Abstract:
A method for shared estimation of parameters (ε, φ, |C 1 |, C 0 , α, Δω) is described, which together with an error vector e(k), describe the connection between a digitally modulated reference signal inputted to a transmission channel and a received receiver signal z(k) which is at an end of the transmission channel. The method includes the following steps: forming the error vector e(k) in dependence of the parameters (ε, φ, |C 1 |, C 0 , α, Δω), a reference signal s(k), and the receiver signal z(k); linearizing the error vector e(k); substituting a real parameter of the linearized error vector through components of a estimation vector, wherein a substituted error vector is produced; inserting the substituted error vector into the cost function; and determining the estimation vector through gradient development of the cost function and subsequently setting the gradient to zero.

Description:
[0001]    This nonprovisional application claims priority under 35 U.S.C. §119(a) on Patent Application No. 101 57 247.6 filed in Germany on Nov. 22, 2001, which is herein incorporated by reference.  
         BACKGROUND OF THE INVENTION  
         [0002]    1. Field of the Invention  
           [0003]    The present invention relates to a method and computer program for shared estimation of parameters, in particular to the determination of “Error Vector Magnitude” (hereinafter “EVM”).  
           [0004]    2. Description of the Background Art  
           [0005]    The “Error Vector Magnitude” (EVM) is used often, to estimate the linearity of a digitally modulated mobile radio system. For Example, the standard “GSM 05.05, version 8.5.0, Draft ETSI EN 300 910 V.8.5.0, (2000-07), Annex G” (hereinafter “the standard”) defines the requirements on the EVM for the 8-PSK GSM EDGE-System. However, the standard does not define algorithms in order to determine the EVM.  
           [0006]    [0006]FIG. 1 shows an example configuration, in accordance with the above given standard, of a transmission channel  20  having different parameters ε, w, C 1 , and C 0 . The parameter ε represents a time shift, that determines the signal in the delay  21  of the configuration, e(k) is an error vector which is added in the configuration in a adder  22 , C 1  is a complex amplification which is added in the multiplier  23 , and C 0  represents a constant level of a DC-offset. The parameter W k  is used to model the time response during a burst (transmit block), for example due to a heating up of the amplifier.  
           [0007]    The following allocations are applied:  
           [0008]    T s : symbol period;  
           [0009]     The sequence of the configuration, are present before the symbol clock of the time points kT s .  
           [0010]    s(k): reference signal: is a trouble-free input signal after the measurement filter in the receiver to the symbol-time points kT s ;  
           [0011]    e(k): error vector;  
           [0012]    ε: resultant time shift due to a non-ideal estimation of the preceding coarse time shift estimation;  
           [0013]    C 1 : complex amplification (gain) of the measurement signal;  
           [0014]    C 0 : constant level of a (DC) offset in the measurement signal; and  
           [0015]    w=e α+jΔωT     s    α describes the change in amplitude of the measurement signal, which, for example, because of the heating up of the amplifier, causes a higher signal level to arise within the bursts.  
           [0016]     Furthermore, through Δω the resultant frequency shift is modeled due to the preceding non-ideal coarse frequency estimation.  
           [0017]    From the reference signal s(k), the following received signal z(k) results:  
             z ( k )={ C   0   +C   1   ·[s ( k )+ e ( k )]}· w   k .  (1)  
           [0018]    The error vector e(k) is determined by:  
               e        (   k   )       =           z        (   k   )       ·     w     -   k           C   1       -       C   0       C   1       -       s        (     k   -   ɛ     )       .               (   2   )                               
 
           [0019]    In view of this model, a total of seven real parameters have to be estimated. It is noted that the time shift ε, in view of the excessive sampled sequence, is to be understood to fulfill the sample theorem.  
           [0020]    The “Error-Vector magnitude” (EVM) is calculated over a burst and is defined as follows:  
             EVM   =           ∑   k          |     e        (   k   )            |   2          /     ∑   k       |     s        (   k   )            |   2           .             (   3   )                               
 
           [0021]    To determine the “Error-Vector magnitude” (EVM), the parameters ε, C 0 , C 1  and w, must be estimated such that a minimum of the “Error-Vector magnitude” (EVM) per burst results. Through the use of this parameter, the individual error vector e(k) can be calculated for each symbol.  
           [0022]    The article “A Method for Computing Error Vector Magnitude in GSM EDGE Systems—Simulation Results,” IEEE Communications Letters, VOL. 5, NO. 3, March 2001, pages 88 to 91, discloses a method to determine the parameters ε, C 0 , C 1  and w. This conventional method is, however, not very efficient. For one, the conventional method has the disadvantage that the time shift ε is not subjected to a common estimation with the parameters C 0 , C 1 , and w, but that only a coarse estimation of the time shift ε is performed before the common estimation of the parameters C 0 , C 1  and w. Moreover, the conventional method has the disadvantage that a gradient method has to be used, which converges relatively slowly. The conventional method requires therefore, a relatively large number of iterations, which are dependent on the arbitrary start values for C 0 , C 1  and w.  
         SUMMARY OF THE INVENTION  
         [0023]    It is, therefore, an object of the present invention to provide a method to commonly estimate several parameters, which together with the error vector describes the connection between a digitally modulated reference signal fed through the transmission channel and a received signal that is received at the end of the transmission channel, which method utilizes a fewer number of iterations and converges quickly. The invention also provides a computer program to execute the method.  
           [0024]    A preferred embodiment of the method of the invention, uses a linearization and a substitution to calculate the parameters analytically. Because of linearization, a minor error arises. Through iterative repetition, the linearization error can be desirably reduced. In the norm, two iterations are sufficient. These are substantially fewer iterations than those needed in the conventional method.  
           [0025]    Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0026]    The present invention will become more fully understood from the detailed description given herein below and the accompanying drawings which are given by way of illustration only, and thus, are not limitive of the present invention, and wherein:  
         [0027]    [0027]FIG. 1 is a configuration of a transmission channel;  
         [0028]    [0028]FIG. 2 is a table which represents the elements M i,j  of the Matrix M and the components b i  of the vector b; and  
         [0029]    [0029]FIG. 3 is a block diagram, illustrating a preferred embodiment.  
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0030]    The estimation method according to a preferred embodiment of the invention is described herein below, wherein estimated parameters are a time shift ε, a phase shift φ, a amplification |C 1 |, a constant level shift C 0 , a amplitude change α, and a frequency shift Δω, which determine a reference signal s(k) in the transmission channel. The method according to the invention is not limited to this application example, and is also suitable for the estimation of other parameters, which characterize the transmission channel.  
         [0031]    The estimated parameters are determined through the minimization of the cost function:  
               L        (     x   ~     )       =       ∑   k          |       e   ~          (   k   )            |   2                 (   4   )                               
 
         [0032]    wherein K is the symbol number within the evaluation area (“useful part,” e.g. a burst). Generally, in this invention, a test parameter is represented by a “snake” and the estimated parameter is represented by a “roof,” that is, {circumflex over (x)} describes generally the parameter that is to be estimated, and {tilde over (e)}(k) describes a therefrom resultant test-error vector.  
         [0033]    Subsequently, the estimation according to a preferred embodiment is deduced. In the deduction, for the purpose of improving the overview, no iteration specific nomenclature is used.  
         [0034]    In C 1  the amplification (gain) |C 1 | and the remaining phase shift φ is modeled through the non-ideal preceding phase compensation according to:  
           C   1   =|C   1   |·e   jφ   (5)  
         [0035]    In w, according to:  
           w=e   α+jΔωT     s   .  (6)  
         [0036]    the amplitude change α in the measurement signal and the resultant frequency shift Δω, is modeled.  
         [0037]    By substituting the equations (5) and (6) into equation (2) the error vector is determined  
               e        (   k   )       =         1     |     C   1     |       ·     z        (   k   )       ·     e         -   α                   k     -     j                 Δ                 ω                   kT     s   -     j                 ϕ                 -       C   0       C   1       -     s        (     k   -   ɛ     )                 (   7   )                               
 
         [0038]    Due to the preceding coarse estimation, a linearization in equation (7) is allowable: for a complex x, via Taylor series expansion, e x  is generally linearized by  
           e   x ≈1 +x.   (8)  
         [0039]    Furthermore, the time shift s(k−ε) is linearized by  
           s ( k −ε)= s ( k )−ε ·s   d ( k ).  (9)  
         [0040]    It is noted that the normed derivative s d (k) is not allowed to be calculated from s(k), because s(k) does not fulfill the sample theorem. Rather, the over-sampled sequence s ov (k) should be used.  
         [0041]    By substituting equations (8) and (9) into equation (7), the linearization error vector is obtained:  
               e        (   k   )       =           1     |     C   1     |       ·   z            (   k   )     ·     [     1   -     α                 k     -       j   ·   Δ                   ω                 kTs     -     j                 ϕ       ]         -       C   0       C   1       -       [       s        (   k   )       -     ɛ   ·       s   d          (   k   )           ]     .               (   10   )                               
 
         [0042]    Through substitution, the real parameters x i  of the vector x is determined, according to:  
               e        (   k   )       =         z        (   k   )       ·     [       1       |     C   1     |            x   1           -       α       |     C   1     |            x   7           ·   k     -     j   ·       Δ                 ω                   T   s           |     C   1     |            x   2           ·   k     -     j   ·     ϕ       |     C   1     |            x   3               ]       -       C   0         C   1              x   4     +     j   ·     x   5               +       ɛ          x   6         ·       s   d          (   k   )         -       s        (   k   )       .               (   11   )                               
 
         [0043]    The real estimation value vector is defined through:  
           x =( x   1   x   2   x   3   x   4   x   5   x   6   x   7 ) T    
         [0044]    Through conversion, according to equation (11), the estimation values to be focused on from the estimation value vector x are determined according to:  
         | C   1 |=1 /x   1    
         Δω T   s   =x   2   ·|C   1 | 
         Δφ= x   3   ·|C   1 | 
         
       C 
       1 
       =|C 
       1 
       |·e 
       jφ 
     
           C   0   =C   1 ·( x   4   +j·x   5 )  
         ε=x 6    
         α= x   7   ·|C   1 |  (12)  
         [0045]    by defining the function f i (k), equation (10) results in:  
         e        (   k   )       =         ∑     i   =   1     N                       x   i     ·       f   i          (   k   )           -     s        (   k   )                               
 
         [0046]    with  
           f   1 ( k )= z ( k )  f   2 ( k )=− j·k·z ( k )  f   3 ( k )=− j·z ( k )  f   4 ( k )=−1  f   5 ( k )=− j f   6 ( k )= s   d ( k )  f   7 ( k )=− z ( k )· k   (13)  
         [0047]    Through gradient development, the cost function L(x) and the subsequent zero setting of the gradient, the estimation value vector {circumflex over (x)} is obtained according to:  
           {circumflex over (x)}=M   −1   ·b   (14)  
         [0048]    with the matrix and vector elements being:  
                     M   ij     =     Re        {       ∑   k              f   i   *          (   k   )       ·       f   j          (   k   )           }                     b   i     =     Re          {       ∑   k              f   i   *          (   k   )       ·     s        (   k   )           }     .                     (   15   )                               
 
         [0049]    By substituting equation (13) into equation (15) the Matrix M and the Vector b is obtained, which is shown in FIG. 2.  
         [0050]    By linearizing equation (8) and equation (9), the error-prone to the estimation vector {circumflex over (x)} in equation (14) is negligible. According to a preferred advancement of the method of the invention, several iterations are performed. The error can be desirably reduced through several iterations. In the norm, the error is negligible after 2 iterations.  
         [0051]    The following is applied:  
                                       Iteratio:   The number of iterations to be performed;       loop=[1,Iteration]:   The parameter loop shows which iteration is           currently being performed;       x (loop) :   The index  (loop)  describes the value x of the loop-ed           iteration (example: {circumflex over (ε)} (loop) , M (loop) ;       z ov   (loop) (K):   Over-sampled measurement signal of the loop-ed           iteration, with the linearized estimated parameters           compensated; and       z (comp) (k):   Measurement signal, with all estimated parameters           compensated. From this sequence, the EVM-error           E{circumflex over (V)}M(k) is calculated.                  
 
         [0052]    [0052]FIG. 3 is a block diagram illustrating the iterative method for estimating parameters. Before the embodied refined parameter estimation, a coarse estimation and compensation of the frequency ω, phase φ, and time shift ε, has to be performed.  
         [0053]    On the inputs  2  and  3  of a refined estimator  1 , the over-sampled measurement sequence (receiver sequence) z ov (k), and the reference sequence s ov (k), are given, respectively. On outputs  4   a  and  4   b  the estimated parameters are present, and on an output  5  the relative C 0  and C 1  from a compensator  18  having a compensator receiver sequence z (comp) (k) (in a symbol pulse), are present.  
         [0054]    From the over-sampled reference signal s ov (k), the normed differential sequence is calculated with the impulse answer h diff (k) in a filter  6 . Subsequently, in a reducing rate sampler  7  the down-sampling-factor ov is down sampled, followed by time slotting by a multiplier  8 . Therewith, on the input  9  of the estimation block  10 , lies the sequence s d (k) in a symbol pulse. Through a sampling rate reducer  11  and a multiplier  12 , in which the time slotting takes place, the unfiltered, down-sampled and slotted reference sequence s(k) can be fed to an input  17  of the estimation block  10 .  
         [0055]    For the estimation, only the valid symbols (“useful symbols”) are used, wherefore a slotting before the estimation must be performed. In the over-sampled input signals a pre-run and post-run are needed. The reason therefore is that a FIR (finite impulse response) filter  6  needs a rise time for the differentiation and also for the non-pictured interpolation filter, to compensate the estimated time shift {circumflex over (ε)}. If a plurality of iterations are performed, the measurement sequence z ov (k), at the beginning of the next iteration, has to be compensated with the actual total estimation value in a compensator  13 , and before the compensated measurement sequence z ov   (loop) (k) is fed to an input  16 , it goes through the reducing rate sampler  14  and the multiplier  15 , in which the time slotting takes place.  
         [0056]    The following points have to be thereby regarded:  
         [0057]    Only the linearized estimation parameters ({circumflex over (ε)}, ŵ, and {circumflex over (φ)}) are compensated at the beginning of a new iteration.  
         [0058]    For the linearized estimation parameters it applies that: the linearized (refined)-estimation value of the loop-ed iteration are {circumflex over (ε)} (loop) , ŵ (loop)  and {circumflex over (φ)} (loop) . The total estimation value according to the loop-ed iteration results through addition of all of the past estimation values according to:  
                     ɛ   ^     =       ∑     l   =   1     loop                       ɛ   ^       (   l   )                       w   ^     =       ∑     l   =   1     loop                       w   ^       (   l   )                       ϕ   ^     =       ∑     l   =   1     loop                       ϕ   ^       (   l   )                       (   16   )                               
 
         [0059]    With these instantaneous total estimation values, the measurement sequence will be compensated in the next iteration.  
         [0060]    With every new iteration, the measurement sequence z ov (k) is compensated with the actual total estimation values {circumflex over (ε)}, ŵ and {circumflex over (φ)} of the linearized parameters.  
         [0061]    The non-linearized estimation values (Ĉ 0  and |Ĉ 1 |) are not compensated for, in the single iterations, but are newly calculated in every iteration. Otherwise, false reproductions may arise because of the linearization error in the single iterations.  
         [0062]    It is to be heeded, that the estimated time shift {circumflex over (ε)} is not compensated in the reference signal, but in the measurement signal (input signal). Through which, according to the measurement regulation, the standards are achieved, in that the measurement signal is interpolated on the inter-symbol-interference-free symbol time point.  
         [0063]    After the last iteration loop-iteration, the equation (16) of the resultant total estimation value of the linearized parameter is present. The non-linearized parameters are taken from the calculation of the last iteration. Finally, the compensated measurement sequence z (comp) (k) in FIG. 3, must be calculated, which is needed for the calculation of the estimated EVM-vector, according to:  
                 z     (   comp   )            (   k   )       =           z     (   loop   )            (   k   )         |       C   ^     1     |       -         C   ^     0         C   ^     1                 (   17   )                               
 
         [0064]    When the method according to the invention is utilized in a CDMA (Code Division Multiple Access) signal, the reference signal comprises a plurality of superimposed partial signals from different code channels and always one parameter for every partial signal describes the different amplifications of the different code channels. The amplification-parameter of the different partial signals is estimated simultaneously with the method according to the invention.  
         [0065]    The invention being thus described, it will be obvious that the same may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are to be included within the scope of the following claims.