Patent Publication Number: US-8995576-B2

Title: Method and module for estimating frequency bias in a digital-telecommunications system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a national stage filing under section 371 of International Application No. PCT/EP2012/063194, filed on Jul. 5, 2012, and published in French on Jan. 17, 2013, as WO 2013/007613 and claims priority of French application No. 1156304 filed on Jul. 11, 2011, the entire disclosure of these applications being hereby incorporated herein by reference. 
     FIELD OF THE INVENTION 
     The present invention relates to the field of digital telecommunications. The present invention more specifically relates to the estimating of a frequency bias negatively affecting a frame of symbols transmitted by a terminal and received by a station of a digital telecommunication system. 
     STATE OF THE ART 
     The invention can be particularly advantageously used in wireless telecommunications on a carrier frequency. 
     “On a carrier frequency” means that the transmission of a frame of symbols by a terminal comprises a step of frequency shifting of said frequency frame, aiming at modifying a central frequency of the frequency spectrum of the frequency frame. 
     Indeed, a frame of symbols is in practice generated around a zero frequency, in “baseband”, and the frame of symbols has to be shifted in order to be around a non-zero carrier frequency, in particular for frequency resource sharing reasons. 
     The transmission of a frame of symbols on a carrier frequency is performed in the form of a radio-frequency signal, which is then received by a station of the telecommunication system. The station then has to extract the data transmitted by the terminal, which extraction comprises, in particular, one or several steps of shifting the radio-frequency signal frequency, aiming at bringing the frame of symbols back to baseband, as well as a step of analog-to-digital (A/D) conversion of the received signal to extract the data with digital calculation means. 
     However, the digital signal, representative of the radio-frequency signal received by the station, is generally negatively affected by a frequency bias which, if it is not sufficiently compensated, disturbs the data extraction. 
     Such a frequency bias may especially result from:
         a frequency drift of frequency synthesis means of the terminal, causing an error on the central frequency of the frequency spectrum of the transmitted radio-frequency signal, which is different from the desired carrier frequency,   an error in the estimate of the central frequency of the frequency spectrum of the radio-frequency signal at the station,   a frequency drift of frequency synthesis means of the terminal, causing an error on the central frequency used to shift the frequency of the received radio-frequency signal to bring the frame of symbols back to baseband,   a relative displacement of the terminal with respect to the station, which goes along with an unwanted frequency shifting of the frequency spectrum of the radio-frequency signal, known as Doppler effect, etc.       

     Accordingly, the digital signal, from which the data transmitted by the terminal are to be extracted, may be negatively affected by a frequency bias corresponding to a difference between a supposed central frequency of the frequency spectrum of the digital signal, generally the zero frequency, and a real central frequency of said frequency spectrum of the digital signal. 
       FIG. 1  shows an example of disturbances introduced by a residual frequency bias negatively affecting a digital signal corresponding to a BPSK (Binary Phase Shift Keying) frame of symbols. This drawing shows that the amplitude of the BPSK symbols strongly varies, and that a sign inversion of said BPSK symbols may occur. It should thus be understood that, if the frequency bias is not estimated and corrected, the performance of the extraction of data transmitted by the terminal will be very adversely affected. 
     The insertion of training sequences into the frame of symbols is known, especially in cell mobile telecommunication systems such as GSM (Global System for Mobile Communications). A training sequence is a set of symbols known offhand by the terminal and the station and which accordingly do not correspond to useful data transmitted by the terminal. Due to the fact that the station knows the symbols forming such training sequences, it can estimate the frequency bias by comparison of the training sequences with the symbols of the digital signal corresponding to the training sequences. 
     However, the insertion of such training sequences decreases the efficiency of the data exchange between a terminal and a station, which efficiency corresponds to the ratio of useful data (that is, data which are not known offhand by the receiving station) per frame. 
     SUMMARY OF THE INVENTION 
     The present invention aims at providing a solution enabling to estimate a frequency bias negatively affecting a digital signal which does not require inserting training sequences in a frame of symbols (that is, the frequency bias can be estimated “blindly”). 
     The present invention can be advantageous used, without this being a limitation, in low bit rate telecommunication systems where the transmitted frames comprise a small number of symbols, for example, at least a few tens of symbols. 
     The present invention also more generally aims at providing a digital telecommunication system where the terminals are simple and inexpensive to implement. 
     According to a first aspect, the invention relates to a method of estimating a frequency bias negatively affecting a digital signal representative of a frame of symbols transmitted by a terminal to a station of a digital telecommunication system, said frequency bias corresponding to a difference between a supposed central frequency of a frequency spectrum of the digital signal and a real central frequency of said frequency spectrum. According to the invention, the estimation method comprises the steps of:
         generating the digital signal by sampling of an analog signal, representative of the frame of symbols, with a sampling period Te shorter than a predefined duration of each of the frame symbols, such that the digital signal comprises at least three samples per symbol,   estimating the frequency bias negatively affecting the digital signal according to values calculated for Np pairs of samples selected so that several of said Np pairs necessarily belong to a same symbol of the frame, each value being representative of a phase difference between the samples of the considered pair of samples, the samples of each of the Np pairs being separated by a same non-zero number D of sampling periods.       

     Due to the fact that the digital signal comprises at least three samples per symbol, it should be understood that it is possible to have several pairs having their samples all belonging to a same symbol (by selecting D such that the digital signal comprises at least two consecutive pairs of samples per symbol). For example, if the digital signal comprises exactly three samples per symbol, then each symbol will comprise two pairs of samples by selecting D equal to one. 
     The phase difference between two samples belonging to a same symbol being independent from the symbol phase, it should be understood that it is advantageous, in order to “blindly” estimate the frequency bias, to consider values calculated for pairs of samples belonging to a same symbol. Further, by considering several pairs of samples belonging to a same symbol, it should be understood that the frequency bias can be estimated even if the frame comprises a small number of symbols. 
     According to specific embodiments, the frequency bias estimation method comprises one or a plurality of the following characteristics, taken alone or in all technically possible combinations. 
     Preferably, the frequency bias is estimated according to values calculated for Np pairs of samples selected so that all the samples of said Np pairs necessarily belong to at most two consecutive samples of the frame. Preferably, number D is equal to one, so that a single pair, from among the Np pairs of samples, may be formed of samples belonging to different symbols. 
     Preferably, sampling period Te is such that the digital signal comprises at least ten samples per symbol, preferably at least one hundred samples per symbol. 
     Preferably, frequency bias f EST  is estimated according to the following relation: 
               f   EST     =         1     2   ·   q   ·   D   ·   π   ·   Te       ·     arg   ⁡     (       ∑     n   =   0       Np   -   1       ⁢           ⁢       (       r   ⁡     (       n   0     +   D   +   n     )       ·       r   *     ⁡     (       n   0     +   n     )         )     q       )         -     F   0             
where:
         r(n) is a sample of the digital signal corresponding to sampling time n·Te, r(n 0 ) being the first sample of the samples of the Np considered pairs,   r*(n) is the conjugate complex of r(n),   arg(x) corresponds to the phase of complex number x,   q is either equal to one, or equal to an even number,   F 0  is the supposed central frequency of the digital signal.       

     Preferably, a plurality of estimates of the frequency bias are performed according to values calculated for different sets of pairs of samples, and the method comprises a step of low-pass filtering of said estimates of the frequency bias. 
     According to a second aspect, the invention relates to a telecommunications method data exchange between a terminal and a station of a digital telecommunication system, said data being exchanged in the form of a frame of symbols. The telecommunications method comprises the steps of:
         transmission, by the terminal, of a frame of symbols in the form of a radio-frequency signal having its instantaneous frequency spectrum of a width smaller than a frequency drift of frequency synthesis means of said terminal,   reception of said radio-frequency signal by the station,   estimating a frequency bias negatively affecting a digital signal representative of the radio-frequency signal in accordance with an estimation method according to the invention,   compensating for the frequency bias negatively affecting the digital signal according to the estimate of said frequency bias,   extracting the data transmitted by the terminal.       

     According to a third aspect, the invention relates to a module for estimating a frequency bias negatively affecting a digital signal representative of a frame of symbols transmitted by a terminal to a station, said frequency bas corresponding to a difference between, on the one hand, a supposed central frequency of a frequency spectrum of the digital signal and, on the other hand, a real central frequency of said frequency spectrum. According to the invention, the estimation module comprises means configured to estimate the frequency bias negatively affecting the digital signal in accordance with an estimation method according to the invention. 
     According to a fourth aspect, the invention relates to a station of a digital telecommunication system, said station comprising a frequency bias estimation module according to the invention. 
     According to a fifth aspect, the invention relates to a digital telecommunication system comprising:
         a station according to the invention,   at least one terminal configured to transmit data in the form of radio-frequency signal shaving an instantaneous frequency spectrum of a width smaller than a frequency drift of frequency synthesis means of said at least one terminal.       

    
    
     
       DESCRIPTION OF THE DRAWINGS 
       The present invention will be better understood on reading of the following description provided as an example only in relation with the accompanying drawings, among which: 
         FIG. 1 : already described, an example of disturbances introduced by a residual frequency bias negatively affecting a digital signal, 
         FIG. 2 : a simplified representation of a telecommunication system comprising a station and a plurality of terminals, 
         FIG. 3 : a diagram schematically showing the main steps of a frequency bias estimation method, 
         FIG. 4 : a diagram schematically showing the main steps of a telecommunications method, 
         FIG. 5 : a simplified representation of an example of occupation of a frequency sub-band by a radio-frequency signal transmitted by a terminal, 
         FIG. 6 : a simplified representation of an example of variation, as a function of temperature, of the occupation of a frequency sub-band by a terminal, 
         FIG. 7 : a simplified representation of an embodiment of a station of the telecommunication system. 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
       FIG. 2  very schematically shows a telecommunication system  1  comprising several terminals  10  and a station  20 . 
     In the context of the invention, “station” generally designates any receiver device capable of receiving radio-frequency signals. Station  20  for example is any of terminals  10 , or a specific device such as a point of access to a wire or wireless telecommunications network, centralizing the data transmitted by each of terminals  10 . 
     “Radio-frequency signal” designates an electromagnetic wave propagating via wireless means, having its frequencies in the traditional radio-frequency wave spectrum (from a few hertz to several hundreds of gigahertz) or in neighboring frequency bands. 
     It should be noted that the case of a data transmission from terminals  10  to station  20  is mainly considered. The possible data transmission from station  20  to terminals  10  does not pertain to the framework of the invention. 
     Terminals  10  comprise means for transmitting radio-frequency signals considered as known by those skilled in the art. Each radio-frequency signal preferably is a single-carrier radio-frequency signal (as opposed to a multi-carrier radio-frequency signal of OFDM—Orthogonal Frequency Division Multiplexing—type). Further, a terminal  10  preferably comprises a central processing unit comprising a processor connected to one or a plurality of electronic memories having computer program code instructions stored therein. According to certain embodiments, a terminal  10  comprises one or several programmable logic circuits of FPGA, PLD, CPLD, or other type. 
     Station  20  comprises means for receiving radio-frequency signals considered as known by those skilled in the art. Further, station  20  preferably comprises a central processing unit of the type comprising a processor connected to one or a plurality of electronic memories having computer program code instructions stored therein. According to certain embodiments, station  20  comprises one or several programmable logic circuits of FPGA, PLD, CPLD, or other type. 
     The present invention first relates to a method  30  of estimating a frequency bias representative of a frame of symbols emitted by a terminal  10 , said estimation method being implemented at station  20 . 
       FIG. 3  schematically shows the main steps of such an estimation method  30 , which are:
           300  obtaining the digital signal by sampling of an analog signal representative of the frame of symbols transmitted by terminal  10 ,     302  calculating values for a plurality of pairs of samples of the digital signal, each value being representative of a phase difference between the samples of a pair of samples,     304  estimating the frequency bias negatively affecting the digital signal according to values calculated for several pairs of samples.       

     During step  300  of obtaining the digital signal, the sampling of the analog signal is performed with a sampling period Te shorter than a predefined duration of each of the frame symbols. 
     Thereby, it is ascertained that the digital signal comprises several samples per symbol. Sampling period Te is selected, as compared with duration Ts, so that the digital signal comprises at least Ne samples per symbol, Ne being greater than or equal to three. 
     Ne is defined as being equal to the integer part of ratio Ts/Te, so that the digital signal will generally comprise Ne samples per symbol, but may also comprise (Ne+1) samples per symbol. The following description considers the non-limiting case where Ts is proportional to Te, so that the digital signal always comprises Ne samples per symbol. 
     Preferably, sampling period Te is selected so that Ne is much greater than three, for example, equal to or greater than ten, or even one hundred. The advantage of having such values of Ne is that the frequency bias estimation can be improved and/or accelerated. 
     It should further be understood that, in the case of a low bit rate telecommunication system where the transmitted frames comprise a small number of symbols, the fact of having a plurality of samples per symbol enables to compensate for the fact that the frames comprise few symbols usable to estimate the frequency bias. 
     Step  300  enables to obtain a digital signal formed of several samples, the sample corresponding to time n·Te being designated hereafter as r(n). Sample r(n) can for example be expressed as follows, neglecting possible additional noise: 
     
       
         
           
             
               
                 
                   
                     r 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       s 
                       ⁡ 
                       
                         ( 
                         
                           E 
                           ⁡ 
                           
                             ( 
                             
                               
                                 n 
                                 + 
                                 nd 
                               
                               Ne 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     · 
                     
                       ⅇ 
                       
                         j 
                         · 
                         2 
                         · 
                         π 
                         · 
                         
                           ( 
                           
                             
                               F 
                               0 
                             
                             + 
                             fd 
                           
                           ) 
                         
                         · 
                         n 
                         · 
                         Te 
                       
                     
                   
                 
               
               
                 
                   ( 
                   e1 
                   ) 
                 
               
             
           
         
       
     
     Expression (e1)) is an approximate expression where:
         fd is the frequency bias affecting the digital signal,   j is the imaginary unit (such that j 2 =−1),   E(x) corresponds to the integer part of x,   s(m) is the symbol at time m·Ts,   nd represents a time shift, representative of the fact that the times of transition between a frame symbol and the next symbol of this frame,   F 0  is a supposed central frequency of the frequency spectrum of the digital signal.       

     It should be noted that supposed central frequency F 0  may for example be:
         the carrier frequency of the radio-frequency signals transmitted by terminal  10 ; in such a case, the sampled analog signal corresponds to the signal received on the carrier frequency, which is possible if the carrier frequency is not too high (so that it can be oversampled in order to have at least three samples per symbol, or even more),   an intermediate frequency, lower than the carrier frequency, back to which the signal received on the carrier frequency has been taken,   the zero frequency, in which case the digital signal is said to be in “baseband”.       

     The rest of the description considers the non-limiting case where the transmitted symbols are BPSK symbols and the case where s(m)=±1. 
     During step  302 , values representative of phase differences between the samples of said pairs are calculated for a plurality of pairs of samples of the digital signal. The samples of each considered pair are separated by a same non-zero number D of sampling periods. 
     Further, D is selected so that the digital signal comprises a plurality of different pairs of samples per symbol of the frame. Two pairs of samples are different as soon as they have at most one common sample. In practice, to ascertain that the digital signal comprises at least two pairs of different samples per symbol of the frame, D should be equal to or smaller than (Ne−2). 
     In a preferred embodiment, the calculated values are the following:
 
 g ( n )= r ( n+D )· r *( n )
 
     According to expression (e1), the calculated values g(n) can be expressed as follows: 
     
       
         
           
             
               
                 
                   
                     g 
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     
                       s 
                       ⁡ 
                       
                         ( 
                         
                           E 
                           ⁡ 
                           
                             ( 
                             
                               
                                 n 
                                 + 
                                 D 
                                 + 
                                 nd 
                               
                               Ne 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     · 
                     
                       
                         s 
                         * 
                       
                       ⁡ 
                       
                         ( 
                         
                           E 
                           ⁡ 
                           
                             ( 
                             
                               
                                 n 
                                 + 
                                 nd 
                               
                               Ne 
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     · 
                     
                       ⅇ 
                       
                         j 
                         · 
                         2 
                         · 
                         π 
                         · 
                         
                           ( 
                           
                             
                               F 
                               0 
                             
                             + 
                             fd 
                           
                           ) 
                         
                         · 
                         D 
                         · 
                         Te 
                       
                     
                   
                 
               
               
                 
                   ( 
                   e2 
                   ) 
                 
               
             
           
         
       
     
     It should be understood that, if samples r(n+D) and r(n) belong to the same BPSK symbol, then: 
                 s   ⁡     (     E   ⁡     (       n   +   D   +   nd     Ne     )       )       ·       s   *     ⁡     (     E   ⁢     (       n   +   nd     Ne     )       )         =   1         
and:
 
 g ( n )= e   j·2·π·(F     0     +fd)·D·Te  
 
     In this case, the only unknown value is frequency bias fd. 
     If, on the contrary, samples r(n+D) and r(n) do not belong to the same BPSK symbol, then: 
                 s   ⁡     (     E   ⁡     (       n   +   D   +   nd     Ne     )       )       ·       s   *     ⁡     (     E   ⁢     (       n   +   nd     Ne     )       )         =     ±   1           
and:
 
 g ( n )=± e   j·2·π·(F     0     +fd)·D·Te   (e3)
 
     In this case, a π phase jump adds when the BPSK symbols to which samples r(n+D) and r(n) belong do not have the same value. The values of said symbols are not known offhand when it is not a training sequence, so that it is not known offhand whether the phase jump is present. 
     In all cases, the calculated values g(n) are however well representative of the phase difference between samples r(n+D) and r(n). 
     Nothing excludes, according to other examples, considering other expressions for the calculation of said values representative of the phase difference between samples of a pair. 
     During step  304 , the frequency bias negatively affecting the digital signal is estimated according to Np values calculated for pairs of samples selected so that several of said Np pairs necessarily belong to a same symbol of the frame. 
     It should indeed be understood that since the digital signal comprises Ne samples per symbol and D is selected so that the digital signal comprises several different pairs of samples per symbol in the frame, the Np pairs can easily be selected so that a plurality of said Np pairs belong to a same symbol. 
     This will necessarily be the case when successive pairs of samples are considered, that is, pairs {r(n+D+k),r(n+k)}, with 0≦k≦Np−1. 
     It should be understood that, by selecting the Np pairs of samples so that a plurality of samples belong to a same symbol, the number of values capable of comprising a phase jump such as previously discussed in reference to expression (e3) is considerably decreased. 
     In a particularly preferred embodiment, the frequency bias is estimated according to values calculated for Np pairs of samples selected so that all the samples of said Np pairs necessarily belong to at most two consecutive symbols of the frame. This is for example true when only considering consecutive pairs of samples, and selecting Np so that Np Ne-D+1. 
     In preferred embodiments, D is equal to one (D=1) to maximize the number of pairs of samples per symbol, in particular when consecutive pairs of samples are considered (each symbol comprising at least (Ne-D) consecutive pairs of samples). 
     In a preferred embodiment, the frequency bias is estimated by means of values calculated for consecutive pairs of samples, the first sample of which is sample r(n 0 ), according to the following expression: 
     
       
         
           
             
               
                 
                   
                     f 
                     EST 
                   
                   = 
                   
                     
                       
                         1 
                         
                           4 
                           · 
                           D 
                           · 
                           π 
                           · 
                           Te 
                         
                       
                       · 
                       
                         arg 
                         ⁡ 
                         
                           ( 
                           
                             
                               ∑ 
                               
                                 n 
                                 = 
                                 0 
                               
                               
                                 Np 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 ( 
                                 
                                   
                                     r 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           n 
                                           0 
                                         
                                         + 
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                                         + 
                                         n 
                                       
                                       ) 
                                     
                                   
                                   · 
                                   
                                     
                                       r 
                                       * 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
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                       0 
                     
                   
                 
               
               
                 
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                     ⁢ 
                     
                         
                     
                     ⁢ 
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                   ) 
                 
               
             
           
         
       
     
     It should be noted that, in expression (e4), values g(n) are squared, so that in the case of BPSK symbols, a phase jump, possibly introduced when the samples of a pair belong to two consecutive symbols, is suppressed. 
     More generally, the frequency bias can be estimated according to the following expression: 
                     f   EST     =         1     4   ·   q   ·   D   ·   π   ·   Te       ·     arg   ⁡     (       ∑     n   =   0       Np   -   1       ⁢           ⁢       (       r   ⁡     (       n   0     +   D   +   n     )       ·       r   *     ⁡     (       n   0     +   n     )         )     q       )         -     F   0               (     e   ⁢           ⁢   5     )               
where q is an even integer equal to or greater than two, so that in the case of BPSK symbols, a phase jump possibly introduced when the samples of a pair belong to two consecutive symbols, is suppressed.
 
     It should be noted that it is also possible to consider, in expression (e5), a number q equal to one. Indeed, due to the fact that the Np pairs of samples are selected so that several of said pairs belong to a same symbol, the presence of possible phase jumps in certain values can however be suppressed. 
     For example, in the case of Np consecutive pairs of samples, Np being selected to be equal to (Ne−D+1): 
     
       
         
           
             
               
                 
                   
                     arg 
                     ⁡ 
                     
                       ( 
                       
                         
                           ∑ 
                           
                             n 
                             = 
                             0 
                           
                           
                             Ne 
                             - 
                             D 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           
                             
                               
                                 
                                   r 
                                   ⁢ 
                                   
                                     
                                       ( 
                                       
                                         
                                           n 
                                           0 
                                         
                                         + 
                                         D 
                                         + 
                                         n 
                                       
                                       ) 
                                     
                                     · 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     r 
                                     * 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         n 
                                         0 
                                       
                                       + 
                                       n 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                           ) 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     arg 
                     ⁡ 
                     
                       ( 
                       
                         
                           ( 
                           
                             Ne 
                             - 
                             
                               D 
                               ± 
                               1 
                             
                           
                           ) 
                         
                         · 
                         
                           ⅇ 
                           
                             j 
                             · 
                             2 
                             · 
                             π 
                             · 
                             
                               ( 
                               
                                 
                                   F 
                                   0 
                                 
                                 + 
                                 fd 
                               
                               ) 
                             
                             · 
                             Te 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   
                     e 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     6 
                   
                   ) 
                 
               
             
           
         
       
     
     Accordingly: 
               arg   ⁢     (       ∑     n   =   0       Ne   -   D       ⁢           ⁢     (       r   ⁡     (       n   0     +   D   +   n     )       ·       r   *     ⁡     (       n   0     +   n     )         )       )       =     2   ·   π   ·     (       F   0     +   fd     )     ·   Te           
since D is selected so that the digital signal comprises several pairs of different samples per symbol. In the case in point, the digital signal comprises (Ne−D) consecutive pairs of samples, and D accordingly is such that (Ne−D) 2, and so that (Ne−D±1)≧1. It should be understood that a number q equal to one can thus be considered, without for this to alter the performance of the estimate for BPSK symbols (to within the noise, which is not considered in the previous expressions). To improve the performance, in particular to take into account the presence of additional noise and when a number q equal to one is used (q=1), a number Ne of samples per symbol equal to or greater than ten, or even than one hundred, is advantageously considered.
 
     In a specific embodiment, also illustrated in  FIG. 3 , several estimates of the frequency bias are performed according to values calculated for different sets of pairs of samples, and estimation method  30  further comprises a step  306  of low-pass filtering of said estimates of the frequency bias. 
     In other words, low-pass filtering step  306  aims at averaging successive estimates of the frequency bias to decrease the level of possible noise affecting the estimate. 
     Calling f EST (n 0 ) the estimate calculated according to expression (e5), a new estimate F EST  is for example determined during low-pass filtering step  306  according to the following expression: 
                       F   EST     ⁡     (   k   )       =       1   Nf     ·       ∑     i   =   0       Nf   -   1       ⁢           ⁢       f   EST     ⁡     (     k   -   i     )                   (     e   ⁢           ⁢   7     )               
where Nf is the number of averaged estimates f EST (n). Preferably, Nf=2·Ne.
 
     The present invention also relates to a telecommunication method of data exchange between a terminal  10  and a station  20  of telecommunication system  1 . 
       FIG. 4  schematically shows the main steps of a telecommunication method  40  according to the invention, which are:
           400  transmission by terminal  10  of a frame of symbols in the form of a radio-frequency signal, preferably with a single carrier,     402  reception of said radio-frequency signal by station  20 ,     404  estimating a frequency bias negatively affecting a digital signal representative of the radio-frequency signal,     406  compensating for the frequency bias affecting the digital signal according to the estimate of said frequency bias,     408  extracting the data transmitted by terminal  10 .       

       FIG. 5  schematically shows a frequency sub-band used by a terminal  10  to transmit a radio-frequency signal. 
     It should be noted that terminal  10  comprises frequency synthesis means, considered as known by those skilled in the art, implemented to shift the frequency of the signals to be transmitted on the carrier frequency. 
     Such a frequency sub-band is mainly determined by its central frequency, called “terminal typical operating frequency” TTOF and by its width, called “terminal natural operating frequency range” TNOFR. The natural operating frequency range, TNOFR, of a terminal  10  corresponds to the frequency range effectively occupied by a radio-frequency signal along time, taking into account a frequency drift of the frequency synthesis means of terminal  10  and taking into account the instantaneous spectral width of the radio-frequency signals transmitted by terminal  10 , called “terminal occupied bandwidth” TOB. 
     Operating frequency range TNOFR is accordingly substantially equal to occupied bandwidth TOB plus frequency drift D (that is, TOB+D), a frequency drift D of 1 kiloHertz (kHz) being considered as corresponding to an accuracy of ±500 Hz (that is, ±D/2) around typical operating frequency TTOF. 
     Occupied bandwidth TOB is measured as being the bandwidth at −10 decibels (dB), that is, as being the set of frequencies for which the measured energy has an attenuation in the range from 0 dB to −10 dB with respect to the maximum energy measured for a frequency in the radio-frequency signal band. In other words, the frequencies for which the energy has an attenuation greater than −10 dB (that is, −20 dB, −30 dB, etc.) are not taken into account in the measurement of occupied bandwidth TOB. 
     The frequency drift of the frequency synthesis means of terminal  10  results in that the instantaneous central frequency of the spectrum of radio-frequency signals transmitted by terminal  10 , called “terminal real operating frequency” TROF, may be substantially different from typical operating frequency TTOF. 
       FIG. 6  illustrates this frequency drift of real operating frequency TROF with respect to typical operating frequency TTOF due, for example, to temperature. Portions a), b), and c) show real operating frequency TROF in operating frequency range TNOFR for three different temperatures. 
     Preferably, the instantaneous frequency spectrum of the radio-frequency signals transmitted by terminal  10  during transmission step  400  has an occupied bandwidth TOB smaller than the frequency drift of frequency synthesis means of terminal  10 , or even significantly smaller than said frequency drift. 
     “Significantly smaller” means that occupied bandwidth TOB is at last five times smaller than operating frequency range TNOFR. In other words, operating frequency range TNOFR of terminal  10  is, due to the frequency drift of the frequency synthesis means of said terminal, at least five times greater than bandwidth TOB of the instantaneous frequency spectrum of the radio-frequency signals transmitted by said terminal. 
     According to specific embodiments, occupied bandwidth TOB is at least ten times smaller than operating frequency range TNOFR, or even at least one hundred times smaller. 
     It should be understood that the smaller the ratio of occupied bandwidth TOB to operating frequency range TNOFR, the greater the frequency drift. It should however be understood that the greater the tolerated frequency drift, the more low-cost frequency synthesis means can be used in each of terminals  10 . 
     Further, the lack of intrinsic frequency stability of terminals  10  (that is, their frequency drift) can be statistically taken advantage of, to decrease the probability of collision between radio-frequency signals transmitted by different terminals  10 . Thus, when two terminals  10  use a same typical operating frequency TTOF, frequency drift D, which is much greater than occupied bandwidth TOB, enables to multiplex the frequency of the radio-frequency signals transmitted by these terminals  10  around the same typical operating frequency TTOF. 
     It should be understood that the more ratio TOB/TNOFR of occupied bandwidth TOB to operating frequency range TNOFR decreases, the more the probability of collision between radio-frequency signals transmitted by different terminals  10  decreases. 
     As seen, very low bit rate systems, for example, of sensor network type, are a preferred application of the invention, without this being a limitation. In the case of a very low bit rate system, called “narrow-bandwidth system”, occupied bandwidth TOB is for example in the range from a few Hertz to a few hundreds of Hertz. 
     Operating frequency range TNOFR depends on the technology implemented to synthesize typical operating frequencies TTOF. In the case of frequency synthesis means comprising a quartz oscillator, the accuracy will for example be in the range from 2 to 40 ppm (parts per million) so that, for a typical operating frequency TTOF equal to 1 gigahertz, frequency drift D will be substantially in the range from 2 kHz (±1 kHz for the 2-ppm accuracy) to 40 kHz (±20 kHz for the 40-ppm accuracy). In this case, operating frequency range TNOFR will be substantially in the range from 2 kHz to 40 kHz. More specifically, in the case of an occupied bandwidth TOB of 100 Hz, operating frequency range TNOFR will substantially be in the range from 2.1 kHz to 40.1 kHz, and ratio TNOFR/TOB will then substantially be in the range from 21 to 401. 
     During step  402 , station  20  receives the radio-frequency signal transmitted by terminal  10 , by implementing means considered as known by those skilled in the art, some of which are described hereafter in reference to  FIG. 7 , without this being a limitation. 
     During step  404 , frequency bias estimation method  30  according to the invention is preferably implemented. 
     It should be understood that when terminals  10  are provided with frequency synthesis means having a frequency drift much greater than the width of the frequency spectrum of the transmitted radio-frequency signals, the frequency bias to be estimated may vary during a same frame, or even during a same symbol. In practice, the variation of the frequency bias to be estimated can then be of the same order of magnitude as occupied bandwidth TOB. 
     Accordingly, the implementation of the estimation method according to the invention to estimate the frequency bias is quite advantageous. 
     Indeed, said estimation method  30 , in particular when Ne is equal to or greater than ten, enables to estimate the frequency bias over a time period in the order of symbol duration Ts, which is much shorter than the duration of a frame (even for a frame comprising few symbols, for example, less than a few tens of symbols), or even over a time period shorter than symbol duration Ts. Sampling period Te is preferably sufficiently short for the frequency bias to be considered as substantially constant during said period Te, given the frequency drift of the frequency synthesis means of terminals  10 . 
     Further, in the case of a narrow-bandwidth low bit rate telecommunication system (occupied bandwidth TOB in the range from a few Hertz to a few hundreds of Hertz), it should be understood that number Ne of samples per symbol may be large (for example, greater than ten) without requiring the use of too high a sampling frequency. 
     During step  406 , the frequency bias is compensated according to the estimate of this frequency bias. Such a compensation aims at compensating for the phase variation induced from one sample to the other by said frequency bias. Such a compensation may be performed in any adapted manner known by those skilled in the art and which does not pertain to the scope of the invention. 
     For example, the compensation may be performed according to expression:
 
 r   c ( n )= r ( n )· e   −j·2·π·f     EST     ·n·Te  
 
or, when estimation method  30  comprises a low-pass filtering step  306 , according to expression:
 
 r   c ( n )= r ( n )· e   −j·2·F     EST     ·n·Te  
 
     During step  408 , the data transmitted by terminal  10  are determined from samples r c (n). The exact implementation of data extraction step  408  depends on a predefined protocol of shaping the data transmitted by terminals  10 , and implements means considered as known by those skilled in the art. 
       FIG. 7  schematically shows a preferred embodiment of station  20 . It should be noted that station  20  may also comprise other elements, not shown in  FIG. 7 . 
     In this non-limiting example, station  20  mainly comprises an analog unit  200  and a digital unit  210 . 
     As illustrated in  FIG. 7 , analog unit  200  especially comprises:
         an antenna  201  capable of receiving radio-frequency signals in a multiplex channel MC where terminals  10  are likely to transmit,   a bandpass filter  202 , called “antenna filter”, capable of filtering unwanted signals outside of multiplex channel MC,   a low-noise amplifier  203 ,   a local oscillator  204  capable of forming a substantially sinusoidal signal, called LO I , having a frequency substantially equal to a central frequency of multiplex channel MC, called multiplex channel central frequency MCCF,   a phase shifter  205  capable of forming a replica in phase quadrature of signal LO I , called LO Q ,   two mixers  206  capable of mixing an output signal of antenna filter  202  respectively with signal LO I  and signal LO Q ,   two low-pass filters  207  respectively at the output of each mixer  206 , called anti-aliasing filters, having a cut-off frequency for example equal to half multiplex channel bandwidth MCB of the multiplex channel (that is, MCB/2).       

     As illustrated in  FIG. 7 , digital unit  210  particularly comprises two analog-to-digital converters (A/D)  211  capable of sampling the respective output signals of each anti-aliasing filter  207 , for example, with a sampling frequency substantially equal to the multiplex channel bandwidth MCB. 
     The output signals of A/D converters  211  respectively correspond to the real part and to the imaginary part of a complex signal called S T . This complex representation is schematized in  FIG. 7  by the addition of the output signals of A/D converters  211 , one of said signals being previously multiplied by imaginary unit j. 
     Digital unit  210  then comprises several functional units. 
     First, digital unit  210  comprises a FFT (Fast Fourier Transform) unit  212  capable of transposing complex signal S T  from the time domain to the frequency domain, to obtain a complex signal S F  representative of the frequency spectrum of complex signal S T . 
     Digital unit  210  then comprises a detector unit  213  capable of searching in complex signal S F  frequencies for which energy peaks are obtained, capable of corresponding to the presence of a radio-frequency signal transmitted by a terminal  10 . 
     Indeed, station  20  does not necessarily know the frequencies used by the different terminals  10 , in particular due to the fact that the real operating frequency TROF of a terminal  10  may be very different from the typical operating frequency TTOF of this terminal due to the frequency drift. The use of FFT unit  212  and of detector unit  213  accordingly enables to determine whether terminals  10  are transmitting radio-frequency signals and, if so, to estimate their real operating frequencies TROF. 
     For this purpose, FFT unit  212  should be capable of delivering a complex signal S F  with a granularity in the frequency domain enabling to detect a radio-frequency signal of occupied bandwidth TOB. In the case where several occupied bandwidths are possible, the minimum occupied bandwidth TOB MIN  is preferably considered. For example, considering a sampling frequency substantially equal to multiplex channel bandwidth MCB, FFT unit  212  is for example configured to obtain frequency samples, in the bandwidth ranging from 0 Hz to MCB, with a step equal to MCB/TOB MIN , that is, for elementary frequencies 0, TOB MIN , 2.TOB MIN , 3.TOB MIN , . . . , MCB-TOB MIN . 
     Detector unit  213  for example measures the energy for each elementary frequency. A criterion for the detection of a signal transmitted by a terminal  10  is for example verified when the power measured for an elementary frequency is greater than a predefined threshold value. 
     When a signal has been detected by detector unit  213 , for example, around an elementary frequency of value F e0 , value F e0  is delivered at the input of a variable local oscillator  214 , which generates a complex sinusoidal signal of frequency F e0  (comprising samples of the type exp(j·2·π·F e0 ·n/MCB)). 
     Complex signal S T  is multiplied with the conjugate complex of the complex sinusoidal signal of frequency F e0  by means of a multiplier unit  215 . This multiplication enables to bring back the signal, detected around the elementary frequency of value F e0 , around zero frequency 0 Hz. 
     Digital unit  210  then comprises a low-pass filtering unit  216 , having a cut-off frequency substantially equal to half occupied bandwidth TOB (that is, TOB/2). In the case where several occupied bandwidths are possible, maximum occupied bandwidth TOB MAX  is preferably considered (that is, a cut-off frequency substantially equal to TOB MAX /2). 
     Digital unit  210  then comprises a frequency bias estimation unit  217 . 
     Estimation unit  217  comprises means configured to estimate the frequency bias negatively affecting the digital signal in accordance with an estimation method  30  according to the invention. Said means of estimation unit  217  are for example software means in the form of computer program code instructions, stored in a non-volatile memory of the central processing unit of station  20 , which, when executed by said central processing unit, implement the different steps of estimation method  30 . 
     As a variation or as a complement, said means of estimation unit  217  comprise one or a plurality of programmable logic circuits of FPGA, PLD, CPLD, or other type, configured to provide all or part of the different steps of estimation method  30 . 
     In the non-limiting example illustrated in  FIG. 7 , estimated value F EST  of the frequency bias is provided at the input of variable local oscillator unit  214 . Said variable local oscillator unit then generates a complex sinusoidal signal of frequency (F e0 +F EST ) comprising samples of the type exp(j·2·π·(F e0 +F EST )·n/MCB)), having its conjugate complex multiplied with complex signal S T  by means of multiplier unit  215 . 
     It should be noted that estimation unit  217  may keep all the samples received from low-pass filtering unit  216 , where above-mentioned sampling period Te is equal to 1/MCB. As a variation, estimation unit  217  performs a sub-sampling of the samples received from low-pass filter unit  216 : in this case, above-mentioned sampling frequency Te is greater than 1/MCB, for example, equal to K/MCB, K being a predefined sub-sampling factor. 
     Digital unit  210  then comprises a decoder unit  218  capable of extracting the data transmitted by a terminal  10 . The exact implementation of decoding unit  218  depends on a predefined protocol for shaping the data transmitted by terminals  10 , and implements means considered as known by those skilled in the art. 
     It should be noted that detector unit  213  may have to detect several elementary frequencies capable of corresponding to signals transmitted by terminals  10 . For example, detector unit  213  may have to detect a number Ns of such elementary frequencies. In this case, variable locator oscillator unit  214 , multiplier unit  215 , low-pass filtering unit  216 , estimation unit  217 , and decoder unit  218  are advantageously replicated Ns times to process in parallel the signals around each of the Ns elementary frequencies capable of being used by a terminal  10 . 
     The above description clearly illustrates that by its different features and advantages, the present invention achieves its objects. 
     In particular, the invention provides a frequency bias estimation method  30  particularly adapted to narrow-bandwidth low bit rate telecommunication systems, in particular such systems where the transmitted frames comprise few symbols. 
     Indeed, estimation method  30  does not require training sequences, which would too significantly decrease the efficiency of the telecommunication system. 
     Further, estimation method  30  enables to estimate the frequency bias by considering samples in a frequency window having a duration in the order of symbol duration Ts, or even shorter than said symbol duration Ts, especially due to the fact that the processed digital signal comprises many samples per symbol. Thereby, estimation method  30  also enables to follow the frequency bias variation during a same frame of symbols. Accordingly, low-cost frequency synthesis means may be used in each of terminals  10 , including means for which the frequency drift is much greater than the bandwidth TOB of the instantaneous frequency spectrum of the radio-frequency signals transmitted by terminals  10 .