Abstract:
A method for frequency offset estimation in frequency domain is provided. The method comprises the following steps. First, a phase angle of a signal field of the input signal after processed by Fast Fourier Transformation (FFT) and channel equalization is calculated. A frequency offset error originated from at least one frequency offset estimation process in time domain is then estimated according to the phase angle.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. application Ser. No. 11/250,669, now U.S. Pat. No. 7,539,125, filed on Oct. 14, 2005, the contents of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     The present invention relates to the baseband processor of the orthogonal frequency division multiplexing (OFDM) receiver, and more particularly, to an OFDM baseband processor for the wireless LAN (WLAN) IEEE 802.11a or IEEE 802.11g standards. 
     Orthogonal frequency division multiplexing (OFDM) is a modulation technique for wireless LAN standards such as IEEE 802.11a and 802.11g. In the IEEE 802.11a standard, the carrier frequency is 5 GHz. There are 64 implied subcarrier frequencies with a spacing of 312.5 kHz (=20 MHz/64, wherein 20 MHz is the channel bandwidth). Among the 64 implied subcarriers, there are 52 nonzero subcarriers, which includes 48 data subcarriers carrying data and four pilot subcarriers used as pilot tones. Each subcarrier hums away at 312.5 k symbols/second. Data is blocked into 3.2-microsecond frames with an additional 0.8 microsecond of cyclic prefix tacked on for mitigation of intersymbol interference, and the data frame and the cyclic prefix thereof forms a data symbol lasting for 4 μs. A 64-point fast Fourier transform is performed over 3.2 microseconds to extract the 48 data symbols on the 48 QAM signals. For binary phase-shift keying (BPSK), with 1 bit per symbol, that is 48 bits in 4 microseconds, for an aggregate data rate of 12 Mbits/s. Half-rate convolutional coding brings the net rate down to 6 Mbits/s. For 64 QAM, the aggregate data rate is six times higher, or 72 Mbits/s. 
       FIG. 1  illustrates the main function blocks of the transmitter end  100  of the OFDM baseband processor according to the IEEE 802.11a standard. The main function blocks of the transmitter end include a signal mapper  102 , a serial to parallel converter  104 , an inverse fast Fourier transform (IFFT) block  106 , a parallel to serial converter  108 , a cyclic prefix (CP) adding block  110 , a digital to analog converter (DAC)  112 , and a radio frequency (RF) transmitter  114 . OFDM is a multi-carrier modulation technique. First, the data stream is modulated with signal mapper  102  using modulation techniques such as Quadrature Amplitude Modulation (QAM) or Binary Phase Shift keying (BPSK). The next step in OFDM modulation is to convert the serial data into parallel data streams with the serial to parallel converter  104 . The Inverse Fast Fourier transform (IFFT) is performed on the modulated data with the IFFT block  106 . The IFFT is at the heart of the OFDM modulation, as it provides a simple way to modulate data streams onto orthogonal subcarriers. The data streams before and after IFFT are designated as X[n] and x[n] to represent frequency domain data and time domain data respectively, wherein n represents the order number of the subcarriers. After the IFFT, the parallel data streams are concatenated into a single data stream by the parallel to serial converter  108 . Finally a characteristic cyclic prefix (CP) is added to each OFDM symbol being transmitted in the single data stream with the cyclic prefix adding block  110 . The OFDM symbol is now ready, and after conversion from digital to analog form by the DAC  112  and modulation by the RF transmitter with a carrier frequency fc, the symbol is sent over channel  150  as RF signals to the receiver end. 
       FIG. 2  illustrates the main function blocks of the receiver end  200  of the OFDM baseband processor according to the IEEE 802.11a standard. The main function blocks of the receiver end  200  include a RF receiver  202 , a sampler  204 , a synchronization block  206 , a cyclic prefix remover  208 , a serial to parallel converter  210 , a fast Fourier transform (FFT) block  212 , a channel estimation and equalization block  214 , a parallel to serial converter  216 , and a signal demapper  218 . The receiver end  200  performs the inverse of the transmitter end  100 . After transmitting through channel  150 , the signal is received by the RF receiver  202  with carrier frequency fc′. The received signal is then passed to the sampler  204  and sampled. Then, the data samples are compensated for carrier frequency offset (CFO) with the CFO correction block  226  inside the synchronization block  206  wherein the CFO is caused by the difference between the carrier frequency of transmitter end  100  and receiver end  200  (fc and fc′). The other function blocks inside the synchronization block  206  are frame detection block  220  and timing synchronization block  224 . Frame detection detects the symbol frame of the data samples, and timing synchronization detects the symbol boundary of the data samples inside a data frame. The receiver end  200  must determine the symbol boundary to ensure that only the signal part of every OFDM symbol is written into the FFT and no part of the cyclic prefix. Implementing timing synchronization can also avoid Inter Symbol Interference (ISI) caused by sampling timing errors. After the cyclic prefix of symbols are removed with the CP removal block  208 , the data samples are converted form serial to parallel, and applied to the FFT block  212 . The Fast Fourier Transform (FFT) converts the time domain samples back into a frequency domain. Because the signal through channel  150  has suffered from frequency selective attenuation, the data samples are passed to the channel estimation and equalization block  214  to equalize the attenuation. The parallel to serial converter block  216  converts the parallel data samples into a serial data stream. Finally, the data stream is demodulated with QAM or BPSK schemes by signal demapper  218  to recover the original input data. 
       FIG. 3  shows the OFDM burst mode frame structure  300  which actually has four distinct regions. The first is the short preamble  302 . This is followed by a long preamble  304  and, finally, by the signal symbol  306  and data symbols  308 . Guard intervals  312 ,  314 ,  316  and  318  are inserted between each burst section. The short preamble  302  consists of 10 identical short OFDM training symbols  322 , and each short training symbol  322  lasts for 0.8 μs and contains 16 data samples. The long preamble  304  consists of two identical long training symbols (LTS)  324  and  326 , and each long training symbol lasts for 3.2 μs and contains 64 data samples. Between the short and long OFDM symbols, there is a guard interval (GI 2 )  312  of length 1.6 μs (32 data samples) that constitutes the cyclic prefix of the long symbols. Short training symbol  302  is used for frame detection, coarse timing synchronization, and carrier frequency offset (CFO) estimation. Long training symbols  324  and  326  are used for fine timing synchronization and channel estimation. Signal symbol  328  contains information about data rate, data length, and modulation scheme. Data symbols  330  and  332  contain the payload data and are of variable length. 
     There are many sources of frequency offset in wireless systems. The main sources are the difference between local oscillators at the transmitter and the receiver and the Doppler shift. The frequency offset destroys the orthogonality between the OFDM symbol subcarriers and introduces inter-channel interference (ICI) at the output of the OFDM demodulator. Therefore the CFO correction block  226  shown in  FIG. 2  is required to compensate the samples for CFO.  FIG. 4  shows a delay correlation circuit  400  for implementing frequency offset estimation in time domain with short preamble  302  or long preamble  304 , and the delay correlation circuit  400  can be used for realizing the CFO correction block  226  shown in  FIG. 2 . The samples are delivered to a delay line  402  which delays the samples for N sampling periods, and the number N is determined with the number of samples of the short training symbol  322  (N=16) or the long training symbol  324  or  326  (N=64). The conjugate of the delayed sample from a conjugate block  404  is then multiplied by the current sample with a complex multiplier  406  to generate a product value. The adder  410  and the delay block  412  then accumulate the product value, and a delayed product value from another delay line  408  is subtracted from the accumulated value from delay block  412 . The remainder is then delivered to a phase calculator  416  for retrieving its phase angle, and the phase angle is then averaged to generate the estimated frequency offset. 
     However, there is still some remnant CFO uncompensated in the traditional method. Because the OFDM system is far more vulnerable to the carrier frequency offset than single-carrier systems, even the remnant CFO of a small fraction of the subcarrier spacing can cause serious performance degradation if not properly compensated. Hence, there is a need for estimating the frequency offset of signals in frequency domain (after FFT) to reduce the error of the prior frequency offset estimation in time domain. 
     SUMMARY 
     Therefore the present invention provides a method and circuit for frequency offset estimation in frequency domain for a receiver of an orthogonal frequency division multiplexing (OFDM) system for IEEE 802.11a or 802.11g wireless local area network (LAN) standards, and an input signal of the receiver of the OFDM system is transmitted via 52 subcarriers. 
     A method for frequency offset estimation in the frequency domain is provided. An exemplary embodiment of a method comprises the following steps. First, a phase angle of a signal field of the input signal after processed by Fast Fourier Transformation (FFT) and channel equalization is calculated. A frequency offset error originating from at least one frequency offset estimation process in time domain is then estimated according to the phase angle. 
     A circuit for frequency offset estimation in the frequency domain is also provided. An exemplary embodiment of a circuit comprises a fast Fourier transformation module, for processing the input signal with fast Fourier transformation (FFT) to generate a first signal. The circuit also comprises a channel estimation module, coupled to the fast Fourier transformation module, for estimating a channel estimation coefficient of a k-th subcarrier of the 52 subcarriers, wherein the index k ranges from 1 to 52 and represents the order of subcarrier. 
     The circuit also comprises: an equalizer, coupled to the fast Fourier transformation module and the channel estimation module, for compensating the first signal for channel distortion with the channel estimation coefficient to generate a second signal; a square circuit, coupled to the channel estimation module, for calculating a square of an absolute value of the channel estimation coefficient of the k-th subcarrier; a multiplier, coupled to the equalizer and the square circuit, for multiplying the signal field of the second signal on the k-th subcarrier by its real part and the square of the absolute value of the channel estimation coefficient of the k-th subcarrier to generate a product value of the k-th subcarrier; an accumulator, coupled to the multiplier, for accumulating the product value of all 52 subcarriers to generate an accumulation value; an ArTan module, coupled to the accumulator, for calculating a phase angle of the accumulation value. Thus, a frequency offset error originating from at least one frequency offset estimation process in the time domain can be estimated according to the phase angle. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       The invention can be more fully understood by reading the subsequent detailed description in conjunction with the examples and references made to the accompanying drawings, wherein: 
         FIG. 1  illustrates the main function blocks of the transmitter end of the OFDM baseband processor according to the IEEE 80.2.11a standard; 
         FIG. 2  illustrates the main function blocks of the receiver end of the OFDM baseband processor according to the IEEE 802.11a standard; 
         FIG. 3  shows the OFDM burst mode frame structure; 
         FIG. 4  shows a delay correlation circuit for implementing frequency offset estimation in time domain with short or long preamble; 
         FIG. 5  is a flowchart illustrating an embodiment of a method for signal processing in an OFDM baseband receiver; 
         FIG. 6  is a flowchart illustrating an embodiment of a method for frequency offset error estimation with signal field in frequency domain; 
         FIG. 7  shows the main function blocks of an embodiment of a circuit for frequency offset error estimation with signal field in frequency domain; 
         FIG. 8  illustrates the timing of samples of the signal field of the signals; 
         FIG. 9  illustrates the relationship between the OFDM frame structure and the phases of samples based by the formula inferring the value of frequency offset. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 5  is a flowchart illustrating an embodiment of a method  500  for signal processing in an OFDM baseband receiver. The method  500  combines the frequency offset error estimation step provided by this invention to reduce the frequency offset estimation error of signals in the frequency domain. The method  500  begins with step  502 , which detects the existence of the OFDM signal. If the OFDM signal is detected in step  504 , step  506  estimates the frequency offset with the short preamble  302  of the signal, and the estimation value here based on short preamble is represented by SPFOE. Step  506  can be implemented with the delay correlation circuit  400  shown in  FIG. 4 . Because the signal has not been processed by the fast Fourier transformation (FFT) block  212 , the signal is still a time domain signal, and the signal after FFT is a frequency domain signal. Then, step  508  implementing a synchronization process as in timing synchronization block  224  shown in  FIG. 2 . If the synchronization process is achieved in step  510 , step  512  estimates the frequency offset with the long preamble  304  of the signal, and the estimation value here based on long preamble is represented by LPFOE. Step  512  can be implemented with the delay correlation circuit  400  shown in  FIG. 4 . Step  514  then performs the fast Fourier transformation (FFT) of the signal. Step  516  then executes the channel equalization to compensate the signal for channel distortion according to a channel estimation coefficient H k  of the k-th subcarrier. Because the SPFOE in step  506  and LPFOE in step  512  cannot be accurate enough and there is still some frequency offset error left meanwhile, which can affect the performance of the following signal processing processes, thus, step  518  estimates the frequency offset estimation error of the equalized signal in frequency domain with the signal field  328  of the equalized signal, and the OFDM receiver can compensate for the frequency offset error according to the estimation in step  518 . 
       FIG. 6  is a flowchart illustrating an embodiment of a method  600  for frequency offset error estimation with signal field  328  in frequency domain. The method  600  begins with step  602 , which performs FFT of the long preamble  304  of the signal. Step  604  then estimates a channel estimation coefficient H k  of the k-th subcarrier according to the long preamble processed by step  602 . Step  606  performs FFT of the signal field  328  of the signal. Step  608  extracts signal field S k  of the k-th subcarrier from the signal after processing with FFT and channel equalization. Step  610  calculates the value Re[S k ]×S k ×|H k | 2 , wherein the Re[S k ] is the real part of the signal field S k  and |H k | 2  is the square of the absolute value of the channel coefficient H k . Step  612  then accumulates the value Re[S k ]×S k ×|H k | 2  through all 52 subcarriers to generate the accumulated value 
               ∑     k   =   1     52     ⁢           ⁢       Re   ⁡     [     S   k     ]       ×     S   k     ×              H   k          2     .             
In step  614  the phase angle of the accumulated value
 
               ∑     k   =   1     52     ⁢           ⁢       Re   ⁡     [     S   k     ]       ×     S   k     ×            H   k          2             
is obtained, and in step  616  the frequency offset estimation error can be calculated according to the phase angle. The algorithm of step  616  for calculating the frequency offset estimation error will be further described with  FIG. 9 .
 
       FIG. 7  shows the main function blocks of an embodiment of a circuit  700  for frequency offset error estimation with signal field in frequency domain. The signal field  328  of input signal is first delivered to an FFT block  702  for fast Fourier transformation. After transformation, the signal field  328  is fed to an equalizer  706  for compensating for channel distortion to generate a signal field S k  of the k-th subcarrier according to a channel estimation coefficient H k  of the k-th subcarrier, which is generated from a channel estimation block  704 . The square circuit  708  then calculates the square of the absolute value of the channel estimation coefficient H k  to generate |H k | 2 , and the real part Re[S k ] of the signal field S k  is multiplied with the signal field S k  and |H k | 2  to produce the product value Re[S k ]×S k ×|H k | 2  with the multiplier  710 . The accumulator  712  then accumulates the product value Re[S k ]×S k ×|H k | 2  through all the 52 subcarriers to generate the accumulated value 
                 ∑     k   =   1     52     ⁢           ⁢       Re   ⁡     [     S   k     ]       ×     S   k     ×            H   k          2         ,         
and the ArTan block  714  retrieves the phase angle of the accumulated value
 
               ∑     k   =   1     52     ⁢           ⁢       Re   ⁡     [     S   k     ]       ×     S   k     ×              H   k          2     .             
Thus, the baseband receiver can calculate the frequency offset estimation error value according to the phase angle and compensate the signal for frequency offset error. The equation between the frequency offset error estimation value and the phase angle will be described in the following.
 
       FIG. 8  illustrates the timing of samples of the signal field  800  of the signals. Because signal field  800  lasts for 3.2 μs and the sampling period is 0.5 μs, there are 64 samples belonging to signal field  800 . Assume the frequency offset while the samples of signal field  800  is transformed with FFT is Δf. If the phase of the first sample of signal field  800  is θ, then the phase of the last sample of signal field  800  is θ+2πΔf64T s , wherein Ts is the sampling period, because there are 64 samples in the signal field  800 . Thus, the average of the phase of the signal field is θ+2πΔf32T s . Therefore we can use the phase of the signal field on 52 subcarriers to estimate the frequency offset Δf according to this formula. 
       FIG. 9  illustrates the relationship between the OFDM frame structure  900  and the phases of samples based by the formula inferring the value of frequency offset. The long preamble region contains guarding interface  902 , first long training symbol  904 , and second long training symbol  906 , and each of them contains 32, 64, and 64 samples respectively. The signal field region contains guarding interface  908  and signal field  910 , and each of them contains 16 and 64 samples respectively. Because there are two frequency offset estimations in the time domain based on short preamble (step  506  shown in  FIG. 5 ) and long preamble (step  512  shown in  FIG. 5 ), we assume that the value of the frequency offset based on the short preamble is SPFOE and the value of the frequency offset based on the long preamble is LPFOE. The following describes a situation with no frequency offset estimation based on the long preamble (i.e. LPFOE=0) first, and a situation where frequency offset estimation based on the long preamble is then described thereafter. 
     Assume that LPFOE=0. If the phase of the last sample  920  of short preamble  912  is θ 1 , the phase θ SG,2  of the last sample  930  of signal field  910  due to the frequency offset estimation error after compensated for SPFOE (represented by Δf SP  here) will be:
 
θ SG,2 =θ i +2 πΔf   SP ( N   LP   +N   SG ) T   S =θ i +2 πΔf   SP 240 T   S ,  (1)
 
     wherein (N LP +N SG ) is the number of samples between  920  and  930 , and N LP =32+64+64=160 and N SG =16+64=80. Accordingly, the phase θ SG,1  of the first sample  928  of signal field  910  due to the frequency offset estimation error will be:
 
θ SG,1 =θ i +2 πΔf   SP ( N   LP   +N   GI ) T   S =θ i +2 πΔf   SP 176 T   S ,  (2)
 
wherein (N LP +N GI ) is the number of samples between  920  and  928 , and N LP =160 and N GI =16. Thus, according to equations (1) and (2), the phase θ SG,FFT  of signal field  910  after FFT (step  514 ) is:
 
θ SG,FFT =θ i +2 πΔf   SP [(176+240)/2 ]T   S =θ i +2 πΔf   SP 208 T   S .  (3)
 
If channel estimation has been applied to the signal, the compensation of phase θ CE  due to channel estimation must be calculated. The compensated phase θ CE,1  by channel estimation with the first long training symbol is:
 
θ CE,1 =θ i +2 πΔf   SP [(32+96)/2 ]T   S =θ i +2 πΔf   SP 64 T   S ,  (4)
 
wherein the 32 is the number of samples between  920  and the first sample  922  of the first long training symbol  904 , and  96  is the number of samples between  920  and the last sample  924  of the first long training symbol  904 . Accordingly, the compensated phase θ CE,2  by channel estimation with the second long training symbol is:
 
θ CE,2 =θ i +2 πΔf   SP [(96+160)/2 ]T   S =θ i +2 πΔf   SP 128 T   S ,  (5)
 
wherein the 96 is the number of samples between  920  and the first sample  924  of the second long training symbol  906 , and  160  is the number of samples between  920  and the last sample  926  of the second long training symbol  906 . Thus, according to equations (4) and (5), the compensated phase θ CE  by channel estimation using both long training symbols is:
 
θ CE =(θ CE,1 +θ CE,2 )/2=θ i =2 πΔf   SP 96 T   S .  (6)
 
Therefore, the phase θ SG  of signal field  910  after channel equalization (step  516 ) is:
 
θ SG =θ SG,FFT −θ CE =2 πΔf   SP 112 T   S .  (7)
 
The phase θ SG  of signal field  910  after channel equalization can be determined by the following equation:
 
                       θ   SG     =     Ar   ⁢           ⁢     Tan   [       ∑     k   =   1     52     ⁢           ⁢       Re   (     S   k     )     ×     S   k     ×            H   k          2         ]         ,           (   8   )               
wherein S k  is signal field  910  signal on the k-th subcarrier, and H k  is the channel estimation coefficient. Since the value of θ SG  is known from equation (8), the SPFOE error Δf SP  can be obtained with the following equation deduced from equation (7):
 Δ f   SP =θ SG /(2π×112 ×T   S ) (Hz).  (9) 
The 112 in denominator of equation (9) can be simplified as 113 to be quantized to (½ 7 +½ 10 ).
 
     Next, we consider the situation in which the frequency offset estimation based on the long preamble is applied. Assume the estimate LPFOE of the frequency offset estimation based on long preamble is f LP . Thus, the phase θ SG,2  of the last sample  930  of signal field  910  due to the frequency offset estimation error after compensated for SPFOE (represented by Δf SP  here) and LPFOE (represented by f LP ) will be 
                           θ     SG   ,   2       =       θ   i     +     2   ⁢           ⁢   π   ⁢           ⁢   Δ   ⁢           ⁢       f   SP     ⁡     (       N   LP     +     N   SG       )       ⁢     T   S       -     2   ⁢           ⁢   π   ⁢           ⁢     f   LP     ⁢     N   SG     ⁢     T   S                     =       θ   i     +     2   ⁢           ⁢   π   ⁢           ⁢   Δ   ⁢           ⁢     f   SP     ⁢   240   ⁢     T   S       -     2   ⁢           ⁢   π   ⁢           ⁢     f   LP     ⁢   80   ⁢       T   S     .                       (   10   )               
Accordingly, the phase θ SG,1  of the first sample  928  of signal field  910  due to the frequency offset estimation error will be:
 
                           θ     SG   ,   1       =       θ   i     +     2   ⁢           ⁢   π   ⁢           ⁢   Δ   ⁢           ⁢       f   SP     ⁡     (       N   LP     +     N   GI       )       ⁢     T   S       -     2   ⁢           ⁢   π   ⁢           ⁢     f   LP     ⁢     N   GI     ⁢     T   S                     =       θ   i     +     2   ⁢           ⁢   π   ⁢           ⁢   Δ   ⁢           ⁢     f   SP     ⁢   176   ⁢     T   S       -     2   ⁢           ⁢   π   ⁢           ⁢     f   LP     ⁢   16   ⁢       T   S     .                       (   11   )               
Thus, according to equation (10) and (11), the phase θ SG,FFT  of signal field  910  after FFT (step  514 ) is:
 θ SG,FFT =(θ SG,1 +θ SG,2 )/2=θ i +2 πΔf   SP 208 T   S −2 πf   LP 48 T   S ,  (12) 
The compensated phase θ CE  by channel estimation is still determined by equation (6). Therefore, the phase θ SG  of signal field  910  after channel equalization (step  516 ) is:
 θ SG =θ SG,FFT −θ CE =2 πΔf   SP 112 T   S −2 πf   LP 48 T   S .  (13) 
If we substitute the SPFOE error Δf SP  by Δf LP +f LP , wherein the Δf LP =Δf SP −f LP  is the frequency offset estimation error after compensation for SPFOE Δf SP  and LPFOE f LP , the equation (13) becomes:
 θ SG =2π(Δ f   LP   +f   LP )112 T   S −2 πf   LP 48 T   S .  (14) 
Since the value of θ SG  is still determined by equation (8), the LPFOE error Δf LP  can be obtained with the following equation deduced from equation (14):
 Δ f   LP =(θ SG −2 π×f   LP ×64 ×T   S ) (Hz).  (15) 
     In this disclosure, we provide a simple method for estimating frequency offset estimation errors with signal field in the frequency domain in the IEEE 802.11a/g OFDM system. The estimation is done with signal field after FFT, that is, in the frequency domain compared to the delay-correlation circuit in the time domain. Because the estimation of frequency offset estimation error is enforced after the frequency offset estimation based on the short and long preambles, it can reduce the error of frequency offset estimation by delay-correlation circuit. 
     Finally, while the invention has been described by way of example and in terms of the above, it is to be understood that the invention is not limited to the disclosed embodiment. On 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.