Abstract:
An apparatus for synchronizing pilots contained in symbols received by a receiver in a multicarrier transmission system and a method thereof are provided. Frequency or Time-frequency correlation-based scheme, with exploitation of time-frequency correlation characteristics of the pilots, may be used for identifying the positions of the pilots in frequency or time and frequency dimensions consisting of received symbols. In one example, the apparatus includes a pilot compensator and a signal selector for determining at least one correlation set, a correlator for generating one correlation set result for each of the correlation set, and a judgment or processing unit for determining positions of the pilots in response to the correlation set result.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part application of U.S. patent application Ser. No. 11/153,105, titled “TIME-FREQUENCY CORRELATION-BASED SYNCHRONIZATION FOR COHERENT OFDM RECEIVER” and filed on Jun. 15, 2005, which claimed the benefit of U.S. Provisional Application No. 60/620,725, titled “FAST SYNCHRONIZATION FOR COHERENT OFDM DEMODULATORS” and filed on Oct. 22, 2004. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention generally relates to digital broadcasting systems. More particular, the present invention relates to frequency or time-frequency correlation-based synchronization for coherent Orthogonal Frequency Division Multiplexing (OFDM) receivers in a multi-carrier digital broadcasting system, such as Digital Video Broadcasting-Terrestrial (DVB-T), Digital Video Broadcasting-Handheld (DVB-H), and Integrated Service Digital Broadcasting-Terrestrial (ISDB-T) system. 
     OFDM transmission technique, being one kind of the multi-carrier modulation schemes, has been widely applied for modern high-data-rate digital communications and broadcasting due to its extreme efficacy on dealing with the multipath propagation effects. The OFDM technique has been adopted by several broadcasting systems such as Digital Audio Broadcasting (DAB), DVB-T, DVB-H and ISDB-T, and, moreover, by local area networks such as the HiperLAN/2 and IEEE 802.11a/g/n. Specifically, the (inverse) fast Fourier transform (FFT) technique is employed in an OFDM transmission system for efficiently implementing multi-carrier modulation and demodulation. 
     For coherent OFDM-based systems such as the DVB-T/H and ISDB-T systems, certain scattered pilots (known as SPs hereinafter) regularly posited in time- and frequency-dimensions are transmitted with predetermined known values together with information data at OFDM transmitters&#39; end and used for channel estimation and equalization at OFDM receivers&#39; end. Referring to  FIG. 1 , a diagram illustrating positions of SPs defined in DVB-T/H systems with respect to the time-frequency dimension in the frequency domain is provided. The positions of SPs in DVB-T/H systems can be expressed as follows: 
     For the OFDM symbol of index l (ranging from 0 to 67), carriers for which index k belongs to the subset {k=K min +3×(l mod 4)+12p|p integer, p≧0, kε[K min , K max ]} are SPs, wherein p is an integer that takes all possible values greater than or equal to zero, provided that the resulting value for k does not exceed the valid range [K min , K max ]. K max  is 1704 for the 2K mode, 3408 for the 4K mode and 6816 for the 8K mode as defined by DVB-T/H standards. 
     The positions of the SPs should be detected and identified by means of a synchronization sequence (or synchronization procedure) at a coherent OFDM receiver. Assume that the received Radio Frequency (RF) signal is first down converted to the baseband using a tuner and a carrier recovery loop. A typical DVB-T/H baseband synchronization sequence  20  is illustrated in  FIG. 2 . After the start-up, pre-FFT synchronization is performed in step  21  in which all metrics are derived in time-domain from guard interval correlation. The baseband signal is then transformed to the frequency-domain through FFT. Subsequently, post-FFT synchronization is performed in frequency-domain in step  22  based on correlating the Continual Pilots (CP) of two consecutive OFDM symbols. Specifically, the pre-FFT and post-FFT synchronization blocks perform the sampling clock, OFDM symbol timing and carrier frequency synchronization. 
     After sampling clock, OFDM symbol timing and carrier frequency synchronization have been achieved via the pre-FFT and post-FFT synchronization, the positions of the SPs within an OFDM symbol has to be determined before channel estimation can be performed in step  24 . As shown in  FIG. 2 , Transmission Parameters Signaling (TPS) decoding procedure is utilized in step  23  which determines the positions of the SPs by detecting a frame boundary as the scattered pilot positions (known as SPPs hereinafter) are directly related to the OFDM frame. The detection of the frame boundary is so-called “frame synchronization.” Typically, the frame synchronization takes a variable synchronization time of 68˜136 OFDM symbols, 68˜136 T OFDM , which is around 50%˜70% of the overall synchronization time associated with the total synchronization procedure  20 . Thus, the conventional frame synchronization is considerably time-consuming. In particular, for DVB-H time-slicing purposes of burst-mode transmission, the receiver may prepare for the required frame synchronization time even longer than the data burst duration of interest. Therefore, the conventional frame boundary detection based SPPs identification (or SPs synchronization) scheme is especially inefficient in the sense of power reduction for receiving the time-sliced DVB-H signals. 
     BRIEF SUMMARY OF THE INVENTION 
     In one example, a method for synchronizing pilots contained in symbols received by a receiver in a multicarrier transmission system is provided. The pilots have predetermined known values, are posited among data carriers in a frequency dimension containing the received symbols, and have a predetermined position pattern in the frequency dimension. The predetermined position pattern may include a finite number of sub-position patterns each corresponding to positions of pilots contained in one of the symbols. The method may include: determining at least one correlation set in the frequency dimension between two sub-carriers of at least one symbol; generating a correlation set result in response to each the correlation set; and determining positions of the pilots in the frequency dimension in response to the correlation set results. 
     In another example, an apparatus for synchronizing pilots contained in symbols received by a receiver in a multicarrier transmission system is provided. The pilots have predetermined known values, are posited among data carriers in a frequency dimension containing the received symbols, and have a predetermined position pattern in the frequency dimension. The predetermined position pattern may include a finite number of sub-position patterns each corresponding to positions of pilots contained in one of the symbols such that at least one correlation set in the frequency dimension between at least two sub-carriers of at least one symbol can be determined. The apparatus includes: a pilots compensator and a signal selector for determining the at least one correlation set; a correlator for generating one correlation set result for each of the correlation set; and a processing unit for determining positions of the pilots in response to the correlation set result. 
     In further another example, an apparatus for synchronizing pilots contained in symbols received by a receiver in a multicarrier transmission system is provided. The pilots have predetermined known values, are posited among data carriers in time and frequency dimensions including the received symbols, and have a predetermined position pattern in the time and frequency dimensions. The predetermined position pattern may include a finite number of sub-position patterns each corresponding to positions of pilots contained in one of the symbols such that at least one correlation set in the time and frequency dimensions between at least two of the symbols in response to the sub-position pattern can be determined. The apparatus include: a pilots compensator and a signal selector for determining the at least one correlation set; a correlator for generating one correlation set result for each the correlation set; and a processing unit for determining positions of the pilots in response to the correlation set result. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The foregoing summary, as well as the following detailed description of the invention, will be better understood when read in conjunction with the appended drawings. For the purpose of illustrating the invention, the drawings are merely exemplary. It should be understood, however, that the invention is not limited to the precise arrangements and instrumentalities shown. 
       In the drawings: 
         FIG. 1  is a diagram illustrating positions of SPs in DVB-T/H systems; 
         FIG. 2  is a diagram illustrating a typical DVB-T/H synchronization sequence (or synchronization procedure); 
         FIG. 3  is a diagram illustrating a prior art time correlation-based SPPs identification scheme; 
         FIG. 4  is a diagram illustrating a prior art power-based SPPs identification scheme; 
         FIG. 5  is a diagram illustrating positions of SPs for explaining an embodiment in accordance with a time-frequency correlation-based scheme; 
         FIG. 6  is a block diagram of one example to implement the embodiment of  FIG. 5 ; 
         FIGS. 7A and 7B  are diagrams illustrating the minimum protection ratio (MPR) associated with the time-frequency correlation-based scheme of the present invention, the conventional time correlation-based and power-based schemes upon simulation results; 
         FIG. 8  is a diagram illustrating positions of SPs for explaining another embodiment in accordance with a time-frequency correlation-based scheme; 
         FIG. 9  is a diagram illustrating positions of SPs for explaining an embodiment in accordance with a frequency correlation-based scheme; 
         FIG. 10  is a block diagram of one example to implement the embodiment of  FIG. 9 ; 
         FIG. 11  is a diagram illustrating positions of SPs for explaining another embodiment in accordance with a frequency correlation-based scheme; and 
         FIG. 12  is a diagram illustrating an application of the present invention in the synchronization procedure of DVB-T/H receivers. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     According to the present invention, a frequency or time-frequency correlation-based scheme that exploits frequency or time-frequency correlation characteristics of the SPs is provided for robust SP synchronization without TPS synchronization. It is to be understood that the present invention may be implemented in various forms of hardware, software, firmware, special purpose processors, or a combination thereof. 
     It is to be further understood that, because some of the constituent system components and method steps depicted in the accompanying figures are preferably implemented in a combination of hardware and software, the actual connections between the system components (or the process steps) may differ depending upon the manner in which the present invention is programmed. Given the teachings herein, one of ordinary skill in the related art will be able to contemplate these and similar implementations or configurations of the present invention. 
     For ease of presenting the concept and the methods of the present invention, let us consider the SPPs identification for the DVB-T/H systems as an example. It is to be understood that the concept and the methods of the present invention can be applied to any coherent OFDM-based systems. Referring to  FIG. 1 , SPPs are designated by solid circles which appear as regular position pattern. The position pattern associated with the SPPs further comprises of four sub-position patterns:  101 ,  102 ,  103  and  104  in  FIG. 1 , wherein each sub-position pattern in the time-dimension will repeat once for every four OFDM symbols. The four sub-position patterns  101 ,  102 ,  103  and  104  are denoted as sub-position patterns  1 ,  2 ,  3 , and  4 , respectively. Moreover, the SPPs shift three subcarriers in view of the frequency-dimension between two adjacent OFDM symbols, and eleven data carriers are arranged between two scattered pilots in each OFDM symbol. For ease of presentation, R l,k  is defined as the received baseband signal on the kth sub-carrier of the lth OFDM symbol. For example, the signal in the position  120  is denoted by R 1,0  and the signal in the position  140  is denoted by R 9,18 . 
       FIG. 3  is a diagram illustrating a prior art time correlation-based SPPs identification scheme as disclosed in L. Schwoerer and J. Vesma, “Fast Scattered Pilot Synchronization for DVB-T and DVB-H,”  Proc.  8 th    International OFDM Workshop , Hamburg, Germany, Sep. 24-25, 2003. As can be observed from  FIG. 3 , four sets of correlation are performed for the four possible SPPs along the time-dimension and both the current and the last fourth OFDM symbols have to be accessed for each correlation set. The four correlation sets T i (l), iε{1, 2, 3, 4} are given as follows: 
     
       
         
           
             
               
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     Theoretically, the SPs are correlated while the data symbols are uncorrelated. Thus, a correlation magnitude maximum is found for the sub-position pattern of the current SPP as 
                   SPP   T     ⁡     (   l   )       =     arg   ⁢           ⁢       max   i     ⁢     (       T   i     ⁡     (   l   )       )           ;     i   ∈       {     1   ,   2   ,   3   ,   4     }     .             
This approach exploits features of the SPs themselves instead of the TPS such that the time needed for SPPs identification is reduced to 5 T OFDM . However, the time correlation-based SPPs identification scheme is quite sensitive to Doppler effects and sampling clock frequency offset (ScFO) effects.
 
       FIG. 4  is a diagram illustrating another prior art power-based SPPs identification scheme as disclosed in L. Schwoerer, “Fast Pilot Synchronization Schemes for DVB-H,”  Proc. Wireless and Optical Communications , Banff, Canada, Jul. 8-10, 2004, pp. 420-424. As can be observed from  FIG. 4 , four sets of power estimators are performed for the four possible SPPs and only the current OFDM symbol needs to be accessed for each set of power estimators. The four power estimation sets E i (l), iε{1, 2, 3, 4} are given as follows: 
     
       
         
           
             
               
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     Definitely, the power of SPs is higher than the data symbols. Thus, a power maximum is found for the sub-position pattern of the current SPP as 
                   SPP   E     ⁡     (   l   )       =     arg   ⁢           ⁢       max   i     ⁢     (       E   i     ⁡     (   l   )       )           ;     i   ∈       {     1   ,   2   ,   3   ,   4     }     .             
This approach exploits features of the SPs themselves instead of the TPS such that the time needed for SPPs identification is reduced to 1 T OFDM . However, the power-based SPPs identification scheme is quite sensitive to noise effects and ill-conditioned channel effects (e.g., echo in single-frequency networks (SFN)).
 
     Based upon the characteristics of the SPPs above, the present invention sets forth a frequency or time-frequency correlation-based scheme for the purpose of fast and robust SPs synchronization for OFDM receivers. Referring to  FIG. 5 , a diagram illustrating the SPPs for explaining a time-frequency correlation-based scheme in accordance with one embodiment of the present invention is depicted schematically. As shown in  FIG. 5 , four correlation sets C 1 (l), C 2 (l), C 3 (l), C 4 (l) (i.e.,  501 ,  502 ,  503  and  504 ) in view of two adjacent OFDM symbols are used for SPPs identification. The four correlation sets C i (l), iε{1, 2, 3, 4} are given as follows: 
                       C   1     ⁡     (   l   )       =            ∑     p   =   0       p   max       ⁢       (       R     l   ,       12   ⁢   p     +   3         ·     P       12   ⁢   p     +   3         )     ·     (       R       l   -   1     ,     12   ⁢   p       *     ·     P     12   ⁢   p     *       )                              C   2     ⁡     (   l   )       =            ∑     p   =   0       p   max       ⁢       (       R     l   ,       12   ⁢   p     +   6         ·     P       12   ⁢   p     +   6         )     ·     (       R       l   -   1     ,       12   ⁢   p     +   3       *     ·     P       12   ⁢   p     +   3     *       )                              C   3     ⁡     (   l   )       =            ∑     p   =   0       p   max       ⁢       (       R     l   ,       12   ⁢   p     +   9         ·     P       12   ⁢   p     +   9         )     ·     (       R       l   -   1     ,       12   ⁢   p     +   6       *     ·     P       12   ⁢   p     +   6     *       )                              C   4     ⁡     (   l   )       =            ∑     p   =   0       p   max       ⁢       (       R     l   ,       12   ⁢   p     +   12         ·     P       12   ⁢   p     +   12         )     ·     (       R       l   -   1     ,       12   ⁢   p     +   9       *     ·     P       12   ⁢   p     +   9     *       )                          
wherein P k =±1 with kεS SP ={0, 3, 6, 9, . . . , K max } (a set of all subcarrier indices associated with all SPPs) is the (sign of the) value of the SP on kth sub-carrier defined by the DVB-T/H standard and (p max , K max )=(141, 1704), (283, 3408) and (567, 6816) for 2K, 4K and 8K modes respectively. Note that P k &#39;s required by computing the correlation C i (l) are used for SPs compensation such that (R l,k ·P k ) and (R l−1,k−3 ·P k−3 ) could be positively correlated if R l,k  carries an SP. Then, a clear distinct correlation magnitude maximum should be found for the sub-position pattern of the current SPP as
 
     
       
         
           
             
               
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     As an example, if Symbol  0  and Symbol  1  shown in  FIG. 1  are used to generate four correlations C 1 ( 1 ), C 2 ( 1 ), C 3 ( 1 ), C 4 ( 1 ), wherein Symbol  1  is the current OFDM symbol, i.e., l=1. The correlation C 1 ( 1 ) is then greater than the other three correlations C 2 ( 1 ), C 3 ( 1 ), C 4 ( 1 ), and thus the current SPP corresponds to sub-position pattern index SPP( 1 )=2 (i.e., sub-position pattern  2 ). Moreover, if Symbol  1  and Symbol  2  shown in  FIG. 1  are utilized to generate four correlations C 1 ( 2 ), C 2 ( 2 ), C 3 ( 2 ), C 4 ( 2 ), wherein Symbol  2  is the current OFDM symbol, i.e., l=2. The correlation C 2 ( 2 ) is then greater than the other three correlations C 1 ( 2 ), C 3 ( 2 ), C 4 ( 2 ), and thus the current SPP corresponds to sub-position pattern index SPP( 2 )=3 (i.e., sub-position pattern  3 ). Furthermore, if Symbol  2  and Symbol  3  shown in  FIG. 1  are utilized to generate four correlations C 1 ( 3 ), C 2 ( 3 ), C 3 ( 3 ), C 4 ( 3 ), wherein Symbol  3  is the current OFDM symbol, i.e., l=3. The correlation C 3 ( 3 ) is then greater than the other three correlations C 1 ( 3 ), C 2 ( 3 ), C 4 ( 3 ), and thus the current SPP corresponds to sub-position pattern index SPP( 3 )=4 (i.e., sub-position pattern  4 ). In addition, if Symbol  3  and Symbol  4  shown in  FIG. 1  are utilized to generate four correlations C 1 ( 4 ), C 2 ( 4 ), C 3 ( 4 ), C 4 ( 4 ), wherein Symbol  4  is the current OFDM symbol, i.e., l=4. The correlation C 4 ( 4 ) is then greater than the other three correlations C 1 ( 4 ), C 2 ( 4 ), C 3 ( 4 ), and thus the current SPP corresponds to a sub-position pattern index SPP( 4 )=1 (i.e., sub-position pattern  1 ). 
     It is to be noted that, instead of accumulating all available (p max +1) complex values of (R l,12p+3i ·P 12p+3i )·(R* l−1,12p+3(i−1) ·P 12p+3(i−1) ) for C i (l), iε{1, 2, 3, 4}, accumulation of only partial set of complex values of (R l,12p+3i ·P 12p+3i )·(R* l,12p+3(i−1) ·P* 12p+3(i−1) ) may suffice for robust SPPs identification. Therefore, the four correlation sets C i (l), iε{1, 2, 3, 4} can be generalized as 
                 C   i     ⁡     (   l   )       =            ∑     p   ∈   Z               ⁢       (       R     l   ,       12   ⁢   p     +     3   ⁢   i           ·     P       12   ⁢   p     +     3   ⁢   i           )     ·     (       R       l   -   1     ,       12   ⁢   p     +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢   p     +     3   ⁢     (     i   -   1     )         *       )                    
wherein Z⊂{0, 1, 2, . . . , p max }.
 
     Referring to  FIG. 6 , a block diagram of one example to implement the time-frequency correlation-based scheme of the present invention as depicted in  FIG. 5  is provided. As shown in  FIG. 6 , the time-frequency correlation-based scheme of the present invention basically comprises an SP compensator and signal selector  630 , four correlators  660 A,  660 B,  660 C and  660 D, and a judgment or processing block  670 . Signals  610  and  620  applied to the SP compensator and signal selector  630  are the received baseband signal R l,k  from an OFDM receiver and known P k  wherein kεS SP ={0, 3, 6, 9, . . . , K max }. The SP compensator and signal selector  630  is employed to obtain sub-signals  640 A,  640 B,  640 C,  640 D,  650 A,  650 B,  650 C, and  650 D, which are associated to (R l,12p+3 ·P 12p+3) , (R l,12p+6 ·P 12p+6) , (R l,12p+9 ·P 12p+9) , (R l,12p+12 ·P 12p+12) , (R l−1,12p ·P 12p ), (R l−1,12p+3 ·P 12p+3 ), (R l−1,12p+6 ·P 12p+6 ) and (R l−1,12p+9 ·P 12p+9 ), respectively, wherein pεZ⊂{0, 1, 2, . . . , p max }. Preferably, the SP compensator and signal selector  630  includes a buffer to receive the signals  610  for storing the signals of the previous OFDM symbol l−1. Sub-signals  640 A and  650 A are applied to the correlator  660 A, sub-signals  640 B and  650 B are applied to the correlator  660 B, sub-signals  640 C and  650 C are applied to the correlator  660 C, and sub-signals  640 D and  650 D are applied to the correlator  660 D. The correlators  660 A,  660 B,  660 C and  660 D are employed to compute four correlation set results  501 ,  502 ,  503  and  504 , which are associated to the correlation sets C 1 (l), C 2 (l), C 3 (l) and C 4 (l) as depicted in  FIG. 5 , respectively. Preferably, the correlator  660 A includes a complex conjugate function to generate the conjugate part of a signal, a complex multiplier and an accumulator, while correlators  660 B,  660 C and  660 D can be implemented the same. Subsequently, the four correlation set results  501 ,  502 ,  503  and  504  are all supplied to a judgment or processing block  670  to determine the maximum thereof and generate a judgment or processing result  680  as SPP(l) indicating the sub-position pattern exhibited by the SPs in the current lth OFDM symbol accordingly. Preferably, the judgment or processing unit  680  includes a peak detector or a comparator so as to determine the maximum of correlation set results  501 ,  502 ,  503  and  504 . It is to be understood that, because some of the sub-signals  640 A,  640 B,  640 C,  640 D,  650 A,  650 B,  650 C, and  650 D appear in different time, one of ordinary skill in the related art such as time-sharing based hardware design will be able to obtain the four correlation set results  501 ,  502 ,  503  and  504  with only one correlator  660 A. 
     It is to be noted that, in virtue of the fact that (R l,k ·P k ) and (R l−1,k3 ·P k−3 ) could be positively correlated if R l,k  carries an SP, the four correlation sets C i (l), iε{1, 2, 3, 4} can be further simplified as 
                 C   i     ⁡     (   l   )       =            ∑     p   ∈   Z               ⁢     Re   ⁢     {       (       R     l   ,       12   ⁢   p     +     3   ⁢   i           ·     P       12   ⁢   p     +     3   ⁢   i           )     ·     (       R       l   -   1     ,       12   ⁢   p     +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢   p     +     3   ⁢     (     i   -   1     )         *       )       }                    
wherein Z⊂{0, 1, 2, . . . , p max }. Therefore, instead of obtaining the result of (R l,12p+3i ·P 12p+3i )·(R l−1,12p+3(i−1) ·P 12p+3(i−1) ) by a complex multiplier, only two real multipliers and one adder suffice for computing
 
               Re   ⁢     {       (       R     l   ,       12   ⁢   p     +     3   ⁢   i           ·     P       12   ⁢   p     +     3   ⁢   i           )     ·     (       R       l   -   1     ,       12   ⁢   p     +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢   p     +     3   ⁢     (     i   -   1     )         *       )       }       =       Re   ⁢       {       R     l   ,       12   ⁢   p     +     3   ⁢   i           ·     P       12   ⁢   p     +     3   ⁢   i           }     ·   Re     ⁢     {       R       l   -   1     ,       12   ⁢   p     +     3   ⁢     (     i   -   1     )             ·     P       12   ⁢   p     +     3   ⁢     (     i   -   1     )             }       +     Im   ⁢       {       R     l   ,       12   ⁢   p     +     3   ⁢   i           ·     P       12   ⁢   p     +     3   ⁢   i           }     ·   Im     ⁢     {       R       l   -   1     ,       12   ⁢   p     +     3   ⁢     (     i   -   1     )             ·     P       12   ⁢   p     +     3   ⁢     (     i   -   1     )             }               
for C i (l), iε{1, 2, 3, 4}.
 
     As compared with the conventional time correlation-based scheme of the required synchronization time 5T OFDM , the time-frequency correlation-based scheme of this example may require only two adjacent OFDM symbols in order to compute the correlation set results C 1 (l), C 2 (l), C 3 (l), C 4 (l) and then determine the maximum thereof to be associated with the judgment or processing result  680  indicating the correct SPPs of the current symbol. The time-frequency correlation-based scheme of this example hence benefits not only the ability of fast synchronization speed but also the robustness against Doppler effects due to less stringent requirement on the channel coherence time. In addition, the time-frequency correlation-based scheme of this example may be less sensitive to ScFO effects than the conventional time correlation-based scheme. On the other hand, as compared with the conventional power-based scheme requiring a synchronization time of T OFDM , the time-frequency correlation-based scheme of this example may provide robustness against noise effects due to the correlation gain at the cost of slightly longer synchronization time 2T OFDM . Furthermore, another advantage of the example over both time correlation-based and power-based schemes is that the time-frequency correlation-based scheme is free from the correlation-interference caused by CP defined in DVB-T/H wherein the CP are continuously located at the same subset S CP  of subcarriers over all OFDM symbols with S CP ⊂S SP . 
     Some of the simulation results (for 8 k mode in DVB-T/H with a guard interval of ¼ useful symbol length) are shown in  FIGS. 7A and 7B  for supporting the efficacy and robustness of the time-frequency correlation-based scheme in one example.  FIGS. 7A and 7B  plot the minimum protection ratio (MPR), a performance index used by L. Schwoerer, “Fast Pilot Synchronization Schemes for DVB-H,”  Proc. Wireless and Optical Communications , Banff, Canada, Jul. 8-10, 2004, pp. 420-424. In particular,  FIGS. 7A and 7B  are the MPR plot of an example of the time-frequency correlation-based scheme and of the conventional time correlation-based and power-based schemes over 1000 independent runs for static AWGN channel model with various carrier-to-noise ratio (C/N) and typical urban channel model with various Doppler frequencies (with C/N=5 dB), respectively. The MPR for the time-frequency correlation-based scheme of this example is defined as 
               MPR   =       min   n     ⁢     (     PR   ⁡     (   n   )       )         ;     n   ∈     {     1   ,   2   ,   …   ⁢           ,   1000     }             
wherein PR(n) is the protection ratio associated with the nth independent run and is defined as
 
                 PR   ⁡     (   n   )       =       min   i     ⁢     (         C     i   true       (   n   )       ⁡     (   l   )           C   i     (   n   )       ⁡     (   l   )         )         ;     i   ∈         {     1   ,   2   ,   3   ,   4     }     ⁢           ⁢   and   ⁢           ⁢   i     ≠     i   true               
in which i true ε{1, 2, 3, 4} is the sub-position pattern index corresponding to the true SPPs associated with the lth OFDM symbol. The MPRs for the conventional time correlation-based and power-based schemes are defined in a similar way with C i   (n) (l) replaced by T i   (n) (l) and E i   (n) (l), respectively. It is noted that the higher the MPR value the more robust the performance of the SPPs identification scheme, wherein MPR&lt;1 implies at least one erroneous detection of the SPPs exists over the 1000 independent runs.
 
     In  FIGS. 7A and 7B , curves  70 A and  70 B are associated with the time-frequency correlation-based scheme of one example, wherein curves  72 A and  72 B correspond to the conventional time correlation-based scheme and curves  74 A and  74   b  correspond to the conventional power-based scheme. 
     As shown in  FIG. 7A , both the time-frequency correlation-based scheme of one example and the conventional time correlation-based scheme are uniformly more robust against noise effects than the conventional power-based scheme due to the correlation gain. The time-frequency correlation-based scheme in some examples may outperform the conventional time correlation-based scheme under higher C/N because the latter may suffer from the correlation-interference due to CP that dominates the performance for low noise condition. As shown in  FIG. 7B , the conventional power-based scheme is as expected insensitive to Doppler effects and the time-frequency correlation-based scheme may be more robust against Doppler effects than the conventional time correlation-based scheme whose performance is significantly degraded for Doppler frequency larger than 60 Hz because the latter requires longer coherence time. In summary, the time-frequency correlation-based scheme may outperform the conventional time correlation-based and power-based schemes in view of robustness against both Doppler and noise effects. 
     The time-frequency correlation-based scheme can further provide a flexible design for the trade-off between hardware cost and synchronization time in some examples. Referring to  FIG. 8 , a diagram illustrating the SPPs for explaining another embodiment in accordance with the time-frequency correlation-based scheme. As compared with the embodiment of  FIG. 5 , this embodiment makes use of only one correlation set, for example, C 1 (l), to determine the correct SPP of the current symbol. If the time-frequency correlation-based scheme of  FIG. 8  is implemented in the same manner as  FIG. 6 , three sets of correlators  660 B,  660 C and  660 D can be omitted with certain modification on the SPPs identification scheme. One possible modification involved is that the judgment or processing block  670  should include a detector provided with threshold detection approach so that the current SPPs are identified as sub-position pattern  2  if C 1 (l) is larger than a threshold value. Another possible modification is that the correlator  660 A should be performed four times to obtain C 1 (l), C 1 (l−1), C 1 (l−2) and C 1 (l−3) using the (l,l−1), (l−1,l−2), (l−2,l−3) and (l−3,l−4) OFDM symbols pairs, respectively. Then, a clear distinct correlation magnitude maximum among C 1 (l), C 1 (l−1), C 1 (l−2) and C 1 (l−3) should be found by the judgment or processing block  670 . Denoting 
                   l   max     =     arg   ⁢           ⁢       max   m     ⁢     (       C   1     ⁡     (   m   )       )           ;     m   ∈     {     l   ,     l   -   1     ,     l   -   2     ,     l   -   3       }         ,         
the SPPs of the l max th OFDM symbol are thus identified as sub-position pattern  2 . For the same reason, any combination of two or three of the correlation-sets C 1 (l), C 2 (l), C 3 (l) and C 4 (l) can be used in a similar way as a direct extension of the second embodiment shown in  FIG. 8  to reduce the number of the required correlators in exchange of the increased synchronization time 2˜5T OFDM .
 
     Referring to  FIG. 9 , in another example, a frequency correlation-based scheme may be implemented. The implementation may be based on the characteristics of the SPPs noted above and, in some examples, may be used for providing fast and robust SPs synchronization for OFDM receivers. The implementation may be used to increase the processing speed of an OFDM receiver and improve SP synchronization. Referring to  FIG. 9 , in an example of having one OFDM symbol, one correlation set, such as F 1 (l), F 2 (l), F 3 (l) and F 4 (l) illustrated as in  FIG. 9 , may be used to determine the correct SPP of the current symbol. For example, the correlation set F 1 (l), iε{1, 2, 3, 4} may be given as: 
     
       
         
           
             
               
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     In one example, the P k &#39;s required for computing the correlation may be used for SP compensation such that (R l,k ·P k ) and (R l,k+12 ·P k+12 ) could be positively correlated if R l,k  carries an SP. Then, a distinct correlation magnitude maximum may be found, which may correspond to the sub-position pattern of the current SPP as 
     
       
         
           
             
               
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     As an example, if Symbol  0  shown in  FIG. 1  is used to generate four correlations F 1 ( 0 ), F 2 ( 0 ), F 3 ( 0 ), F 4 ( 0 ), wherein Symbol  0  is the current OFDM symbol, i.e., l=0. The correlation F 1 ( 0 ) would be greater than the other three correlations F 2 ( 0 ), F 3 ( 0 ), F 4 ( 0 ). Therefore, the sub-position pattern of the current SPP is SPP( 0 )=1 (sub-position pattern  1 ). Moreover, if Symbol  1  shown in  FIG. 1  is used to generate four correlations F 1 ( 1 ), F 2 ( 1 ), F 3 ( 1 ), F 4 ( 1 ), wherein Symbol  1  is the current OFDM symbol, i.e., l=1. The correlation F 2 ( 1 ) would be then greater than the other three correlations F 1 ( 1 ), F 3 ( 1 ), F 4 ( 1 ), and therefore corresponds to sub-position pattern of the current SPP SPP( 1 )=2 (sub-position pattern  2 ). Furthermore, if Symbol  2  shown in  FIG. 1  is used to generate four correlations F 1 ( 2 ), F 2 ( 2 ), F 3 ( 2 ), F 4 ( 2 ), wherein Symbol  2  is the current OFDM symbol, i.e., l=2. The correlation F 3 ( 2 ) would be greater than the other three correlations F 1 ( 2 ), F 2 ( 2 ), F 4 ( 2 ), and therefore corresponds to sub-position pattern of the current SPP SPP( 2 )=3 (sub-position pattern  3 ). Similarly, if Symbol  3  shown in  FIG. 1  is used to generate four correlations F 1 ( 3 ), F 2 ( 3 ), F 3 ( 3 ), F 4 ( 3 ), wherein Symbol  3  is the current OFDM symbol, i.e., l=3. The correlation F 4 ( 3 ) would be greater than the other three correlations F 1 ( 3 ), F 2 ( 3 ), F 3 ( 3 )), and therefore corresponds to sub-position pattern of the current SPP SPP( 3 )=4 (sub-position pattern  4 ). 
     It is to be noted that, instead of accumulating all available (P max+1 ) complex values of (R l,12p ·P 12p )·(R* l,12(p+1)+3(i−1) ·P* 12(p+1)+3(i−1) ) for F i (l), iε{1, 2, 3, 4}, accumulation of only partial set of complex values of (R l,12p ·P 12p )·(R* l,12(p+1)+3(i−1) ·P* 12(p+1)+3(i−1) ) may suffice for providing robust SPPs identification. Therefore, the four correlation sets F i (l), iε{1, 2, 3, 4} can be generalized as 
                   F   i     ⁡     (   l   )       =            ∑     p   ∈   Z       ⁢       (       R     l   ,     12   ⁢   p         ·     P     12   ⁢   p         )     ·     (       R     l   ,       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )         *       )                ,         
wherein Z⊂{0, 1, 2, . . . , p max }.
 
     The block diagram of  FIG. 6  may be applicable to the exemplary implementation described in  FIG. 9  and above paragraphs.  FIG. 10  illustrates an exemplary block diagram for implementing a frequency correlation-based scheme. Referring to  FIG. 10 , the frequency correlation-based scheme may include an SP compensator and signal selector  1030 , four correlators  1060 A,  1060 B,  1060 C and  1060 D, and a judgment or processing block  1070 . Signals  1010  and  1020  applied to the SP compensator and signal selector  1030  are the received baseband signal R l,k  from an OFDM receiver with known P k  wherein kεS SP ={0, 3, 6, 9, . . . , K max }. The SP compensator and signal selector  1030  may be employed to obtain sub-signals  1040 A,  1040 B,  1040 C,  1040 D, and  1050 D, which are associated to (R l,12p ·P 12p ), (R l,12p+3 ·P 12p+3 ), (R l,12p+6 ·P 12p+6 ), (R l,12p+9 ·P 12p+9 ), (R l,12(p+1) ·P 12(p+1) ), (R l,12(p+1)+3 ·P 12(p+1)+3 ), (R l,12(p+1)+6 ·P 12(p+1)+6 ), and (R l,12(p+1)+9 ·P 12(p+1)+9 ), wherein pεZ⊂{0, 1, 2, . . . , p max }. In one example, sub-signal  1040 A and  1050 A may be applied to correlator  1060 A; sub-signal  1040 B and  1050 B may be applied to correlator  1060 B; sub-signal  1040 C and  1050 C may be applied to correlator  1060 C; sub-signal  1040 D and  1050 D may be applied to correlator  1060 D. 
     Correlators  1060 A,  1060 B,  1060 C and  1060 D may be used to compute four correlation set results  901 ,  902 ,  903  and  904 , which are respectively correlated to correlation sets F 1 (l), F 2 (l), F 3 (l) and F 4 (l) illustrated in  FIG. 9 . In one example, correlator  660 A may include a complex conjugate function to generate the conjugate part of a signal, a complex multiplier, and an accumulator, and correlators  660 B,  660 C and  660 D may be implemented in the same or similar manner. Subsequently, four correlation set results  901 ,  902 ,  903  and  904  may be submitted to judgment or processing block  1070  to determine the maximum among them and generate a judgment or processing result  1080  as SPP(l), which may indicate the sub-position pattern of the SP for the current lth OFDM symbol accordingly. 
     In one example, the judgment or processing unit  1080  may include a peak detector or a comparator so as to determine the maximum of correlation set results  901 ,  902 ,  903  and  904 . It is noted that some of the sub-signals  1040 A,  1040 B,  1040 C,  1040 D,  1050 A,  1050 B,  1050 C, and  1050 D may appear at different times. Accordingly, one of ordinary skill in the related art, such as in the field of time-sharing or resource-sharing hardware design, may be able obtain the four correlation set results  901 ,  902 ,  903  and  904  with a less number of correlators, such as with only one correlator  1060 A. 
     It is to be noted that, due to the fact that (R l,k ·P k ) and (R l,k+12 ·P k+12 ) could be positively correlated if R l,k  carries an SP, the four correlation sets F i (l), iε{1, 2, 3, 4} can be simplified as 
                 F   i     ⁡     (   l   )       =            ∑     p   ∈   Z       ⁢     Re   ⁢     {       (       R     l   ,     12   ⁢   p         ·     P     12   ⁢   p         )     ·     (       R     l   ,       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )         *       )       }                    
wherein Z⊂{0, 1, 2, . . . , p max }. Therefore, instead of obtaining the result of (R l,12p ·P 12p ), (R* l,12(p+1)+3(i−1) ·P* 12(p+1)+3(i−1) ) by a complex multiplier, only two real-number multipliers and one adder are sufficient for computing
 
               Re   ⁢     {       (       R     l   ,     12   ⁢   p         ·     P     12   ⁢   p         )     ·     (       R     l   ,       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )           *     ·     P       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )         *       )       }       =       Re   ⁢       {       R     l   ,     12   ⁢   p         ·     P     12   ⁢   p         }     ·   Re     ⁢     {       R     l   ,       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )             ·     P       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )             }       +     Im   ⁢       {       R     l   ,     12   ⁢   p         ·     P     12   ⁢   p         }     ·   Im     ⁢     {       R     l   ,       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )             ·     P       12   ⁢     (     p   +   1     )       +     3   ⁢     (     i   -   1     )             }               
for F i (l), iε{1, 2, 3, 4}.
 
     As compared with the conventional time correlation-based scheme of the required synchronization time 5T OFDM , the frequency correlation-based scheme in these examples requires only one OFDM symbol in order to compute the correlation set results F 1 (l), F 2 (l), F 3 (l), F 4 (l) and determine the maximum of the results. The judgment or processing result  1080  may identify the correct SPPs of the current symbol. Accordingly, a frequency correlation-based scheme may improve the ability of fast synchronization speed and/or improve the robustness against Doppler effects due to a less stringent requirement on the channel coherence time. In addition, a frequency correlation-based scheme may be less sensitive to ScFO effects when compared with conventional time correlation-based schemes. In some examples, when compared with the conventional power-based scheme of the required synchronization time T OFDM , the frequency correlation-based scheme may provide robustness against noise effects due to the correlation gain at the cost of slightly longer synchronization time 2T OFDM . Furthermore, a frequency correlation-based scheme may be free from the correlation-interference caused by CP defined in DVB-T/H. 
     The frequency correlation-based scheme noted in the examples above may provide a flexible design taking into consideration of both hardware cost and synchronization time.  FIG. 11  illustrates another example of implementing a frequency correlation-based scheme. Referring to  FIG. 11 , this example uses only one correlation, such as F 1 ( l ) to determine the correct SPP of a current symbol. When the design illustrated in  FIG. 10  is used for such implementation, the SPP identification components may be modified to remove three correlators  1060 B,  1060 C, and  1060 D. One example is to have judgment or processing block  1070  include a threshold value detecting device, such that when F 1 ( l ) is larger than a certain threshold, the current SPP may be identified as sub-position pattern  1 . Another example is to execute correlator  660 A for four times in order to use the lth, l-1th, l-2th, and l-3th OFDM symbols to respectively obtain F 1 ( l ), F 1 ( l −1), F 1 ( l −2), and F 1 ( l −3). Thereafter, judgment or processing block  1070  may uncover a distinct maximum of correlation magnitude, which may be labeled as 
                   l   max     =     arg   ⁢           ⁢       max   m     ⁢     (       F   1     ⁡     (   m   )       )           ;     m   ∈     {     l   ,     l   -   1     ,     l   -   2     ,     l   -   3       }         ,         
and the SPP of the l max th OFDM symbol are thus identified as sub-position pattern  1 . Applying the technique noted here, any combination of two or three of the correlation sets F 1 (l), F 2 (l), F 3 (l) and F 4 (l) can be used in a similar way as a variation of the examples in  FIG. 11  to reduce the number of correlators required with increased synchronization time of 1˜4 T OFDM .
 
       FIG. 12  is a diagram illustrating an application of the present invention in the synchronization procedure of DVB-T/H receivers. Compared to the typical DVB-T/H synchronization sequence shown in  FIG. 2 , SPPs required by channel estimation are identified through the present invention without TPS synchronization. 
     It will be appreciated by those skilled in the art that changes could be made to the embodiments described above without departing from the broad inventive concept thereof. It is understood, therefore, that this invention is not limited to the particular embodiments disclosed, but it is intended to cover modifications within the spirit and scope of the present invention as defined by the appended claims. 
     Further, in describing representative embodiments, the specification may have presented the method and/or process of the present invention as a particular sequence of steps. However, to the extent that the method or process does not rely on the particular order of steps set forth herein, the method or process should not be limited to the particular sequence of steps described. As one of ordinary skill in the art would appreciate, other sequences of steps may be possible. Therefore, the particular order of the steps set forth in the specification should not be construed as limitations on the claims. In addition, the claims directed to the method and/or process of the present invention should not be limited to the performance of their steps in the order written, and one skilled in the art can readily appreciate that the sequences may be varied and still remain within the spirit and scope of the present invention.