# Patent

## Title
Apparatus and method for generating preamble sequences in an OFDM communication system

## Abstract

An apparatus for generating a preamble sequence in an orthogonal frequency division multiplexing (OFDM) communication system using A subcarriers in a frequency domain. A preamble sequence generator generates a length−M+N+k preamble sequence, where M+N+k is less than A, by combining a length−N Golay complementary sequence with a length−M Golay complementary sequence. An inverse fast Fourier transform (IFFT) processor assigns elements constituting the preamble sequence to the M+N+k subcarriers among the A subcarriers on a one-to-one mapping basis, assigns null data to remaining subcarriers excluding the M+N+k subcarriers from the A subcarriers, and then IFFT-transforms the assigned result into time-domain data.

## Background
PRIORITY
This application claims priority under 35 U.S.C. § 119 to an application entitled “Apparatus and Method for Generating Preamble Sequences in an OFDM Communication System” filed in the Korean Intellectual Property Office on Jun. 16, 2003 and assigned Ser. No. 2003-38815, the contents of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates generally to a communication system utilizing an Orthogonal Frequency Division Multiplexing (OFDM) scheme, and in particular, to an apparatus and method for generating a preamble sequence having a minimum peak-to-average power ratio using a complex Golay complementary sequence.
2. Description of the Related Art
In general, a wireless communication system supporting a wireless communication service comprise a plurality of Node Bs and user equipments (UEs). The Node Bs and the UEs support a wireless communication service using transmission frames. Therefore, the Node Bs and the UEs must acquire mutual synchronization for transmission and reception of the transmission frames.
In order to synchronize, a Node B transmits a synchronization signal so that a UE can detect the start of a frame transmitted by the Node B. The UE then detects frame timing of the Node B by receiving the synchronization signal transmitted by the Node B, and demodulates received frames according to the detected frame timing. Commonly, a specific preamble sequence previously established by the Node B and the UE is used for the synchronization signal.
In addition, a preamble sequence having a low peak-to-average power ratio (PAPR) is used as the preamble sequence in an OFDM communication system. Further, a preamble that is created by concatenating a long preamble, which is necessary for performing coarse synchronization, to a short preamble, which is necessary for performing fine frequency synchronization, is used for the preamble transmitted from a Node B to a UE. Only the short preamble is used for the preamble transmitted from the UE to the Node B for acquiring fine frequency synchronization.
The preamble sequence having a low PAPR must be used as a preamble sequence of the OFDM communication system because the OFDM communication system, which is a multicarrier communication system, uses a plurality of carriers, i.e., a plurality of subcarriers, in which orthogonality between the subcarriers is important. Therefore, phases of the subcarriers are appropriately set so that orthogonality between the subcarriers should be secured, and if the phases are changed during signal transmission/reception through the subcarriers, signals on the subcarriers may overlap each other. In this case, the amplitude of the signals that overlap due to the phase change deviates from a linear region of an amplifier included in the OFDM communication system, thereby disabling normal signal transmission/reception. Therefore, the OFDM communication system uses a preamble sequence having a minimal PAPR.
Further, the OFDM communication system transmits data for several users, or UEs, by time-multiplexing a single frame. In the OFDM communication system, a frame preamble, which indicates a start of a frame, is transmitted for a predetermined period beginning at a start point of the frame. Because data may be irregularly transmitted to the respective UEs within one frame, a burst preamble indicting the start of data is located at a front part of each data block. Therefore, a UE must receive a data frame in order to identify a transmission start point of the data. The UE should be synchronized to a start point of data in order to receive the data, and to this end, the UE must acquire a preamble sequence used commonly by all systems for synchronization, before receiving signals.
The OFDM communication system is identical to a non-OFDM communication system in a source coding scheme, a channel coding scheme, and a modulation scheme. While a code division multiple access (CDMA) communication system spreads data before transmission, the OFDM communication system performs inverse fast Fourier transform (IFFT) on data and inserts a guard interval in the IFFT-transformed data before transmission. Therefore, when compared with the CDMA communication system, the OFDM communication system transmits a wideband signal using relatively simpler hardware. In the OFDM communication system, if a parallel bit/symbol stream generated by parallel converting a plurality of serial bit/symbol streams is applied as a frequency-domain IFFT input after modulation is performed on data, an IFFT-transformed time-domain signal is output. The time-domain output signal is obtained by multiplexing a wideband signal with several narrowband subcarrier signals, and a plurality of modulation symbols are transmitted for a one-OFDM symbol period through the IFFT process.
However, in the OFDM communication system, if the IFFT-transformed OFDM symbol is transmitted as it is, interference between a previous OFDM symbol and a current OFDM symbol is unavoidable. In order to remove the inter-symbol interference, a guard interval is inserted. The guard interval is used to insert null data for a predetermined period. However, in a method of transmitting null data for the guard interval, if a receiver incorrectly estimates a start point of an OFDM symbol, interference occurs between subcarriers, causing an increase in error probability of a received OFDM symbol. Therefore, a “cyclic prefix” scheme or a “cyclic postfix” scheme has been proposed for the guard interval.
In the cyclic prefix scheme, a predetermined number of last bits in a time-domain OFDM symbol are copied and then inserted in an effective OFDM symbol, and in the cyclic postfix scheme, a predetermined number of first bits in a time-domain OFDM symbol are copied and then inserted in an effective OFDM symbol. The bits used in the cyclic prefix scheme and the cyclic postfix scheme are preset bits, and in the OFDM communication system, a length of the preset bits is previously determined. A receiver may acquire time/frequency synchronization of a received OFDM symbol using a characteristic of the guard interval created by copying a part of a time-domain OFDM symbol, i.e., a beginning part or a last part of one OFDM symbol, and then repeatedly arranging the copied OFDM symbols.
In any radio frequency (RF) system, a transmission signal transmitted by a transmitter is distorted when it passes through a radio channel, and thus, a receiver receives a distorted transmission signal. The receiver acquires time/frequency synchronization of the received distorted transmission signal, using a preamble sequence previously set between the transmitter and the receiver, performs channel estimation, and then demodulates the channel-estimated signal into frequency-domain symbols through fast Fourier transform (FFT). After demodulating the channel-estimated signal into frequency-domain symbols, the receiver performs channel decoding and source decoding corresponding to the channel coding applied in the transmitter on the demodulated symbols, thereby decoding the demodulated symbols into information data.
The OFDM communication system uses a preamble sequence for frame timing synchronization, frequency synchronization, and channel estimation. The OFDM communication system may perform frame timing synchronization, frequency synchronization, and channel estimation using a guard interval and a pilot subcarrier in addition to the preamble. The preamble sequence is used to transmit known symbols at a beginning part of every frame or data burst, and update estimated time/frequency/channel information at a data transmission part, using information on the guard interval and the pilot subcarrier.
FIG. 1 is a diagram illustrating a structure of a long preamble sequence for a conventional OFDM communication system. However, before a description of FIG. 1 is given, it should be noted that a current OFDM communication system uses the same preamble sequence in both a downlink (DL) and an uplink (UP).
Referring to FIG. 1, in the long preamble sequence, a length−64 sequence is repeated 4 times and a length−128 sequence is repeated 2 times. According to a characteristic of the OFDM communication system, the above-stated cyclic prefix (CP) is added to a front end of the 4 repeated length−64 sequences and to a front end of the 2 repeated length−128 sequences. In addition, as described above, signals obtained before performing IFFT are frequency-domain signals, and signals obtained after performing IFFT are time-domain signals. The long preamble sequence illustrated in FIG. 1 represents a time-domain long preamble sequence obtained after performing IFFT.
Frequency-domain long preamble sequences obtained before performing IFFT are illustrated below.




  
    
      
        
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Numerals specified in the frequency-domain long frequency sequences S(−100:100) and P(−100:100) represent subcarriers+ positions applied while IFFT is performed, and a detailed description thereof will be made with reference to FIG. 3 herein below. S(−100:100) represents a frequency-domain preamble sequence obtained by repeating a length−64 sequence 4 times, and P(−100:100) represents a frequency-domain preamble sequence obtained by repeating a length−128 sequence 2 times. In the expression of S(−100:100) and P(−100:100), ‘sqrt(2)’ means ‘root 2’, and ‘sqrt(2)*sqrt(2)’ means performing double amplification to increase transmission power of S(−100:100) and P(−100:100).
FIG. 2 is a diagram illustrating a structure of a short preamble sequence for a conventional OFDM communication system. Referring to FIG. 2, in the short preamble sequence, a length−128 sequence is repeated 2 times. According to a characteristic of the OFDM communication system, the above-stated cyclic prefix (CP) is added to a front end of the 2 repeated length−128 sequences. In addition, the short preamble sequence illustrated in FIG. 2 represents a time-domain short preamble sequence obtained after performing IFFT, and a frequency-domain short preamble sequence equals the P(−100:100) described in connection with FIG. 1.
The long preamble sequence stated above must be generated taking the following conditions under consideration.
(1) The long preamble sequence should have a low PAPR.
In order to maximize transmission efficiency of a power amplifier (PA) in a transmitter of an OFDM communication system, a PAPR of an OFDM symbol must be low. That is, because an IFFT-transformed signal is applied to a power amplifier and because of a non-linear characteristic of the power amplifier, a low PAPR is required. A PAPR of an OFDM symbol must be low in a ratio of maximum power to average power of a time-domain OFDM symbol corresponding to an IFFT output terminal of the transmitter. For a low ratio of the maximum power to the average power, uniform distribution must be provided. In other words, a PAPR of an output becomes low if symbols having a low cross correlation are combined in an IFFT processor's input terminal of the transmitter, i.e., in a frequency domain.
(2) The long preamble sequence should be suitable for parameter estimation needed for communication initialization.
The parameter estimation includes channel estimation, frequency offset estimation, and time offset estimation.
(3) The long preamble sequence should have low complexity and low overhead.
(4) Coarse frequency offset estimation should be possible.
A function of the long preamble sequences generated considering the foregoing conditions will now be described herein below.
(1) A sequence obtained by repeating a length−64 sequence 4 times is used for time offset estimation and coarse frequency offset estimation.
(2) A sequence obtained by repeating a length−128 sequence 2 times is used for fine frequency offset estimation.
As a result, the long preamble sequence has the following uses in an OFDM communication system.
(1) The long preamble sequence is used as a first preamble sequence of a downlink protocol data unit (PDU).
(2) The long preamble sequence is used for initial ranging.
(3) The long preamble sequence is used for bandwidth request ranging.
Further, the short preamble sequence has the following uses in the OFDM communication system.
(1) The short preamble sequence is used as an uplink data preamble sequence.
(2) The short preamble sequence is used for periodic ranging.
In the OFDM communication system, because accurate synchronization is acquired by performing initial ranging and periodic ranging, the uplink preamble sequence is mainly used for channel estimation. For channel estimation, PAPR, performance and complexity should be taken into consideration. In the case of the existing short preamble sequence, a PAPR shows 3.5805|dB|, and various channel estimation algorithms such as a minimum mean square error (MMSE) algorithm and a least square (LS) algorithm are used.
FIG. 3 is a diagram schematically illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in a conventional OFDM communication system. It is assumed in FIG. 3 that if the number of all of the subcarriers for an OFDM communication system is 256, the 256 subcarriers include −128th to 127th subcarriers, and if the number of subcarriers actually in use is 200, the 200 subcarriers include −100th, . . . ,−1st, 1st, . . . ,100th subcarriers.
In FIG. 3, input numerals at an IFFT processor's front end represent frequency components, i.e., unique numbers of subcarriers. Here, of the 256 subcarriers, only 200 subcarriers are used. That is, only 200 subcarriers excluding a 0th subcarrier, the −128th to −101st subcarriers, and the 101st to 127th subcarriers from the 256 subcarriers are used. Null data, or 0-data, is inserted in each of the 0th subcarrier, −128th to −101st subcarriers and 101st to 127th subcarriers, before being transmitted.
The null data is inserted into the 0th subcarrier because the 0th subcarrier, after performing IFFT, represents a reference point of a preamble sequence in a time domain, i.e., represents a DC (Direct Current) component in a time domain. In addition, the reason for inserting null data into 28 subcarriers of the −128th to −101st subcarriers and 27 subcarriers of the 101st to 127th subcarriers is to provide a guard interval in a frequency domain because the 28 subcarriers of the −128th to −101st subcarriers and the 27 subcarriers of the 101st to 127th subcarriers correspond to a high frequency band in the frequency domain.
As a result, if a frequency-domain preamble sequence of S(−100:100) or P(−100:100) is applied to an IFFT processor, the IFFT processor maps the frequency-domain preamble sequence of S(−100:100) or P(−100:100) to corresponding subcarriers, IFFT-transforms the mapped preamble sequence, and outputs a time-domain preamble sequence.
FIG. 4 is a block diagram schematically illustrating a structure of a transmitter in a conventional OFDM communication system. Referring to FIG. 4, if information bits to be transmitted are generated, the information bits are applied to a symbol mapper 411. The symbol mapper 411 symbol-maps the input information bits by a preset modulation scheme, and then provides the symbol-mapped bits to a serial-to-parallel (S/P) converter 413. Here, quadrature phase shift keying (QPSK) or 16-ary quadrature amplitude modulation (16QAM) can be used for the modulation scheme. The serial-to-parallel converter 413 parallel-converts symbols received from the symbol mapper 411 so that the number of the received symbols is matched to an A-point, which is the number of inputs of an inverse fast Fourier transformer (IFFT processor) 419, and then provides the parallel-converted symbols to a selector 417. A preamble sequence generator 415, under the control of a controller (not shown), generates a corresponding preamble sequence and provides the generated preamble sequence to the selector 417. The selector 417 selects a signal output from the serial-to-parallel converter 413 or a signal output from the preamble sequence generator 415 according to scheduling at a corresponding time, and provides the selected signal to the IFFT processor 419.
The IFFT processor 419 performs A-point IFFT on a signal output from the selector 417, and provides its output to a parallel-to-serial (P/S) converter 421. In addition to the signal output from the IFFT processor 419, a cyclic prefix with a length L is applied to the parallel-to-serial converter 421. The parallel-to-serial converter 421 serial-converts the signal output from the IFFT processor 419 and the cyclic prefix, and provides its output to a digital-to-analog (D/A) converter 423. The digital-to-analog converter 423 analog-converts a signal output from the parallel-to-serial converter 421, and provides the analog-converted signal to a radio frequency (RF) processor 425. The RF processor 425, which includes a filter and a front-end unit, RF-processes a signal output from the digital-to-analog converter 423 so that it can be transmitted over the air. The RF signal is then transmitted via an antenna.
A description will be made herein below of disadvantages of a preamble sequence used in a conventional OFDM communication system, and a method for generating the preamble sequence.
(1) In the existing OFDM communication system, a full search method must be used in order to acquire a preamble sequence having a minimal PAPR. Additionally, the full search method has an undesirably long processing time.
For example, assuming that in the OFDM communication system, a length of a preamble sequence is X and the number of types of values that elements of the preamble sequence can have is Y, if the full search is performed in order to generate a preamble sequence having the minimum PAPR, the search must be performed YX times. For example, if Y=2 and X=100, the search must be performed 2100 times in order to acquire a preamble sequence having the minimal PAPR. However, the number of 2100 operations is a very large number, and is a huge load on the OFDM communication system.
(2) There is a method for generating a preamble sequence using a Golay complementary sequence as a method for generating a preamble sequence not using the full search method in the existing OFDM communication system. When a preamble sequence is generated using the Golay complementary sequence, a preamble sequence having a minimum PAPR is generated within a relatively short time, compared with when a preamble sequence is generated using the full search method. Further, when a preamble sequence is generated using the Golay complementary sequence, it is advantageous in that a preamble sequence having a minimum PAPR is generated within a relatively short time. However, because the preamble sequence is generated using the Golay complementary sequence, it is disadvantageous in that a length of the preamble sequence is limited to 2α10β26γ (where α, β, γ≧0). Here, the reason that the length of the preamble sequence is limited to 2α10β26γ is caused by a characteristic of the Golay complementary sequence. Because a length of the Golay complementary sequence is limited to 2α10β26γ, a length of a preamble sequence generated using the Golay complementary sequence is also limited to 2α10β26γ. Therefore, when a length limit condition of the Golay complementary sequence does not satisfy a length of a preamble sequence needed in the OFDM communication system, the preamble sequence cannot be used.
In order to solve such problems, there is a demand for a method for generating a preamble sequence having a minimum PAPR with a minimized number of operations within a short time. In addition, there is a demand for a method for generating a preamble sequence capable of satisfying a length of a preamble sequence needed in the OFDM communication system.
SUMMARY OF THE INVENTION
It is, therefore, an object of the present invention to provide an apparatus and method for generating a preamble sequence in an OFDM communication system.
It is another object of the present invention to provide an apparatus and method for generating a preamble sequence having a minimum PAPR in an OFDM communication system.
It is further another object of the present invention to provide an apparatus and method for generating a preamble sequence for minimizing a number of operations in an OFDM communication system.
It is still another object of the present invention to provide an apparatus and method for generating a preamble sequence using a complex Golay complementary sequence in an OFDM communication system.
It is still another object of the present invention to provide an apparatus and method for generating a preamble sequence, the length of which is not limited, using a complex Golay complementary sequence in an OFDM communication system.
The above and other objects are achieved by providing an apparatus for generating a preamble sequence in an orthogonal frequency division multiplexing (OFDM) communication system using A subcarriers in a frequency domain. In the apparatus, a preamble sequence generator generates a length−M+N+k preamble sequence, where M+N+k is less than A, by combining a length−N Golay complementary sequence with a length−M Golay complementary sequence. An inverse fast Fourier transform (IFFT) processor assigns elements constituting the preamble sequence to the M+N+k subcarriers among the A subcarriers on a one-to-one mapping basis, assigns null data to remaining subcarriers excluding the M+N+k subcarriers from the A subcarriers, and then IFFT-transforms the assigned result into time-domain data.
Additionally, the above and other objects are achieved by providing a method for generating a preamble sequence in an orthogonal frequency division multiplexing (OFDM) communication system using A subcarriers in a frequency domain. The method comprises: generating a length−M+N+k preamble sequence, where M+N+k is less than A, by combining a length−N Golay complementary sequence with a length−M Golay complementary sequence; and assigning elements constituting the preamble sequence to the M+N+k subcarriers among the A subcarriers on a one-to-one mapping basis, assigning null data to remaining subcarriers excluding the M+N+k subcarriers from the A subcarriers, and then IFFT (Inverse Fast Fourier Transform)-transforming the assigned result into time-domain data.



BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects, features, and advantages of the present invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which:
FIG. 1 is a diagram illustrating a structure of a long preamble sequence for a conventional OFDM communication system;
FIG. 2 is a diagram illustrating a structure of a short preamble sequence for a conventional OFDM communication system;
FIG. 3 is a diagram illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in a conventional OFDM communication system;
FIG. 4 is a block diagram schematically illustrating a structure of a transmitter in an OFDM communication system;
FIG. 5 is a block diagram illustrating a structure of a preamble sequence generator according to an embodiment of the present invention;
FIG. 6 is a block diagram illustrating a structure of a complex Golay complementary sequence generation apparatus according to an embodiment of the present invention;
FIG. 7 is a diagram schematically illustrating a rule for mapping a complex Golay complementary sequence to an IFFT processor's input terminal according to an embodiment of the present invention;
FIG. 8 is a diagram schematically illustrating a rule for mapping a length−104 complex Golay complementary sequence to a 256-point IF=f processor's input terminal according to an embodiment of the present invention;
FIG. 9 is a block diagram illustrating a structure of the Golay complementary sequence pair generator 611 as illustrated in FIG. 6;
FIG. 10 is a block diagram illustrating a structure of a length−52 Golay complementary sequence pair generator;
FIG. 11 is a diagram schematically illustrating a complex Golay complementary sequence pair combing rule according to an embodiment of the present invention;
FIG. 12 is a diagram schematically illustrating a procedure for generating a length−104 complex Golay complementary sequence pair [E,F,G,H] by combining a length−52 Golay complementary sequence pair [A,B] with a length−52 Golay complementary sequence pair [C,D];
FIG. 13 is a block diagram illustrating a structure of the Golay complementary sequence conjugate pair generator 915 as illustrated in FIG. 9;
FIG. 14 is a block diagram schematically illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in an OFDM communication system according an embodiment of the present invention;
FIG. 15 is a block diagram schematically illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in an OFDM communication system having 256 subcarriers; and
FIG. 16 is a flowchart illustrating a preamble sequence mapping procedure according to an embodiment of the present invention.



DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
Several preferred embodiments of the present invention will now be described in detail herein below with reference to the annexed drawings. In the following description, a detailed description of known functions and configurations incorporated herein has been omitted for conciseness.
The present invention provides an apparatus and method for generating a preamble sequence having a minimum peak-to-average power ratio (PAPR) in an orthogonal frequency division multiplexing (OFDM) communication system in which a total number of subcarriers is A and unique numbers of subcarriers actually in use are −B, −B+1, . . . , −1, 1, . . . , B−1, B. In the OFDM communication system, although the total number of subcarriers is A, the number of subcarriers into which a preamble sequence is actually inserted becomes 2B, because null data, or 0-data, is inserted into a 0th subcarrier indicating a DC component in a time domain and subcarriers (−Ath to (−B−1)th subcarriers and (B+1)th to (A−1)th subcarriers) indicating a high frequency band in a frequency domain, i.e., a guard interval in a time domain, as described in the related art section. In addition, a preamble sequence proposed in the present invention has no limitation in its length because it is generated using a Golay complementary sequence and a complex Golay complementary sequence.
As described above, the preamble sequence is classified into a long preamble sequence and a short preamble sequence. In the long preamble sequence, a length-A/4 sequence is repeated 4 times and a length-A/2 sequence is repeated 2 times, and according to a characteristic of the OFDM communication system, a cyclic prefix (CP) is added to a front end of the 4 repeated length-A/4 sequences and a front end of the 2 repeated length-A/2 sequences. Here, A represents the number of points, or inputs, of inverse fast Fourier transform (IFFT). For example, if it is assumed that the IFFT has 256 points (256-point IFFT), in the long preamble sequence, a length−256/4=64 sequence is repeated 4 times and a length−256/2=128 sequence is repeated 2 times. Further, in the short preamble sequence, a length-A/2 sequence is repeated 2 times, and according to a characteristic of the OFDM communication system, the cyclic prefix (CP) is added to a front end of the 2 repeated length-A/2 sequences as described in the related art section.
In an OFDM communication system in which information symbols are transmitted after being IFFT-transformed, if a Golay complementary sequence is applied to all input terminals, i.e., all subcarriers, before performing the IFFT, then the information symbols after performing the IFFT have a minimum PAPR according to a characteristic of the Golay complementary sequence. Here, the Golay complementary sequence represents a sequence in which the sum of an aperiodic autocorrelation function for all intervals of a particular sequence and an aperiodic autocorrelation function for the same interval of a complementary sequence becomes 0. That is, the Golay complementary sequence can be expressed as follows:



  
    
      
        
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CA(u) and CB(u) satisfying the above condition become a Golay complementary sequence pair. That is, two sequences constitute one Golay complementary sequence pair
The complex Golay complementary sequence represents a sequence in which the sum of an aperiodic autocorrelation function for all intervals of a particular sequence and an aperiodic autocorrelation function for the same interval of three complementary sequences becomes 0. That is, the complex Golay complementary sequence can be expressed as follows:



  
    
      
        
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A pair [A,B,C,D] satisfying the above condition becomes a complex Golay complementary sequence pair. That is, four sequences constitute one complex Golay complementary sequence.
For example, if an IFFT processor is a 256-point IFFT processor, a length−256 complex Golay complementary sequence is applied to an input terminal of the IFFT processor, and the elements making up the length−256 complex Golay complementary sequence are matched with 256 corresponding points of the IFFT processor. That is, IFFT, is performed in such a manner that 256 subcarriers of −128th subcarrier to 127th subcarrier are mapped to 256 elements constituting the complex Golay complementary sequence on a one-to-one basis.
However, in an actual OFDM communication system, null data must be inserted into a subcarrier corresponding to a DC component, i.e., 0th subcarrier, and subcarriers corresponding to a guard interval component. Therefore, it is impossible to insert respective elements constituting the complex Golay complementary sequence into all subcarriers on the IFFT processor's input terminal on a one-to-one mapping basis. Because it is impossible to insert the complex Golay complementary sequence into the IFFT processor's input terminal on a one-to-one basis, the present invention proposes a rule for inserting the complex Golay complementary sequence into the IFFT processor's input terminal by mapping, thereby making the best use of a characteristic of the OFDM communication system.
1. Complex Golay Complementary Sequence Mapping Rule
If respective elements constituting a complex Golay complementary sequence are inserted into specific subcarriers on an IFFT processor's input terminal to maintain a specific interval between the respective elements of the complex Golay complementary sequence and then null data is inserted in the remaining subcarriers into which the elements constituting the complex Golay complementary sequence are not inserted, after performing IFFT, their outputs have a PAPR less than 6|dB|. For example, if a specific interval at which complex Golay complementary sequence elements are inserted into the IFFT processor's input terminal is 1, respective elements constituting the complex Golay complementary sequence are mapped to subcarriers on the IFFT processor's input terminal on a one-to-one basis and then sequentially inserted into the IFFT processor's input terminal. That is, if the specific interval is 1 when a length-256 complex Golay complementary sequence is inserted into a 256-point IFFT processor, 256 elements of the complex Golay complementary sequence are inserted into 256 subcarriers of the IFFT processor, respectively.
However, in the OFDM communication system, null data should always be inserted into subcarriers corresponding to a DC component and a guard interval component in a high frequency band. Therefore, if a length of the complex Golay complementary sequence exceeds 1⁄2 of the number of the remaining subcarriers excluding the subcarriers corresponding to the DC component and the guard interval component from all the subcarriers, it is impossible to continuously insert respective elements constituting the complex Golay complementary sequence into the IFFT processor's input terminal.
As another example, if the specific interval is 2, there is provided a structure in which respective elements constituting the complex Golay complementary sequence are inserted into the subcarriers on the IFFT processor's input terminal every other subcarrier. In addition, null data is inserted into all of the remaining subcarriers into which elements of the complex Golay complementary sequence are not inserted. Here, if a subcarrier corresponding to a DC component exists in a position other than in positions of the subcarriers in which the elements of the complex Golay complementary sequence are inserted, the Golay complementary sequence can be sequentially arranged on the IFFT processor's input terminal at regular intervals. As a result, after performing the IFFT, an output has a PAPR less than 6 [dB].
A description will now be made of a method of inserting elements constituting a short preamble sequence into positions of −100th to 100th subcarriers on a 256-point IFFT processor's input terminal at every other subcarrier. Because null data must be inserted into a DC component, i.e., a 0th subcarrier on the IFFT processor's input terminal, it is impossible that data of +1 or −1, not null data, is inserted in the IFFT processor's input terminal at regular intervals. That is, because a start position at which elements constituting the short preamble sequence are inserted is a −100th subcarrier, elements of the short preamble sequence are actually mapped even to the 0th subcarrier when elements of the short preamble sequence are inserted every other subcarrier. However, when elements constituting the short preamble sequence are inserted at every other subcarrier beginning at a −99th subcarrier on the 256-point IFFT processor's input terminal, elements of the short preamble sequence are not mapped to the 0th subcarrier. As a result, it is possible to insert all elements of the short preamble sequence into the IFFT processor's input terminal at regular intervals without mapping an element of the short preamble sequence to the 0th subcarrier, so that a length−100 complementary Golay complementary sequence is inserted into the 256-point IFFT processor's input terminal as follows:

[−99,−97, . . . ,−3,−1,1,3, . . . ,97,99]

If null data is inserted in the remaining subcarriers other than the subcarriers identified by [−99, −97, . . . , −3, −1,1,3, . . . ,97,99], i.e., a 0th subcarrier, −128th to −100th subcarriers, and 100th to 127th subcarriers, then a PAPR after performing IFFT becomes less than 6 [dB].
The present invention generates a preamble sequence using the Complex Golay Complementary Sequence Mapping Rule as described above. In addition, the present invention proposes a method for generating a length−104 complex Golay complementary sequence for supporting the Complex Golay Complementary Sequence Mapping Rule. In the forgoing description, the Complex Golay Complementary Sequence Mapping Rule has been described for a short preamble sequence with reference to a length−104 complex Golay complementary sequence. However, a preamble sequence used in the OFDM communication system can have a length other than the length 104.
FIG. 7 is a diagram schematically illustrating a rule for mapping a complex Golay complementary sequence to an IFFT processor's input terminal according to an embodiment of the present invention. It is assumed in FIG. 7 that in an OFDM communication system in which the number of subcarriers on an IFFT processor's input terminal is A, data is inserted into only the subcarriers identified by [−B, −(B−1), . . . ,−1,1, . . . , B−1,B], null data is inserted into the remaining subcarriers, and a specific interval at which a Golay complementary sequence is inserted is I (where I≧2).
In this case, B=Ik+D (where 0≦D≦I−1). Thus, constituent elements of the complex Golay complementary sequence are inserted in the subcarriers identified by [−(B−E),−(B−E−I), . . . ,B−F−I,B−F] on the IFFT processor's input terminal, and null data is inserted in the other subcarriers. The parameters D, E, and F will be described herein below.
When B is a multiple of I, i.e., when B=Ik, if subcarrier mapping of the IFFT processor's input terminal begins at a −Bth subcarrier, a value of +1 or −1, not null data, should be necessarily inserted in a 0th subcarrier. For B=Ik, because null data is inserted into the 0th subcarrier, it is impossible to map the complex Golay complementary sequence to a preamble sequence. In order to prevent null data from being inserted into the 0th subcarrier, B for determining a position on the IFFT processor's input terminal, at which insertion of respective elements of the complex Golay complementary sequence is started, is set to Ik+D. Here, if 0≦D≦(I−1), all integers B can be included. In addition, a parameter E is defined in order to prevent a value of +1 or −1, not null data, from being mapped to the 0th subcarrier. Moreover, a parameter F is defined in order to match a mapping relation for inserting the last part of the complex Golay complementary sequence.
If the complex Golay complementary sequence is represented by J and a preamble sequence output after performing IFFT on the complex Golay complementary sequence J is represented by L, then a complex Golay complementary sequence mapping rule is given by Equation (1).




  
    
      
        
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In Equation (1), GPM(n) is an index function, wherein n in GPM(n) represents an index of elements constituting a complex Golay complementary sequence. A result value of the GPM(n) represents an index of elements constituting a preamble sequence. The GPM(n) is defined in Equation (2).

GPM(n)=−(B−E−nI)  (2)

In Equation (2), −B≦i≦B, and 0≦n≦(M+N+k−1). That is, the parameter i has a value of −B, −(B−1), . . . , −1, 1, . . . ,B−1, B, and if there is n satisfying i=FPM(n), J(n) is inserted in a corresponding subcarrier on an input terminal of an IFFT processor. If there is no n satisfying i=GPM(n), null data is inserted into a corresponding subcarrier on the input terminal of the IFFT processor. The parameter k is an integer, which is larger than or equal to a smaller one of −N and −M, i.e., an integer satisfying k≧min(−N,−M). A relation between the parameters D, E, and F will be described herein below, considering a situation where data of +1 or −1 should not be inserted into a 0th subcarrier indicating a DC component and respective elements of the complex Golay complementary sequence are inserted into subcarriers on an IFFT processor's input terminal at regular intervals as described above.
(1) For D=0, the parameters are set so that E=1, 2, . . . , I−1 and F=I−E.
When D=E=0, data of +1 or −1, not null data, is inserted into the0th subcarrier on the IFFT processor's input terminal.
(2) For D=1, . . . , I−1, the parameters are set so that E=0, . . . , I−1 (D+E≠F) and F=((B−F) mod I=D+E) (where 0≦F≦I−1).
This prevents data of +1 or −1, not null data, from being inserted into the 0th subcarrier.
A description of FIG. 7 has been made for the situation in which in an A-point IFFT processor, −Bth, −(B−1)th, . . . , 1st, 1st, . . . , (B−1)th, Bth subcarriers are actually used, a length of a complex Golay complementary sequence is M+N+k, and the complex Golay complementary sequence elements are mapped to the IFFT processor's input terminal at intervals of I. An operation of actually mapping the complex Golay complementary sequence to the seer processor's input for mapping of a preamble sequence is performed by a complex Golay complementary sequence/preamble sequence mapper 710, and the connection between the complex Golay complementary sequence/preamble sequence mapper 710 and other hardware structures will be described herein below.
FIG. 8 is a diagram schematically illustrating a rule for mapping a length−104 complex Golay complementary sequence to a 256-point IFFT processor's input terminal according to an embodiment of the present invention. It is assumed in FIG. 8 that in the Complex Golay Complementary Sequence Mapping Rule described in FIG. 7, a point value A of the IFFT processor is 256, an integer B for determining a subcarrier position where mapping of the complex Golay complementary sequence is actually started is 104, and a specific interval I at which elements of the complex Golay complementary sequence are inserted is 2.
In this case, D=0 by the Complex Golay Complementary Sequence Mapping Rule described in FIG. 7, and because D=0, the parameters are set such that E=1 and F=I−E=2−1=1. The index function GPM(n) becomes GPM(n)=−(103−2n) (where 0≦n≦103), so that elements of the length−104 complex Golay complementary sequence are mapped to subcarriers corresponding to indexes [−103, −101, −99, −97 . . . , −1, 1, . . . , 97, 99, 101, 103] among the elements constituting a preamble sequence, i.e., subcarriers corresponding to [−103, −101, −99, −97, . . . , −1, 1, . . . , 97, 99, 101, 103] among 256 subcarriers on an IFFT processor's input terminal. Null data is inserted into the remaining subcarriers to which the complex Golay complementary sequence is not mapped.
FIG. 6 is a block diagram illustrating a structure of a complex Golay complementary sequence generation apparatus according to an embodiment of the present invention. FIG. 6 proposes a method for generating a length−M+N+k complex Golay complementary sequence. Parameters A, B, C, D, E, F, G, and H used in describing the method and method for generating a length−M+N+k complex Golay complementary sequence represent parameters being substantially different from the parameters described in FIGS. 7 and 8. That is, the parameters A, B, C, and D represent Golay complementary sequences, and the parameters E, F, G, and H represent complex Golay complementary sequences. Here, M and N are integers satisfying a condition of 2α10β26γ, where α, β, γ≧0, and k is an integer being larger than a smaller one of −M and −N.
Referring to FIG. 6, a Golay complementary sequence pair generator 611 receives a parameter pNum0 and a parameter seed0 from a controller (not shown), and generates a length−N Golay complementary sequence pair [A,B] according to the pNum0 and seed0. The parameter pNum0 is an integer between 0 and K−1. The parameter K represents the number of length−N primitive Golay complementary sequence pairs. Therefore, the parameter pNum0 is a parameter for selecting a primitive Golay complementary sequence pair to be used among the K primitive Golay complementary sequence pairs. Further, the parameter K is different from the above-stated parameter k representing an integer larger than a smaller one of −M and −N. The parameter seed0 is an integer between 0 and 63 and is a parameter for selecting a conjugate pair of the primitive Golay complementary sequence pair. The parameter seed0 is an integer between 0 and 63 because a Golay complementary sequence pair has 64 conjugate pairs. The primitive Golay complementary sequence pair is a Golay complementary sequence pair that cannot be generated through combining of Golay complementary sequence pairs, which are shorter in length than the primitive Golay complementary sequence. A procedure for actually generating the Golay complementary sequence pair by the Golay complementary sequence pair generator 611 will be described in detail with reference to FIG. 9.
A Golay complementary sequence pair generator 613 receives a parameter pNum1 and a parameter seed1, and generates a length−M Golay complementary sequence pair [C,D] according to the pNum1 and seed1. The parameter pNum1 is an integer between 0 and L−1. The parameter L represents the number of length−M primitive Golay complementary sequence pairs. Therefore, the parameter pNum1 is a parameter for selecting a conjugate pair of a length−M primitive Golay complementary sequence pair.
A complex Golay complementary sequence pair combiner 615 combines the length−N Golay complementary sequence pair [A,B] generated from the Golay complementary sequence pair generator 611 with the length−M Golay complementary sequence pair [C,D] generated from the Golay complementary sequence pair generator 613 according to a complex Golay complementary sequence pair combining rule provided from the controller, and generates a length−M+N+k complex Golay complementary sequence pair [E,F,G,H]. The complex Golay complementary sequence pair combing rule will be described in more detail herein below with reference to FIG. 11.
Finally, a selector 617 receives a select signal from the controller, and selects one of the complex Golay complementary sequence pairs [E,F,G,H] output from the complex Golay complementary sequence pair combiner 615 according to the provided select signal, and outputs a final length−M+N+k complex Golay complementary sequence J. The select signal is an integer between 0 and 3, and the selector 617 selects E for the select signal=0, F for the select signal=1, G for the select signal=2, and H for the select signal=3, and outputs the selected signal as the complex Golay complementary sequence J.
FIG. 5 is a block diagram illustrating a structure of a preamble sequence generator according to an embodiment of the present invention. Referring to FIG. 5, a preamble sequence generator comprises a complex Golay complementary sequence generator 511, a complex Golay complementary sequence/preamble sequence mapper 513, and a selector 515. The complex Golay complementary sequence generator 511 receives parameters pNum0, pNum1, seed0, seed1, and a select signal, and generates a length−M+N+k complex Golay complementary sequence J(0:(M+N+k−1)) using the received parameters pNum0, pNum1, seed0, and seed1, and the received select signal.
A procedure for actually generating a complex Golay complementary sequence by the complex Golay complementary sequence generator 511 has already been described above with reference to FIG. 6. Therefore, a detailed description thereof will be omitted here.
The length−M+N+k complex Golay complementary sequence J(0:(M+N+k−1)) generated from the complex Golay complementary sequence generator 511 is applied to the complex Golay complementary sequence/preamble sequence mapper 513, and the complex Golay complementary sequence/preamble sequence mapper 513 generates a preamble sequence corresponding to an IFFT processor's input using the length−M+N+k complex Golay complementary sequence J(0:(M+N+k−1)) and a parameter‘interval’ provided from a controller. Here, Sg represents a sequence inserted in a leading preamble sequence of a long preamble sequence, Pg represents a sequence inserted in a short preamble sequence, and B represents the same value as the B of FIG. 7.
Although FIG. 5 has been described while assuming that the parameter ‘interval’ is set to 2 or 4, a value of the ‘interval’ can be varied according to circumstances. Here, Sg(−B,B) is generated for the parameter ‘interval’=4, and Pg(−B,B) is generated for the parameter ‘interval’=2.
Additionally, an operation of the complex Golay complementary sequence/preamble sequence mapper 513 has been described with reference to FIG. 7. Therefore, a detailed description thereof will be omitted at this time.
The Sg(−B:B) or Pg(−B:B) output from the complex Golay complementary sequence/preamble sequence mapper 513 is applied to the selector 515, and the selector 515 selects the Sg(−B:B) or the Pg(−B:B) as a preamble sequence according to circumstances.
FIG. 9 is a block diagram illustrating a structure of the Golay complementary sequence pair generator 611 as illustrated in FIG. 6. Referring to FIG. 9, if it is assumed that the number of length−N primitive Golay complementary sequence pairs 911 is K, a parameter pNum0 is an integer of 0 to K−1. The parameter pNum0 is applied to a selector 913. The selector 913 selects a length−N primitive Golay complementary sequence pair [T0,T0C] among the length−N primitive Golay complementary sequence pairs 911, using the parameter pNum0, and provides the selected length−N primitive Golay complementary sequence pair [T0,T0C] to a Golay complementary sequence conjugate pair generator 915. The Golay complementary sequence conjugate pair generator 915 generates a Golay complementary sequence conjugate pair [A,B] by receiving the length−N primitive Golay complementary sequence pair [T0,T0C] output from the selector 913 and a parameter seed0 provided from the controller.
FIG. 10 is a block diagram illustrating a structure of a length−52 Golay complementary sequence pair generator. Referring to FIG. 10, there is one length−52 primitive Golay complementary sequence pair 1011, which is as follows:



  
    
      
        
          
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Because there is one length−52 primitive Golay complementary sequence pair 1011, the parameter pNum0 is 0, and a selector 1013 selects a primitive Golay complementary sequence pair and outputs the selected primitive Golay complementary sequence pair [T0,T0C]. A Golay complementary sequence conjugate pair generator 1015 generates a Golay complementary sequence conjugate pair [A,B] using the sequence pair [T0,T0C] output from the selector 1013 and a parameter seed0 provided from the controller.
2. Complex Golay Complementary Sequence Pair Combing Rule
FIG. 11 is a diagram schematically illustrating a complex Golay complementary sequence pair combing rule according to an embodiment of the present invention. Referring to FIG. 11, the complex Golay complementary sequence pair combiner 615, which is illustrated in FIG. 6, combines a length−M+N+k Golay complementary sequence pair according to a complex Golay complementary sequence pair combing rule. The complex Golay complementary sequence pair combing rule is as follows:



  
    
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In the complex Golay complementary sequence pair combing rule, ai and bi represent elements constituting a length−N Golay complementary sequence pair [A,B], ci and di represent elements constituting a length−M Golay complementary sequence pair [C,D], and ei, fi, gi, and hi represent elements constituting a length−M+N+k complex Golay complementary sequence pair [E,F,G,H]. Here, the parameter ‘i’ satisfies a condition of Equation (3) below.

0≦i≦M+N+k  (3)

As a result, in the complex Golay complementary sequence generation apparatus illustrated in FIG. 6, if the controller assigns a parameter ‘i’ according to the Complex Golay Complementary Sequence Pair Combining Rule, the complex Golay complementary sequence pair combiner 615 generates a length−M+N+k complex Golay complementary sequence pair [E,F,G,H] by combining a length−N Golay complementary sequence pair [A,B] with a length−M Golay complementary sequence pair [C,D].
3. Length−104 Complex Golay Complementary Sequence Pair Combining Rule
FIG. 12 is a diagram schematically illustrating a procedure for generating a length−104 complex Golay complementary sequence pair [E,F,G,H] by combining a length−52 Golay complementary sequence pair [A,B] with a length−52 Golay complementary sequence pair [C,D]. Referring to FIG. 12, the complex Golay complementary sequence pair combiner 615, which was described in conjunction with FIG. 6, generates a length−104 complex Golay complementary sequence pair [E,F,G,H] according to the Complex Golay Complementary Sequence Pair Combining Rule from the controller. The Length−104 Complex Golay Complementary Sequence Pair Combining Rule will be described herein below.



  
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In the Length−104 Complex Golay Complementary Sequence Pair Combining Rule, ai and bi represent elements constituting a length−52 Golay complementary sequence pair [A,B], ci and di represent elements constituting a length−52 Golay complementary sequence pair [C,D], and ei, fi, gi, and hi represent elements constituting a length−52+52+0=104 complex Golay complementary sequence pair [E,F,G,H].
FIG. 13 is a block diagram illustrating a structure of the Golay complementary sequence conjugate pair generator 915 as illustrated in FIG. 9. Referring to FIG. 13, the Golay complementary sequence conjugate pair generator 915 is provided with a parameter ‘seed’ for selecting a conjugate pair of a primitive Golay complementary sequence pair from the controller, and generates a Golay complementary sequence conjugate pair according to the provided parameter ‘seed’. A procedure for actually generating a Golay complementary sequence conjugate pair according to the parameter ‘seed’ by the Golay complementary sequence conjugate pair generator 915 will be described in more detail herein below.
The parameter ‘seed’ is applied to a binary converter 1311, which converts the parameter ‘seed’ into a binary number. Here, because there are 64 Golay complementary sequence conjugate pairs, the parameter ‘seed’ is an integer of 0 to 63. Accordingly, the binary converter 1311 converts the parameter ‘seed’ into a 6-digit binary number, and each of the converted 6 binary digits will be represented by bseed[n]. That is, bseed[0] represents a value of a digit corresponding to 20 in the 6-digit binary number, bseed[1] represents a value of a digit corresponding to 21 in the 6-digit binary number, bseed[2] represents a value of a digit corresponding to 22 in the 6-digit binary number, bseed[3] represents a value of a digit corresponding to 23 in the 6-digit binary number, bseed[4] represents a value of a digit corresponding to 24 in the 6-digit binary number, and bseed[5] represents a value of a digit corresponding to 25 in the 6-digit binary number. For example, if the parameter ‘seed’ is 3, then bseed[5]=0, bseed[4]=0, bseed[3]=0, bseed[2]=0, bseed[1]=1, and bseed[0]=1.
In this way, the binary converter 1311 binary-converts the parameter ‘seed’ and outputs bseed[5], bseed[4], bseed[3], bseed[2], bseed[l], and bseed[0]. The bseed[5], bseed[4], bseed[3], bseed[2], bseed[l], and bseed[0] are applied to a Golay complementary sequence pair converter 1313, a first sequence's order converter 1315, a second sequence's order converter 1317, a first sequence's sign converter 1319, a second sequence's sign converter 1321, and a Golay complementary sequence pair's odd sign converter 1323, respectively.
A length−N primitive Golay complementary sequence pair [T0,T0C] is applied to the Golay complementary sequence pair converter 1313. If bseed[5] output from the binary converter 1311 is 1, the Golay complementary sequence pair converter 1313 converts order of the length−N primitive Golay complementary sequence pair [T0,T0C] into [T0C,T0], and outputs [T1,T1C]. Here, the [T1,T1C] represents a Golay complementary sequence output from the Golay complementary sequence pair converter 1313. However, if bseed[5] output from the binary converter 1311 is 0, the Golay complementary sequence pair converter 1313 outputs [T1,T1C], without converting the order of the length−N primitive Golay complementary sequence pair [T0,T0C].
The [T1,T1C] output from the Golay complementary sequence pair converter 1313 is applied to the first sequence's order converter 1315. If bseed[4] output from the binary converter 1311 is 1, the first sequence's order converter 1315 converts order of a first sequence T1 of the [T1,T1C] to generate it as T2, and generates T1 as T2C, without order conversion. However, if bseed[4] output from the binary converter 1311 is 0, the first sequence's order converter 1315 generates [T1,T1C] as [T2,T2C], without order conversion.
The [T2,T2C] output from the first sequence's order converter 1315 is applied to the second sequence's order converter 1317. If bseed[3] output from the binary converter 1311 is 1, the second sequence's order converter 1317 converts order of a second sequence T2C of the [T2,T2C] to generate it as T3C, and generates T2 as T3, without order conversion. However, if bseed[3] output from the binary converter 1311 is 0, the second sequence's order converter 1317 generates [T2,T2C] as [T3,T3C], without order conversion.
The [T3,T3C] output from the second sequence's order converter 1317 is applied to the first sequence's sign converter 1319. If bseed[2] output from the binary converter 1311 is 1, the first sequence's sign converter 1319 converts a sign of a first sequence T3 of the [T3,T3C] to generate it as T4, and generates T3 as T4, without sign conversion. However, if bseed[2] output from the binary converter 1311 is 0, the first sequence's sign converter 1319 generates [T3,T3C] as [T4,T4C], without sign conversion.
The [T4,T4C] output from the first sequence's sign converter 1319 is applied to the second sequence's sign converter 1321. If bseed[1] output from the binary converter 1311 is 1, the second sequence's sign converter 1321 converts a sign of a second sequence T4C of the [T4,T4C] to generate it as T5C, and generates T4 as T5, without sign conversion. However, if bseed[1] output from the binary converter 1311 is 0, the second sequence's sign converter 1321 generates [T4,T4C] as [T5,T5C], without sign conversion.
The [T5,T5C] output from the second sequence's sign converter 1321 is applied to the Golay complementary sequence pair's odd sign converter 1323. If bseed[0] output from the binary converter 1311 is 1, the Golay complementary sequence pair's odd sign converter 1323 converts a sign of odd constituent elements of the two sequences T5 and T5C of the [T5,T5C] to generate T6 and T6C. However, if bseed[0] output from the binary converter 1311 is 0, the Golay complementary sequence pair's odd sign converter 1323 generates [T5,T5C] as [T6,T6C], without sign conversion.
As a result, the [T6,T6C] output from the Golay complementary sequence pair's odd sign converter 1323 becomes an output of the Golay complementary sequence conjugate pair generator 915. Also, all of the sequences generated by sequence conversion by the Golay complementary sequence pair converter 1313, the first sequence's order converter 1315, the second sequence's order converter 1317, the first sequence's sign converter 1319, the second sequence's sign converter 1321, and the Golay complementary sequence pair's odd sign converter 1323 have a characteristic of a Golay complementary sequence pair. Therefore, it is possible to generate 64 Golay complementary sequence conjugate pairs using the characteristic of the Golay complementary sequence pair.
FIG. 14 is a block diagram schematically illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in an OFDM communication system according an embodiment of the present invention. It is assumed in FIG. 14 that the total number of subcarriers of the OFDM communication system is A and unique numbers of subcarriers actually in use among the A subcarriers are [−B, −B+1, . . . , −1, 1, . . . , B−1, B]. In FIG. 14, numerals at an IFFT processor's input terminal represent unique numbers of subcarriers in the OFDM communication system.
As described above, null data is inserted into a 0th subcarrier because the 0th subcarrier, after performing IFFT, represents a reference point of a preamble sequence in a time domain, i.e., represents a DC component in a time domain. In addition, null data is also inserted into −(A/2)th to −(B+1)th subcarriers and (B+1)th to (A/2−1)th subcarriers, excluding the 2B subcarriers actually in use and the 0th subcarrier. Null data is inserted into the −(A/2)th to −(B+1)th subcarriers and the (B+1)th to (A/2−1)th subcarriers because the −(A/2)th to −(B+1)th subcarriers and the (B+1)th to (A/2−1)th subcarriers correspond to a guard interval. Therefore, if the frequency-domain preamble sequence Sg(−B:B) or Pg(−B:B) is applied to the IFFT processor, the IFFT processor performs IFFT after mapping the received frequency-domain preamble sequence Sg(−B:B) or Pg(−B:B) to corresponding subcarriers, and outputs a time-domain preamble sequence. The Sg(−B:B) is applied to the IFFT processor for a leading preamble sequence period in a long preamble period, while the Pg(−B:B) is applied to the IFFT processor for a short preamble sequence period.
FIG. 15 is a block diagram schematically illustrating a mapping relation between subcarriers and a preamble sequence during IFFT processing in an OFDM communication system having 256 subcarriers. It is assumed in FIG. 15 that there are 256 subcarriers of −128th to 127th subcarriers, and the number of subcarriers actually in use is 208, including −104th, . . . , −1st, 1st, . . . , 104th subcarriers. As described in conjunction with FIG. 14, because a 0th subcarrier functions as a DC component and −128th to −105th subcarriers and 105th to 127th subcarriers function as a guard interval, null data is inserted therein. Thus, a frequency-domain preamble sequence Sg(−104:104) or Pg(−104:104) is inserted into an input terminal of an IFFT processor, and the IFFT processor performs IFFT on the received Sg(−104:104) or Pg(−104:104) and outputs a time-domain preamble sequence. The Sg(−104:104) is inserted into the input terminal of the IFFT processor for a leading preamble sequence period in a long preamble period, and the Pg(−104:104) is inserted into the input terminal of the IFFT processor for a short preamble sequence period.
The Sg(−104:104) or Pg(−104:104) is generated by the preamble sequence generator as illustrated in FIG. 5. The present invention has been described while assuming that the preamble sequence generator generates the Pg(−104:104). All preamble sequences generated by the preamble sequence generator have a PAPR less than 6 [dB], and the lowest PAPR is 2.8666 [dB] among PAPRs of all complex Golay complementary sequences that can be obtained by a combination of all parameters M, N, pNum0, pNum1, seed0, seed1, seed2, and ‘select’used in the M+N+k complex Golay complementary sequence generator illustrated in FIG. 6. However, the parameters M, N, pNum0, pNum1, seed0, seed1, seed2, and ‘select’for generating a complex Golay complementary sequence for the PAPR=2.8666 [dB]can have different values. For pNum0=pNum1=select=0, seed0 and seed1 having the lowest PAPR can have various values. For example, for seed0=1 and seed1=4, a preamble sequence Pg(−104:104) is given by




  
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Describing the Pg(−104:104), it should be noted that data of +1 or −1 is inserted into odd elements and null data, or 0, is inserted into even elements.
FIG. 16 is a flowchart illustrating a preamble sequence mapping procedure according to an embodiment of the present invention. Referring to FIG. 16, a transmitter of an OFDM communication system determines whether a current signal transmission period is a preamble sequence transmission period in step 1611. If the current signal transmission period is not a preamble sequence transmission period, but a data transmission period, the transmitter proceeds to step 1613. In step 1613, the transmitter maps transmission data to corresponding subcarriers on an IFFT processor's input terminal, and then returns to step 1611.
However, if it is determined in step 1611 that the current signal transmission period is a preamble sequence transmission period, the transmitter proceeds to step 1615, where the transmitter determines whether the preamble sequence transmission period is a period for which a leading preamble sequence of a long preamble sequence is transmitted. Here, in the preamble sequence transmission period, the leading preamble sequence of a long preamble sequence is a sequence Sg(−B:B). If it is determined that the preamble sequence transmission period is a period for which a leading preamble sequence of a long preamble sequence is transmitted, the transmitter proceeds to step 1617.
In step 1617, the transmitter generates a leading preamble sequence Sg(−B:B) of the long preamble sequence, maps the generated preamble sequence Sg(−B:B) to corresponding subcarriers on the IFFT processor's input terminal, and then returns to step 1611. “−B:B” represents unique numbers of subcarriers where data is actually used in the OFDM communication system.
However, if it is determined in step 1615 that the preamble sequence transmission period is not a period for which a leading preamble sequence Sg(−B:B) of a long preamble sequence is transmitted, i.e., if the preamble sequence transmission period is a period for which a short preamble sequence Pg(−B:B) is transmitted, then the transmitter proceeds to step 1619. In step 1619, the transmitter generates the short preamble sequence Pg(−B:B), maps the generated short preamble sequence Pg(−B:B) to corresponding subcarriers on the IFFT processor's input terminal, and then returns to step 1611.
As is understood from the foregoing description, the present invention generates a preamble sequence having a minimum PAPR, thereby improving the overall performance of an OFDM communication system. In addition, the present invention generates a preamble sequence using a complex Golay complementary sequence, making it possible to generate a preamble sequence having a minimum PAPR with a minimized number of operations within a shorter time. Moreover, the present invention generates a preamble sequence using a complex Golay complementary sequence, thereby generating a preamble sequence without limitation in its length.
While the present invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the appended claims.

## Claims

1. An apparatus for generating a preamble sequence in an orthogonal frequency division multiplexing (OFDM) communication system using A subcarriers in a frequency domain, the apparatus comprising:
a preamble sequence generator for generating a length−M+N+k preamble sequence, where M+N+k is less than A, by combining a length−N Golay complementary sequence with a length−M Golay complementary sequence, wherein k is an integer larger than a smaller one of−N and −M; and
an inverse fast Fourier transform (IFFT) processor for assigning elements constituting the preamble sequence to the M+N+k subcarriers among the A subcarriers, on a one-to-one mapping basis, assigning null data to remaining subcarriers excluding the M+N+k subcarriers from the A subcarriers, and IFFT-transforming the assigned results into time-domain data.

2. The apparatus of claim 1, wherein the preamble sequence is a complex Golay complementary sequence.

3. The apparatus of claim 1, wherein the preamble sequence generator comprises:
a complex Golay complementary sequence generator for generating the length−M+N+k complex Golay complementary sequence by combining the length−N Golay complementary sequence with the length−M Golay complementary sequence; and
a complex Golay complementary sequence/preamble sequence mapper for generating the preamble sequence such that elements constituting the length−M+N+k complex Golay complementary sequence are mapped to the M+N+k subcarriers among the A subcarriers at a preset interval on a one-to-one basis.

4. The apparatus of claim 3, wherein the complex Golay complementary sequence generator comprises:
a first Golay complementary sequence pair generator for generating a length−N Golay complementary sequence pair;
a second Golay complementary sequence pair generator for generating a length−M Golay complementary sequence pair;
a complex Golay complementary sequence pair combiner for combining the length−N Golay complementary sequence pair with the length−M Golay complementary sequence pair according to a complex Golay complementary sequence pair combining rule, and outputting the length−M+N+k complex Golay complementary sequence pair; and
a selector for selecting any one of the length−M+N+k complex Golay complementary sequence pair as the length−M+N+k complex Golay complementary sequence.

5. The apparatus of claim 4, wherein the first Golay complementary sequence pair generator comprises:
a selector for selecting one primitive Golay complementary sequence pair among length−N primitive Golay complementary sequence pairs; and
a first Golay complementary sequence conjugate pair generator for generating a length−N Golay complementary sequence pair by selecting one primitive Golay complementary sequence conjugate pair from conjugate pairs of the selected primitive Golay complementary sequence pair.

6. The apparatus of claim 4, wherein the second Golay complementary sequence pair generator comprises:
a selector for selecting one primitive Golay complementary sequence pair among length−M primitive Golay complementary sequence pairs; and
a second Golay complementary sequence conjugate pair generator for generating a length−M Golay complementary sequence pair by selecting one primitive Golay complementary sequence conjugate pair from conjugate pairs of the selected primitive Golay complementary sequence pair.

7. The apparatus of claim 4, wherein the complex Golay complementary sequence pair combiner combines the length−M+N+k complex Golay complementary sequence pair according to the following complex Golay complementary sequence pair combining rule,



  
    
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                          i
                        
                        -
                        
                          c
                          
                            i
                            -
                            N
                            -
                            k
                          
                        
                      
                      ,
                    
                  
                  
                    
                      
                        N
                        +
                        k
                      
                      ≤
                      i
                      <
                      N
                    
                  
                
                
                  
                    
                      
                        c
                        
                          i
                          -
                          N
                          -
                          k
                        
                      
                      ,
                    
                  
                  
                    
                      N
                      ≤
                      i
                      <
                      
                        M
                        +
                        N
                        +
                        k
                      
                    
                  
                
              
              ⁢
              
                

              
              ⁢
              
                g
                i
              
            
            =
            
              {
              
                
                  
                    
                      
                        
                          
                            b
                            i
                          
                          ,
                        
                      
                      
                        
                          0
                          ≤
                          i
                          <
                          
                            N
                            +
                            k
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              b
                              i
                            
                            +
                            
                              d
                              
                                i
                                -
                                N
                                -
                                k
                              
                            
                          
                          ,
                        
                      
                      
                        
                          
                            N
                            +
                            k
                          
                          ≤
                          i
                          <
                          N
                        
                      
                    
                    
                      
                        
                          
                            d
                            
                              i
                              -
                              N
                              -
                              k
                            
                          
                          ,
                        
                      
                      
                        
                          N
                          ≤
                          i
                          <
                          
                            M
                            +
                            N
                            +
                            k
                          
                        
                      
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    h
                    i
                  
                
                =
                
                  {
                  
                    
                      
                        
                          
                            
                              
                                
                                  b
                                  i
                                
                                ,
                              
                            
                            
                              
                                0
                                ≤
                                i
                                <
                                
                                  N
                                  +
                                  k
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    b
                                    i
                                  
                                  -
                                  
                                    d
                                    
                                      i
                                      -
                                      N
                                      -
                                      k
                                    
                                  
                                
                                ,
                              
                            
                            
                              
                                
                                  N
                                  +
                                  k
                                
                                ≤
                                i
                                <
                                N
                              
                            
                          
                          
                            
                              
                                
                                  d
                                  
                                    i
                                    -
                                    N
                                    -
                                    k
                                  
                                
                                ,
                              
                            
                            
                              
                                N
                                ≤
                                i
                                <
                                
                                  M
                                  +
                                  N
                                  +
                                  k
                                
                              
                            
                          
                        
                        ⁢
                        
                          

                        
                        ⁢
                        0
                      
                      ≤
                      i
                      <
                      
                        M
                        +
                        N
                        +
                        
                          k
                          ⁢
                          
                            

                          
                          ⁢
                          k
                        
                      
                      ≥
                      
                        0
                        ⁢
                        
                          

                        
                        ⁢
                        
                          e
                          i
                        
                      
                    
                    =
                    
                      {
                      
                        
                          
                            
                              
                                
                                  
                                    a
                                    i
                                  
                                  ,
                                
                              
                              
                                
                                  0
                                  ≤
                                  i
                                  <
                                  N
                                
                              
                            
                            
                              
                                
                                  0
                                  ,
                                
                              
                              
                                
                                  N
                                  ≤
                                  i
                                  <
                                  
                                    N
                                    +
                                    k
                                  
                                
                              
                            
                            
                              
                                
                                  
                                    c
                                    
                                      i
                                      -
                                      N
                                      -
                                      k
                                    
                                  
                                  ,
                                
                              
                              
                                
                                  
                                    N
                                    +
                                    k
                                  
                                  ≤
                                  i
                                  <
                                  
                                    M
                                    +
                                    N
                                    +
                                    k
                                  
                                
                              
                            
                          
                          ⁢
                          
                            

                          
                          ⁢
                          
                            f
                            i
                          
                        
                        =
                        
                          {
                          
                            
                              
                                
                                  
                                    
                                      
                                        a
                                        i
                                      
                                      ,
                                    
                                  
                                  
                                    
                                      0
                                      ≤
                                      i
                                      <
                                      N
                                    
                                  
                                
                                
                                  
                                    
                                      0
                                      ,
                                    
                                  
                                  
                                    
                                      N
                                      ≤
                                      i
                                      <
                                      
                                        N
                                        +
                                        k
                                      
                                    
                                  
                                
                                
                                  
                                    
                                      
                                        -
                                        
                                          c
                                          
                                            i
                                            -
                                            N
                                            -
                                            k
                                          
                                        
                                      
                                      ,
                                    
                                  
                                  
                                    
                                      
                                        N
                                        +
                                        k
                                      
                                      ≤
                                      i
                                      <
                                      
                                        M
                                        +
                                        N
                                        +
                                        k
                                      
                                    
                                  
                                
                              
                              ⁢
                              
                                

                              
                              ⁢
                              
                                g
                                i
                              
                            
                            =
                            
                              {
                              
                                
                                  
                                    
                                      
                                        
                                          
                                            b
                                            i
                                          
                                          ,
                                        
                                      
                                      
                                        
                                          0
                                          ≤
                                          i
                                          <
                                          N
                                        
                                      
                                    
                                    
                                      
                                        
                                          0
                                          ,
                                        
                                      
                                      
                                        
                                          N
                                          ≤
                                          i
                                          <
                                          
                                            N
                                            +
                                            k
                                          
                                        
                                      
                                    
                                    
                                      
                                        
                                          
                                            d
                                            
                                              i
                                              -
                                              N
                                              -
                                              k
                                            
                                          
                                          ,
                                        
                                      
                                      
                                        
                                          
                                            N
                                            +
                                            k
                                          
                                          ≤
                                          i
                                          <
                                          
                                            M
                                            +
                                            N
                                            +
                                            k
                                          
                                        
                                      
                                    
                                  
                                  ⁢
                                  
                                    

                                  
                                  ⁢
                                  
                                    h
                                    i
                                  
                                
                                =
                                
                                  {
                                  
                                    
                                      
                                        
                                          
                                            
                                              
                                                b
                                                i
                                              
                                              ,
                                            
                                          
                                          
                                            
                                              0
                                              ≤
                                              i
                                              <
                                              N
                                            
                                          
                                        
                                        
                                          
                                            
                                              0
                                              ,
                                            
                                          
                                          
                                            
                                              N
                                              ≤
                                              i
                                              <
                                              
                                                N
                                                +
                                                k
                                              
                                            
                                          
                                        
                                        
                                          
                                            
                                              
                                                -
                                                
                                                  d
                                                  
                                                    i
                                                    -
                                                    N
                                                    -
                                                    k
                                                  
                                                
                                              
                                              ,
                                            
                                          
                                          
                                            
                                              
                                                N
                                                +
                                                k
                                              
                                              ≤
                                              i
                                              <
                                              
                                                M
                                                +
                                                N
                                                +
                                                k
                                              
                                            
                                          
                                        
                                      
                                      ⁢
                                      
                                        

                                      
                                      ⁢
                                      0
                                    
                                    ≤
                                    i
                                    <
                                    
                                      M
                                      +
                                      N
                                      +
                                      k
                                    
                                  
                                
                              
                            
                          
                        
                      
                    
                  
                
              
            
          
        
      
    
  



where ai, and i represent elements constituting a length−N Golay complementary sequence pair [A,B], ci and di represent elements constituting a length−M Golay complementary sequence pair [C,D], and ei, fi,gi and hi represent elements constituting a length−M+N+k Golay complementary sequence pair [E,F,G,H], where i and k satisfy
0≦i<M+N+k.

8. The apparatus of claim 3, wherein the complex Golay complementary sequence/preamble sequence mapper performs a control operation such that elements having a value of +1 or −1 among elements constituting the length−M+N+k complex Golay complementary sequence are not mapped to a subcarrier corresponding to a time-domain direct current (DC) component among the M+N+k subcarriers.

9. The apparatus of claim 3, wherein the complex Golay complementary sequence/preamble sequence mapper performs a control operation such that elements having a value of −1 or −1 among elements constituting the length M+N+k complex Golay complementary sequence are mapped to odd subcarriers among the M+N+k subcarriers.

10. The apparatus of claim 3, wherein the complex Golay complementary sequence/preamble sequence mapper performs a control operation such that elements constituting the length M+N+k complex Golay complementary sequence are mapped to the M+N+k subcarriers at a preset interval in accordance with




  
    L
    ⁡
    
      (
      i
      )
    
  
  =
  
    {
    
      
        
          
            
              J
              ⁡
              
                (
                n
                )
              
            
            ,
          
        
        
          
            i
            =
            
              GPM
              ⁢
              
                
              
              ⁢
              
                (
                n
                )
              
            
          
        
      
      
        
          
            0
            ,
          
        
        
          
            i
            ≠
            
              GPM
              ⁢
              
                
              
              ⁢
              
                (
                n
                )
              
            
          
        
      
    
  




where n represents an index of elements constituting a complex Golay complementary sequences, GPM(n) represents an index of elements constituting a preamble sequence, J represents the complex Golay complementary sequence, and L represents the preamble sequence output after performing an IFFT on the complex Golay complementary sequence J.

11. The apparatus of claim 10, wherein the GPM(n) is defined as


GPM(n)=−(B−E−nI)


where −B≦i≦B, 0≦n≦(M+N+k−1), −B represents an initial subcarrier number of subcarriers excluding the subcarriers where the null data is inserted among the A subcarriers, and B represents a last subcarrier number.

12. The apparatus of claim 3, wherein the preset interval is defined as


B=Ik+D(for 0≦D≦(I−1))


where I represents the preset interval, wherein if a parameter D=0, then E=1,2, . . . , I−1 and F=I−E, and if D=1, . . . , I−1, then E=0, . . . , I−1 (D+E≠F) and F=((B−F) mod I=D+E) for 0≦F≦(I−1).

13. The apparatus of claim 1, wherein the preamble sequence generator generates a preamble sequence Pg(−104:104) for A=256, wherein




  
    Pg
    ⁡
    
      (
      
        
          -
          104
        
        ⁢
        
          :
        
        ⁢
        104
      
      )
    
  
  =
  
    
      
        
          {
          0
        
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        
          0
          }
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
  




where “−n:n” represents −nth to nth subcarriers.

14. A method for generating a preamble sequence in an orthogonal frequency division multiplexing (OFDM) communicating system using A subcarriers in a frequency domain, the method comprising the steps of:
generating a length−M+N+k preamble sequence, where M+N+k is less than A, by combining a length−N Golay complementary sequence with a length−M Golay complementary sequence, wherein k is an integer larger than a smaller one of −N and −M;
assigning elements constituting the preamble sequence to the M+N+k subcarriers among the A subcarriers on a one-to-one mapping basis;
assigning null data to retaining subcarriers excluding the M+N+k subcarriers from the A subcarriers; and
IFFT (Inverse Fast Fourier Transform)—transforming the assigned result into time-domain data.

15. The method of claim 14, wherein the preamble sequence is a complex Golay complementary sequence.

16. The method of claim 14, wherein the step of generating the preamble sequence comprises the steps of:
generating the length−M+N+k complex Golay complementary sequence by combining the length−N Golay complementary sequence with the length−M Golay complementary sequence; and
generating the preamble sequence such that elements constituting the length−M+N+k complex Golay complementary sequence are mapped to the M+N+k subcarriers among the A subcarriers at a preset interval on a one-to-one basis.

17. The method of claim 16, wherein the step of generating the length−M+N+k complex Golay complementary sequence comprises the steps of:
generating a length−N Golay complementary sequence pair;
generating a length−M Golay complementary sequence pair;
combining the length−N Golay complementary sequence pair with the length−M Golay complementary sequence pair according to a complex Golay complementary sequence pair combining rule;
outputting the length−M+N+k complex Golay complementary sequence pair; and
selecting any one of the length−M+N+k complex Golay complementary sequence pair as the length−M+N+k complex Golay complementary sequence.

18. The method of claim 17, wherein the step of generating the length−N Golay complementary sequence pair comprises the steps of:
selecting one primitive Golay complementary sequence pair among length−N primitive Golay complementary sequence pairs; and
selecting one primitive Golay complementary sequence conjugate pair from conjugate pairs of the selected primitive Golay complementary sequence pair.

19. The method of claim 17, wherein the step of generating the length−M Golay complementary sequence pair comprises the steps of:
selecting one primitive Golay complementary sequence pair among length−M primitive Golay complementary sequence pairs; and
selecting one primitive Golay complementary sequence conjugate pair from conjugate pairs of the selected primitive Golay complementary sequence pair.

20. The method of claim 17, wherein the length−M+N+k complex Golay complementary sequence pair is combined according to the following complex Golay complementary sequence pair combining rule,



  
    
      -
      N
    
    ≤
    k
    <
    0
  




  
    
      e
      i
    
    =
    
      {
      
        
          
            
              
                
                  
                    a
                    i
                  
                  ,
                
              
              
                
                  0
                  ≤
                  i
                  <
                  
                    N
                    +
                    k
                  
                
              
            
            
              
                
                  
                    
                      a
                      i
                    
                    +
                    
                      c
                      
                        i
                        -
                        N
                        -
                        k
                      
                    
                  
                  ,
                
              
              
                
                  
                    N
                    +
                    k
                  
                  ≤
                  i
                  <
                  N
                
              
            
            
              
                
                  
                    c
                    
                      i
                      -
                      N
                      -
                      k
                    
                  
                  ,
                
              
              
                
                  N
                  ≤
                  i
                  <
                  
                    M
                    +
                    N
                    +
                    k
                  
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            f
            i
          
        
        =
        
          {
          
            
              
                
                  
                    
                      
                        a
                        i
                      
                      ,
                    
                  
                  
                    
                      0
                      ≤
                      i
                      <
                      
                        N
                        +
                        k
                      
                    
                  
                
                
                  
                    
                      
                        
                          a
                          i
                        
                        -
                        
                          c
                          
                            i
                            -
                            N
                            -
                            k
                          
                        
                      
                      ,
                    
                  
                  
                    
                      
                        N
                        +
                        k
                      
                      ≤
                      i
                      <
                      N
                    
                  
                
                
                  
                    
                      
                        c
                        
                          i
                          -
                          N
                          -
                          k
                        
                      
                      ,
                    
                  
                  
                    
                      N
                      ≤
                      i
                      <
                      
                        M
                        +
                        N
                        +
                        k
                      
                    
                  
                
              
              ⁢
              
                

              
              ⁢
              
                g
                i
              
            
            =
            
              {
              
                
                  
                    
                      
                        
                          
                            b
                            i
                          
                          ,
                        
                      
                      
                        
                          0
                          ≤
                          i
                          <
                          
                            N
                            +
                            k
                          
                        
                      
                    
                    
                      
                        
                          
                            
                              b
                              i
                            
                            +
                            
                              d
                              
                                i
                                -
                                N
                                -
                                k
                              
                            
                          
                          ,
                        
                      
                      
                        
                          
                            N
                            +
                            k
                          
                          ≤
                          i
                          <
                          N
                        
                      
                    
                    
                      
                        
                          
                            d
                            
                              i
                              -
                              N
                              -
                              k
                            
                          
                          ,
                        
                      
                      
                        
                          N
                          ≤
                          i
                          <
                          
                            M
                            +
                            N
                            +
                            k
                          
                        
                      
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    h
                    i
                  
                
                =
                
                  {
                  
                    
                      
                        
                          
                            
                              
                                
                                  b
                                  i
                                
                                ,
                              
                            
                            
                              
                                0
                                ≤
                                i
                                <
                                
                                  N
                                  +
                                  k
                                
                              
                            
                          
                          
                            
                              
                                
                                  
                                    b
                                    i
                                  
                                  -
                                  
                                    d
                                    
                                      i
                                      -
                                      N
                                      -
                                      k
                                    
                                  
                                
                                ,
                              
                            
                            
                              
                                
                                  N
                                  +
                                  k
                                
                                ≤
                                i
                                <
                                N
                              
                            
                          
                          
                            
                              
                                
                                  d
                                  
                                    i
                                    -
                                    N
                                    -
                                    k
                                  
                                
                                ,
                              
                            
                            
                              
                                N
                                ≤
                                i
                                <
                                
                                  M
                                  +
                                  N
                                  +
                                  k
                                
                              
                            
                          
                        
                        ⁢
                        
                          

                        
                        ⁢
                        0
                      
                      ≤
                      i
                      <
                      
                        M
                        +
                        N
                        +
                        
                          k
                          ⁢
                          
                            

                          
                          ⁢
                          k
                        
                      
                      ≥
                      
                        0
                        ⁢
                        
                          e
                          i
                        
                      
                    
                    =
                    
                      {
                      
                        
                          
                            
                              
                                
                                  
                                    a
                                    i
                                  
                                  ,
                                
                              
                              
                                
                                  0
                                  ≤
                                  i
                                  <
                                  N
                                
                              
                            
                            
                              
                                
                                  0
                                  ,
                                
                              
                              
                                
                                  N
                                  ≤
                                  i
                                  <
                                  
                                    N
                                    +
                                    k
                                  
                                
                              
                            
                            
                              
                                
                                  
                                    c
                                    
                                      i
                                      -
                                      N
                                      -
                                      k
                                    
                                  
                                  ,
                                
                              
                              
                                
                                  
                                    N
                                    +
                                    k
                                  
                                  ≤
                                  i
                                  <
                                  
                                    M
                                    +
                                    N
                                    +
                                    k
                                  
                                
                              
                            
                          
                          ⁢
                          
                            

                          
                          ⁢
                          
                            f
                            i
                          
                        
                        =
                        
                          {
                          
                            
                              
                                
                                  
                                    
                                      
                                        a
                                        i
                                      
                                      ,
                                    
                                  
                                  
                                    
                                      0
                                      ≤
                                      i
                                      <
                                      N
                                    
                                  
                                
                                
                                  
                                    
                                      0
                                      ,
                                    
                                  
                                  
                                    
                                      N
                                      ≤
                                      i
                                      <
                                      
                                        N
                                        +
                                        k
                                      
                                    
                                  
                                
                                
                                  
                                    
                                      
                                        -
                                        
                                          c
                                          
                                            i
                                            -
                                            N
                                            -
                                            k
                                          
                                        
                                      
                                      ,
                                    
                                  
                                  
                                    
                                      
                                        N
                                        +
                                        k
                                      
                                      ≤
                                      i
                                      <
                                      
                                        M
                                        +
                                        N
                                        +
                                        k
                                      
                                    
                                  
                                
                              
                              ⁢
                              
                                

                              
                              ⁢
                              
                                g
                                i
                              
                            
                            =
                            
                              {
                              
                                
                                  
                                    
                                      
                                        
                                          
                                            b
                                            i
                                          
                                          ,
                                        
                                      
                                      
                                        
                                          0
                                          ≤
                                          i
                                          <
                                          N
                                        
                                      
                                    
                                    
                                      
                                        
                                          0
                                          ,
                                        
                                      
                                      
                                        
                                          N
                                          ≤
                                          i
                                          <
                                          
                                            N
                                            +
                                            k
                                          
                                        
                                      
                                    
                                    
                                      
                                        
                                          
                                            d
                                            
                                              i
                                              -
                                              N
                                              -
                                              k
                                            
                                          
                                          ,
                                        
                                      
                                      
                                        
                                          
                                            N
                                            +
                                            k
                                          
                                          ≤
                                          i
                                          <
                                          
                                            M
                                            +
                                            N
                                            +
                                            k
                                          
                                        
                                      
                                    
                                  
                                  ⁢
                                  
                                    

                                  
                                  ⁢
                                  
                                    h
                                    i
                                  
                                
                                =
                                
                                  {
                                  
                                    
                                      
                                        
                                          
                                            
                                              
                                                b
                                                i
                                              
                                              ,
                                            
                                          
                                          
                                            
                                              0
                                              ≤
                                              i
                                              <
                                              N
                                            
                                          
                                        
                                        
                                          
                                            
                                              0
                                              ,
                                            
                                          
                                          
                                            
                                              N
                                              ≤
                                              i
                                              <
                                              
                                                N
                                                +
                                                k
                                              
                                            
                                          
                                        
                                        
                                          
                                            
                                              
                                                -
                                                
                                                  d
                                                  
                                                    i
                                                    -
                                                    N
                                                    -
                                                    k
                                                  
                                                
                                              
                                              ,
                                            
                                          
                                          
                                            
                                              
                                                N
                                                +
                                                k
                                              
                                              ≤
                                              i
                                              <
                                              
                                                M
                                                +
                                                N
                                                +
                                                k
                                              
                                            
                                          
                                        
                                      
                                      ⁢
                                      
                                        

                                      
                                      ⁢
                                      0
                                    
                                    ≤
                                    i
                                    <
                                    
                                      M
                                      +
                                      N
                                      +
                                      k
                                    
                                  
                                
                              
                            
                          
                        
                      
                    
                  
                
              
            
          
        
      
    
  



where ai and bi represent elements constituting a length−N Golay complementary sequence pair [A,B], ci and di represent elements constituting a length−M Golay complementary sequence pair [C,D], and ei, fi, gi, and hi represent elements constituting a length−M+N+k Golay complementary sequence pair [E,F,G,H], where i and k satisfy


0≦i≦M+N+k.

21. The method of claim 16, wherein the step of mapping elements constituting the length−M+N+k complex Golay complementary sequence to the M+N+k subcarriers comprises the step of performing a control operation such that elements having a value of +1 or −1 among elements constituting the length−M+N+k complex Golay complementary sequence are not mapped to a subcarrier corresponding to a time-domain direct current (DC) component among the M+N+k subcarriers.

22. The method of claim 16, wherein the step of mapping elements constituting the length−M+N+k complex Golay complementary sequence to the M+N+k subcarriers comprises the step of performing a control operation such that elements having a value of +b 1 or −1 among elements constituting the length M+N+k complex Golay complementary sequence are mapped to odd subcarriers among the M+N+k subcarriers.

23. The method of claim 16, wherein the step of mapping elements constituting the length−M+N+k complex Golay complementary sequence to the M+N+k subcarriers comprises the step of performing a control operation such that elements constituting the length M+N+k complex Golay complementary sequence are mapped to the M+N+k subcarriers at a preset interval in accordance with




  
    L
    ⁡
    
      (
      i
      )
    
  
  =
  
    {
    
      
        
          
            
              J
              ⁡
              
                (
                n
                )
              
            
            ,
          
        
        
          
            i
            =
            
              GPM
              ⁡
              
                (
                n
                )
              
            
          
        
      
      
        
          
            0
            ,
          
        
        
          
            i
            ≠
            
              GPM
              ⁡
              
                (
                n
                )
              
            
          
        
      
    
  




where n represents an index of elements constituting a complex Golay complementary sequence, GPM(n) represents an index of elements constituting a preamble sequence, J represents the complex Golay complementary sequence, and L represents the preamble sequence output after performing an IFFT on the complex Golay complementary sequence J.

24. The method of claim 23, wherein the GPM(n) is defined as


GPM(n)=−(B−E−nI)


where −B≦i≦B, 0≦n≦(M+N+k−1), −B represents an initial subcarrier number of subcarriers excluding the subcarriers where the null data is inserted among the A subcarriers, and B represents a last subcarrier number.

25. The method of claim 16, wherein the preset interval is defined as


B=Ik+D(for 0≦D≦(I−1))


where I represents the preset interval, wherein if a parameter D=0, then E=1,2, . . . , I−1 and F=I−E, and if D=1, . . . , I−1, then E=0, . . . , I−1 (D+E≠F) and F=((B−F) mod I=D+E) for 0≦F≦(I−1).

26. The method of claim 14, wherein for A=256, a preamble sequence Pg(−104:104) is generated, wherein




  
    Pg
    ⁡
    
      (
      
        
          -
          104
        
        ⁢
        
          :
        
        ⁢
        104
      
      )
    
  
  =
  
    
      
        
          {
          0
        
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
    
    
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
    
    
      
        0
      
      
        
          -
          1
        
      
      
        0
      
      
        1
      
      
        
          0
          }
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
      
        
          
        
      
    
  




where “−n:n” represents −nth to nth subcarriers.