Abstract:
A DC offset estimation system is disclosed. A DC offset estimation system includes a carrier frequency offset estimator receiving an input signal and estimating a carrier frequency offset value, a symbol timing recovery unit providing a symbol boundary of the input signal, and a DC offset estimator estimating a DC offset value to compensate the input signal based on the input signal, the carrier frequency offset value, and the symbol boundary.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention relates to DC offset estimation system and method. 
     2. Description of the Related Art 
     In wireless communication, DC offset is generated both in transmitter and receiver. At the transmitter, one possible reason for DC offset generation is that the DAC (digital to analog converter) is not ideal, and the input digital data may not even contain a DC value, the converted data might also contain DC offset. Additionally, the nonlinear feature of other analog elements of the transmitter may also cause unwanted DC offset. As to the receiver, if the receiver has Zero IF configuration, the DC offset effect is more obvious.  FIG. 1  and  FIG. 2  show schematic diagrams of DC offset generation in a receiver. Since the Zero IF receiver utilizes only one stage conversion to convert a radio frequency signal to a baseband signal, the signal COS ω LO t easily leaks to combine with the input signal S 1  if the conductive line to the mixer is not completely isolated from the conductive line for transmitting the input signal S 1 , thus, the next one radio frequency signal carries the unwanted leakage signal, and the converted baseband signal carries a DC offset value.  FIG. 2  shows another DC offset generation event. Since the Zero IF receiver converts a radio frequency signal to a baseband signal dircectly, the input signal S 1  easily leaks to combine with the signal COS ω LO t if the conductive line to the mixer is not completely isolated from the conductive line for transmitting the input signal S 1 . 
       FIG. 3  is a schematic block diagram of a conventional OFDM receiver  300  for performing DC estimation and compensation for long training symbols. This implementation attempts to determine the estimated value of the signal, s(n), in order to estimate the DC offset. The signal s(n) shown in  FIG. 3  may be referred to as DC offset distortion at subcarrier  0 . The DC offset is estimated based on the two local oscillator (LO) offset-corrected long training symbols that are components of an OFDM preamble. Since the OFDM spectrum may contain severe carrier leakage, the DC estimation based on subcarrier  0  of one OFDM symbol may be distorted and not useful. Thus, the difference of two successive DC estimations is used, canceling out the constant carrier leakage value at subcarrier  0 , but retaining some value representing the receiver DC offset (signal r(n) in  FIG. 3 ). 
     As shown in  FIG. 3 , the sum of all 34 input time domain samples is computed for the long training symbols x(n) (from the long training symbol buffer  305 ) by the summation unit  320  to generate a signal, s(n). The signal s(n) is fed through a delay unit  325  and subtracted (block  326 ) from the current value of s(n) to generate signal r(n). 
     To calculate the true DC level at the input (i.e., the output of the analog-to-digital converters), the output r(n) is processed to compensate for the Local Oscillator offset compensation (the difference between the transmitter and receiver local oscillators). To accomplish this, the LO offset phasor  328  is down sampled by a factor of 64 (block  330 ) and complex conjugated, the difference of two consecutive phasor values is calculated (block  340 ), and the result q(n) is multiplied (block  327 ) with r(n) to produce t(n). The LO offset frequency  343  is then processed with a compensation factor  345  and multiplied (block  328 ) with t(n). The result is the receiver DC offset estimate DC RX    329 . It should be noted that block  340  comprises a delay unit  332  and subtraction unit  333  that operate in a manner similar to that of delay unit  325  and subtraction unit  326 . 
     The remainder of the circuitry in  FIG. 3  is designed to compensate for the DC offset DC RX    329 , local oscillator offset (LOO), and the effects of subcarrier rotation. The computed receiver DC offset estimate DC RX    329  is passed through the compensation processing block  380  to calculate the DC contribution in the frequency domain (Davg(i)). Block  350  determines the DC power contribution to each subcarrier (sinc shape) as a function of the LO offset frequency  343 . Block  360  is a compensation factor to compensate for the effect of the sub carrier rotation. The down sampled local oscillator offset phasor is averaged over two samples (block  358 ) to produce the local oscillator offset used by block  380  (block  380  comprises multiplier units  365 - 367 ). 
     The buffer long training symbols  305  are also delayed (block  370 ) and summed (block  371 ) to derive the required 64 time samples for input to the FFT block  372 . The DC contribution in the frequency domain (Davg(i)) is then added (block  385 ) to the output of the fast fourier transform (performed by FFT  372 ) to generate the DC free channel estimation  390 . It is noted that the DC free channel estimation  390  is obtained after removing the training data symbols per subcarrier. The removal of the DC offset from each subcarrier should take into account the fact that the Long Training Symbols are averaged over two DC estimations (done by means of block  358 ). 
     In  FIG. 3 , the DC offset estimation method is based on the carrier frequency offset, and at least two repeated training symbols or OFDM symbols are required for DC offset estimation. However, the preambles and the OFDM symbols in 802.16e standard, for example, do not have the ideal repetition feature, thus, the conventional DC offset estimation method based on the carrier frequency offset cannot be applied in 802.16e standard. 
     BRIEF SUMMARY OF THE INVENTION 
     The invention of a DC offset estimation system comprises a carrier frequency offset estimator, a symbol timing recovery unit and a DC offset estimator. The carrier frequency offset estimator receives an input signal and estimates a carrier frequency offset value. The symbol timing recovery unit provides a symbol boundary on the input signal. The DC offset estimator estimates a DC offset value to compensate the input signal based on the input signal, the carrier frequency offset value, and the timing information. 
     The invention of a DC offset estimation method comprises estimating a fractional carrier frequency offset value of a input signal; determining a DC offset value by averaging plural OFDM symbols in response to the fractional carrier frequency offset value does not exceed a predetermined value; determining the DC offset value by a CP-based DC offset estimation method based on the fractional carrier frequency offset value in response to the fractional carrier frequency offset value exceeds a predetermined value. 
     The invention of a DC offset estimation system comprises a correction term generator, a first mixer, a difference value generator, and a second mixer. The correction term generator receives a carrier frequency offset data to generate a correction term. The first mixer receives and mixes an input signal with the carrier frequency offset data to compensate carrier frequency offset. The difference value generator generates a difference value based on a pair of compensated input samples. The second mixer receives the correction term and the difference value to generate a DC offset value. 
     The invention of a DC offset estimation method, comprises estimating a carrier frequency offset value; compensating an input signal with the carrier frequency offset value; calculating a cosecant value based on the carrier frequency offset value; estimating a difference value based on a pair of compensated input samples; calculating a correction term based on the carrier frequency offset value; determining a DC offset value based on the correction term and the difference value. 
     A detailed description is given in the following embodiments with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein: 
         FIG. 1  and  FIG. 2  show schematic diagrams of DC offset generation in a receiver. 
         FIG. 3  is a schematic block diagram of a conventional OFDM receiver  300  for performing DC estimation and compensation for the long training symbols. 
         FIG. 4  is a block diagram of the DC offset signal model in the OFDM system. 
         FIG. 5  is a block diagram of a DC offset estimation system of one embodiment of the invention based on the expressions (1)˜(6). 
         FIG. 6  is a block diagram of a DC offset estimation system of one embodiment of the invention based on the expressions (7) and (8). 
         FIG. 7  is another embodiment of a DC offset estimation system based on another aspect of invention. 
         FIG. 8  shows a determination mechanism for DC offset estimation. 
         FIG. 9  shows a DC offset estimation method based on an averaged signal calculated by averaging a plurality of OFDM symbols. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the appended claims. 
       FIG. 4  is a block diagram of the DC offset signal model in the OFDM system. As shown in  FIG. 4 , both in the transmitter end and receiver end, the DC offsets d tx  and d rx  are generated and are respectively added by adders  42   a  and  42   c . When the signal is transmitted in channel  43 , noise z(n) and carrier frequency offset exp(j(Δωn+φ)) are also generated. Amplifiers  41   a  and  41   b  respectively provide gain factors K and G to adjust the signal amplitude in a predetermined range for better A/D conversion performance in A/D converter  45 . Supposing the parameter K and G are 1, the received signal r(n) can be expressed by the following expression: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     The function h(n) represents an equivalent transmission function when the signal is transmitted in channel  43 . The signal z(n) representing the AWGN noise is added to the received signal r(n) by adder  42   b . The term exp(j(Δωn+φ)) represents the carrier frequency offset between the transmitter and the receiver and is imposed on the signal s(n) by the multiplier  44   a . The carrier frequency offset (CFO) comprises both integer carrier frequency offset and fractional carrier frequency offset, and expressed by the following expression: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ω 
                       
                       = 
                       
                         
                           k 
                           ⁢ 
                           
                               
                           
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                               N 
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                     ⁢ 
                     
                       
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                         ⁢ 
                         
                           
 
                         
                         - 
                         
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                           / 
                           
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                       &lt; 
                       
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                         k 
                       
                       = 
                       0 
                     
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                   ⁢ 
                   
                       
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In expression (2), k is the number of integer frequency offset. Substituting (2) into (1), the received signal r(n) is expressed by the following expression:
 
 r ( n )= y ( n ) e   j((2πk/N     FFT     +δω)n+φ)   +d′   tx   e   j((2πk/N     FFT     +δω)n+φ)   +z′ ( n )+ d   rx  
 
     After the received signal r(n) is compensated by a the carrier frequency offset value e −j(Δωn+θ)  in the mixer  44   b , the received signal r(n) is expressed by the following expression:
 
 r ′( n )= r ( n ) e   −j(Δωn+θ)   =y ( n ) e   j(φ−θ)   +d′   tx   e   j(φ−θ)   +z″ ( n )+ d   rx   e   −j(Δωn+θ)   (3)
 
     Since the OFDM symbol comprises the cylix prefix (CP) and signals transmitted in CP has the feature shown as the following:
 
 s ( n+N   FFT )= s ( n )
 
     Thus, signal s(n+N FFT ) can be expressed by the following expression: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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                             rx 
                           
                           ⁢ 
                           
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                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Subtract (3) from (4), to obtain expression (5) as shown in the following: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
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                                 ″ 
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                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     The DC offset estimation value in receiver can be expressed by the following expression (6): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
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                                 / 
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                         = 
                         
                           
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                             rx 
                           
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                                 ⁢ 
                                 
                                   
                                     z 
                                     
                                       ″ 
                                       ⁢ 
                                       ′ 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     n 
                                     ) 
                                   
                                 
                               
                               2 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               csc 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     
                                       N 
                                       FFT 
                                     
                                     2 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   ω 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       Δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         ( 
                                         
                                           n 
                                           + 
                                           
                                             
                                               N 
                                               FFT 
                                             
                                             / 
                                             2 
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             d 
                             rx 
                           
                           + 
                           
                             ζ 
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     In expression (6), we can find that the DC offset estimation value is a product of a correction term of carrier frequency offset and a difference value between one point data in CP period and its corresponding point data in the compensated signal. 
     According the described derivation, a block diagram of a DC offset estimation system of one embodiment of the invention based on the expressions (1)˜(6) is shown in  FIG. 5 . Symbol timing recovery unit  53  provides the symbol boundary for the DC offset estimation method and provides plural sampled data to a DC offset estimator  54  based on the input signal r(n) and the timing. Numerically controlled oscillator (NCO)  52  generates a correction term, e −j(δωn+θ) , composed of sine and cosine waves mixed with the incoming signal r(n) to correct the frequency error by mixer  57 . The fractional CFO estimator  51  receives the incoming signal r(n) to estimate the value of fractional carrier frequency offset δω. The integer CFO estimator  55  generates the integer carrier frequency offset 
               2   ⁢   π   ⁢           ⁢   k       N   FFT           
based on the output signal of mixer  57 . The adder  58  adds the integer carrier frequency offset
 
               2   ⁢   π   ⁢           ⁢   k       N   FFT           
and the fractional carrier frequency offset δω to generate the carrier frequency offset Δω. The DC offset estimator  54  receives the input signal r(n), sampled data from the symbol timing recovery  53 , and the carrier frequency offset Δω to estimate a DC offset value, {circumflex over (d)} rx . The adder  56  subtracts the DC offset value {circumflex over (d)} rx  from the input signal r(n).
 
     In the system shown in  FIG. 5 , note that the DC offset value is estimated after the integer carrier frequency offset and the fractional carrier frequency offset had been estimated. This defers the time of obtaining DC offset estimates. Thus, in another aspect of the invention the DC offset compensation method only requires the fractional carrier frequency offset value. The signal after compensating the fractional carrier frequency offset is expressed as shown in the following: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               r 
                               ~ 
                             
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             n 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             r 
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               - 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       δω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             2 
                                             ⁢ 
                                             π 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               k 
                                               / 
                                               
                                                 N 
                                                 FFT 
                                               
                                             
                                           
                                           + 
                                           δω 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     ϕ 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               d 
                               tx 
                               ′ 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             2 
                                             ⁢ 
                                             π 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             
                                               k 
                                               / 
                                               
                                                 N 
                                                 FFT 
                                               
                                             
                                           
                                           + 
                                           δω 
                                         
                                         ) 
                                       
                                       ⁢ 
                                       n 
                                     
                                     + 
                                     ϕ 
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               
                                 z 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 n 
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                             ⁢ 
                             
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                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           + 
                           
                             
                               d 
                               rx 
                             
                             ⁢ 
                             
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                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
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                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       kn 
                                       / 
                                       
                                         N 
                                         FFT 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
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                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
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                                     - 
                                     θ 
                                   
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                           + 
                           
                             
                               d 
                               tx 
                               ′ 
                             
                             ⁢ 
                             
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                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       kn 
                                       / 
                                       
                                         N 
                                         FFT 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     - 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               
                                 z 
                                 ~ 
                               
                               ″ 
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                           + 
                           
                             
                               d 
                               rx 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δ 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         n 
                                       
                                       + 
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Replacing {tilde over (r)}′(n) by {tilde over (r)}′(n+N FFT ) 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               r 
                               ~ 
                             
                             ′ 
                           
                           ⁡ 
                           
                             ( 
                             
                               n 
                               + 
                               
                                 N 
                                 FFT 
                               
                             
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       
                                         k 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             n 
                                             + 
                                             
                                               N 
                                               FFT 
                                             
                                           
                                           ) 
                                         
                                       
                                       / 
                                       
                                         N 
                                         FFT 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
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                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     - 
                                     θ 
                                   
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                               tx 
                               ′ 
                             
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                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       
                                         k 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             n 
                                             + 
                                             
                                               N 
                                               FFT 
                                             
                                           
                                           ) 
                                         
                                       
                                       / 
                                       
                                         N 
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                                   ) 
                                 
                               
                             
                             ⁢ 
                             
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                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     - 
                                     θ 
                                   
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                         ⁢ 
                         
                           
                             
                               
                                 z 
                                 ~ 
                               
                               ″ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 n 
                                 + 
                                 
                                   N 
                                   FFT 
                                 
                               
                               ) 
                             
                           
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                               d 
                               rx 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 - 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         δω 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             n 
                                             + 
                                             
                                               N 
                                               FFT 
                                             
                                           
                                           ) 
                                         
                                       
                                       + 
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                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                             ⁢ 
                             
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                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       kn 
                                       / 
                                       
                                         N 
                                         FFT 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     - 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             
                               d 
                               
                                 tx 
                                 ⁢ 
                                 
                                     
                                 
                               
                               ′ 
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     2 
                                     ⁢ 
                                     π 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       kn 
                                       / 
                                       
                                         N 
                                         FFT 
                                       
                                     
                                   
                                   ) 
                                 
                               
                             
                             ⁢ 
                             
                               ⅇ 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     ϕ 
                                     - 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           + 
                           
                             
                               
                                 z 
                                 ~ 
                               
                               ″ 
                             
                             ⁡ 
                             
                               ( 
                               
                                 n 
                                 + 
                                 
                                   N 
                                   FFT 
                                 
                               
                               ) 
                             
                           
                           + 
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           
                             d 
                             rx 
                           
                           ⁢ 
                           
                             ⅇ 
                             
                               - 
                               
                                 j 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     
                                       δω 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           n 
                                           + 
                                           
                                             N 
                                             FFT 
                                           
                                         
                                         ) 
                                       
                                     
                                     + 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     According to expression (7) and (8), the DC offset estimation value in receiver can be expressed by the following expression: 
     
       
         
           
             
               
                 
                   
                     
                       
                         d 
                         ^ 
                       
                       rx 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         j 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   ~ 
                                 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   n 
                                   + 
                                   
                                     N 
                                     FFT 
                                   
                                 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   r 
                                   ~ 
                                 
                                 ′ 
                               
                               ⁡ 
                               
                                 ( 
                                 n 
                                 ) 
                               
                             
                           
                           ) 
                         
                       
                       2 
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         j 
                         ⁡ 
                         
                           ( 
                           
                             
                               δω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                             + 
                             θ 
                           
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       csc 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               N 
                               FFT 
                             
                             2 
                           
                           ⁢ 
                           δω 
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       ⅇ 
                       
                         jδω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             N 
                             FFT 
                           
                           / 
                           2 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       d 
                       rx 
                     
                     + 
                     
                       
                         
                           j 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               
                                 z 
                                 ~ 
                               
                               
                                 ″ 
                                 ⁢ 
                                 ′ 
                               
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                         
                         2 
                       
                       ⁢ 
                       csc 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             
                               N 
                               FFT 
                             
                             2 
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           δω 
                         
                         ) 
                       
                       ⁢ 
                       
                         ⅇ 
                         
                           j 
                           ⁡ 
                           
                             ( 
                             
                               
                                 δω 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     n 
                                     + 
                                     
                                       
                                         N 
                                         FFT 
                                       
                                       / 
                                       2 
                                     
                                   
                                   ) 
                                 
                               
                               + 
                               θ 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       d 
                       rx 
                     
                     + 
                     
                       
                         ζ 
                         ~ 
                       
                       ⁡ 
                       
                         ( 
                         n 
                         ) 
                       
                     
                   
                 
               
             
           
         
       
     
       FIG. 6  is a block diagram of a DC offset estimation system of one embodiment of the invention based on the expressions (7) and (8). Symbol timing recovery unit  62  provides a symbol boundary for the DC offset estimation method and provides a plurality of sampled data to a DC offset estimator  63  based on the input signal r(n) and the timing. The fractional CFO estimator  61  receives the incoming signal r(n) to estimate the value of fractional carrier frequency offset δω. The DC offset estimator  63  receives the input signal r(n), and the fractional carrier frequency offset δω to estimate a DC offset value, {circumflex over (d)} rx . The adder  64  subtracts the DC offset value {circumflex over (d)} rx  from the input signal r(n). 
       FIG. 7  is another embodiment of a DC offset estimation system. According to the DC offset estimation system shown in  FIG. 4 to 6 , it is revealed that the DC value is estimated based on a correction term of carrier frequency offset and a difference value between one point data in CP period and its corresponding point data in the compensated signal. The correction term generator  72  receives a carrier frequency offset data (CFO data) to generate a correction term. The first mixer  73   a  receives and mixes an input signal with the carrier frequency offset data to compensate carrier frequency offset. The difference value generator, including the FIFO register  74  and adder  75   a , computes the difference between the data sample in CP period and its corresponding sample in the compensated signal. The second mixer  73   b  receives the correction term and the difference value to generate a distorted DC offset estimate. The accumulator  76 , including a delay unit  76   a  and adder  75   b , receives a plurality of distorted DC offset estimates to output an estimation error suppressed DC offset signal. The cosecant value generator  71  receives the carrier frequency offset data to generate a cosecant value based on the carrier frequency offset value. The correction term generator  72  comprises a coordinate rotation digital calculation (CORDIC) unit  72   a , a computing unit  72   b  and an IQ swap unit  72   c . The coordinate rotation digital calculation unit  72   a  receives the carrier frequency offset data and generates the sine and cosine sequences with the frequency equal to the carrier frequency offset. The computing unit  72   b  coupled to the coordinate rotation digital calculation unit  72   a  receives and calculates a complex conjugate of the coordinate rotation digital calculation unit output data. The IQ swap mapping unit  72   c  receives and multiplies a j to the output signal of the computing unit  72   b . In this embodiment, the mixer  73   a  receives and mixes an input signal with the rotated carrier frequency offset data from the correction term generator  72  to compensate carrier frequency offset. 
       FIG. 8  shows a determination mechanism for DC offset estimation. Please refer to the expression (2). In step S 81 , the value of the term |δω| is determined whether the term is smaller than a predetermined value α. If |δω|&lt;α, the determination mechanism jumps to the step S 83 , and the DC offset value is determined by averaging over a plurality of OFDM symbols comprising preamble, data or frame control head (FCH). If |δω|&gt;α, the determination mechanism jumps to the step S 82 , and the method of DC offset estimation considers both integer carrier frequency offset and fraction carrier frequency offset, a CP based DC offset estimation method is applied to calculate the DC offset value. 
       FIG. 9  shows a DC offset estimation method based on an averaged signal calculated by averaging a plurality of OFDM symbols. A first signal value is calculated by averaging over N FFT  samples of the first OFDM symbol starting from the middle of the first cyclic prefix (CP)  91 . A second signal value is calculated by averaging over N FFT  samples of the second OFDM symbol starting from the middle of the second CP  93 . A third signal value is calculated by averaging over N FFT  samples of the third OFDM symbol starting from the middle of the third CP  95 . An adder is applied to sum and average the first signal value, the second signal value, and the third signal value. Then, the DC offset estimation method estimates the DC offset value based on the averaged signal value. In one embodiment, at least four OFDM symbols are required to estimate the DC offset value based on the averaged signal value of the OFDM symbols. 
     While the invention has been described by way of example and in terms of preferred embodiment, it is to be understood that the invention is not limited thereto. To the contrary, it is intended to cover various modifications and similar arrangements (as would be apparent to those skilled in the art). Therefore, the scope of the appended claims should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements.