Abstract:
Provided is a synchronization apparatus and method for a receiver that performs synchronization in a digital domain and detects a transmission signal. The synchronization apparatus includes an Analog-to-Digital (A/D) converter for converting a received signal into a digital signal, a frequency synchronizer for synchronizing a frequency using the digital signal output from the A/D converter, a signal detection unit for detecting a transmission symbol from a signal synchronized by the frequency synchronizer, and a residual phase detector for compensating for a residual phase of the transmission symbol output from the signal detection unit and outputting the resulting transmission symbol. The frequency synchronizer is capable of accurately and efficiently compensating for a frequency offset by minimizing the time delay caused by subcarrier synchronization using an improved CORDIC algorithm.

Description:
PRIORITY  
       [0001]     This application claims priority under 35 U.S.C. § 119 to an application entitled “Frequency Synchronization Apparatus and Method for Orthogonal Frequency Division Multiplexing System” filed in the Korean Intellectual Property Office on Apr. 27, 2005 and assigned Serial No. 2005-35296, the contents of which are incorporated herein by reference.  
       BACKGROUND OF THE INVENTION  
       [0002]     1. Field of the Invention  
         [0003]     The present invention generally relates to an Orthogonal Frequency Division Multiplexing (OFDM)-based communication system, and in particular, to a frequency synchronization apparatus and method using an improved Coordinated Rotation Digital Computer (CORDIC) algorithm for an OFDM system.  
         [0004]     2. Description of the Related Art  
         [0005]     OFDM is a technique for multicarrier transmission in which a signal is transmitted using multiple carriers. By using a plurality of subcarriers that are orthogonal to each other, OFDM can use a frequency effectively and implement high-speed modulation/demodulation through Inverse Fast Fourier Transform/Fast Fourier Transform. OFDM can extend a symbol period for each subcarrier by the number of subcarriers while maintaining data transmission speed in the transmission of high-speed data having a short symbol period in a wireless communication channel having a multipath fading phenomenon. In this regard, OFDM is more robust to a frequency-selective fading channel than a single-carrier transmission scheme.  
         [0006]     OFDM transmission is performed in a symbol unit. When an OFDM symbol is transmitted through a multipath channel, the currently transmitted symbol may be affected by a previously transmitted symbol, which is called Inter Symbol Interference (ISI). To mitigate ISI, a guard interval longer than the maximum delay spread of a channel is inserted between successive OFDM symbols. Thus, a symbol period is a sum of an effective symbol interval in which actual data is transmitted and a guard interval. A receiver detects and demodulates data associated with the effective symbol interval after removing the guard interval. To prevent orthogonality from being destroyed due to the delay of a subcarrier, a signal of the last part of the effective symbol interval is copied and inserted, and the copied and inserted signal is referred to as a cyclic prefix (CP).  
         [0007]     Generally, a signal received through a channel has a frequency offset due to phase jitter or Doppler shift. This subcarrier frequency offset causes interference between subcarriers and thus distorts power and phase of the signal. In other words, if subcarrier frequencies of a transmitter and a receiver are different from each other, the subcarrier frequency offset occurs and causes interference between subcarriers, thus destroying orthogonality of a channel and increasing an error rate. Therefore, the receiver should complete frequency synchronization between the transmitter and the receiver before performing a Fourier transform.  
         [0008]     A wireless modem using OFDM transmits a training symbol used for channel estimation and initial synchronization at the beginning of a data symbol period. For example, a burst modem for a wireless Local Area Network (LAN) such as an IEEE 802.11a or ETSI HIPERLAN/2 system uses in a time domain a short training symbol composed of 10 repeated sequences, each of which is 16 samples long, and a long training symbol composed of 2 repeated sequences, each of which is 64 samples long.  
         [0009]     A conventional carrier frequency synchronization apparatus estimates a frequency offset in a digital domain using a training symbol and then controls a Voltage Controlled Oscillator (VCO) using an output signal of a loop filter according to the estimated frequency offset. The VCO is widely used for subcarrier synchronization in an analog domain, and a Numerical Controlled Oscillator (NCO) for compensating for a subcarrier offset in the digital domain may be used.  
         [0010]     However, a subcarrier synchronization method in the analog domain, which is applied to a conventional OFDM system, cannot provide reliable frequency offset compensation for data detection and accurate subcarrier synchronization due to the time delay caused by generation of a VCO control signal using an estimated frequency offset and subcarrier synchronization using an output of the VCO.  
         [0011]     A subcarrier synchronization method in a complete digital domain uses a Coordinated Rotation Digital Computer (CORDIC) algorithm or a lookup table to implement an arctangent function or a log function. The subcarrier synchronization method using the CORDIC algorithm can be implemented with a simple structure, but has low computation speed and accuracy. The subcarrier synchronization method using the lookup table has high computation speed and accuracy, but requires frequency memory use and thus is not easy to implement, and requires difficult table address generation.  
       SUMMARY OF THE INVENTION  
       [0012]     It is, therefore, an object of the present invention to provide a frequency synchronization apparatus and method using an improved CORDIC algorithm, which provides high computation speed and improves estimation accuracy.  
         [0013]     It is another object of the present invention to provide a frequency synchronization apparatus and method capable of accurately and efficiently compensating for a frequency offset by minimizing the time delay caused by subcarrier synchronization using an improved CORDIC algorithm.  
         [0014]     According to one aspect of the present invention, there is provided a synchronization apparatus for a receiver that performs synchronization in a digital domain and detects a transmission signal. The synchronization apparatus includes an Analog-to-Digital (A/D) converter for converting a received signal into a digital signal, a frequency synchronizer for synchronizing a frequency using the digital signal output from the A/D converter, a signal detection unit for detecting a transmission symbol from a signal synchronized by the frequency synchronizer, and a residual phase detector for compensating for a residual phase of the transmission symbol output from the signal detection unit and outputting the resulting transmission symbol.  
         [0015]     Preferably, the frequency synchronizer includes an estimation unit for estimating a frequency offset of the received signal and a compensation unit for compensating for the frequency offset estimated by the estimation unit.  
         [0016]     Preferably, the estimation unit includes a shift register for delaying a sample of the received signal and simultaneously outputting conjugate complex numbers of a predetermined received signal and a next received signal, a first complex multiplier for performing complex multiplying with respect to the output conjugate complex numbers, a first accumulator for accumulating an output of the first complex multiplier, a first preprocessor for performing preprocessing for phase rotation transform with respect to an output of the first accumulator, a vector-mode Coordinated Rotation Digital Computer (CORDIC) calculator for outputting a phase value by vector-mode CORDIC calculation with respect to an output of the first preprocessor, and a first phase adjustor for estimating the frequency offset from the phase value output from the vector-mode CORDIC calculator.  
         [0017]     Preferably, the compensation unit includes a bit extender for dividing the frequency offset output from the estimation unit into samples of a predetermined size, a second accumulator for accumulating a frequency offset of each of the samples output from the bit extender to generate a log function table address, a log function processor for outputting a trigonometric function value by referring to the log function table address generated by the second accumulator, a second phase adjustor for generating a complex number using the trigonometric function value output from the log function processor and an output of the second accumulators and a second complex multiplier for compensating for the signal offset by multiplying the digital signal output from the A/D converter by the complex number output from the second phase adjustor.  
         [0018]     Preferably, the residual phase detector includes a pilot extractor for extracting a pilot signal from a baseband signal output from the signal detection unit, a third accumulator for accumulating the extracted pilot signal, a second preprocessor for performing preprocessing for CORDIC calculation with respect to a signal output from the third accumulator, a compact CORDIC calculator for simultaneously performing a vector-mode CORDIC calculation and rotation-mode CORDIC calculation with respect to a signal output from the second preprocessor and outputting the phase value, a third phase adjustor for estimating the frequency offset from the phase value output from the compact CORDIC calculator, and a third complex multiplier for compensating for the residual phase by multiplying the baseband signal output from the signal detection unit by the complex value output from the third phase adjustor.  
         [0019]     Preferably, the compact CORDIC calculator includes a vector-mode unit for performing vector-mode CORDIC calculation with respect to the signal output from the second preprocessor, a rotation-mode unit for performing rotation-mode CORDIC calculation using a predetermined initial value, and a counter for counting the number of repetitions of CORDIC calculation.  
         [0020]     Preferably, the vector-mode unit includes a first register for receiving and temporarily storing a real part of the signal output from the second preprocessor, a second register for receiving and temporarily storing an imaginary part of the signal output from the second preprocessor, a first shifter for shifting an output of the second register according to the number of repetitions output from the counter, a first complementary operator for performing a complementary operation with respect to 1 for the output of the first shifter, a first multiplexer for multiplexing an output of the first complementary operator and an output of the first shifter, a first Carry Lookahead Adder (CLA) for adding an output of the first multiplexer to the output of the first register and feeding back the result to the first register, a second shifter for shifting the output of the first register according to the number of repetitions output from the counter, a second complementary operator for performing a complementary operation with respect to 1 for the output of the second shifter, a second multiplexer for multiplexing an output of the second complementary operator and the output of the second shifter, and a second CLA for adding an output of the second multiplexer to the output of the second register and feeding back the result to the second register.  
         [0021]     Preferably, the rotation-mode unit includes a third register for receiving and temporarily storing a real part of a signal output from the fourth preprocessor, a fourth register for receiving and temporarily storing an imaginary part of the signal output from the fourth preprocessor, a third shifter for shifting an output of the fourth register according to the number of repetitions output from the counter, a third complementary operator for performing a complementary operation with respect to 1 for an output of the third shifter, a third multiplexer for multiplexing an output of the third complementary operator and the output of the third shifter, a third CLA for adding an output of the third multiplexer to the output of the third register and feeding back the result to the third register, a fourth shifter for shifting the output of the third register according to the number of repetitions output from the counter, a fourth complementary operator for performing a complementary operation with respect to 1 for the output of the fourth shifter, a fourth multiplexer for multiplexing an output of the fourth complementary operator and the output of the fourth shifter, and a fourth CLA for adding an output of the fourth multiplexer to the output of the fourth register and feeding back the result to the fourth register.  
         [0022]     Preferably, the signal detection unit includes a Fourier transformer for performing Fast Fourier Transform (FFT) with respect to a signal output from the frequency synchronizer, an equalizer for equalizing a signal output from the Fourier transformer, and a channel estimator for estimating a channel value from a signal output from the equalizer and inputting the estimated channel to the Fourier transformer.  
         [0023]     According to another aspect of the present invention, there is provided a synchronization method for a receiver that performs synchronization in a digital domain and detects a transmission signal. The synchronization method includes converting a received signal into a digital signal, synchronizing a frequency using the digital signal, detecting a transmission symbol from the synchronized signal, and compensating for a residual phase of the output transmission symbol and outputting the resulting transmission symbol.  
         [0024]     Preferably, the step of synchronizing the frequency includes estimating a frequency offset of the received signal and compensating for the estimated frequency offset.  
         [0025]     Preferably, the step of estimating the frequency offset includes delaying a sample of the received signal and simultaneously outputting conjugate complex numbers of a predetermined received signal and a next received signal, performing complex multiplying with respect to the output conjugate complex numbers, accumulating the result of complex multiplying, performing preprocessing for phase rotation transform with respect to the accumulated result of complex multiplying, outputting a phase value by vector-mode CORDIC calculation with respect to the result of preprocessing, and estimating the frequency offset from the output phase value.  
         [0026]     Preferably, the step of compensating for the frequency offset includes dividing the estimated frequency offset into samples of a predetermined size, accumulating a frequency offset of each of the samples output to generate a log function table address, outputting a trigonometric function value by referring to the generated log function table address, generating a complex number using the output trigonometric function value and the generated log function table address, and compensating for the signal offset by multiplying the output digital signal by the generated complex number.  
         [0027]     Preferably, the step of preprocessing for phase rotation transform includes performing Exclusive OR (XOR) operations on the accumulated result of complex multiplying, performing OR operations on the result of XOR operations, and multiplexing the result of OR operations and outputting the result of preprocessing.  
         [0028]     Preferably, the step of compensating for the residual phase of the transmission symbol includes extracting a pilot signal from the transmission symbol, accumulating the extracted pilot signal, performing preprocessing for CORDIC calculation with respect to the accumulated pilot signal, simultaneously performing vector-mode CORDIC calculation and rotation-mode CORDIC calculation with respect to the preprocessed signal and outputting the phase value, estimating the frequency offset from the output phase value, and compensating for the residual phase by multiplying the transmission symbol by the complex number corresponding to the estimated frequency offset. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0029]     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:  
         [0030]      FIG. 1  is a block diagram illustrating the internal structure of an OFDM receiver using a frequency synchronizer according to the present invention;  
         [0031]      FIG. 2  is a block diagram illustrating the internal structure of the frequency synchronizer of  FIG. 1  according to the present invention;  
         [0032]      FIG. 3  illustrates the internal structure of a first preprocessor of  FIG. 2 ;  
         [0033]      FIG. 4  is a conceptual view of an operation of the first preprocessor of  FIG. 2 ;  
         [0034]      FIG. 5  is a block diagram illustrating the internal structure of a residual phase detector of  FIG. 1 ; and  
         [0035]      FIG. 6  is a block diagram illustrating the internal structure of a compact CORDIC calculator of  FIG. 5 . 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0036]     A preferred embodiment of the present invention will now be described in detail 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.  
         [0037]      FIG. 1  is a block diagram of an OFDM receiver using a frequency synchronizer according to the present invention.  
         [0038]     Referring to  FIG. 1 , the OFDM receiver includes a Radio Frequency (RF) receiver  100  for processing an RF signal received through an antenna, an analog-to-digital (A/D) converter  200  for converting an analog signal output from the RF receiver  100  into a digital signal, a frequency synchronizer  300  for synchronizing a frequency offset of the digital signal output from the A/D converter  200 , a Fourier transformer  400  for performing Fast Fourier Transform (FFT) with respect to a signal output from the frequency synchronizer  300 , an equalizer  500  for equalizing a signal output from the Fourier transformer  400 , a residual phase detector  600  for extracting a pilot signal from a signal output from the equalizer  500 , detecting a residual phase, and compensating for a data symbol with the detected residual phase, and a demodulator  700  for demodulating a signal output from the residual phase detector  600  and outputting the demodulated signal to a viterbi decoder (not shown). The frequency synchronizer  300  estimates an integer or decimal frequency offset of a received signal according to a control signal output from a controller  10  and compensates for the received signal with the estimated frequency offset. The equalizer  500  performs equalization using channel information that is estimated by a channel estimator  450  from a signal output from the Fourier transformer  400 .  
         [0039]     When both a short training symbol and a long training symbol are used, the frequency synchronizer  300  compensates for a frequency offset of the long training symbol by estimating a frequency offset of the short training symbol (coarse mode) and compensates for the frequency offset of the long training symbol again by re-estimating the compensated frequency offset of the long training symbol (fine mode). A data symbol is compensated for with a sum of the frequency offset of the short training symbol and the frequency offset of the long training symbol. When only one of the short training symbol and the long training symbol is used, the frequency synchronizer  300  estimates a frequency offset of the short training symbol or the long training symbol for compensation.  
         [0040]      FIG. 2  is a block diagram of the frequency synchronizer  300  according to the present invention.  
         [0041]     In  FIG. 2 , the frequency synchronizer  300  includes an estimation unit  310  for estimating a frequency offset or a residual phase of a received signal using a digital signal output from the A/D converter  200  and a compensation unit  320  for compensating for the estimated frequency offset according to a control signal.  
         [0042]     The estimation unit  310  includes a shift register  311  for delaying a sample of a received signal and simultaneously outputting conjugate complex numbers of a predetermined received signal and a next received signal, a first complex multiplier  312  for performing complex multiplying with respect to a signal output from the shift register  311 , a first accumulator  313  for accumulating an output of the first complex multiplier  312  according to a mode signal output from the controller  10 , a first preprocessor  314  for performing preprocessing for phase rotation transform with respect to a value accumulated by the first accumulator  313 , a vector-mode CORDIC calculator  315  for estimating an arctangent value using a signal processed by the first preprocessor  314 , and a first phase adjustor  316  for adjusting a phase using the arctangent value estimated by the vector-mode CORDIC calculator  315 .  
         [0043]     The compensation unit  320  includes a bit extender  321  for dividing the frequency offset output from the first phase adjustor  316  of the estimation unit  310  into samples of a predetermined size according to the control signal of the controller  10 , a second accumulator  322  for accumulating a frequency offset of each of the samples obtained by the bit extender  321  to generate a log function table address, a log function processor  323  for outputting a trigonometric function value by referring to the log function table address generated by the second accumulator  322 , a second phase adjustor  324  for generating a complex number to be compensated for using outputs of the log function processor  323  and the second accumulator  322 , and a second complex multiplier  325  for compensating for a signal output from the A/D converter  200  using the complex number output from the second phase adjustor  324 . It is noted that the second phase adjustor  324  generates a log function table address by accumulating a frequency offset of each of samples output from the bit extender  321 . The output value of the second accumulator  322  is a value to accumulate the frequency offset of each sample output from each bit extender  321 . Thus, the log function processor includes the output value of the second accumulator  322 .  
         [0044]      FIG. 3  illustrates the internal structure of the first preprocessor  314  and  FIG. 4  is a conceptual view for explaining an operation of the first preprocessor  314 . It is assumed herein that an output of the first accumulator  313  is composed of L bits and m bits are calculated in the vector-mode CORDIC calculator  315 .  
         [0045]     As illustrated in  FIGS. 3 and 4 , the first preprocessor  314  includes Exclusive OR (XOR) gates  32 - 1  through  32 - n  and  33 - 1  through  33 - n  for performing an XOR function on an output of the first accumulator  313 , OR gates  34 - 1  through  34 - n  for performing an OR function on outputs of the XOR gates  32 - 1  through  32 - n  and  33 - 1  through  33 - n , and a multiplexer  35  for multiplexing outputs of the OR gates  34 - 1  through  34 - n . The first preprocessor  314  uses a feature that x and y values stored in a real-part memory and an imaginary-part memory (not shown) are not absolute but are relative values in CORDIC calculation. Thus, the first preprocessor  314  detects the position of a Most Significant Bit (MSB) indicating  1  in the real part and imaginary part of an output of the first accumulator  313  and selects m bits including “0” or “1” of 2 bits from the detected value to prevent calculation overflow. To implement the first preprocessor  314 , (L−m−1)*2 XOR gates and (L−m−1) OR gates are required and the multiplexer  35  having a size of (L−m−1)*1 is required.  
         [0046]     The first preprocessor  314  according to the present invention functions in the same manner as a conventional normalization block that performs a division operation, but performs more accurate normalization by referring to the bit value of an input signal and the position of the bit value.  
         [0047]      FIG. 5  is a block diagram illustrating the internal structure of the residual phase detector  600 .  
         [0048]     As illustrated in  FIG. 5 , the residual phase detector  600  includes a pilot extractor  601  for extracting a pilot signal from a signal output from the equalizer  500 , a third accumulator  602  for accumulating the pilot signal extracted by the pilot extractor  601 , a second preprocessor  610  for performing preprocessing for CORDIC calculation with respect to a signal output from the third accumulator  602 , a compact CORDIC calculator  611  for estimating an arctangent value using a signal processed by the second preprocessor  610 , a third phase adjustor  606  for adjusting a phase using the arctangent value estimated by the compact CORDIC calculator  611 , and a third complex multiplier  607  for correcting a phase of a signal estimated by the equalizer  500  by reflecting an output of the third phase adjustor  606 .  
         [0049]      FIG. 6  is a block diagram illustrating the internal structure of the compact CORDIC calculator  611 , and is useful in explaining its operation. The compact CORDIC calculator  611  simultaneously performs vector-mode CORDIC calculations and rotation-mode CORDIC calculations and can process vector-mode CORDIC calculations and rotation-mode CORDIC calculations by a single repeated process.  
         [0050]     As illustrated in  FIG. 6 , the compact CORDIC calculator  611  according to the present invention includes a vector-mode unit  650  for performing a vector-mode operation, a rotation-mode unit  670  for performing a rotation-mode operation, and a counter  690  for counting the number of repetitions.  
         [0051]     The vector-mode unit  650  includes a first register  651  for receiving and temporarily storing a real part x of the signal output from the second preprocessor  610 , a second register  661  for receiving and temporarily storing an imaginary part y of the signal output from the second preprocessor  610 , a first shifter  652  for shifting an output of the second register  661  according to the number of repetitions output from the counter  690 , a first complementary operator  653  for performing a complementary operation with respect to 1 for the output of the first shifter  652 , a first multiplexer  654  for multiplexing an output of the first complementary operator  653  and an output of the first shifter  652 , a first Carry Lookahead Adder (CLA)  655  for adding an output of the first multiplexer  654  to the output of the first register  651  and feeding back the result to the first register  651 , a second shifter  662  for shifting the output of the first register  651  according to the number of repetitions output from the counter  690 , a second complementary operator  663  for performing a complementary operation with respect to 1 for the output of the second shifter  662 , a second multiplexer  664  for multiplexing an output of the second complementary operator  663  and the output of the second shifter  662 , and a second CLA  665  for adding an output of the second multiplexer  664  to the output of the second register  661  and feeding back the result to the second register  661 . The first multiplexer  654  and the second multiplexer  664  and the first CLA  655  and the second CLA  665  perform multiplexing and carry operations by referring to the MSB of a signal stored in the second register  661 .  
         [0052]     The rotation-mode unit  670  includes a third register  671  and a fourth register  681  whose initial values are set to 1/K and 0, a third shifter  672  for shifting an output of the fourth register  681  according to the number of repetitions output from the counter  690 , a third complementary operator  673  for performing a complementary operation with respect to 1 for an output of the third shifter  672 , a third multiplexer  674  for multiplexing an output of the third complementary operator  673  and the output of the third shifter  672 , a third CLA  675  for adding an output of the third multiplexer  674  to the output of the third register  671  and feeding back the result to the third register  671 , a fourth shifter  682  for shifting the output of the third register  671  according to the number of repetitions output from the counter  690 , a fourth complementary operator  683  for performing a complementary operation with respect to 1 for the output of the fourth shifter  682 , a fourth multiplexer  684  for multiplexing an output of the fourth complementary operator  683  and the output of the fourth shifter  682 , and a fourth CLA  685  for adding an output of the fourth multiplexer  684  to the output of the fourth register  681  and feeding back the result to the fourth register  681 . The third multiplexer  674  and the fourth multiplexer  684  and the third CLA  675  and the fourth CLA  685  perform multiplexing and carry operations by referring to the MSB of the signal stored in the second register  661 .  
         [0053]     Hereinafter, an operation of the frequency synchronizer  300  of  FIG. 1  will be described in detail with reference to the accompanying drawings.  
         [0054]     First, a short training symbol transmitted through the OFDM receiver of  FIG. 1  can be expressed in Equation (1) as follows:  
                 s   ⁡     (   n   )       =       ∑     k   =   0       N   -   1       ⁢       S   ⁡     (   k   )       ⁢   exp   ⁢     {       j2π   ⁢           ⁢   nk     N     }           ,     n   =   0     ,   1   ,   2   ,   ⋯   ⁢           ,     N   -   1     ,           (   1   )             
 
         [0055]     where S(k) indicates a short training symbol of a frequency domain, N indicates an FFT/IFFT size, s(n) indicates a short training symbol in a time domain and is composed of N/D repeated sequences, each of which is D samples long, during a single symbol interval,  
         [0000]     j generally indicates a symbol placed before an imaginary number, and k indicates a constant.  
         [0056]     Since a short training symbol received through a channel has a frequency offset due to phase jitter or Doppler shift, the received short training symbol can be expressed in Equation (2) as follows:  
                     r   ⁡     (   n   )       =       ⁢       ∑     k   ⁢           =           ⁢   0               ⁢     N   ⁢           -           ⁢   1         ⁢       S   ⁡     (   k   )       ⁢     H   ⁡     (   k   )                           ⁢     exp   ⁢     {       j2π   ⁢     (     k   ⁢           +           ⁢   ɛ     )     ⁢           ⁢   n               ⁢   N       }                       ⁢         exp   ⁢     {       j2π   ⁡     (       n             ⁢   0       ⁢           +           ⁢     Δ   ⁢           ⁢   t       )       N     }       +     W   ⁡     (   n   )         ,                   (   2   )             
 
         [0057]     where ε=( f   offset / Δ f)  
         [0058]     indicates a normalized frequency offset, f offset  and Δf indicate a normalized frequency offset interval and a subchannel interval, and H(k) indicates a frequency response of a channel. Δt indicates the start point (n=0) of signal reception, 2πΔt/N indicates initial phase rotation, n 0  indicates the start point of a coarse mode, and W(n) indicates additive noise.  
         [0059]     As can be seen from Equation (2), since the received signal is composed of N/D repeated sequences, each of which is D samples long, an integer frequency offset and a decimal frequency offset can be estimated using an autocorrelation property of Equation (3) when the influence of noise is excluded.  
                       ɛ   ^     =       N             ⁢     2   ⁢           ⁢   π   ⁢           ⁢   D         ⁢     arg   ⁡     (       ∑     n   =   0       L   -   1       ⁢       r   ⁡     (     n   +   D     )       ⁢       r   ⁡     (   n   )       *         )                     =       N             ⁢     2   ⁢           ⁢   π   ⁢           ⁢   D         ⁢     arg   (         ∑     n   =   0       L   -   1       ⁢     Im   ⁡     (       r   ⁡     (     n   +   D     )       ⁢       r   ⁡     (   n   )       *       )             ∑     n   =   0       L   -   1       ⁢     Re   ⁡     (       r   ⁡     (     n   +   D     )       ⁢       r   ⁡     (   n   )       *       )           )               ,           (   3   )             
 
         [0060]     where D indicates an interval of repeated two symbols. As can be seen from Equation (3), after delaying a sample using a repeated training symbol, a frequency offset is estimated using the autocorrelation property. The estimation range of the integer frequency offset is −2-2 when D=16 and the estimation range of the decimal frequency offset is −0.5-0.5 when D=64.  
         [0061]     When the arctangent function is implemented using a CORDIC calculation, a simpler and more accurate normalization can be achieved by using a compact preprocessor according to the present invention than using a conventional normalization block that performs a division operation.  
         [0062]     As illustrated in  FIG. 3 , the first preprocessor  314  compares bit values of a real part and an imaginary part of an output of the first accumulator  313  for normalization. When the output of the first accumulator  313  is composed of L bits and m bits are calculated in the vector-mode CORDIC calculator  315 , the first preprocessor  314  requires (L−m−1)*2 XOR gates, (L−m−1) OR gates, and a multiplexer having a size of (L−m−1)*1. Using CORDIC calculation, values calculated in x and y registers of the vector-mode CORDIC calculator  315  are not absolute values, but are relative values Thus, when selecting an effective bit for CORDIC calculation, the first preprocessor  314  selects the position of the MSB indicating 1 in a real part and an imaginary part of an output of the first accumulator  313  irrespective of the number system of the output of the first accumulator  313 , selects m bits including “0” of 2 bits to prevent calculation overflow, and performs normalization.  
         [0063]     In conventional normalization using a division operation, the sizes of a real part and an imaginary part cannot be previously known. As a result, the quotient of the division operation should include an integer part of several bits for a case where the imaginary part is greater than the real part. However, when the imaginary part is less than the real part, bits for expressing the integer part are not required, resulting in waste of bits and thus degradation in estimation accuracy due to a small amount of information.  
         [0064]     A signal output from the third accumulator  602  of the residual phase detector  600  can be expressed in Equation (4) as follows:  
                         ϕ   ^     n     =       tan     -   1       ⁢       ∑     p   =   0       P   -   1       ⁢         R   n     ⁡     (   k   )       ⁢       P   n   *     ⁡     (   k   )                         =       tan     -   1       ⁢     {         ∑     p   =   0       P   -   1       ⁢     Im   ⁡     (         R   n     ⁡     (   k   )       ⁢       P   n   *     ⁡     (   k   )         )             ∑     p   =   0       P   -   1       ⁢     Re   ⁡     (         R   n     ⁡     (   k   )       ⁢       P   n   *     ⁡     (   k   )         )           }               ,           (   4   )             
 
         [0065]     where R n (k) indicates a k th  subcarrier of an n th  received symbol, P n (k) indicates a k th  pilot subcarrier of an n th  symbol, {circumflex over (φ)} n  indicates an estimated phase of the n th  symbol, and P indicates the number of pilot carriers.  
         [0066]     In conventional CORDIC-based frequency offset synchronization, the arctangent operation is performed using a vector-mode CORDIC calculation and a trigonometric operation is performed with respect to a value estimated by the arctangent operation using a rotation-mode CORDIC calculation.  
         [0067]     The compact CORDIC calculator  611  according to the present invention can process vector-mode CORDIC calculations and rotation-mode CORDIC calculations by a single repeated process. A phase estimated in conventional vector-mode CORDIC calculations can be expressed in Equation (5) as follows: 
 
 z   V ( m+ 1)=− d   v ( m )α (m)   −d   v ( m− 1)α (m−1)   − . . . −d   v (0)α (0)   (5) 
 
         [0068]     where z V (m+1) indicates a phase estimated after m repetitions in a vector mode, α (m)  indicates an m th  phase stored in a memory, and d V (m) indicates a sign selected by referring to the sign of a value of a y memory in an m th  repetition. Rotation-mode CORDIC calculation is performed using the estimated phase and a sign d R (m) of a rotation mode is selected in rotation-mode CORDIC calculation such that a phase converges to 0. The sign of the rotation mode after m repetitions can be expressed in Equation (6) as follows:  
                         z   R     ⁡     (     m   +   1     )       =       ⁢         z   V     ⁡     (     m   +   1     )       -                     ⁢     {         -     d             ⁢   R         ⁢     (   m   )     ⁢     α     (   m   )         -         d             ⁢   R       ⁡     (     m   -   1     )       ⁢     α     (     m   -   1     )         -   ⋯   -         d             ⁢   R       ⁡     (   0   )       ⁢     α     (   0   )           }                 =       ⁢       {         -     d             ⁢   v         ⁢     (   m   )     ⁢     α     (   m   )         -       d             ⁢   v       ⁢     (     m   -   1     )     ⁢     α     (     m   -   1     )         -   ⋯   -       d             ⁢   v       ⁢     (   0   )     ⁢     α     (   0   )           }     -                     ⁢     {         -     d             ⁢   R         ⁢     (   m   )     ⁢     α     (   m   )         -         d             ⁢   R       ⁡     (     m   -   1     )       ⁢     α     (     m   -   1     )         -   ⋯   -         d             ⁢   R       ⁡     (   0   )       ⁢     α     (   0   )           }             ,           (   6   )             
 
         [0069]     d R (m) is selected in a rotation-mode CORDIC calculation such that Z R (m+1) converges to 0, and it can be seen from Equation (6) that d R (m) is opposite to d V (m).  
         [0070]     The present invention is configured such that vector-mode CORDIC calculations and rotation-mode CORDIC calculations are simultaneously performed by a single repetition using the characteristics described above. Because of aiming at compensation value estimation, the compact CORDIC calculator  611  according to the present invention does not require a memory for storing α (m)  used for phase tracking.  
         [0071]     A compact CORDIC algorithm according to the present invention can be expressed in Equation (7) as follows: 
 
 x   V ( i+ 1)= x   V ( i )− d   i   y   V ( i )2 −i  
 
 y   V ( i+ 1)= y   V ( i )+ d   i   x   V ( i )2 −i  
 
x R ( i+ 1)= x   R ( i )+ d   i   y   R ( i )2 −i  
 
 y   R ( i+ 1)= y   R ( i )− d   i   x   R ( i )2 −i   (7) 
 
         [0072]     where d i =1 if y V (i)&lt;0, else d i =−1  
         [0073]     Thus, initial values x V (0) and y V (0) of the first register  651  and the second register  661  of the vector-mode unit  650  use a real part and an imaginary part output from the second preprocessor  610 , and initial values x R (0) and y R (0) of the third register  671  and the fourth register  681  of the rotation-mode unit  670  use 1/K and 0. After repeating Equation (7) m times, x R (m+1) and y R (m+1) remain in the third register  671  and the fourth register  681  and a residual phase is compensated for using x R (m+1) and y R (m+1).  
         [0074]     As described above, according to the present invention, by introducing a preprocessor for performing normalization by referring to the optimal bit of an input signal and the position of the optimal bit, instead of performing conventional normalization using a division operation, the accuracy of CORDIC-based frequency offset estimation can be improved and calculation complexity can be reduced.  
         [0075]     Furthermore, a memory for storing a phase for each mode is not required, thereby reducing manufacturing cost. Moreover, a vector-mode process and a rotation-mode process are performed simultaneously, thereby minimizing operation processing delay.  
         [0076]     While the present invention has been shown and described with reference to a preferred embodiment 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 invention.