Patent Publication Number: US-7596181-B2

Title: Apparatus and method for frequency synchronization in OFDM system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit under 35 U.S.C. §119(a) of Korean Patent Application No. 10-2004-0074890 entitled “Apparatus And Method For Initial Frequency Synchronization In OFDM System” filed in the Korean Intellectual Property Office on Sep. 18, 2004, the entire disclosure of which is hereby incorporated by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method and an apparatus for data transmission in an Orthogonal Frequency Division Multiplexing (OFDM) system. More particularly, the present invention relates to a method and an apparatus for initial frequency synchronization for data transmission by using OFDM symbols. 
     2. Description of the Related Art 
     The OFDM scheme is a fourth generation (4G) modulation scheme which is expected to be adopted as a standard for digital televisions in European countries, Japan and Australia. The OFDM scheme was initially recommended for a Local Area Network (LAN) technology and is now being developed to provide mobility to an OFDM-based wireless LAN technology for a cellular system for wireless Internet service. 
     The band spread technology of the OFDM scheme distributes data to a plurality of sub-carriers at the exact same frequency interval. This frequency interval provides “orthogonality” within a technology preventing a demodulator from referring to frequencies other than its own frequency. Further, the OFDM scheme is a kind of multi-carrier modulation scheme and shows an excellent performance in a multi-path mobile reception environment. Therefore, the OFDM scheme is now attracting attention as a modulation scheme that is well suited for ground wave digital televisions and digital voice broadcasting. Although the OFDM scheme has been researched and developed mainly in the field of communication, it is now being actively researched and developed in the field of broadcasting, especially in the case of broadcasting after the OFDM scheme is employed as a modulation scheme of a Digital Audio Broadcast (DAB) system proposed by the European Broadcasting Union (EBU). 
       FIG. 1  is a block diagram illustrating the structure of a transmitter and a receiver in a physical layer of a typical OFDM system. 
     Referring to  FIG. 1 , an input bit stream to be transmitted is transferred through an encoder  111  to a serial/parallel converter  112 . Then, the serial/parallel converter  112  collects N number of symbols and transfers the N symbols to an Inverse Fast Fourier Transform (IFFT) converter  113  which converts the symbols from symbols of the frequency domain into time domain symbols. Thereafter, a parallel/serial converter  114  converts the time domain symbols into serial symbols. In the above process, the N collected symbols are referred to as ‘OFDM’ symbols. Then, a Cyclic Prefix (CP) inserter  115  adds a CP to each of the serial time domain symbols obtained by the parallel/serial converter  114  in order to remove the influence of the multi-path channels. Then, the CP-added symbols in a digital domain are converted to an analog signal by a digital/analog converter  116 , and the converted analog signal is then transmitted through a channel  120  to a receiver side. 
     When the transmitted signal is received by the receiver  130  through the channel  120 , an analog/digital converter  131  converts the received analog signal into a digital signal, and a CP remover  132  removes CP from the OFDM symbol contaminated due to the multi-path. The CP-removed signal is converted into a frequency domain signal by a Fast Fourier Transform (FFT) converter  134  after passing through a serial/parallel converter  133 . The converted frequency domain signal passes through an equalizer  135  for eliminating channel interference, a parallel/serial converter  136  and a decoder  137 , and is then output as an output bit stream at the receiver terminal. 
       FIG. 2  is a graph showing data symbols transmitted in a typical OFDM system, which are illustrated according to frequency and time. 
     In an OFDM system as described above with reference to  FIG. 1 , N number of data symbols within one OFDM symbol are transmitted by N number of sub-carriers. The N data symbols carried by the N sub-carriers constitute one OFDM symbol  201 , and M number of OFDM symbols constitute one frame  202 . The start symbol of the frame  202  usually includes a pilot symbol for frequency synchronization and channel estimation, by which a preamble, control information and so forth, is transmitted. 
     The OFDM system has an excellent performance for a mobile reception environment and a good frequency band use efficiency. However, in the OFDM system, the sub-carriers orthogonal to each other are compactly disposed with small intervals. Therefore, the OFDM system is relatively weak with regard to frequency offset in comparison with the single sub-carrier system. 
     Hereinafter, an example of the orthogonality between sub-carriers in the OFDM system will be described with reference to  FIG. 3 . 
     Referring to the graph in  FIG. 3 , three sub-carriers a shown. It is noted that data is transmitted by using frequency f n−1    301 , frequency f n    302  and frequency f n+1    303  adjacent to each other. The data transmitted through each of the frequencies  301  to  303  has a sinusoidal waveform, and each of the first frequency signal  304 , second frequency signal  305  and third frequency signal  306  is exactly located at the frequency of a corresponding sub-carrier. Therefore, the three signals give no interference to each other. 
       FIG. 4  is a graph showing interference between sub-carriers when there are frequency offsets in a typical OFDM system. 
     If each sub-carrier has a frequency offset of Δf  401  from an exact frequency of the sub-carrier, the receiver fails to catch the exact frequency location of the sub-carrier and instead takes a data sample at a location deviated Δf  401  from the exact location. Therefore, interference occurs between the three sub-carriers shown in  FIG. 4 , including the first sub-carrier signal  402 , the second sub-carrier signal  403  and the third sub-carrier signal  404 . For example, a signal sample  405  having a frequency offset of Δf  401  from the second sub-carrier signal  403  is subject to interference by the first sub-carrier signal  407  and the third sub-carrier signal  406  at a corresponding frequency location. As described above, the OFDM system has orthogonality between sub-carriers, which reduces the interval between the sub-carriers and causes the sub-carriers to be compactly arranged. Therefore, the OFDM system is largely influenced by interference due to the frequency offset. 
     According to a conventional initial frequency synchronization scheme in order to compensate for frequency offsets in the OFDM system as described above, the initial frequency synchronization is performed by using two pilot OFDM symbols. The conventional initial frequency synchronization includes two steps, that is, a first step of fine frequency synchronization (that is, compensation for frequency offsets within a band twice as wide as the sub-carrier band) and a second step of frequency ambiguity resolution for a part corresponding to a multiple of the band that is twice as wide as the sub-carrier band. 
       FIG. 5  illustrates an example of the format of pilot OFDM symbols according to the conventional initial frequency synchronization method in an OFDM system. 
     The first pilot OFDM symbol  501 , which is a symbol for the fine frequency synchronization (hereinafter, referred to as “the first frequency synchronization”) in the first step for the frequency synchronization, has values other than zero for the sub-carriers in an even number order and ‘0’ for the sub-carriers in an odd number order. The first pilot OFDM symbol  501  is identical to the repetition of pilot symbols each having a half symbol length in the time domain. The process for the first frequency synchronization corresponds to a process of obtaining the decimal part of the frequency offset. 
     The second pilot OFDM symbol  502  is a symbol for the frequency ambiguity resolution in the second step for the frequency synchronization, which will be referred to as the second frequency synchronization process. The second pilot OFDM symbol  502  has values for all sub-carriers. The second frequency synchronization process corresponds to a process of obtaining the integer part of the frequency offset. 
     In other words, the frequency offset includes a decimal part expressed as being smaller than twice the sub-carrier band, and an integer part expressed as being a multiple of twice the sub-carrier band, which can be expressed by equation (1) below.
 
Δ f=φ /(π T )+2 g/T   (1)
 
     In equation (1), Δf denotes the entire frequency offset, φ denotes the decimal part of the frequency offset and T denotes the symbol length. Further, g denotes the integer part of the frequency offset corresponding to an integer being a multiple of twice the sub-carrier band. 
     If one data symbol is expressed by using an N point Fast Fourier Transform (FFT), a received symbol signal w(t) having a frequency offset can be expressed by equation (2) below. 
     
       
         
           
             
               
                 
                   
                     
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     If one received data symbol located at the first half OFDM symbol of the first pilot symbol is set as w(t 0 ), and another received data symbol located at the second half OFDM symbol corresponding to the same location of the first half OFDM symbol is set as w(t 0 +T/2), a relation as expressed by equation (3) below is established. 
     
       
         
           
             
               
                 
                   
                     
                       
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     If the phase of the correlation value of the repeated half OFDM symbol length from equation (3), a relation defined by equation (4) below can be established between the decimal part φ of the frequency offset and the entire frequency offset Δf.
 
φ=πΔfT  (4)
 
     That is, it is possible to estimate the decimal part of the frequency offset through phase estimation by taking the correlation coefficient of the repeated part of the first pilot symbol. 
     The conventional frequency offset estimation method teaches the use of the function as defined by equation (5) below in order to enhance the precision in the estimation. 
     
       
         
           
             
               
                 
                   
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     If it is possible to guarantee that the absolute value of the initial frequency offset is within a range smaller than the sub-carrier band, the entire frequency offset can be estimated as equation (6) below.
 
Δ {circumflex over (f)} ={circumflex over (φ)}/(π T )  (6)
 
     However, it is actually not always possible to guarantee that the absolute value of the initial frequency offset is within a range smaller than the sub-carrier band, and there exists an ambiguity corresponding to a multiple of twice the sub-carrier band. 
     Therefore, in order to finally determine the frequency offset, it is necessary to resolve the ambiguity of the integer part of the frequency offset corresponding to the integer g in equation (1) in advance, for which the second pilot symbol is used. First, an estimation for the part corresponding to the decimal part of the frequency offset in the first frequency synchronization process is performed. Then, only the part corresponding to 2g/T remains in the frequency offset. 
     The frequency conversion values of the first and second pilot symbols are set as X 1,k  and X 2,k , respectively, and the second pilot symbol is determined such that the differentially modulated values of the frequency conversion value of the first pilot symbol and the frequency conversion value of the even number-th sub-carriers of the second pilot symbol have a particular pattern. Further, according the conventional method, in order to determine g which is the integer part of the frequency offset, correlation coefficients of a predetermined pattern and differences between the first and second pilot symbols for possible g values are obtained. Then, a g value having the largest correlation value from among the obtained correlation values is determined as the final value. Through the above process, the frequency offset is estimated. 
       FIG. 6  is a block diagram illustrating a structure of a transmitter and a receiver for initial frequency synchronization in a physical layer of a conventional OFDM system. 
     In the transmitter  610  of  FIG. 6 , for transmission through the first and second OFDM symbols of each frame as described above, pilot bits pass through the serial/parallel converter  612 , are converted into symbols of the time domain, and are then converted into a serial pilot bits. The Cyclic Prefix (CP) inserter  615  inserts CPs to the converted pilot bits, which are then converted from the digital signal to an analog signal by the digital/analog converter  616 . Then, the converted analog signal is transmitted through the channel  620  to the receiver  630 . 
     The signal received through the channel  620  is converted again from the analog signal to a digital signal by the analog/digital converter  631  and the converted digital signal is then transferred to the correlator  638 . Then, in order to acquire the first frequency synchronization, the correlator  638  finds the repeated pattern of the first pilot OFDM symbol of the received signal and revises the decimal part of the frequency offset. After the decimal part of the frequency offset is revised, the CP remover  632  removes CPs from the received signal, the serial/parallel converter  633  converts the signal into a parallel signal, and then the FFT converter  634  converts the signal into a signal of the frequency domain. Then, in order to acquire the second frequency synchronization, the ambiguity resolution unit  640  checks the correlation value between the differential values of the first and second pilot symbols in the frequency domain and thereby solves the ambiguity of the frequency offset, that is, revises the integer part of the frequency offset. Then, the initial frequency synchronization is acquired as a result. 
     The conventional frequency synchronization method as described above is known as a method that is capable of obtaining an exact initial frequency offset. However, in the OFDM based wireless system, the conventional method uses two OFDM symbols within one frame for pilot transmission in order to revise the initial offset, thereby causing an excessively large overhead. In order to solve this problem, a method has been developed that is capable of acquiring the initial frequency offset while using only one pilot OFDM symbol for revising the initial frequency offset. 
     According to this method which uses only one pilot OFDM symbol, the second pilot OFDM symbol as shown in  FIG. 5  is not transmitted, and only the first pilot OFDM symbol is transmitted, so that the symbol corresponding to the second pilot OFDM symbol can be used in transmitting data and thus can reduce the overhead. In the method for initial frequency synchronization by using only one pilot OFDM symbol, it is also necessary to perform both the first frequency synchronization step for finding the decimal part of the frequency offset, and the second frequency synchronization step for resolving the ambiguity of the multiple of the sub-carrier band by finding the integer part of the frequency offset. That is, the same process as that using equation (6) is also used in the method for initial frequency synchronization by using only one pilot OFDM symbol. 
     However, although the method using only one pilot OFDM symbol can reduce the overhead of the system in comparison with the method using two pilot OFDM symbols, the method using only one pilot OFDM symbol is based on an assumption that the channel does not change for a predetermined number of sub-carriers in resolving the ambiguity for determining the integer part of the frequency offset. Therefore, the method using only one pilot OFDM symbol has a degraded performance in acquiring the initial frequency synchronization for a channel environment having a selectivity in the frequency domain. 
     Accordingly, a need exists for a system and method that is capable of substantially guaranteeing an improved performance for initial frequency synchronization while reducing the overhead of the system. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention has been made to solve the above-mentioned and other problems occurring in the prior art, and an object of the present invention is to provide a method and an apparatus for initial frequency synchronization which can reduce the overhead of the system in the process for initial frequency synchronization of an OFDM system. 
     It is another object of the present invention to provide a method and an apparatus which can acquire initial frequency synchronization without transmitting a pilot OFDM symbol in an OFDM system. 
     It is another object of the present invention to provide a method and an apparatus which can acquire initial frequency synchronization by using a cyclic prefix in an OFDM system. 
     It is another object of the present invention to provide a method and an apparatus which can acquire initial frequency synchronization in the time domain without transmitting a preamble in an OFDM system. 
     It is another object of the present invention to provide a method and an apparatus which can acquire initial frequency synchronization by adjusting the data size of a data OFDM symbol in an OFDM system. 
     In order to accomplish this object, a method is provided for frequency synchronization in an Orthogonal Frequency Division Multiplexing (OFDM) system, the method comprising the steps of: transmitting OFDM symbols such that a data symbol size of a particular OFDM symbol is set to be smaller than a data symbol size of typical OFDM symbols within a frame; receiving the particular OFDM symbol and calculating respectively correlation coefficients of the particular OFDM symbol based on both a time interval of corresponding data symbols and a time interval of data symbols of the typical OFDM symbol; taking respectively phases of corresponding correlation coefficients calculated from the particular OFDM symbol and estimating a decimal part of a frequency offset; and determining an integer part of the frequency offset corresponding to the decimal part of the frequency offset for estimating a substantially entire frequency offset and acquiring the frequency synchronization. 
     In accordance with another aspect of the present invention, a method is provided for transmitting Orthogonal Frequency Division Multiplexing (OFDM) symbols by a transmitter for frequency synchronization in an OFDM system, the method comprising the steps of performing Inverse Fast Fourier Transform (IFFT) on the OFDM symbols after setting a data symbol size of a particular OFDM symbol in each frame to be smaller than a data symbol size of a typical OFDM symbol within the frame, and inserting cyclic prefixes into data symbols of the particular OFDM symbol and then transmitting the OFDM symbols. 
     In accordance with another aspect of the present invention, a method is provided for receiving Orthogonal Frequency Division Multiplexing (OFDM) symbols by a receiver for frequency synchronization in an OFDM system, the method comprising the steps of: receiving a particular OFDM symbol having a data symbol size smaller than a data symbol size of typical OFDM symbols and calculating respectively correlation coefficients of the particular OFDM symbol based on both a time interval of the corresponding data symbols and a time interval of the typical OFDM symbols; taking respectively phases of corresponding correlation coefficients calculated from the particular OFDM symbol and estimating a decimal part of a frequency offset; and determining an integer part of the frequency offset corresponding to the decimal part of the frequency offset for estimating a substantially entire frequency offset and acquiring the frequency synchronization. 
     In accordance with another aspect of the present invention, an Orthogonal Frequency Division Multiplexing (OFDM) system is provided for frequency synchronization for communication, the system comprising: a transmitter for transmitting OFDM symbols such that a data symbol size of a particular OFDM symbol is set to be smaller than a data symbol size of typical OFDM symbols within a frame; and a receiver for receiving the particular OFDM symbol and calculating respectively correlation coefficients of the particular OFDM symbol both a time interval of corresponding data symbols and a time interval of data symbols of the typical OFDM symbol, taking respectively phases of corresponding correlation coefficients calculated from the particular OFDM symbol and estimating a decimal part of a frequency offset, and determining an integer part of the frequency offset corresponding to the decimal part of the frequency offset for estimating a substantially entire frequency offset and acquiring the frequency synchronization. 
     In accordance with another aspect of the present invention, an apparatus is provided for transmitting Orthogonal Frequency Division Multiplexing (OFDM) symbols for frequency synchronization in an OFDM system, the apparatus comprising a conversion unit for performing Inverse Fast Fourier Transform (IFFT) on the OFDM symbols after setting a data symbol size of a particular OFDM symbol in each frame to be smaller than a data symbol size of a typical OFDM symbol within the frame, and a transmission unit for inserting cyclic prefixes into data symbols of the particular OFDM symbol and then transmitting the OFDM symbols. 
     In accordance with another aspect of the present invention, an apparatus is provided for receiving Orthogonal Frequency Division Multiplexing (OFDM) symbols for frequency synchronization in an OFDM system, the apparatus comprising: a correlation unit comprising at least one correlator for receiving a particular OFDM symbol having a data symbol size smaller than a data symbol size of typical OFDM symbols and for calculating respectively correlation coefficients of the particular OFDM symbol based on both a time interval of the corresponding data symbols and a time interval of the typical OFDM symbols, and taking respectively phases of corresponding correlation coefficients calculated from the particular OFDM symbol and estimating a decimal part of a frequency offset; and an estimation unit for estimating a substantially entire frequency offset by determining an integer part of the frequency offset corresponding to the decimal part of the frequency offset and acquiring the frequency synchronization. 
    
    
     
       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 taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a block diagram illustrating the structure of a transmitter and a receiver in a physical layer of a typical OFDM system; 
         FIG. 2  is a graph illustrating data symbols transmitted in a typical OFDM system, which are illustrated according to frequency and time; 
         FIG. 3  is a graph illustrating an example of the orthogonality between sub-carriers in the OFDM system; 
         FIG. 4  is a graph illustrating interference between sub-carriers when there are frequency offsets in a typical OFDM system; 
         FIG. 5  illustrates an example of a format of pilot OFDM symbols according to a conventional initial frequency synchronization method in an OFDM system; 
         FIG. 6  is a block diagram illustrating a structure of a transmitter and a receiver for initial frequency synchronization in a physical layer of a conventional OFDM system; 
         FIG. 7  is a block diagram illustrating a structure of a transmitter and a receiver for initial frequency synchronization in an OFDM system according to an embodiment of the present invention; 
         FIG. 8  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to an embodiment of the present invention; 
         FIG. 9  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to another embodiment of the present invention, in which one OFDM symbol in each frame is transmitted after being divided into two FFTs; 
         FIG. 10  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to another embodiment of the present invention, in which one OFDM symbol in each frame is transmitted in a state of having a size of N 1  smaller than N; 
         FIG. 11  is a flowchart of an operation of a transmitter in an OFDM system according to an embodiment of the present invention; and 
         FIG. 12  is a flowchart of an operation of a receiver in an OFDM system according to an embodiment of the present invention. 
     
    
    
     Throughout the drawings, like reference numerals will be understood to refer to like parts, components and structures. 
     DETAILED DESCRIPTION OF THE EXEMPLARY EMBODIMENTS 
     Hereinafter, exemplary embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, detailed descriptions of known functions and configurations incorporated herein are omitted for clarity and conciseness. 
     In contrast with the conventional method which uses two pilot OFDM symbols for the initial frequency synchronization, a principle of embodiments of the present invention lies in that one OFDM symbol in each frame is divided into at least two parts which can be converted by FFTs having sizes of N 1  and N 2  smaller than N, which is an FFT size of a typical OFDM symbol. 
     That is, according to embodiments of the present invention, the transmitter arranges the OFDM symbols carrying data such that they have different FFT sizes each frame, and the receiver having received an OFDM symbol, calculates a correlation coefficient between data in the OFDM symbol and the cyclic prefix either with a time interval of N data symbols, or with a time interval of N 1  data symbols, or with a time interval of N 1  and N 2  data symbols. Further, it is possible in accordance with the embodiments of the present invention to acquire the initial frequency synchronization by acquiring the first frequency synchronization by taking a phase for the correlation value exceeding a predetermined threshold value and acquiring the second frequency synchronization by resolving the ambiguity of the frequency offset. Therefore, it is possible in accordance with the embodiments of the present invention to acquire the initial frequency synchronization even without transmitting a particular preamble or pilot OFDM symbol. 
     In the method according to embodiments of the present invention as described above, the process for acquiring the first frequency synchronization corresponds to a process of determining the decimal part of the frequency offset, and the process for acquiring the second frequency synchronization corresponds to a process of determining the integer part of the frequency offset. 
     Hereinafter, exemplary embodiments of the present invention provided for initial frequency synchronization will be described with reference to the accompanying drawings. 
       FIG. 7  is a block diagram illustrating a structure of a transmitter and a receiver for initial frequency synchronization in an OFDM system according to an embodiment of the present invention. The structure of  FIG. 7  comprises a transmitter  710  and a receiver  730 . 
     Referring to  FIG. 7 , the transmitter  710  comprises an encoder  711 , a serial/parallel converter  712 , a parallel/serial converter  714 , a CP inserter  715 , and a digital/analog converter  716 . Although a pilot bit is transmitted for frequency synchronization in the conventional method, the transmitter  710  of embodiments of the present invention transmits data bits without transmitting a separate pilot bit. The transmitter  710  further comprises an Inverse Fast Fourier Transform (IFFT) unit  713  that is capable of IFFT-converting data bits and also IFFT-converting typical OFDM symbols having an IFFT size of N into OFDM symbols having a size (e.g. N 1  or N 2 ) smaller than N. The serial/parallel converter  712  converts the data bits encoded by the encoder  711  into parallel signals and transfers the converted parallel signals to the IFFT unit  713 . The output of the IFFT unit  713  is transferred to the parallel/serial converter  714 . 
     In embodiments of the present invention, the IFFT unit  713  comprises, for example, a plurality of IFFT converters  713   a ,  713   b  and  713   c  having sizes of N, N 1  and N 2 , respectively. The IFFT converter  713   a  having the size of N performs an N sized IFFT for processing typical OFDM symbols for the input data bits, and the IFFT converter  713   b  having the size of N 1  performs an N 1  sized IFFT for processing OFDM symbols having an FFT size smaller than N which are located at each frame. Further, when at least one OFDM symbol located at each frame is divided into two parts respectively having sizes of N 1  and N 2 , the IFFT unit  713  simultaneously performs an N 1  sized IFFT and an N 2  sized IFFT by means of the IFFT converters  713   b  and  713   c.    
     Although two cases having N 1  and N 2  as an FFT size of the OFDM symbol are described in regard to the exemplary embodiment, it is possible for the IFFT unit  713  to have a construction that is capable of processing an OFDM symbol including at least two parts each having a size smaller than N. 
     The parallel/serial converter  714  converts the IFFT-converted data into a serial data and inputs the serial data to the CP inserter  715 . The CP inserter  715  inserts CPs into the input serial data and then inputs the CP inserted data to the digital/analog converter  716 , which then converts the data into an analog signal. The converted analog signal is then transmitted to the receiver through the channel  720 . 
     The receiver  730  which receives the signal transmitted through the channel  720  from the transmitter, comprises an analog/digital converter  731  for converting the received signal into a digital signal, a correlation unit  738  for acquiring a first frequency synchronization by receiving the digitalized OFDM symbol and calculating a correlation value between the data in the OFDM symbol and the cyclic prefix, and an ambiguity resolution unit  740  for acquiring a second frequency synchronization by resolving ambiguity of the output correlation value. It should be noted that other general elements of a receiver of an OFDM system such as a CP remover, an FFT converter and so forth are omitted in  FIG. 7  for clarity and conciseness. 
     When the correlation unit  738  receives an OFDM symbol, the correlation unit  738  calculates correlation coefficients between data within the OFDM symbol and the cyclic prefix by using a time interval of an N sized data symbol and a time interval of a data symbol having a size smaller than N, and takes a phase for the correlation coefficient exceeding a predetermined threshold and determines the decimal part of the frequency offset for the phase (that is, the first frequency synchronization). 
     Referring to  FIG. 7 , the correlation unit  738  receives the OFDM symbol which has been converted into a digital signal by the analog/digital converter  731 . The received OFDM symbol simultaneously passes through the correlator # 0   738   a  for an OFDM symbol having been subjected to an N sized IFFT, the correlator # 1   738   b  for an OFDM symbol having been subjected to an N 1  sized IFFT, and the correlator # 2   738   c  for an OFDM symbol having been subjected to an N 2  sized IFFT when the symbol has been divided into two parts. The correlators  738   a ,  738   b  and  738   c  calculate the correlation coefficients between data within the OFDM symbol and the cyclic prefix by using data symbol time intervals of N, N 1  and N 2 . Also, the correlators  738   a ,  738   b  and  738   c  check if the calculated correlation coefficients are larger than a predetermined threshold value and takes a phase for the correlation coefficient exceeding the threshold value, thereby estimating the decimal part of the frequency offset. 
     When the correlation unit  738  has estimated at least one decimal part of the frequency offset, the correlation unit  738  transfers the correlation values to the ambiguity resolution unit  740 . The ambiguity resolution unit  740  acquires the second frequency synchronization by determining the integer part of the frequency offset by using the frequency synchronization estimation algorithm of embodiments of the present invention as described below. Therefore, the receiver  730  having acquired both the first and second frequency synchronization by the above-described exemplary embodiment constructions and methods can determine the frequency offset and acquire the initial synchronization even without receiving the pilot OFDM symbol. 
     Hereinafter, a frequency synchronization estimation algorithm of embodiments of the present invention will be described in greater detail. 
     According to an exemplary embodiment of the present invention, the initial frequency synchronization is estimated by calculating the correlation coefficient between data in the OFDM symbol and the cyclic prefix at one OFDM symbol within each frame having an FFT size different from that of the typical OFDM symbol. Equation (7) below can be derived from an OFDM symbol having an FFT size of N.
 
Δ {circumflex over (f)}={circumflex over (φ)}   0 /(2π T )+ ĝ   0   /T   (7)
 
     In equation (7), {circumflex over (φ)} 0  denotes the decimal part of the frequency offset of the OFDM symbol having an FFT size of N, and ĝ 0  denotes the integer part of the frequency offset corresponding to a multiple of the sub-carrier band. Further, the frequency offset for an OFDM symbol having a reduced FFT size of N 1  can be estimated by equation (8) below.
 
Δ {circumflex over (f)}={circumflex over (φ)}   1 /(2 πT 1)+ ĝ   1   /T 1  (8)
 
     In equation (8), {circumflex over (φ)} 1  denotes the decimal part of the frequency offset of the OFDM symbol having an FFT size of N 1 , ĝ 1  denotes the integer part of the frequency offset corresponding to a multiple of the sub-carrier band and T 1  denotes a time interval corresponding to a data except for the length of the cyclic prefix of the symbol having an FFT size of N 1 . 
     In contrast to equation (1) showing the repetition of the pilot data having a half OFDM symbol length, equation (8) shows a frequency offset estimation using a correlation coefficient between an OFDM symbol data of one OFDM symbol length difference and the cyclic prefix. Therefore, the range of the decimal part of the frequency offset is estimated within an absolute value of the half length of the sub-carrier band, and the ambiguity occurs by an integer multiplied by the sub-carrier band instead of by an integer multiplied by twice the sub-carrier band. 
     When one OFDM symbol of each frame is divided into two FFT parts having sizes of N 1  and N 2  and the data subjected to the second FFT part having the size of N 2  is used, the frequency offset can be estimated by equation (9) below.
 
Δ {circumflex over (f)}={circumflex over (φ)}   2 /(2 πT 2)+ ĝ   2   /T 2  (9)
 
     In equation (9), {circumflex over (φ)} 2  denotes the decimal part of the frequency offset of the OFDM symbol having an FFT size of N 2 , ĝ 2  denotes the integer part of the frequency offset corresponding to a multiple of the sub-carrier band, and T 2  denotes a time interval corresponding to data excluding the length of the cyclic prefix of the symbol having an FFT size of N 2 . 
     By using equations (7) through (9), it is possible to determine the single frequency offset Δf according to selection of N 1  or N 2  with respect to N. 
     For the case in which one OFDM symbol within each frame is transmitted after being subjected to an FFT having a size of N 1  or after being divided into two parts by FFTs having sizes of N 1  and N 2  as described above, various examples of transmission of the cyclic prefix and OFDM data according to time and frequency coordinates will be described in detail with reference to  FIGS. 8 through 10 . 
       FIG. 8  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to an embodiment of the present invention. 
     Referring to  FIG. 8 , a cyclic prefix  802  repeating the sample at the rear end of an OFDM symbol  801  with a length of L in the time domain, is added to the front end of the OFDM symbol  801  that has been subjected to the N sized FFT conversion and the OFDM symbol  801  is then transmitted. Further, the transmitted OFDM symbol having been subjected to the N 1  and N 2  sized FFT conversion comprises the FFT part and accompanies an N 1  sized FFT part  803  with a corresponding cyclic prefix  805  and an N 2  sized FFT part  804  with a corresponding cyclic prefix  806 . In this case, if a frequency offset of Δf has occurred, the frequency offset has a different decimal part and integer part depending on the size of the FFT conversion. 
     For example, if it is assumed in this example that N=16, N 1 =9 and N 2 =7, then T/T 1 =1.178 and T/T 2 =2.286. As noted from Table 1 below, if Δf*T=2.5, the decimal part of the frequency offset in the OFDM symbol having an N sized FFT is 1.0π (φ 0 =1.0π) and the decimal parts of the frequency offset in the OFDM symbol having N 1  and N 2  sized FFTs are 1.444π and 0.428π, respectively (that is, φ 1 =1.444π and φ 2 =0.428π). Therefore, it is theoretically possible to obtain the decimal parts φ 0 , φ 1  and φ 2 , and the integer parts g 0 , g 1  and g 2  of the frequency offset coinciding with Δf. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
            
               
                   
                 Δf * T = 2.5 
                   
                 g 0  = 2 
                 φ 0  = 1.0π 
               
               
                   
                 Equation (8) 
                 T/T1 = 1.178 
                 g 1  = 1 
                 φ 1  = 1.444π 
               
               
                   
                 Equation (9) 
                 T/T2 = 2.286 
                 g 2  = 1 
                 φ 2  = 0.428π 
               
               
                   
                   
               
            
           
         
       
     
     Further, the integer parts corresponding to the decimal parts of the frequency offset may be provided in the form of table information at the receiver. 
     In an actual estimation of the frequency offset, an estimation error may be added to make it difficult to achieve an exact estimation of the frequency offset. The estimation error may be reduced by properly setting up the value N 1  or the values N 1  and N 2 . Further, it is possible to obtain a more exact and clearer frequency offset through repetition of the estimation, revision and then estimation of the frequency offset again. 
     In the OFDM system according to embodiments of the present invention, one OFDM symbol including N number of data samples is transmitted together with L number of cyclic prefixes. In the exemplary embodiment shown in  FIG. 8 , the cyclic prefixes are arranged at two locations based on the FFT, and the total length of the cyclic prefixes is equal to that in the case of the OFDM symbol having an N sized FFT. However, in this case, the reception performance may be degraded due to the delay length of the multi-path fading. 
       FIG. 9  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to another embodiment of the present invention, in which one OFDM symbol in each frame is transmitted after being divided into two FFTs. 
     Referring to  FIG. 9 , cyclic prefixes  903  and  904  having the same size of L as that of the typical OFDM symbol having an N sized FFT are put in front of the two parts  901  and  902  having sizes of N 1  and N 2 . The sizes N 1  and N 2  of the two data parts may be reduced in consideration of the size of the cyclic prefixes in order to insert additional cyclic prefixes within a range defined by one OFDM symbol and the number of all samples of corresponding cyclic prefixes. 
       FIG. 10  is a graph illustrating a method for transmission of a cyclic prefix and OFDM data according to another embodiment of the present invention, in which one OFDM symbol in each frame is transmitted in a state of having a size of N 1  smaller than N. 
     Referring to  FIG. 10 , one OFDM symbol  1003  in each frame is subjected to an N 1  sized FFT and the other data OFDM symbols  1001  are subjected to an N sized FFT, and they are then transmitted together with cyclic prefixes each having a size of L. For the cyclic prefix  1004  for the OFDM symbol  1003  subjected to the N 1  sized FFT, an extended cyclic prefix  1004  may be transmitted because the FFT size has been reduced from N to N 1 . 
     As described above,  FIGS. 8 through 10  illustrate examples of improvements in the performance of the initial frequency synchronization by using OFDM symbols converted by an FFT with a size smaller than N instead of the OFDM symbols converted by an N sized FFT, by which embodiments of the present invention are not limited. 
     Hereinafter, an exemplary operation of a transmitter and receiver according to embodiments of the present invention will be described with reference to  FIGS. 11 and 12 . The following operation is an example of transmission of OFDM symbols having been divided into parts corresponding to N 1  and N 2  sized FFTs for initial frequency synchronization. 
       FIG. 11  is a flowchart of an operation of a transmitter in an OFDM system according to an embodiment of the present invention. 
     Referring to  FIG. 11 , when the data transmission begins, the transmitter determines whether to select an FFT with a size of N or an FFT with a size smaller than N at step  1101 . As a result of the determination, when it is necessary to transmit an OFDM symbol corresponding to the N sized FFT, the transmitter takes N number of data symbols at step  1102  and performs N sized IFFT conversion for the data symbols to shift the symbols into the time domain at step  1103 . Then, the transmitter inserts L sized cyclic prefixes into the data symbols of the time domain at step  1104 , transmits the OFDM symbols at step  1105 , and then returns to step  1101 . 
     As a result of the determination in step  1101 , when it is necessary to transmit an OFDM symbol corresponding to an FFT having a size smaller than N, the transmitter takes N 1  number of or (N 1 +N 2 ) number of data symbols at step  1110  and performs N 1  sized IFFT conversion for the data symbols at step  1112 . Then, the transmitter performs N 2  sized IFFT conversion for the data symbols at step  1113 . Here, step  1113  may be omitted if necessary. When step  1113  is performed, an N 2  point IFFT conversion of the data symbols is first performed, and the N OFDM symbols are then divided into N 1  symbols and N 2  symbols for FFT conversion (wherein each N 1  and N 2  is smaller than N) as shown in  FIGS. 9 and 10 . However, in the example shown in  FIG. 11 , an IFFT is performed only for N 1  number of data symbols. Thereafter, the transmitter inserts CPs into the IFFT converted data symbols and outputs the OFDM symbols to be transmitted at step  1114  and then transmits the OFDM symbols having been subjected to an IFFT of a size smaller than N at step  1105 . 
     Hereinafter, an operation of a receiver having received OFDM symbols transmitted from the transmitted operating as described above will be described with reference to  FIG. 12 . 
       FIG. 12  is a flowchart of an operation of a receiver in an OFDM system according to an embodiment of the present invention. 
     In step  1201 , the receiver receives and accumulates OFDM symbols including CPs. Whenever it receives each of the OFDM symbols, the receiver renewals an ODFM symbol received newly. Then, the receiver calculates a correlation coefficient between data in the OFDM symbol and a corresponding cyclic prefix with a time interval of N data symbols for each of the received OFDM symbols at step  1202  and calculates a correlation coefficient between data in the OFDM symbol and a corresponding cyclic prefix with a time interval of N 1  data symbols. When one OFDM symbol has been divided into two FFT parts, the correlation value is calculated with a time interval of N 1  data symbols at step  1203 , and also with a time interval of N 2  data symbols at step  1204 . 
     Thereafter, in steps  1205  and  1206 , the receiver determines if the calculated correlation values for time intervals of the N and N 1  data symbols are larger than preset first and second threshold values, respectively. Further, when one OFDM symbol has been divided into two parts for FFT conversion as shown in  FIGS. 9 and 10 , the receiver determines if the calculated correlation value in relation to the time interval of the N 2  data symbols exceeds a preset third threshold value at step  1207 . 
     When each of the calculated correlation value satisfies a condition by the preset threshold values in steps  1205  through  1207 , the receiver acquires the first frequency synchronization by taking the phase of the correlation value and estimating the decimal part of the frequency offset at step  1208 . When each of the calculated correlation values fails to satisfy the condition by the preset threshold values, the receiver proceeds to step  1209 . 
     When the decimal part of the frequency offset has been estimated, the receiver checks if at least one decimal part of the frequency offset has been estimated through the OFDM symbol including FFT parts of different sizes. When at least one decimal part of the frequency offset has not been estimated, the process repeatedly performs steps  1201  to  1209 . When it is determined in step  1209  that at least two decimal part of the frequency offset has been estimated, the receiver acquires the second frequency synchronization by resolving the ambiguity and determining the integer part of the frequency offset in order to estimate the entire frequency offset at step  1210 . 
     The entire frequency offset estimated through the process of  FIG. 12  is used to revise the frequency offset. In order to reduce error in the course of the initial frequency synchronization, the estimation of the entire frequency offset can be repeated even after the frequency offset is revised. 
     As described above, the present invention provides a method and an apparatus for initial frequency synchronization which can reduce the overhead of the system in the process for initial frequency synchronization of an OFDM system, and can acquire initial frequency synchronization without transmitting a pilot OFDM symbol in an OFDM system. Also, the present invention provides a method and an apparatus which can acquire initial frequency synchronization in the time domain by using a cyclic prefix and by transmitting a particular OFDM symbol having a data size smaller than that of a typical OFDM symbol through each frame in an OFDM system. 
     While the invention has been shown and described with reference to certain exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.