Abstract:
A speed estimation method is provided, detecting relative speed of a transmitter and a receiver transmitting symbols by OFDM sub-carriers through a channel. First, a first correlation table is established, indicating conceptual relationships between the relative speed and the channel characteristic based on Doppler shift theory. Thereafter, channel characteristic caused by movement is estimated. The first correlation table is checked to determine the relative speed according to the estimated channel characteristic. The channel characteristic is a correlation value generated by auto-correlating received symbols with a delay factor. The first correlation table is established with a first delay factor, associating correlation values to a first plurality of presumed shift frequencies in view of the first delay factor. The first presumed shift frequencies scale from zero to a first maximum value, and the relative speed is proportional to the shift frequencies.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The invention relates to OFDM telecommunications, and in particular, to a speed estimation method detecting relative speeds between a transmitter and a receiver transmitting symbols by OFDM sub-carriers through a channel. 
   2. Description of the Related Art 
   According to Orthogonal Frequency Division Multiplex (OFDM) standard, data is delivered separately through a plurality of sub-carriers with guard interval insertion, efficiently overcoming multi-path interference issues. In a mobile telecommunication system, such as wireless cellular network, a moving transmitter (or a receiver) is accommodated in a mobile station and the receiver (or the transmitter) is accommodated in a base station of a telecommunication system. A channel for mobile communication is challenged by time varying multi-path interferences. The channel response has a variation rate referred to as coherence time T c . The coherence time T c  is a period inversely proportional to Doppler shift frequency f d  estimated between the transmitter and the receiver. Conventionally, the formula is provided as: 
   
     
       
         
           
             
               
                 
                   T 
                   c 
                 
                 = 
                 
                   0.423 
                   
                     f 
                     d 
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   The higher the Doppler shift frequency, the shorter the coherence time. The Doppler shift frequency is also associated with the relative speed between the transmitter and receiver, proportional to the frequency of transmitted signal. Thus a formula is given as: 
   
     
       
         
           
             
               
                 
                   f 
                   d 
                 
                 = 
                 
                   
                     f 
                     c 
                   
                   · 
                   
                     v 
                     c 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   Where c is the speed of light, and f c  is the transmitted frequency. With formula (2), the relative speed v can be estimated since f c  and c are known, and the f d  is detectable. 
   As described in J. Cai, W. Song, and Z. Li, “Doppler Spread Estimation for Mobile OFDM Systems in Rayleigh Fading Channels,” IEEE Tr. Consumer Electronics, vol. 49, issue 4, Nov. 2001, if a transmitter continuously sends a specific pattern while the channel varies with time, the receiver will obtain a correlation value by auto-correlating the received symbols based on a zero order Bessel function expressed as:
 
φ(Δ t )= J   0 (2 πf   d   Δt )  (3)
 
   Where the φ(Δt) is the correlation value corresponding to a delay time Δt. The delay time is a multiple of symbol time T s :
 
Δt=mT s   (4)
 
   Thus, the correlation value φ(Δt) in formula (3) is also represented as:
 
φ( m )= J   0 (2π f   d   mT   s )  (5)
 
   Where T s  represents the duration of one symbol time, and m is a positive integer. 
   Conventionally, speed estimation utilizes complex algorithm and hardware, which is deemed ineffective. To estimate relative speed while either the transmitter or the receiver is moving in communication, a more efficient method is desirable. 
   BRIEF SUMMARY OF THE INVENTION 
   A detailed description is given in the following embodiments with reference to the accompanying drawings. 
   An exemplary embodiment of a speed estimation method is provided, detecting relative speed of a transmitter and a receiver transmitting symbols by OFDM sub-carriers through a channel. First, a first correlation table is established, indicating conceptual relationships between the relative speed and the channel characteristic based on Doppler shift theory. Thereafter, channel characteristics caused by movement are estimated. The first correlation table is checked to determine the relative speed according to the estimated channel characteristic. The channel characteristic is a correlation value generated by auto-correlating received symbols with a delay factor. The first correlation table is established with a first delay factor, associating correlation values to a first plurality of presumed shift frequencies in view of the first delay factor. The first presumed shift frequencies scale from zero to a first maximum value, and the relative speed is proportional to the shift frequencies. 
   The establishment of the first correlation table comprises deriving a plurality of correlation curves corresponding to the first presumed shift frequencies based on Bessel function with the first presumed shift frequencies and delay factors as variables. The first delay factor is substituted to the plurality of correlation curves so that a plurality of correlation values are correspondingly obtained. The first delay factor is selected to render monotonic relationships between the obtained correlation values and the first presumed shift frequencies, by which associations of the obtained correlation values and the first presumed shift frequencies are recorded to form the first correlation table. 
   The determination of relative speed comprises auto-correlating received symbols with the first delay factor to generate a first correlation value. The first correlation table is checked to obtain an estimated shift frequency according to the first correlation value, and the relative speed is calculated by the estimated shift frequency. The first presumed shift frequencies are discontinuously selected from zero to the first maximum value with a first predetermined interval. If the first correlation value maps to a frequency between two presumed shift frequencies thereamong, the estimated frequency is determined by inner interpolation. 
   If the first correlation value maps to a frequency between zero and a least nonzero value among the first presumed frequencies, a second correlation table is established by a second delay factor higher than the first delay factor. The second correlation table associates correlation values to a second plurality of presumed shift frequencies in view of the second delay factor. The second presumed shift frequencies are discontinuously selected from zero to the least nonzero value with a second predetermined interval. The relative speed estimation is performed again with the second delay factor, such that a more accurate relative speed is obtained. 
   The auto-correlation of received symbols comprises a received symbol stream delayed by the delay factor to generate a delayed symbol stream. An expectation of the received symbol stream multiplying the delayed symbol stream is estimated. The expectation is normalized by power of the received symbol stream to generate the correlation value. Derivation of the plurality of correlation curves comprises providing a zero order Bessel function φ(m)=J 0 (2πf d mT s ), where J 0  is the zero order Bessel function, f d  is the shift frequency, m is the delay factor, T s  is the duration of a symbol time, and φ(m) is the correlation value associated with the delay factor. The correlation curves are plotted, where the horizontal axis represents the variation of delay factors m, and the vertical axis is the correlation value φ(m). 

   
     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   a  shows correlation curves of a large scale shift frequencies; 
       FIG. 1   b  shows a first lookup table generated from  FIG. 1   a;    
       FIG. 2   a  shows correlation curves of a medium scale shift frequencies; 
       FIG. 2   b  shows a second lookup table generated from  FIG. 2   a;    
       FIG. 3   a  shows correlation curves of a least scale shift frequencies; 
       FIG. 3   b  shows a third lookup table generated from  FIG. 3   a ; and 
       FIG. 4  is a flowchart of the speed estimation method. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   The following description is of the best-contemplated mode of carrying out the invention. This 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. 1   a  shows correlation curves of a large scale shift frequencies. In the embodiments, correlation tables are established, such that the relative speed can be easily estimated by looking up the tables according to observable channel characteristics.  FIG. 1   a  shows seven correlation curves of shift frequencies f d  from 0 Hz to 240 Hz incrementing every 40 Hz. As defined in DVB-T system, sub-carrier number, symbol time T s  and guard interval size GI vary as different transfer rate. The symbol time T s  can be derived from the guard interval size GI and data duration T u :
   T   s   =T   U (1+ GI )  (6) 
   For example, if the guard interval size GI is chosen to be ⅛ in 8K mode, the correlation curves can be plotted based on formula (5), with horizontal axis representing the delay factor m, and the vertical axis the correlation value Φ(m). These correlation curves, each representing a presumed shift frequency, show theoretical relationships between the relative speed and the auto-correlation results of the received symbols based on Doppler shift theory. In  FIG. 1   a , if a vertical line corresponding to a fixed delay factor m is drawn crossing the correlation curves, a plurality of cross points are generated, mapping to corresponding correlation values If the delay factor m is carefully chosen, the mapped correlation values may have monotonic relationships with the presumed shift speeds represented by the correlation curves. In  FIG. 1   a , the monotonic relationship is available before the delay factor m reaches first cross point of the 200 Hz and 240 Hz curves. By way of explanation, using the vertical line of m=2, correlation value at 0 Hz is 1, and gradually decreases as the shift frequency increases. Subsequently, the correlation curves of 200 Hz and 240 Hz map to negative correlation values at m=2. That is to say, by selecting a proper delay factor m, a monotonic linear relationship can be found between the shift frequencies and the correlation values. 
     FIG. 1   b  shows a first lookup table  100  generated from  FIG. 1   a . In this case, the delay factor is chosen to be 2, thus a plurality of cross points P 0  to P 240  are obtained, each associating a theoretical correlation value to a shift frequency, and the first lookup table  100  is established thereby. 
   When a transmitter delivers a specific pattern while moving with a relative speed, the receiver may obtain an estimated correlation value by auto-correlating the received symbols. The auto-correlation can be easily implemented by an adder, a multiplier and a delay line. The delay line delays the received symbol by a delay factor m to generate the estimated correlation value. Since the shift frequencies are linear to the correlation values with regards to the delay factor m, an estimated shift frequency f d  can be easily obtained by interpolation of the cross points P 0  to P 240 , and the relative speed ν can be estimated by formula (2) from the f d . 
     FIG. 2   a  shows five correlation curves scaling from 0 Hz to 40 Hz incrementing by 10 Hz. A second lookup table  200  can be established to distinguish more detailed shift frequencies between 0 Hz and 40 Hz as shown in  FIG. 2   b . When the shift frequency is below 40 Hz, the second lookup table  200  provides better distinguishability than the first lookup table  100 . Another delay factor m is chosen within the monotonic range to establish the second lookup table  200 . For example, in  FIG. 2   a , cross points obtained on vertical line m=15 have better distinguishability than those on m=10. On the contrary, points appear on the correlation curves where m=20 are not monotonic with the correlation values, thus a method to select the delay factor m is desirable. As an example, the correlation curve of maximum shift frequency (40 Hz in  FIG. 2   a ) is observed to determine the delay factor m for establishment of the second lookup table  200 . On the 40 Hz curve, correlation value decreases as the delay factor m increases (within a preliminary range). When the correlation value reaches zero, the corresponding delay factor m is chosen to obtain a plurality of cross points from all correlation curves to establish the second lookup table  200 . Alternatively selection of the delay factor m can comprise, when the 40 Hz curve has a turning point where the slope is zero, the delay factor m thereof selected for use. The delay factor m should be an integer, thus the closest integer is selected from the described methods. In  FIG. 2   a , the delay factor is chosen to be 15 to have best distinguishability, and the second lookup table  200  associating cross points P 0  to P 40  to corresponding correlation values, is established thereby. 
     FIG. 3   a  shows six correlation curves scaling from 0 Hz to 10 Hz incrementing by 2 Hz. The cross points P 0  to P 10  mapped by setting the delay factor m to 60, generate a third lookup table  300  as shown in  FIG. 3   b . When the shift frequency is below 10 Hz, the third lookup table  300  has better distinguishability in comparison to the first and second lookup tables. 
   The auto-correlation of received symbols can be implemented by a delay line, a multiplier and an adder. For example, the correlation value of delay factor m=2 is: 
   
     
       
         
           
             
               
                 
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                   ⁡ 
                   
                     ( 
                     2 
                     ) 
                   
                 
                 = 
                 
                   
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                     ⁢ 
                     
                       { 
                       
                         
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                           ⁡ 
                           
                             [ 
                             n 
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                         · 
                         
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                               n 
                               - 
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                       } 
                     
                   
                   
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                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   Where r[n] is a received symbol stream, and r[n−2] is generated by delaying the received symbol stream r[n] by two symbol times. The r[n] and r[n−2] are multiplied to take expectation. The denominator term normalizes the expectation. The received symbol stream r[n], however, may be affected by noise, inducing erroneous correlation values. In practice, the received symbol stream r[n] may be expressed as:
 
 r[n]=s[n]+i[n]   (8)
 
   Where the s[n] is the original signal sent from the transmitter, and i[n] is noise. If i[n] is additive white Gaussian noise (AWGN), the correlation value in formula (7) is rewritten as: 
   
     
       
         
           
             
               
                 
                   ϕ 
                   ⁡ 
                   
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                     2 
                     ) 
                   
                 
                 = 
                 
                   
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                     ⁢ 
                     
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                 ( 
                 9 
                 ) 
               
             
           
         
       
     
   
   To cancel the erroneous term in the denominator of formula (9), an alternative correlation term is defined by: 
   
     
       
         
           
             
               
                 
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                     ( 
                     
                       m 
                       , 
                       1 
                     
                     ) 
                   
                 
                 = 
                 
                   
                     
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                         m 
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                 ( 
                 10 
                 ) 
               
             
           
         
       
     
   
   Thus, an alternative correlation term can also be associated with the Bessel function to plot alternative conceptual correlation curves (not shown): 
   
     
       
         
           
             
               
                 
                   φ 
                   ⁡ 
                   
                     ( 
                     
                       m 
                       , 
                       1 
                     
                     ) 
                   
                 
                 = 
                 
                   
                     
                       J 
                       0 
                     
                     ⁡ 
                     
                       ( 
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
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                           f 
                           d 
                         
                         ⁢ 
                         
                           mT 
                           s 
                         
                       
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                       J 
                       0 
                     
                     ⁡ 
                     
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                         2 
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                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
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                           d 
                         
                         ⁢ 
                         
                           T 
                           s 
                         
                       
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                 ( 
                 11 
                 ) 
               
             
           
         
       
     
   
   Similarly, a plurality of correlation curves may be generated by substituting various shift frequencies f d  to formula (11) to map relationships of correlation value φ(m,1) versus delay factor m. 
     FIG. 4  is a flowchart of the speed estimation method. In step  402 , at least one lookup table is established, mapping correlation values to shift frequencies. The scale of shift frequency depends on practical applications, and different lookup tables may be generated by different delay factor to map different scale shift frequencies. In  FIGS. 1   b ,  2   b  and  2   c , three lookup tables are established to specifically map three different scales. In step  404 , a first correlation value is generated with delay factor m=2, and the first lookup table  100  is checked for corresponding shift frequency. Values between two columns can be obtained by interpolation. In step  406 , the scale of the shift frequency is checked. If the shift frequency is below 40 Hz, step  408  is processed. Otherwise, a relative speed is calculated in step  414  by the checked shift frequency. In step  408 , a second correlation value is generated by delay factor m=15, and the second lookup table is checked. Step  410  determines whether the shift frequency is below 10 Hz, and if so, step  412  is processed. Otherwise the relative speed is estimated in step  414 . In step  412 , a third correlation value is generated by delay factor m=60, and the third lookup table is checked, estimating a shift frequency scaling from 0 Hz to 10 Hz. Thereafter, step  414  is processed. 
   For each lookup table, the number of correlation curves and incremental intervals are not limited by the embodiments. The determination of delay factor m may take various forms. Number of lookup tables depends on practical accuracy requirements, and the scale thereof is also dependent. The generation of relation curves is not limited to Bessel function, and may be adaptable for other algorithms. The speed estimation method is applicable for telecommunication systems utilizing OFDM such as DVB-T, GSM or IEEE 802.11a/b/g standards. 
   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.