Abstract:
The invention relates to a direct conversion receiver for down-converting a received multi-carrier signal comprising at least a first and a second carrier signal at image carrier frequencies to a base band resulting in that the first carrier signal includes an image signal of said second carrier signal. Further, the known direct conversion receiver comprises at least a first and a second digital down-converter unit for separating the first and the second carrier signal from the down-converted multi-carrier signal after digitization. In order to make such receivers less complex and adjust them for fast time varying szenarios it is proposed to provide an error estimating unit to said receivers for calculating a compensating coefficient representing the quota and/or the phase position of the image signal of the second carrier signal being included in the first carrier signal and to remove the undesired image signal in response to said compensating coefficient.

Description:
TECHNICAL FIELD  
         [0001]    The invention relates to a direct conversion receiver DCR, for receiving a multi-carrier signal including at least a first and a second carrier signal, being located at a first and second image carrier frequency, respectively, via an antenna. The invention further relates to a method for receiving such a multi-carrier signal, a computer program for carrying out such a method and an error estimating unit as well as to a compensator stage of such a direct conversion receiver. The invention is based on a priority reference EP 02 360 380.6 which is hereby incorporated by reference.  
         BACKGROUND OF THE INVENTION  
         [0002]    Direct conversion receivers DCR are substantially known in the art. They typically comprise a front end unit for receiving the multi-carrier signal from the antenna and a quadrature demodulator for down-converting said received multi-carrier signal to a base band. Disadvantageously the down-converting process results in that the first carrier signal includes an image signal of said second carrier signal and vice versa.  
           [0003]    [0003]FIG. 7 illustrates the generation of the image signals I 1 , I 2  during a conventional quadrature demodulation process. In the left part of FIG. 7 there is shown the multi-carrier signal as received via the antenna. It comprises for example a first carrier signal C 1  and a second carrier signal C 2  which are both free of image signals. These carrier signals are located at a first and a second mirror carrier frequency, respectively. These mirror carrier frequencies are arranged symmetrically around a center frequency f c . In the right-hand part of FIG. 7 there are shown the carrier signals after the converting process as carried out by the quadrature demodulator. It can be seen that the down-converted first carrier signal C 1  comprises an image signal  12  of the second carrier signal C 2  and that said second carrier signal comprises an image signal  11  of the second carrier signal C 2 . These image signals are undesired because they make a reconstruction of the desired carrier signal more difficult. The difficulty of reconstruction depends on the ratio of image signal to carrier signal which itself depends on the level of impairments in the realisation of the analog quadrature demodulator (gain, phase &amp; quadrature mismatches) as well as similar defects in the A to D converter chain.  
           [0004]    The traditional direct conversion receiver DCR further comprises an analog/digital converter for digitizing the down-converted multi-carrier signal and at least a first and a second down-converter DDC-unit for separating the first and the second carrier signal from the digitized down-converted multi-carrier signal and for translating the separated first and second carrier signal to be centered at a predetermined frequency in the frequency plane. In the right-hand part of FIG. 7 said predetermined frequency is set to 0.  
           [0005]    In the prior art several methods are known to reject the undesired image signals. For quadrature modulators such a method is known for example from the article “Automatic Adjustment of Quadrature Modulators” by Faulkner, Mattsson and Yates in “Electronic Letters”, vol. 27 no. 3, 31 st  Jan. 1991. The method of image rejection disclosed in said article can substantially also be applied to quadrature demodulators. However, said method requires quite complex electronic circuits and/or a special signal for calibration. Further, the method of image rejection proposed by said article is made iteratively with the result that it can not be applied to fast-time varying scenarios, such as those encountered for example in multicarrier receivers used according to GSM standard with fast frequency hopping and uplink discontinuous transmission.  
           [0006]    Starting from that prior art it is the object of the invention to improve a known direct conversion receiver and a method for receiving a multi-carrier signal, a computer program for carrying out said method as well as an error estimating unit and a compensator stage of such a direct conversion receiver such that image rejection can be carried out less complex and with better accuracy and stability.  
           [0007]    This object is solved by the subject-matter of claim  1 . More specifically, for the above-described direct conversion receiver this object is solved by providing an error estimating unit for calculating a compensating complex coefficient representing the quota and/or the phase position of the image signal of the second carrier signal being included in the first carrier signal and at least a first compensator stage for removing the undesired image signal from the first carrier signal in response to said compensating coefficient.  
         SUMMARY OF THE INVENTION  
         [0008]    The implementation of a such constructed direct conversion receiver is rather simple and allows an easy image rejection. It is another advantage of the invention that in all embodiments the compensating coefficient is at once calculated correctly so that a sufficient suppression of the image signals in the carrier signals is achieved and that a further processing of the carrier signal is possible; consequently, for most of the applications no further adaptation of said compensating coefficient, e.g. by carrying out further iterations, is required. The term ‘direct’ in direct conversion receiver means that A to D conversion is done directly in baseband representation of a complex analog signal as opposed to intermediate frequency sampling and digitizing method where the image problem does not exist but exibit much higher performance requirements for the A to D converter. Namely, the patent applies also to a superheterodyne receiver with a 1 st  intermediate frequency band.  
           [0009]    As a summary the patent applies to any receiver where an analog complex representation of the received band is digitized by a set of A to D converters.  
           [0010]    According to a first embodiment the compensating coefficients are calculated from the translated down-converted carrier signals as output by the DDC-units and provided to compensator stages which are connected in series behind said DDC-units, respectively. Due to said open loop construction an iterative adaptation of the compensating coefficient is neither possible nor required because the accuracy of the calculated compensating coefficient is sufficient to achieve a proper removement of the image signals for most applications.  
           [0011]    According to several other embodiments of the invention, the compensating coefficient is calculated in an iterative process in which the at least partially cleaned output signal of the direct conversion receiver are considered.  
           [0012]    However, the process for optimizing the compensating coefficients according to the invention is rather quick so that typically only one iteration loop has to be carried out for achieving a proper compensating coefficient which is already able to suppress the undesired image signals sufficiently and which allows a further processing of the carrier signals. However, for applications which require a rather clean signal these embodiments allow further iteration loops in which the compensating coefficient is further optimized.  
           [0013]    Advantageous embodiments of the DCR, in particular of its compensating stages and of its error estimating unit are subject-matters of the dependent claims.  
           [0014]    The above identified object is further solved by a method for receiving a multi-carrier signal and for rejecting undesired images within these carrier signals and by a computer program for carrying out said method. Moreover, the object is solved by an error estimating unit and by a compensator stage of a direct conversion receiver. The advantages of said solutions correspond to the advantages mentioned above with respect to the direct conversion receiver. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]    The invention will now be described in the form of advantageous embodiments by referring to the seven figures accompanying the description wherein  
         [0016]    [0016]FIG. 1 shows a first embodiment of the direct conversion receiver according to the invention;  
         [0017]    [0017]FIG. 2 shows a second embodiment of the direct conversion receiver according to the invention;  
         [0018]    [0018]FIG. 3 shows a preferred embodiment of an indirect compensator according to the invention as used in the first and the second embodiment of the direct conversion receiver;  
         [0019]    [0019]FIG. 4 shows a third embodiment of the direct conversion receiver according to the invention;  
         [0020]    [0020]FIG. 5 shows a fourth embodiment of the direct conversion receiver according to the invention;  
         [0021]    [0021]FIG. 6 shows a direct compensator according to the invention as used in the embodiments 3 and 4 of the direct conversion receiver; and  
         [0022]    [0022]FIG. 7 shows the variation of carrier signals caused by a quadrature-demodulating process as known in the art. 
     
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0023]    [0023]FIG. 1 shows a first embodiment of the direct conversion receiver DCR  100 ′ according to the invention. Said DCR  100 ′ serves for receiving a multi-carrier signal including at least a first and a second carrier signal —see spot S 1 —being located at image carrier frequencies via an antenna  110 . After passing a front end  120  that can include itself some frequency band transposition the multi-carrier signal is directly down-converted to base band by a quadrature demodulator  130 . The limited image rejection capabilities of said traditional quadrature demodulator  130  cause a superposition of the desired carrier signals and their images as described above by referring to FIG. 7. This effect is further illustrated for a multi-carrier signal comprising four carrier signals C 1 , C 2 , C 3  and C 4  by the spots S 1  and S 2  shown in FIG. 1. The images caused by the carrier signals C 1  . . . C 4  are assigned by the reference numerals I 1  . . . I 4 , respectively.  
         [0024]    After being output by the quadrature demodulator  130  the inphase and quadrature components of the complex baseband are respectively digitized by analog/digital AD-converters  140 . Subsequently, the carriers included in the multi-carrier base band signal are separated by digital down-converters DDCs  150 - 1  . . .  150 - 4  which are individually provided for each of said carriers. In FIG. 1 there are provided four DDCs for separating the four carriers C 1  . . . C 4  as shown in the spots S 1  and S 2 . Further, the DDCs serve for translating the carrier signals in frequency to be centered at 0 Hz in the frequency plane. At the output of the DDCs the image signal components I 1  . . . I 4  are still present within the carrier signals C 1  . . . C 4 .  
         [0025]    According to the proposed invention each of the separated carriers C 1  . . . C 4  is subsequently processed in an individually co-ordinated compensator stage  160 ′- 1  . . .  160 ′- 4 . More specifically, the translated first carrier signal output by the first DDC  150 - 1  is processed by the first compensator stage  160 ′- 1 . The same co-ordination applies to the other DDCs and compensator stages. The compensator stages  160 ′- 1  . . .  160 ′- 4  remove the undesired image signals from the carrier signals in response to a provided compensating coefficient. Consequently, in the first embodiment according to FIG. 1 each of said compensator stages  160 ′- 1  . . .  160 ′- 4  outputs a cleaned carrier signal which is free of an undesired image signal component; this image rejection effect of the compensator stages is illustrated by the spots S 3  and S 4  in FIG. 1. For carrying out said image rejection the compensator stages  160 ′-l . . .  160 ′- 4  need information about the quota/magnitude and/or the phase of the undesired image signal component to be removed. This information is provided to the compensator stages by said compensating coefficients which are individually calculated by an error estimating unit  170  for each of said compensating stages. In order to distinguish the compensating coefficients calculated in the first embodiment from the compensating coefficients calculated in the other embodiments which will be described later, the compensating coefficients in the first embodiment are referred to as first type of compensating coefficients.  
         [0026]    The error estimating unit  170 ′ of the first embodiment is embodied to calculate a first type compensating coefficient representing the amplitude/quota and/or the phase position the undesired image signal within the carrier signal to be cleaned. More specifically, according to FIG. 1 it is assumed that the first carrier signal C 1  includes an undesired image of the second carrier signal C 2  and vice versa. Moreover, it is assumed that the third carrier signal C 3  includes—after down-converting—an image  14  of the fourth carrier signal C 4  and vice versa. Consequently, the first compensator stage  160 - 1  is embodied to reject the image I 2  of the second carrier signal C 2  from the first carrier signal C 1 . For achieving this, the first compensator stage  160 ′- 1  receives both, the first and the second carrier signal as well as its individual compensating coefficient.  
         [0027]    The error estimating unit  170 ′ in principle generates said compensating coefficients by correlating the output of the DDCs for the desired carrier signal with the DDC output of the image carrier. For example, for generating the individual compensating coefficient CC 1  for the first compensator stage  160 ′- 1  the error estimating unit  170 ′ correlates the output of the first DDC  150 - 1  for the first carrier signal which shall be cleaned with the output of the second DDC  150 - 2 , i.e. the translated second carrier signal, an image of which is included in the translated first carrier signal. From said complex compensating coefficient CC 1  and from the levels of the two input signals, i.e. the translated down-converted first and second carrier signals the first compensator stage  160 ′- 1  calculates the cleaned first carrier signal.  
         [0028]    Often, the compensating coefficients only vary slow versus time. For this case it is sufficient to compute these compensating coefficients CC 1  with 1-4 from time to time. The compensating coefficients may be computed sequentially and offline with the result that only limited hardware and/or software resources are required.  
         [0029]    However, if online/real time image rejection is required, the compensator stages  160 ′- 1  . . .  160 ′- 4  have to buffer a certain portion of their above-mentioned input signals in order to await the provision of the corresponding compensating coefficient from the error estimating unit  170 ′. After the error estimating unit  170 ′ has evaluated the translated and down-converted first and second carrier signal the first compensating coefficient CC 1  representing the amplitude/quota and/or the phase position of the image signal of the second carrier signal within the translated and down-converted first carrier signal is calculated.  
         [0030]    Subsequently, this compensating coefficient CC 1  is provided to the first compensator stage  160 ′- 1 . In said compensator stage  160 ′- 1  the buffered input signals are processed by using said compensating coefficient CC 1  in order to generate the desired clean first carrier signal.  
         [0031]    In the whole description, the term “clean” means a lack of image signals within a carrier signal. Due to its individual calculation the compensating coefficient CC 1  it is highly accurate with the result that the undesired image signal components within the cleaned carrier signals are sufficiently suppressed for most applications; usually, no further adaptation of the compensating coefficient CC 1  is necessary and thus the described method is best suited for fast varying scenarios.  
         [0032]    The above-described operation of the error estimating unit  170 ′ and the first compensator stage  160 ′- 1  also applies to the operation of the other compensator stages  160 ′- 2 ,  160 ′- 3  and  160 ′- 4  shown in FIG. 1.  
         [0033]    [0033]FIG. 2 shows a second embodiment of the direct conversion receiver according to the present invention. Here, the antenna  110 , the front end  120 , the quadrature demodulator  130 , the analog/digital converters  140 , the direct down-converters  150 - 1 ,  150 - 4  and the indirect compensator stages  160 ′- 1  . . .  160 ′- 4  as well as the operations of said components are identical to the components being identified by the same reference numerals and operations thereof described above for the first embodiment.  
         [0034]    However, the second embodiment of the DCR according to FIG. 2 differs from the first embodiment in that the input for the error estimating unit  170 ″ is now taken from the output of the compensator stages  160 ′- 1  . . .  160 ′- 4 . The effect is that the error estimation operates in an iterative manner. The remaining image components at the outputs of the compensator stages  160 ′- 1  . . .  160 ′- 4  are used to refine the compensating coefficients CC 1  with i=1-4 in an iteration loop. Advantageously, said proposed iteration converges very fast so that normally only one iteration loop is sufficient for sufficiently suppressing the image signals.  
         [0035]    [0035]FIG. 3 shows a preferred embodiment of the indirect compensator stages  160 ′- 1  . . .  160 ′- 4  as used in the first and second embodiment of the DCR in FIGS. 1 and 2, respectively.  
         [0036]    From FIG. 3 it is apparent that each of the compensator stages receives the real component I desired, in  of the translated carrier signal to be cleaned. Further, the imaginary component Q desired, in  of the translated carrier signal to be cleaned is received. For calculating the cleaned components I desired, out  and Q desired, out  the compensator stages  160 ′ further receive the real component I image, in  of that translated carrier signal, an image of which is included in the translated carrier signal which is desired to be cleaned. Further, the indirect compensator stage  160 ′ receives the imaginary component Q image, in  of the translated carrier signal an image of which is included in the translated carrier signal desired to be cleaned at the port. Finally, the indirect compensator stage  160  receives the real component a and the imaginary component b of the co-ordinated compensating coefficient.  
         [0037]    For calculating the desired cleaned output signal preferably each of the compensator stages  160 ′ comprise a first multiplying unit  161 ′ for multiplying the imaginary component of the translated image carrier signal with a real component of the compensating coefficient a. Further, it comprises a second multiplying unit  162 ′ for multiplying the real component of said translated image carrier signal I image, in  with the real component a of the compensating coefficient. Moreover, it comprises a third multiplying unit  163 ′ for multiplying the real component of the translated image carrier signal I image, in  with the imaginary component b of the compensating coefficient and a fourth multiplying unit  164 ′ for multiplying the imaginary component of the translated image carrier signal Q image, in  with the imaginary component b of the compensating coefficient. Further, each of the compensating stages comprise a first adding unit  165 ′ for generating a real component of the desired cleaned carrier signal by adding the output of the third multiplying unit  163 ′ to the real component of the translated carrier signal desired to be cleaned and by substracting the output of the first multiplying unit  161 ′ therefrom. Finally, each of the compensator stages  160 ′ comprises a second adding unit  166 ′ for generating an imaginary component the of cleaned carrier signal by substracting the output of the second multiplying unit  162 ′ and the output of the fourth multiplying unit  164 ′ from the imaginary component of the translated carrier signal Q desired, in  required to be cleaned.  
         [0038]    Mathematically, the operation of the direct compensator stages  160 ′ can be described by the following transfer function:  
         
       S 
       desired, out 
       =S 
       desired, in 
       −S* 
       image, in 
       ·C  
     
         [0039]    wherein  
         [0040]    S desired, out  represents the desired complex output signal after correction;  
         [0041]    S desired, in  represents the desired complex input signal before correction;  
         [0042]    S* image, in  represents the frequency inverted complex input image signal; and  
         [0043]    c represents a complex scaling factor  
         [0044]    Split up into a real and an imaginary components equation 1 may be written according to:  
           I   desired, out   =I   desired, in   −a·Q   image, in   +b·i   image, in   (2)  
           Q   desired, out   =Q   desired, in   −a·i   image, in   −b·Q   image, in   (3)  
         [0045]    wherein  
         [0046]    I x  represents the real part of a signal (in phase component)  
         [0047]    Q X  represents the imaginary part of a signal (quadrature component)  
         [0048]    a represents the real component of c  
         [0049]    b represents the imaginary component of c.  
         [0050]    [0050]FIG. 4 shows a third embodiment of the direct conversion receiver according to the invention. The operation of the antenna  110 , the front end  120 , the quadrature demodulator  130 , the A/D-converter  140  and of the direct down-converters  150 - 1  . . .  150 - 4  and the operations of these components are the same as described above.  
         [0051]    However, the third embodiment of the direct conversion receiver differs from the second embodiment substantially in that the compensator stages  160 ″- 1  . . .  160 ″- 4  are now connected in series between the A/D-converter  140  and the digital down-converters  150 - 1 . Thus, the digitized multi-carrier signal output by said A/D-converter  140  is now received by said compensator stages  160 ″- 1  . . .  160 ″- 4  and these compensator stages output a cleaned multi-carrier signal; i.e. the output multi-carrier signal is substantially free of undesired image signals. The cleaned multi-carrier signals output by the compensator stages  160 ″- 1  . . .  160 ″- 4  are received by the individually co-ordinated digital down-converters  150 - 1  . . .  150 - 4  for separating individual carriers from said cleaned multi-carrier signal.  
         [0052]    Expressed in other words, in comparison to the embodiments 1 and 2 the cleaning process carried out by the compensator stages is carried out here before the separation process is carried out by the DDCs. However, in difference to embodiments 1 and 2 the compensating coefficients (third type) are now calculated in response to the output signal of the DDCs channels. In that way an individual adaptation of the compensating coefficient with regard to the carrier signal to be selected from the multi-carrier signal can be provided to said compensating stages  160 ″- 1  . . .  160 ″- 4 . The error estimating unit which is embodied to calculate these individual compensating coefficients is in embodiment 3 assigned by the reference numeral  170 ′″.  
         [0053]    [0053]FIG. 5 shows a fourth embodiment of the claimed direct conversion receiver DCR. The construction of that fourth embodiment only differs from the third embodiment in that it is facilitated in the way that the plurality of compensator stages used in the third embodiment is here replaced by only one single compensating stage  160 ″. Due to that facilitation the error estimator unit  170   IV  now generates only one fourth-type compensating coefficient for said single compensator stage  160 ″ in response to the individual signals output by said digital down-converters  150 - 1  . . .  150 - 4 . Because now there is only one compensating coefficient provided to said single compensator stage said compensating coefficient is not individually adapted to each of the carrier signals included within the multi-carrier signal processed by said compensating stage and which are subsequently to be separated by said digital down-converters  150 - 1  . . .  150 - 4 . Consequently, the rejection of undesired image signals within the signals output by said digital down-converters is only suboptimal in comparison to for example embodiment 3. However, like in embodiments 2 and 3, in embodiment 4 the generation of the compensating coefficient is also done in the form of a closed loop. Consequently, also in embodiment 4 an arbitrary accuracy of the compensating coefficient may be achieved perhaps by carrying out the closed loop for some more times than in the other embodiments.  
         [0054]    [0054]FIG. 6 shows a preferred embodiment of the compensator stages  160 ″- 1  . . .  160 ″- 4  or  160 ″ as used in embodiments 3 and 4. As can be seen, said compensator stage receives a real component I desired, multi-in  and an imaginary component Q desired, multi-in  as well as the magnitude k and the phase p of the compensating coefficient for the multi-carrier signal as generated by the error estimating unit  170   IV . For generating the real component I desired, multi-out  of the cleaned multi-carrier signal a constant I2DC is substracted from the received real component I desired, multi-in . For enabling that operation the compensator stage  160 ″ comprises a substracting unit  161 ″.  
         [0055]    Further, the compensator stage  160 ″ comprises a first multiplier  163 ″ for multiplying the real component I desired, multi-out  of the generated cleaned multi-carrier output signal with a first factor x1=k.sin(p) wherein k represents the magnitude of the compensator coefficient and p represents the phase of said compensator coefficient.  
         [0056]    Said first multiplier  163 ″ generates a first intermediate signal. Further, the compensating stage  160 ″ comprises a second substracting unit  164 ″ for generating a second intermediate signal by adding the first intermediate signal to the imaginary component Q desired, multi-in  of the received multi-carrier signal and by substracting a second constant Q2DC therefrom. Finally, for generating the desired imaginary component Q desired, multi-out  of the cleaned multi-carrier signal the compensating stage  160 ″ comprises a second multiplier  165 ″ for multiplying said second intermediate signal with a second factor x2=1: (k.cos(p)).  
         [0057]    The operation of said compensating stage  160 ″ may mathematically be described by the following algorithm:  
         
       I 
       desired, multi-out 
       =I 
       desired, multi-in 
       −I 
       2DC 
       
         
           
             
               Q 
               
                 desired 
                 , 
                 
                   multi 
                    
                   
                     - 
                   
                    
                   out 
                 
               
             
             = 
             
               
                 
                   Q 
                   
                     desired 
                     , 
                     
                       multi 
                        
                       
                         - 
                       
                        
                       i 
                        
                       
                           
                       
                        
                       n 
                     
                   
                 
                 - 
                 
                   Q 
                   
                     2 
                      
                     
                         
                     
                      
                     D 
                      
                     
                         
                     
                      
                     C 
                   
                 
                 + 
                 
                   
                     
                       ( 
                       
                         
                           I 
                           
                             desired 
                             , 
                             
                               multi 
                                
                               
                                 - 
                               
                                
                               i 
                                
                               
                                   
                               
                                
                               n 
                             
                           
                         
                         - 
                         
                           I 
                           
                             2 
                              
                             
                                 
                             
                              
                             D 
                              
                             
                                 
                             
                              
                             C 
                           
                         
                       
                       ) 
                     
                     · 
                     k 
                     · 
                     sin 
                   
                    
                   
                       
                   
                    
                   
                     ( 
                     p 
                     ) 
                   
                 
               
               
                 
                   k 
                   · 
                   cos 
                 
                  
                 
                     
                 
                  
                 
                   ( 
                   p 
                   ) 
                 
               
             
           
         
                 
         
             
         
       
     
         [0058]    Finally, the general operation of the error estimating unit  170   I  . . .  170   IV  as used in all of the embodiments according to the invention shall be mathematically described. The error estimating unit serves—as outlined above—to estimate the unknown compensating coefficients, that means in particular the amplitude and the phase imbalance in case of direct error compensation as used in embodiments 3 and 4 or in the form of a complex scaling factor, that means in the form of real component and imaginary component in the case of an indirect error compensation as used or done in embodiments 1 and 2. According to the invention, error estimation is done by correlating the “frequency inverted” signal of the corresponding image channel with the signal of the desired channel. The scaled complex correlation coefficient is used to compute the scaling factor used for indirect compensation whereas the scaled correlation coefficient is used to compute the amplitude and the phase imbalance of the real and imaginary component of the demodulator. The algorithm is described as follows:  
       xy   =         ∑     i   =   1     n                     (         Q     i   ,   desired       ·     I     i   ,   image         +       I     i   ,   desired       ·     Q     i   ,   image           )       +     j   ·     (         Q     i   ,   desired       ·     Q     i   ,   image         -       I     i   ,   desired       ·     I     i   ,   image           )                 xxw   =         ∑     i   =   1     n          I     i   ,   desired     2       +     Q     i   ,   desired     2               xxi   =         ∑     i   =   1     n          I     i   ,   image     2       +     Q     i   ,   image     2               c   =           xy   xxi     ·     [     1   -     0        ,          5   ·       (     xxw   xxi     )     2           ]                     for                 xxi     ≥   xxw             c   =           xy   xxw     ·     [     1   -     0        ,          5   ·       (     xxi   xxw     )     2           ]                     for                 xxi     &lt;   xxw                           
 
         [0059]    k=1+2,047.imag(c)  
         [0060]    p=−2.real(c)  
         [0061]    k &amp; p formulas are here fist order approximations but precise enough to ensure fast convergence in the iterative embodiment described here.  
         [0062]    with  
         [0063]    x 1  representing a complex correlation coefficient between the desired and image signal;  
         [0064]    xxw representing the energy of desired signal sequence;  
         [0065]    xxi representing the energy of image signal sequence;  
         [0066]    I i  representing the inphase component of sample i;  
         [0067]    Q i  representing the quadrature component of sample i;  
         [0068]    n representing the number of samples taken for correlation, e.g. on radio slot;  
         [0069]    c representing a scaling factor needed for indirect compensator method;  
         [0070]    k representing the amplitude imbalance of IQ demodulator;  
         [0071]    p representing the phase imbalance of the IQ demodulator in rad.  
         [0072]    In all embodiments of the invention the number of DDCs and/or compensator stages preferably corresponds to the number of carriers comprised within the received multi-carrier signal. The numbers are not limited for any embodiment of the invention, even if some embodiments have only been described for two carriers in order to facilitate the illustration.  
         [0073]    The same remark applies for links between imaged carriers. For simplicity of description especially in FIGS. 1 and 2 and associated descriptions, images links have been predetermined.  
         [0074]    In the general case it is assumed to be part of box  170  variants to also detect &amp; predict, especially in frequency hopping mode and discontinuous reception, which are the carriers subject to be coupled with an imaged one.  
         [0075]    In case of no image carrier for a given active carrier, then it is up to box  170  to temporarily stop updating the coefficient update and hold the former value for the time where image will reappear. Also for inputs of boxes  160  the box  170  can in that case force coefficient to zero.