890B82
2FAD16A3A
35C9AD95F


78
3E5C1EBE2
3C65A7691
2394005B6
251B1BB49
1F42BFA23
0E8608C07
24666F55C
11A5214DF


79
323E882C5
2DBFF5E13
3638BC43F
38CC5CBB5
1DBF783FB
0499418C7
2285E5A40
1A61D17E7


80
1E508F19D
0CF345F97
0E5648601
0A0951DF3
1194EE717
0A6C0B374
03C4E19EC
06F725799


81
0B54F4AEF
186A12343
04C4A60C6
27C2CC0E9
3973075A1
392C5EEB7
3933C99B1
005F98CB2


82
021B6635A
3764D0696
20942B266
0155C4EDD
3FDBF7497
37356D442
374F3DB06
2718357FE


83
120DF6F80
0E41F376A
03544C7B2
2D6795EFD
29E8811F1
1B3EFD388
01CA4C48D
2067E8033


84
07703D649
35221AB50
22141A0D7
268061A59
2D9192B05
3834711FF
3A07258C0
36253B5AA


85
1C4A564C1
26804247A
16A4DB29D
0BEF93C88
37A3EAB6C
25547B136
3FC935878
250E3BF1C


86
17049BB43
0D6426761
2BF3A471E
1665820E9
14412A13D
30D5744B0
2ECE5CAE6
01395189C


87
29615B890
0A2C5A664
216DA64F4
3D4AA9D2C
07B98342C
2603F0D76
0574BDFA8
3F9B35D5D


88
3A0414B22
0A8BE885E
155C220E4
2D3B17AA6
3017E1B48
26508C6C8
3FF25EC63
240EFF072


89
2ACD81CE3
0468D7943
2A4108121
1F2E8E67F
3AB446179
33325CA24
3006DD3A5
1A33F3A2C


90
2B038BAF7
070660C4E
30953C7B7
3E7375D04
1D6A39944
001BE5C8D
199A89253
0A82087BB


91
03BF7C836
2CBF9FC48
38EAB1C98
11C303993
3D748807F
1EBD41D17
351085EF2
1C55B94D3


92
116E0BE61
17BC8C403
31BD1EAA2
1CF87C049
2A41CC04D
3883EFEC1
3971BBBE2
190CAE3B7


93
172799BB5
3301DB193
2480B569B
34DBEFE9C
003287827
38DAEA1CB
0B0E25BB4
1972B37E3


94
3EF1F9EF4
189D8C3E0
1941998D3
259838BC9
28E545988
33BFC60D8
3572B10F3
197913B6B


95
24CF96D66
285347801
22BC70E5E
394231BCC
077583F4E
0364420AF
278FBF5CB
3850AFC8B


96
1B38C4A50
04439E0B5
3A7BEB18B
3003A36CD
329D5A2B6
1BB123AFA
049C2CC94
0F604D1DC


97
28D47EF33
24CF66B6B
24B716FA9
34ED7F6BB
186AE44B4
1380D0726
1CC51324E
16BA74F62


98
04422E60A
3424BA16C
3FF1B39DD
1A1E658F7
33457317D
14E822151
3EC02F279
28593D11D


99
0F2DF0912
21BBFA838
32D634EBF
2061148FD
09A565B74
2BCE430B7
34DAAD9FA
228ADAFE5


100
2D7EE0544
25D57B7CA
0FADAF20D
19B4F6444
3A75DF1C1
0AD3EDD56
0A4D61EEA
28C1262A5


101
1B6AEE253
0BFE02772
24AB19547
186A377A5
03089B4E8
128955F60
3A8DA9AC8
2931648B3


102
21BE0200F
00F34B4F5
34FF3261B
1A0E27AED
0A821AEFB
21B0BA404
1C6A644A4
1734EBB33


103
201FBFD73
0592E9D86
053D87C9D
3CAFC7479
22F1BA3FA
3DB25DD15
31D468990
22FF2B539


104
06C77404E
18AE64252
3963D899A
37179C03C
0FD2E3D04
191E64DBB
380B841FB
368E1DEAA


105
3A561759B
156243DE8
04325D217
33993D0B0
0CEAC2109
002242D1B
33C1D9F5E
1EC4195D3


106
17D7A9B74
1F44ABA75
17B572FE3
096008B9B
1F1E00AAE
05489F7A1
17A4C131D
1C018E923


107
0A4ACCEC8
1F294A30D
19CAEE64E
002787A1B
03EB3238D
27C10F626
1C9E656A0
3F73609F0


108
1E0E3C802
1B52D12AA
2F4E003B7
23BA7A6F1
3CAA0998A
32E96C916
168EFA1EE
28147EE33


109
1CEC9799E
215D9302B
176BB6639
003D5E371
12FE4ADB3
3106B64E2
001D9C28E
0F39059DC


110
31570792D
2260D7FEF
1AC830374
118FE7C78
08F982159
23BB2B13A
2C7944305
376396F3C


111
2D340540B
272E94D06
097C70995
0E70DDADA
1DBD644E5
341A72A58
01CBF5334
2C7999AF9


112
3FF17764D
0701DFAD3
146BDBB97
229D2D7F0
03C5DA21D
3A5916EC7
2390AC01D
197D64233


113
3E9759D5A
00B237425
0B7E646B9
190CB4D16
2646AA1D4
1A373103D
337E5EFB1
0199DE4A1


114
3FD5ADE8A
26B843860
0A2D0AA7B
3C351E07F
1B25376AE
05C553CDD
1DBC3F38D
019823A2A


115
30FF187B4
112F9D7A1
1AE977517
3760AF555
004F86368
3700975C2
0518029DE
032427D9B


116
3A86D49BB
057E649D8
2FDE33D7E
31254217C
30E05CE12
10BCC1CD7
1889C5139
38A163ECF


117
2610F5174
02A7ACB27
208B84FF0
14609CA80
0F3526318
38EBC7384
287C57BAA
279661A9C


118
014F6D77B
1036B3D2C
294F1999A
33A059187
26CCE0507
180DF3129
00A6CAE22
2AC0F23A2


119
347C62997
1912A710D
2260C531F
2F54BBEBB
0A2D90305
1BBEE20E4
0AF79997E
2376F3D0F


120
04484EB82
181977944
1C1CC2693
227ECAB0F
23F32982B
19E2F290C
1BA2300F8
0EFB06247


121
0EC048AD8
3B2168495
34FC02DA1
2C0CDEF52
0553CA222
25DFA4581
29CF66B6B
0AB9C21CD


122
2AF502148
3B00632F9
387CDC4BF
3F8B9F716
19084CD65
0354918C7
39D1FD9AA
0F5ABDB77


123
2C6E2557A
3E8A19D6B
3E6756A28
237E6E5BF
24CA57004
1D52401AD
0237F1D80
0FB2B335D


124
228F4B540
07532BF5D
101F67F52
29D8598EE
0421A0E23
2D89C2AFF
0963D2F3B
24C472A63


125
0CF3598E8
196A40BD2
00E63B26D
088A0BFCA
1C78E9016
03835236C
33071A836
3949DC586


126
3E815D747
1588D4E96
073C8D44A
303281AE4
095D31EC8
1F10F69DC
200F057D8
1F270128F


127
34F9ACB6B
384870FF1
257A863DE
34B36BA0F
3FA3D216B
27425041B
0E0DD0BAD
2E95AD35D
















TABEL 13







n = 2 (Segment 2):









blk















q
A
B
C
D
E
F
G
H


















0
13F99E8EC
3CF776C2A
3300A482C
0B2BF4791
17BECDFE8
35998C6D4
05F8CB75C
259B90F0B


1
116913829
05188F2A4
2DB0A8D00
2F770FE4A
185BE5E33
0F039A076
212F3F82C
116635F29


2
004EE1EC6
18EF4FDD9
26C80900E
1A63FB8A7
1DAA917D4
0E6716114
02690646D
0CC94AD36


3
06D4FF377
2716E8A54
16A1720C8
08750246F
393045CCB
1DBCCDE43
114A0CAD6
181690377


4
3DC4EF347
1F53452FC
01584B5D3
11D96034F
1FA62568E
11974FACA
191BE154D
397C9D440


5
05A1B6650
29835ADAD
2F6DDABE4
0976A607B
11BA92926
2456B1943
3E3FD608B
095E7584B


6
00CC66282
0560BE767
21EBAA7C6
2D8E9ACE3
198A9E285
05F3E73DD
13DA751A2
176B75E43


7
03D08ADC1
2254606FC
3C695D892
1DA9E0280
2CD4FF589
19B78A5A4
0CE67A7C6
12535A61C


8
0984647CF
0822BA46B
3EB2BC076
212596F54
11CC2E64E
120BADF9F
0DA72CEDE
30D0E106F


9
083CE5726
1F05DA925
169D93EF6
1FCADF3D3
08A5CF0BC
317C8508F
19BDCCFE7
0FACE3631


10
27583A466
1CB1634D5
03C7849F7
38C6CED00
1161C173A
15A645D3E
281A7ED92
076ADA797


11
33BA1AE8F
187F578EE
32473D69A
2458B703B
267E59071
0F317883B
3E7DEDBF1
3B9859BA7


12
0322609A3
20C4C957C
3FD638746
3FB716D79
36BD0CF1C
333B11B8F
0027ED1F2
3E7471BF3


13
3529922B1
0ECECBE04
1980B9B9E
38D60363F
18904BCED
108E3E5F1
34B95C446
338F51DAC


14
21FD50527
0EA2F7A31
1E294A159
114734A02
120B90BF3
3F3617C92
0129071E2
106640936


15
2B59354BB
275BF9761
39C6FF332
2004B3902
053F9DCB0
19D79A902
2B3125038
20649B43E


16
03A8A7A2B
091AE6721
18651FD9E
1F5415ECD
1B38EA62E
07FB0F422
3EB58896B
077FE4C7C


17
06A13CB38
340099B18
2AE6D6385
1669631F9
28E51A676
19A023391
261855F39
3E518F0BC


18
2A88F831B
09D295831
294C468DF
1477F0A13
37725C6EB
00E7DB222
27D610157
349A8FAB6


19
163E1C44D
3F98B6F4A
1805538DD
01EE3DB4A
22AA1797E
27568753E
16090F219
2C9838C01


20
34B0543DC
121B8EA82
00873B4A0
220FE7C05
2EDBEAE34
1104BDB93
0711E8C0E
0E1C107BD


21
226183AFF
15643DE71
04A4CDECB
2E67FDF8A
26D2A6D40
25E7695F1
1A99778F5
20FE0C1A3


22
0F7EAC09D
12BB72B2A
182E44301
2962EB85A
3477C1B69
3E3CF56F7
29C9D00C6
39788600C


23
31084BEB5
1DC90E345
391736CC1
3C8292AE1
38A0D515C
3977012F6
25D1F6055
36A7D3F8B


24
229D3ABAC
1044BA05F
0C391B88A
0636A90A6
0B14322AB
21ADC33E4
2DC1A3BFE
0D7FF6D1F


25
33C85B393
37BFA31B6
134F872F0
0C5EA36E1
286956ED1
1632092FA
382B4BB10
23DC3EF14


26
38E8B9BF6
0A0CE666B
207D98054
23FF360AD
121BFDA4E
347D442FD
242922C07
23C6E4115


27
263EA8516
36138BD6A
0ED9C55E7
3F0937876
03232BC24
18E5FFF26
3530CF206
3981B7414


28
1D9AC2E79
051B220E9
3F3B09EC8
0D3F6C366
0201A7CB9
3D5477092
22185FF9F
1C5AA5348


29
208D85694
22104E7C5
14BCFD3DD
3592DF665
1F4EC3265
24358076A
2D20A8000
017F2D489


30
36B3A9A2C
3F8E0F162
13ACDCCF2
16951F727
271E73555
1B3EDCDE7
162B45352
1CAFA635A


31
2D30FE705
3EC9BFC8D
1B10F8349
34F973F31
1CA96A349
1A28B4543
1C5367CE6
2DFAB0AE7


32
21D93EB5A
0E49D6211
3C6FCF774
09F44CACF
2D8CD2BEA
037DDAD3D
3BBD06D1D
39CBB996F


33
159B1F948
0183E8DCD
3A484866C
21F8DF1A5
219A58193
2D1B3C399
2275F19BA
0EFF4C612


34
22EB93A82
15047E272
15428D77B
38FFC612E
20609BE54
3226C8254
3E5568DB2
159284EED


35
34529707C
2E84585F4
20DFFB4C5
28288AA00
10EFC1E07
3C4D211FC
379087C3F
25716A7DD


36
20106354F
22AEB9FD7
3A6BAC67D
3126294C6
0FBC874AC
2DFE5675A
391B1DDAA
06BAA74D8


37
348F831C5
2E44BF3C2
3D9F6F454
20746A30E
08D183029
35C6BFEA7
2729B552B
263BB2EBD


38
202D7F08F
0DBE1C144
132F4EC09
184CD9B93
2596F5884
2A55B8217
2BEAE02D8
235A19A43


39
2DDE3FF5F
23932555C
001ED92D7
22FCD3D60
2C0737593
0B27E62FF
0693CFBDC
284D5B33F


40
1DB9AB8E9
2995EE0A1
1ACFE9892
0D41BCB9D
2E3806507
25CCD5D60
3536DF04C
0BB0A5E3B


41
3FFD4DD82
3E69CC1C1
2BC30FB74
3462F70FC
164FAE762
09B83F8AD
1DF593F3C
2DB478034


42
16E24E9B6
0A9FCFBD2
3A018544C
1ED8E2855
0037681E4
05950E1F8
1107DA097
377A25C65


43
03C9318B8
0C70A7749
0D58708C2
0CA2808C4
219E02554
39315B2F2
2E089B00F
302E135C7


44
04DC211E8
1DD20A505
21A50649F
2CA438C04
39CAD66AE
2E1BD969F
002748760
069924211


45
2E84BCF09
226F5D43C
37BE7EB10
07CDC854A
06FB50D48
08966435B
01BA5E5D2
1D34057FA


46
2D8DFD565
0A30D633F
33F93B7C6
0B330E9D2
0E659B262
130669024
19A9D5F64
38059132D


47
17E4777AE
1308F9046
2F7C0483E
1859E0943
0982C9101
05453D92C
001F53877
388A571AB


48
00D29CC63
0A6D3BDED
1CA44D2AF
388C002CA
2A3D70EF7
2DD3F5A6F
39FEAF0B6
11DFE385F


49
3E3A6CEC4
122F5E8BE
360B96301
0632CF244
2E8985A9F
0FD256C87
0449C29D4
26B713C90


50
238150687
3D96F7F7B
0091E6D18
21802352A
02F7A466E
0A5BB6648
350DA85DB
1C97F4544


51
306BA76DE
379A88697
3F0DA31E1
0EBF48C71
27F8A46EB
3F75A19F6
277002F97
275B43715


52
24D946CC1
38DF102DC
3EFE1F5B3
3C316E148
2735B20CF
0688E430F
0316DC923
24919BEA1


53
0EEAF72D2
3C7248573
1087A7BD6
08EDA9BF6
2B5D97BF4
26733DC60
1190D275B
2EC7ABD30


54
37C6AB63E
2FFC9C790
02CAA37A7
1B34A3F84
0022CD5F6
3ECF891BF
193D545E2
0172C674E


55
0848A41C3
1D8150EE7
3D8A8549A
2595F707B
00640B276
2D44EBDAE
1CAF37453
377EF590A


56
16B7A5F7D
1F5AA7998
382300A8B
218916E53
19D00E728
1EDA11790
0BBDEF9C4
1DEB15796


57
3EFB3368D
392AA88AD
29CF3CACD
03F59ED8A
1042098CA
1721B8F3A
2B5DE9312
0CB5E6F23


58
1A8B0FB9E
3FBC09C8B
3D7F3E248
034C9BCB5
1BDD89300
3392476C0
0C10AED4B
23BECA42A


59
0EBC749B6
33453C7F6
304735F5C
334628143
1DAF6E7A9
11BB9C393
226C5E4FF
170372039


60
3F9262CBC
0693308C8
21B563415
09BDCC403
0112C79D4
2DA9F1134
36AA1CD7D
3A1608BFC


61
218AC590E
0FACC734D
02132C9A3
27087557E
076B3ECE7
2EA16BA3D
0E1D452F1
3F70B027A


62
004F9DC68
25BE3AD9C
2CBD3C07B
3F9DECD71
3E771E15A
11FF2F24D
2AEA5DF67
1E838955D


63
3A04BC376
1D19254F1
00F92DD2B
3C57484F3
181D0973E
319F9CEEA
053ADEEDB
1A3C22150


64
0F78BA6BC
2DFE0E681
3035BD77D
0A0FFD148
275F50C66
2246E9053
27B2BF3E9
1741894F8


65
1ACCD0F79
22F0AEA4F
32796ADB5
134A4A876
183D989E3
204C4BF97
22300E86F
3F18744A3


66
3EB6E19EF
1B24EAB88
2E318F810
3F07B618E
26B4C0C87
31CC10EA8
169E1B650
017DF88ED


67
2BD9E8FED
0AB104122
30C9D81A0
09EA73C7F
141357B1D
000A7DB48
1DD06FD41
0AFA8EF72


68
19CA5678F
28A89AA43
1DB945917
262AF69C3
3145A4473
3742CBFF5
1BCD965E9
1B0E7FC84


69
077838B25
2BF7032F8
23DC2E014
028544277
37B411B5F
392FF6CDC
1D66F2BE9
011372DA0


70
39596216C
05A651F63
183A6AE26
0D1FCA203
0FF6F0D22
2FEB8364B
05A438ED8
32D045F13


71
3711AD513
290B237FF
20E2A9B26
0C72A0234
2F1ABBE93
19B505378
354ED915D
0C359F272


72
1D7786BA4
1CCDF053A
36828B333
0ED27AFB6
241326FC4
1A9C37F8B
0A9C3C372
05937E898


73
1053B9CDB
040B97B1D
0D4FF481D
23AD465A8
2906EBDE2
0C4F6C09D
2189C5FEA
2D90D305A


74
39073122B
35FEAA236
1B38B7A90
2E02AB9F7
219FEEA0A
36B3B2EF8
39A3F4C8B
15A42C9DD


75
2C6326A9E
33F7536C1
2A120C75F
37030CAA0
3A011882C
098C8504E
3B92D756B
175811CF9


76
38A0F736B
2BD9E9C32
3B989715A
2A646ADF4
2D02FE38C
11AC7E9E6
3F5464862
0F382B0D8


77
26897D80C
145B21D3E
143F5E320
30549707E
28126710C
122CA92BE
3AF47270C
0B544128F


78
00E931208
2E1E75EAA
374C36E5F
21724DFC5
1DFCD2028
1B3FF774E
3A826A68B
1781CDCA4


79
0C3D7268D
0B7A26BF9
1587CE5CD
1D04E1E60
36240C07D
1AC403449
0417F9622
02B9F8BED


80
1B569F488
08A3F3A46
377F03A18
2DE416045
1ED96E381
33F4F16DC
2C8DAAE4F
33E384AC7


81
13F709786
02A4E32CB
14C7F849E
09EA16987
06C849EA4
219E4B995
243CB7F07
253513BC6


82
09B83FDF2
119D60439
278290BFF
2483E6F2C
0EDEC175D
242A669C1
3EB639EF0
31EBB4CA0


83
22CAEF0E4
0B2FCDED0
19BA79607
343F81C7B
289AA213E
358AC9FFA
23956ADA1
00BC725E7


84
1186F95E3
2F95F4048
3CFBF41E2
1D1E4BE96
26B38BA65
2F715E590
2235C0029
2C89AF93F


85
33437ED6C
12F14DB69
2E70F5611
183752704
142BC8B34
3B90ECD86
1C11EB493
1022D4782


86
248457F60
05B9A28A5
0A2A5DD56
16002D9E7
34C87FB16
2E32BAE0C
21065BD64
1CCE92BB0


87
1DCE3941A
1D940ACE3
30D331B98
3D5A3BAB6
119791607
10FB0D788
2C78E9015
100B598E4


88
39C0BC811
1B886594E
27AF50C73
2DCEA05E6
0805EDCA9
3A5989B08
18AD24255
1683B7CF2


89
186A3D233
09E8B95DA
1ED9F3DBE
1B19A74F8
356CA7443
316C9FBE9
3F8A3162A
3A0BC11CC


90
02F039B63
2F02D3E75
0F5B5E89E
3D062255C
222C6AA4E
25DEA06FB
39488C071
139318BFB


91
27B5B6EE8
22154E0BD
3FF7729F1
1052B1947
3D477BF2B
3EDB6745A
1B30CF849
030F84AF4


92
27B2D40BC
01EE5E9B6
24B0ACF84
3370F65E0
067D8DFA9
1C01B9327
26FF8FDB5
3809C0CA6


93
11F581193
07B9B7A7D
1CA56B4A3
3D088CC6C
11D52C38A
344760F0A
3D3AA336D
0118CBD93


94
096990784
2960D1672
3BFD7D847
2BC297EEE
32168CF28
3912FFF6C
08ED9BAB1
34452C6E5


95
02CD48DC2
186403849
24C6EE1EA
12ED5268A
2718C00E9
27E8F18CF
145913E2D
0B09009BB


96
06B97DD08
2880C9B96
37EB87E03
14C4ED01D
17041E5DC
347A412CB
088CE591B
0BE926B22


97
116250DF7
1745B4329
1102B7093
1CA549C5A
25244AB6C
374E0F19B
274F76015
0FB738F16


98
12841B9E9
1F9C4AEEB
1445F0C98
39FFB6307
02AB688E7
0FD8B499E
28D533072
138F162EA


99
22BD9525E
2030E58C6
25F2CD033
157D93437
1442E92D2
3D6EE9DF3
3CA5B469D
0588A0FAE


100
0FDEC177D
2606157BE
2224E556C
0C6F33897
0F830DE1B
3C3F9C1D8
2AF576923
0D4173E27


101
376EF82C2
30E3C582E
0A82DE29A
1B8D454D9
079ACE6D9
2579984C6
392F28400
24CEAEDF1


102
1CD4AA9D2
1DD6F4DA5
3485B7150
105DE02F9
22168E0FA
24F48AA6C
003771A39
306890843


103
1F8303786
2C981AAE4
0819F22E9
0A1D88D55
3B4C012FD
0214CDF52
19DF3BE8F
02364E19A


104
1364A15C0
16E9F9961
17E598810
2654E5A2C
09B43C7C8
3A5E2AF45
14FC71E26
2B4BA69F4


105
12E128BEF
19166342E
04A1404B7
283D17B66
014836F64
13BE0B4B5
2F8583C08
2B19A7FB4


106
19F83FDE2
361D25170
36354011B
3FF4EC74B
1B2128FF9
0C849EB1B
096B991D8
1CA7A74AA


107
32E0BEF35
11A61714D
34C56D40B
0742C52FE
00ED2F1C4
3997FC7B7
06E414374
180DCD64F


108
18399ED59
224E6C2FF
3450F1BB7
27A1CA959
21B5E00F8
13B67DAE8
0B14C022E
0E41BBEE2


109
318D94D05
2EBB53B17
331C3E6F4
0FBCD71ED
380FF18B8
3E3C75B26
0E0088A18
17553D2A2


110
37AC7E5D5
27C9EADFA
3FC47B5E4
38699BB57
1564F8B27
3579C7FEB
13401BD88
0DB519DE0


111
0FF4D6F22
3C84242F3
2DEAE40AD
305F320A5
244CB97B0
0892DA905
3F09D5CB5
332E7DB02


112
31479E580
1B6AD13E0
16A1CF9E2
33A0A119A
1AC8388E9
3D4105F37
226501835
27AF1310F


113
1CBDAFE39
3E5A30C1C
236E9A029
063430D97
0CD91A825
02F335D7E
1989FE0BE
13C4E2A20


114
10B393370
33CB79316
2CEB44FC0
236019420
248F95ACB
35034B6F0
365691771
34A8FBCB6


115
25463FC5F
082FC0ED2
038ACE1CC
3E959B49D
21B8C04F5
08633F3A0
3A5D18159
12B3EC4C7


116
167B32C3E
06FF88387
34C3F468B
3239005B2
121C913AF
21C90CE16
28B54D557
3811CB0A9


117
221BD0503
0AF619499
21F8D40C1
1B3DA7AEE
3FA2E3B05
348466C50
10F12A28D
0E70B26AB


118
1D79A57C5
315D2460F
1402B8222
28DC66FEA
1BCF748F9
2AD5D4227
0094D2CAD
25EA22A58


119
062B39CFB
310E8818D
0F2D0A235
3F6468866
33F86F342
39CAB5BBC
2E7D6A8BF
3E9218162


120
2FCDEA0E0
1BDD766A4
2827B99BB
0B5F04CC9
1C9E02A9A
1A6675ED4
033497A06
07D4ADD44


121
3CD46CD9D
311A64A85
24DDFE6FF
3411C6FE5
0D0613CDA
0E9276056
178ACC4F8
23DEA3CB0


122
2762D6A40
306FE3843
1402589C8
382B07654
160BA3DEA
3815B54C8
273960105
2076A15E5


123
1C593A744
1562487F6
0C38617B4
2CA68266A
071C4BF93
2593F0BDC
1562436E5
199BEEA49


124
35B8C7503
278F57EAA
34A804061
19C657A74
385734710
3FAC27628
0707BED4E
32F20F45E


125
34994C46C
1C6B99499
1AF24D850
11AD795D3
19288BFE9
1360C1B96
3B5D8DBC0
2554E72D6


126
22D7095A4
34B70502A
3F0CB27D2
04FC214E6
24C0B80C5
03D6F4DC8
1432A099E
26300D70E


127
21C33416F
18B894695
3AC062614
3537CF601
00A20A8B8
1CD10BAF5
394DF1DC0
0925851ED









Simulation: Properties of SA-Preambles Proposed by the Invention
The properties of the sequences listed in Table 11, Table 12 and Table 13 and the extended sequences obtained by complex conjugating the sequences according to the present invention were investigated (256 sequences per segment). As comparison groups, known 114 preamble sequences for the IEEE 802.16e system and known SA-Preamble sequences (256 sequences per segment, refer to Table 10 and IEEE 802.16m-09/0010r2, Table 658 and Table 659) were used. Cross-correlations, differential cross-correlations (Type 1), differential cross-correlations (Type 2), auto-correlations, differential auto-correlations, and boosting levels were measured. The differential cross-correlations (Type 2) were calculated according to the method described by [Equation 26]. The boosting levels are maximum values that do not lead a maximum peak value exceeding 9 dB in the time domain. For the other measurements, refer to [Equation 9] to [Equation 18].




  
    
      
        
          R
          
            a
            ,
            b
          
        
        =
        
          
            1
            
              N
              -
              1
            
          
          ⁢
          
            
              ∑
              
                n
                =
                0
              
              
                N
                -
                2
              
            
            ⁢
            
              
                
                  (
                  
                    
                      a
                      d
                    
                    ⁡
                    
                      (
                      n
                      )
                    
                  
                  )
                
                *
              
              ⁢
              
                
                  b
                  d
                
                ⁡
                
                  (
                  n
                  )
                
              
            
          
        
      
    
    
      
        [
        
          Equation
          ⁢
          
            
          
          ⁢
          26
        
        ]
      
    
  




where zd(n)=(z(n))*z(n+1) and N represents a sequence length.

Table 14 to Table 19 illustrate the simulation results of the properties of the sequences proposed by the present invention (Ex,seg—0 to Ex,seg—2) and the comparison groups (16e, and 16m,seg—0 to 16m,seg—2).









TABLE 14









Cross-correlation
















16mb, seg_0
Exc, seg_0
16m, seg_1
Ex, seg_1
16m, seg_2
Ex, seg_2



16ea (114)
(256)
(256)
(256)
(256)
(256)
(256)


















Min
0.000
0.000
0.000
0.000
0.000
0.000
0.000


Max
0.303
0.403
0.301
0.361
0.303
0.347
0.303


Mean
0.074
0.074
0.074
0.074
0.074
0.074
0.074


Median
0.070
0.069
0.069
0.069
0.069
0.069
0.069


std.
0.039
0.039
0.039
0.039
0.039
0.039
0.039


dev.





a144 known preambles for the IEEE 802.16e system


b256 known BPSK-type SA-Preambles for the IEEE 802.16m system


c256 QPSK-type SA-Preambles according to the present invention















TABLE 15









Differential cross-correlation (type 1)
















16mb, seg_0
Exc, seg_0
16m, seg_1
Ex, seg_1
16m, seg_2
Ex, seg_2



16ea (114)
(256)
(256)
(256)
(256)
(256)
(256)


















Min
0.000
0.000
0.000
0.000
0.000
0.000
0.000


Max
0.236
0.329
0.235
0.310
0.234
0.319
0.235


Mean
0.041
0.041
0.042
0.041
0.042
0.041
0.042


Median
0.037
0.037
0.038
0.037
0.038
0.037
0.038


std.
0.025
0.025
0.025
0.025
0.025
0.025
0.025


dev.





a144 known preambles for the IEEE 802.16e system


b256 known BPSK-type SA-Preambles for the IEEE 802.16m system


c256 QPSK-type SA-Preambles according to the present invention















TABLE 16









Differential cross-correlation (type 2)
















16mb, seg_0
Exc, seg_0
16m, seg_1
Ex, seg_1
16m, seg_2
Ex, seg_2



16ea (114)
(256)
(256)
(256)
(256)
(256)
(256)


















Min
0.000
0.007
0.007
0.007
0.007
0.007
0.007


Max
0.239
0.315
0.237
0.301
0.239
0.315
0.238


Mean
0.065
0.067
0.077
0.067
0.077
0.067
0.077


Median
0.056
0.063
0.073
0.063
0.073
0.063
0.073


std.
0.049
0.050
0.040
0.050
0.040
0.050
0.040


dev.





a144 known preambles for the IEEE 802.16e system


b256 known BPSK-type SA-Preambles for the IEEE 802.16m system


c256 QPSK-type SA-Preambles according to the present invention






Referring to Table 14, Table 15 and Table 16, the QPSK-type SA-Preambles according to the present invention have lower maximum cross-correlations all the time than the known BPSK-type SA-Preambles of the IEEE 802.16m system.









TABLE 17









Auto-correlation















16ea
16mb, seg_0
Exc, seg_0
16m, seg_1
Ex, seg_1
16m, seg_2
Ex, seg_2



(114)
(256)
(256)
(256)
(256)
(256)
(256)


















Min
0.091
0.139
0.126
0.139
0.126
0.139
0.119


Max
0.203
0.333
0.250
0.306
0.237
0.361
0.264


Mean
0.134
0.213
0.178
0.206
0.173
0.212
0.177


Median
0.133
0.222
0.175
0.194
0.169
0.194
0.176


std.
0.020
0.034
0.024
0.034
0.022
0.038
0.023


dev.





a144 known preambles for the IEEE 802.16e system


b256 known BPSK-type SA-Preambles for the IEEE 802.16m system


c256 QPSK-type SA-Preambles according to the present invention















TABLE 18









Differential auto-correlation















16ea
16mb, seg_0
Exc, seg_0
16m, seg_1
Ex, seg_1
16m, seg_2
Ex, seg_2



(114)
(256)
(256)
(256)
(256)
(256)
(256)


















Min
0.127
0.133
0.128
0.133
0.134
0.119
0.144


Max
0.408
0.315
0.253
0.357
0.244
0.357
0.264


Mean
0.216
0.214
0.181
0.218
0.184
0.216
0.184


Median
0.211
0.217
0.179
0.217
0.183
0.217
0.183


std.
0.044
0.035
0.024
0.039
0.023
0.036
0.023


dev.





a144 known preambles for the IEEE 802.16e system


b256 known BPSK-type SA-Preambles for the IEEE 802.16m system


c256 QPSK-type SA-Preambles according to the present invention






Referring to Table 17 and Table 18, the QPSK-type SA-Preambles according to the present invention have lower maximum and mean auto-correlations all the time than the known BPSK-type SA-Preambles of the IEEE 802.16m system.







TABLE 19







SA-preamble signal boosting levels













Ants/FFT
512
2048







16ma
1
1.59 dB
1.49 dB



(FSTD)
2
2.18 dB
2.09 dB




4
2.84 dB
3.11 dB




8
3.54 dB
4.40 dB



Example
1
1.87 dB
1.69 dB



sb
2
2.51 dB
2.42 dB



(FSTDc)
4
4.38 dB
3.50 dB




8
8.67 dB
4.95 dB







aKnown BPSK-type SA-Preambles for the IEEE 802.16 m system



bQPSK-type SA-Preambles proposed by the present invention



cFrequency Switched Transmit Diversity






Referring to Table 19, the QPSK-type SA-Preambles according to the present invention have higher boosting levels than the known BPSK-type SA-Preambles of the IEEE 802.16m system, in all of eight cases for 512-FFT and 2048 FFT. Especially, in the cases of 4 antennas and 8 antennas for 512-FFT, the QPSK-type SA-Preambles according to the present invention have at least twice as high boosting levels as the known BPSK-type SA-Preambles of the IEEE 802.16m system. Thus, it can be concluded that the QPSK-type SA-Preambles according to the present invention have low PAPRs than the known BPSK-type SA-Preambles of the IEEE 802.16m system.
Table 20 illustrates power boosting according to FFT sizes and numbers of antennas. The power boosting was optimized for the sequences listed in Table 11, Table 12 and Table 13. In the time domain, a maximum peak does not exceed 9 dB.












TABLE 20







Ant\FFT
512
1024
2048









1
1.87
1.75
1.69



2
2.51
2.33
2.42



4
4.38
3.56
3.50



8
8.67
6.25
4.95










In Table 20, in the case of a single antenna and 512-FFT, the SA-Preambles are boosted at a boosting level of 1.87. Then a boosted SA-Preamble at a kth subcarrier may be expressed as ck=1.87bk where bk denotes an SA-Preamble (+1, −1, +j, −j) prior to boosting.
Table 21 illustrates block cover sequences for each subblock in an SA-Preamble. A block cover sequence converted to binary values {0, 1} is mapped to {+1, −1}.










TABLE 21





(FFT, number of





antennas)\Segment ID
0
1
2







 (512,1)
00
00
00


 (512,2)
22
22
37


 (512,4)
09
01
07


 (512,8)
00
00
00


(1024,1)
0FFF
555A
000F


(1024,2)
7373
3030
0000


(1024,4)
3333
2D2D
2727


(1024,8)
0F0F
0404
0606


(2048,1)
0F0FFF00
00000FF0
0F000FFF


(2048,2)
7F55AA42
4438180C
3A5A26D9


(2048,4)
1A13813E
03284BF0
391A8D37


(2048,8)
0D0EF8FA
0C0BFC59
03000656









FIG. 16 illustrates exemplary ranging channel structures in the IEEE 802.16m system. A ranging procedure is used for various purposes. For example, the ranging procedure is used for uplink synchronization, uplink resource request, etc.
Referring to FIG. 16, the ranging channel includes a Ranging CP (RCP) of length TRCP and a Ranging Preamble (RP) of length TRP, in the time domain. TRP is proportional to the reciprocal of a ranging subcarrier spacing ΔfRP. Table 22 illustrates the ranging channel structures.











TABLE 22





Format
Ranging Channel





No.
Structure
TRCP
TRP
Δ fRP







0
Structure 1
Tg + k × Tb(a)
2 × Tb
Δ f/2


1
Structure 3





2
Structure 2
m × Tg + n × Tb(b)
2 × 2 × Tb(c)



3
Structure 3
7 × Tg + Tb
8 × Tb
Δ f/8


4
Structure 4
Tg
Tb
Δ f









In Table 22, Tb denotes a useful symbol duration, Tg denotes a CP duration, and ΔfRP denotes a subcarrier spacing. For details, refer to Table 7 and its description. k may be expressed as

k=┌{[Nsym·Ts−2·(TRP+Tg)]/3}·Fs┐/NFFT  [Equation 27]

where Nsym denotes the number of OFDMA symbols in a subframe, Ts denotes an OFDMA symbol duration, FS denotes a sampling frequency, and NFFT denotes an FFT size. m is (Nsym+1)/2, and n is (Nsym−4)/2. For details, refer to Table 7 and its description.

In ranging channel format 0, repeated RCPs and repeated RPs are used as one ranging opportunity in a subframe. Ranging channel format 2 includes one RCP and repeated RPs in a subframe, and ranging channel format 1 includes one RCP and two RPs. If ranging channel format 1 is used, there are two ranging opportunities in a subframe. Ranging channel format 4 user identification card connecting device is identical to ranging channel format 1 in structure and different from ranging channel format 1 in length. In ranging channel format 4, first to fourth RPs RP1, RP2, RP3 and RP4 correspond to first to last parts of a ranging sequence, respectively.
FIG. 17 is a block diagram of a transmitter and a receiver according to an embodiment of the present invention. A transmitter 1810 is a part of a BS and a receiver 1850 is a part of an MS on a downlink, whereas the transmitter 1810 is a part of the MS and the receiver 1805 is a part of the BS on an uplink.
Referring to FIG. 17, a sequence processor 1820 of the transmitter 1810 may perform various operations related to sequence generation, sequence selection, sequence extension, etc., or it may control other modules to perform the operations. The sequence processor 1820 may select a base sequence from a memory or generate a base sequence using a sequence generator. Also, the sequence processor 1820 may generate a new extended sequence out of the base sequence through complex conjugation and/or a reverse operation. The sequence processor 1820 may output the selected/generated/extended sequence to a modulator 1830. The modulator 1830 modulates the received sequence according to the type of the sequence by BPSK, QPSK, 8-PSK, etc. The modulator 1830 may perform complex conjugation and/or the reverse operation on the modulated sequence under the control of the sequence processor 1820. An additional module may be separately configured so as to perform the complex conjugation and/or the reverse operation. The modulated sequence is mapped to subcarriers by the modulator 1830 or an additionally configured module. According to a channel that will carry the sequence, the modulated sequence may be mapped to consecutive or distributed subcarriers. A Radio Frequency (RF) module 1832 generates an RF signal by processing the mapped sequence to be suitable for an air interface (e.g. digital-to-analog conversion, amplification, filtering and frequency upconversion). The RF signal is transmitted to the receiver through an antenna 1834.
The receiver receives the signal at an RF module 1854 from the transmitter 1810 through an antenna 1852. The RF module 1854 provides input samples by processing the received signal (e.g. filtering, amplification, frequency downconversion, and analog-to-digital conversion). A demodulator 1860 provides a sequence by demodulating the input samples. A channel estimator 1880 calculates a channel estimate based on received pilot values. The demodulator 1860 equalizes the received sequence using the channel estimate and thus provides a sequence estimate. A sequence detector 1870 detects or estimates the sequence transmitted by the transmitter 1810 by the exemplary method illustrated in FIG. 6 or any other method.
Controllers/processors 1840 and 1890 manage and control the operations of various processing modules of the transmitter 1810 and the receiver 1850, respectively. Memories 1842 and 1892 store program codes and data for the transmitter 1810 and the receiver 1850, respectively.
The embodiments of the present invention described hereinbelow are combinations of elements and features of the present invention. The elements or features may be considered selective unless otherwise mentioned. Each element or feature may be practiced without being combined with other elements or features. Further, an embodiment of the present invention may be constructed by combining parts of the elements and/or features. Operation orders described in embodiments of the present invention may be rearranged. Some constructions of any one embodiment may be included in another embodiment and may be replaced with corresponding constructions of another embodiment. It is obvious to those skilled in the art that claims that are not explicitly cited in each other in the appended claims may be presented in combination as an embodiment of the present invention or included as a new claim by a subsequent amendment after the application is filed.
In the embodiments of the present invention, a description is made, centering on a data transmission and reception relationship between a BS and an MS. In some cases, a specific operation described as performed by the BS may be performed by an upper node of the BS.
Herein, the term ‘BS’ refers to a terminal node of a network, which communicates directly with the MS. Namely, it is apparent that, in a network comprised of a plurality of network nodes including a BS, various operations performed for communication with an MS may be performed by the BS, or network nodes other than the BS. The term ‘BS’ may be replaced with the term ‘fixed station’, ‘Node B’, ‘enhanced Node B (eNode B or eNB)’, ‘access point’, etc. The term ‘MS’ may be replaced with the term ‘User Equipment (UE)’, ‘Mobile Subscriber Station (MSS)’, ‘mobile terminal’, etc.
The embodiments of the present invention may be achieved by various means, for example, hardware, firmware, software, or a combination thereof. In a hardware configuration, the methods according to the embodiments of the present invention may be achieved by one or more Application Specific Integrated Circuits (ASICs), Digital Signal Processors (DSPs), Digital Signal Processing Devices (DSPDs), Programmable Logic Devices (PLDs), Field Programmable Gate Arrays (FPGAs), processors, controllers, microcontrollers, microprocessors, etc.
In a firmware or software configuration, the embodiments of the present invention may be implemented in the form of a module, a procedure, a function, etc. For example, software code may be stored in a memory unit and executed by a processor. The memory unit is located at the interior or exterior of the processor and may transmit and receive data to and from the processor via various known means.
Those skilled in the art will appreciate that the present invention may be carried out in other specific ways than those set forth herein without departing from the spirit and essential characteristics of the present invention. The above embodiments are therefore to be construed in all aspects as illustrative and not restrictive. The scope of the invention should be determined by the appended claims and their legal equivalents, not by the above description, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.
INDUSTRIAL APPLICABILITY
The present invention is applicable to wireless communication systems, especially wireless communication systems supporting at least one of SC-FDMA, MC-FDMA, and OFDMA. More particularly, the present invention is applicable to a method and apparatus for transmitting and receiving sequences in a wireless communication system.

## Claims

1. A method of transmitting a signal at a base station in a wireless communication system, the method comprising:
transmitting a preamble including a modulation sequence, the modulation sequence being indexed as one of 0 to 2N−1,
wherein the index of the modulation sequence is used to determine a cell identifier and N is a number of pre-defined hexadecimal sequences,
wherein, if the index of the modulation sequence is within 0 to N−1, the modulation sequence is obtained by modulation of one of the pre-defined hexadecimal sequences, and
wherein, if the index of the modulation sequence is within N to 2N−1, the modulation sequence is obtained by using the following equation:


vk(q)=(vk(q-N))* (for N≦q≦2N−1)


where vk(q) is a kth modulation symbol in a modulation sequence of index q, vk(q-N) is a kth modulation symbol in a modulation sequence of index (q−N), k is an integer greater than or equal to 0, and the symbol “*” represents a conjugate operation.

2. The method of claim 1, wherein the one of the pre-defined hexadecimal sequences is modulated by converting each element Xi(q) of a corresponding hexadecimal sequence into two Quadrature Phase Shift Keying (QPSK) symbols vk 2i(x) and vk 2i+1(x) by using the following equation:



  
    
      v
      
        2
        ⁢
        i
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    0
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  1
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  




  
    
      v
      
        
          2
          ⁢
          i
        
        +
        1
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    2
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  3
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  


where Xi(q)=23·bi,0(q)+22·bi,1(q)+21·bi,2(q)+20·bi,3(q), q is an integer of 0 to N−1, and i is an integer greater than or equal to 0.

3. The method of claim 1, wherein the preamble is a Secondary Advanced Preamble (SA-Preamble).

4. The method of claim 3, wherein the SA-Preamble is located on subcarriers given by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  



where n is an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP is a value given for the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

5. The method of claim 4, wherein the cell identifier (IDcell) is determined by the following equation,


IDcell =256×n+Idx

where n is the index of the SA-Preamble carrier set, indicating the segment ID ranging from 0 to 2, and Idx is an integer ranging from 0 to 255, the Idx being obtained from the index of the modulation sequence.

6. A method of receiving a signal at a mobile station in a wireless communication system, the method comprising:
receiving a preamble including a modulation sequence, the modulation sequence being indexed as one of 0 to 2N−1,
wherein the index of the modulation sequence is used to determine a cell identifier and N is a number of pre-defined hexadecimal sequences,
wherein, if the index of the modulation sequence is within 0 to N−1, the modulation sequence is obtained by modulation of one of the pre-defined hexadecimal sequences, and
wherein, if the index of the modulation sequence is within N to 2N−1, the modulation sequence is obtained by using the following equation:


vk(q)=(vk(q-N))* (for N≦q≦2N−1)


where vk(q) is a kth modulation symbol in a modulation sequence of index q, vk(q-N) is a kth modulation symbol in a modulation sequence of index (q−N), k is an integer greater than or equal to 0, and the symbol “*” represents a conjugate operation.

7. The method of claim 6, wherein the one of the pre-defined hexadecimal sequences is modulated by converting each element Xi(q) of a corresponding hexadecimal sequence into two Quadrature Phase Shift Keying (QPSK) symbols vk 2i(x) and vk 2i+1(x) by using the following equation:



  
    
      v
      
        2
        ⁢
        i
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    0
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  1
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  




  
    
      v
      
        
          2
          ⁢
          i
        
        +
        1
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    2
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  3
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  


where Xi(q)=23·bi,0(q)+22·bi,1(q)+21·bi,2(q)+20·bi,3(q), q is an integer of 0 to N−1, and i is an integer greater than or equal to 0.

8. The method of claim 6, wherein the preamble is a Secondary Advanced Preamble (SA-Preamble).

9. The method of claim 8, wherein the SA-Preamble is located on subcarriers given by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  



where n is an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP is a value given for the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

10. The method of claim 9, wherein the cell identifier (IDcell) is determined by the following equation,


IDcell=256×n+Idx

where n is the index of the SA-Preamble carrier set, indicating the segment ID ranging from 0 to 2, and Idx is an integer ranging from 0 to 255, the Idx being obtained from the index of the modulation sequence.

11. A base station used for transmitting a signal in a wireless communication system, the base station comprising:
a Radio Frequency (RF) module; and
a processor configured to transmit a preamble including a modulation sequence, the modulation sequence being indexed as one of 0 to 2N−1,
wherein the index of the modulation sequence is used to determine a cell identifier and N is a number of pre-defined hexadecimal sequences,
wherein, if the index of the modulation sequence is within 0 to N−1, the modulation sequence is obtained by modulation of one of the pre-defined hexadecimal sequences, and
wherein, if the index of the modulation sequence is within N to 2N−1, the modulation sequence is obtained by using the following equation:


vk(q)=(vk(q-N))* (for N≦q≦2N−1)


where vk(q) is a kth modulation symbol in a modulation sequence of index q, vk(q-N) is a kth modulation symbol in a modulation sequence of index (q−N), k is an integer greater than or equal to 0, and the symbol “*” represents a conjugate operation.

12. The base station of claim 11, wherein the one of the pre-defined hexadecimal sequences is modulated by converting each element Xi(q) of a corresponding hexadecimal sequence into two Quadrature Phase Shift Keying (QPSK) symbols vk 2i(x) and vk 2i+1(x) by using the following equation:



  
    
      v
      
        2
        ⁢
        i
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    0
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  1
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  




  
    
      v
      
        
          2
          ⁢
          i
        
        +
        1
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    2
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  3
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  


where Xi(q)=23·bi,0(q)+22·bi,1(q)+21·bi,2(q)+20·bi,3(q), q is an integer of 0 to N−1, and i is an integer greater than or equal to 0.

13. The base station of claim 11, wherein the preamble is a Secondary Advanced Preamble (SA-Preamble).

14. The base station of claim 13, wherein the SA-Preamble is located on subcarriers given by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  



where n is an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP is a value given for the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

15. The base station of claim 14, wherein the cell identifier (IDcell) is determined by the following equation,


IDcell =256×n+Idx

where n is the index of the SA-Preamble carrier set, indicating the segment ID ranging from 0 to 2, and Idx is an integer ranging from 0 to 255, the Idx being obtained from the index of the modulation sequence.

16. A mobile station used for receiving a signal in a wireless communication system, the mobile station comprising:
a Radio Frequency (RF) module; and
a processor configured to receive a preamble including a modulation sequence, the modulation sequence being indexed as one of 0 to 2N−1,
wherein the index of the modulation sequence is used to determine a cell identifier and N is a number of pre-defined hexadecimal sequences,
wherein, if the index of the modulation sequence is within 0 to N−1, the modulation sequence is obtained by modulation of one of the pre-defined hexadecimal sequences, and
wherein, if the index of the modulation sequence is within N to 2N−1, the modulation sequence is obtained by using the following equation:


vk(q)=(vk(q-N))* (for N≦q≦2N−1)


where vk(q) is a kth modulation symbol in a modulation sequence of index q, vk(q-N) is a kth modulation symbol in a modulation sequence of index (q−N), k is an integer greater than or equal to 0, and the symbol “*” represent a conjugate operation.

17. The mobile station of claim 16, wherein the one of the pre-defined hexadecimal sequences is modulated by converting each element Xi(q) of a corresponding hexadecimal sequence into two Quadrature Phase Shift Keying (QPSK) symbols vk 2i(x) and vk 2i+1(x) by using the following equation:



  
    
      v
      
        2
        ⁢
        i
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    0
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  1
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  




  
    
      v
      
        
          2
          ⁢
          i
        
        +
        1
      
      
        (
        x
        )
      
    
    =
    
      exp
      ⁡
      
        (
        
          j
          ⁢
          
            π
            2
          
          ⁢
          
            (
            
              
                2
                ·
                
                  b
                  
                    i
                    ,
                    2
                  
                  
                    (
                    q
                    )
                  
                
              
              +
              
                b
                
                  i
                  ,
                  3
                
                
                  (
                  q
                  )
                
              
            
            )
          
        
        )
      
    
  


where Xi(q)=23·bi,0(q)+22·bi,2(q)+20·bi,3(q), q is an integer of 0 to N−1, and i is an integer greater than or equal to 0.

18. The mobile station of claim 16, wherein the preamble is a Secondary Advanced Preamble (SA-Preamble).

19. The mobile station of claim 18, wherein the SA-Preamble is located on subcarriers given by the following equation,




  
    SAPreambleCarrierSet
    n
  
  =
  
    n
    +
    
      3
      ·
      k
    
    +
    
      40
      ·
      
        
          N
          SAP
        
        144
      
    
    +
    
      ⌊
      
        
          2
          ·
          k
        
        
          N
          SAP
        
      
      ⌋
    
  



where n is an index of an SA-Preamble carrier set, indicating a segment Identifier (ID) ranging from 0 to 2, NSAP is a value given for the SA-Preamble, and k is an integer ranging from 0 to NSAP−1.

20. The mobile station of claim 19, wherein the cell identifier (IDcell) is determined by the following equation,


IDcell =256×n+Idx

where n is the index of the SA-Preamble carrier set, indicating the segment ID ranging from 0 to 2, and Idx is an integer ranging from 0 to 255, the Idx being obtained from the index of the modulation sequence.