Abstract:
A method for reducing the crest factor of a multi-carrier signal includes evaluating an inverse Fourier transform of the multi-carrier signal, thereby generating a transformed multi-carrier signal; defining a signal-to-be-corrected to be the transformed multi-carrier signal; generating a simulated output signal; estimating a signal maximum of the simulated output signal; deriving a first correction variable on the basis of the estimate; correcting the signal-to-be-corrected using at least the first correction variable, thereby generating a corrected output signal having a reduced crest factor; defining the corrected output signal to be the signal-to-be-corrected; and iteratively repeating the last five steps until the corrected output signal has a crest factor below a predetermined threshold, or a predetermined number of iterations has occurred.

Description:
FIELD OF THE INVENTION 
     The present invention relates to digital signal processing, and in particular, to methods for reducing the crest factor of a multi-carrier signal. 
     RELATED APPLICATIONS 
     This application claims priority from German Application Serial No. 10255687.3, filed on Nov. 28, 2002, the entire contents of which are herein incorporated by reference. 
     BACKGROUND 
     Multicarrier signals generally have a high ratio between the signal maximum and the standard deviation of the signal. This ratio is also referred to as the crest factor and places stringent requirements on amplifiers and transmitters in order not to risk saturation effects which could result in loss of data. It is therefore actually necessary to reduce this crest factor for DMT (discrete multitone) and for OFDM (orthogonal frequency division multiplex) signals, in order to prevent saturation of the amplifier and transmitter and, furthermore, to reduce the power consumption of the amplifier and of the transmitter during transmission. If the crest factor is squared, then this results in the so-called PAR (peak-to-average ratio), which should likewise be reduced, for the reason mentioned above. 
     German Laid-Open Specification DE 198 50 642 A1 describes a method for reducing the crest factor of a signal. In this case, a signal is transformed using an IFT device and both a signal maximum and a signal minimum of the output signal are determined, from which a correction variable is derived. The output signal from the IFT device is corrected by means of the correction variable, which is derived from the determined value of the signal maximum and of the signal minimum, and with a second correction value possibly being calculated for correction of the crest factor of a signal. However, this has the disadvantage that any influence on the crest factor from downstream devices (amplifiers, converters, transducers, transformers, filters, etc.) are ignored in the correction process. 
       FIG. 4  shows a simplified block diagram of a number of schematic elements of a DMT or OFDM transmission device. A datastream  10  is subjected to inverse Fourier transformation in an IFT device  11 . The multicarrier signal  12  is then, for example, passed to a high-pass filter  13 , where it is filtered. The filtered output signal  14  is then supplied to an interpolation stage  15  and/or to an interpolation device with a low-pass filter. The filtered and interpolated output signal  16  is then converted in a block  17  to an analog signal, and is then filtered using a low-pass filter, before the output signal  18  from this converter device  17  with a low-pass filter is passed to an amplifier device (not shown). 
     DMT and OFDM signals are subject to the disadvantage that the ratio of the maximum to the standard deviation (crest factor) of the signal is very high. In order to reduce the requirements for a downstream output amplifier, particularly with regard to the linearity and the power consumption of the amplifier device, and for digital filters, as regards resolution, and for D/A converters, various methods are known from the literature which allow the crest factor to be reduced. The subject matter of most of the methods is to reduce the crest factor directly after the IFT device  11 , for example starting at nodes  12 ′. However, this method is subject to the problem that the crest factor will rise again as a result of the downstream filters  13  and the interpolation with low-pass filtering in the block  15 . However, in order to make it possible to reduce the power consumption of the downstream amplifier, it is necessary to reduce the output crest factor of the signal  18 . 
     A more successful reduction to the crest factor can be achieved if the reduction is carried out after the interpolation in the block  15 , that is to say starting for example at the node  16 ′. In the paper “PAR reduction revisited: an extension to Tellado&#39;s method”, which was published in conjunction with the sixth International OFDM Workshop (InOWo) 2001 in Hamburg, Werner Henkel and Valentin Zrno propose an advantageous method such as this which is explained, for example, in the published paper “Further Results on Peak-to-Average Ratio Reduction” by Jose Tellado and John M. Cioffi. According to the article by Henkel, the maximum value of the signal  16  is in this case determined after interpolation in the filter device  15 , for each data frame of the input signal  10 . This information, that is to say the precise sample value of the maximum value of the signal (both on the time axis or in the x direction as well as the amplitude of the maximum value, that is to say relating to the y direction) , is used in order to correct the output signal  12  from the transformation device  11 , for example starting at the point  12 ′. 
     The corrected signal is then once again passed through the high-pass filter  13  and the interpolation device  15  and, if necessary, the described steps are repeated. This implementation according to Henkel and based on Tellado is subject to the disadvantage that all of the filters from the high-pass filter  13  and the interpolation device  15  must be taken into account for each iteration or repetition. This leads to time-consuming computation operations and thus to restricted practical usefulness of the Henkel method according to the prior art. 
     SUMMARY 
     The object of the present invention is therefore to provide a method for reducing the crest factor of a multicarrier signal, which requires less computation complexity. 
     The idea on which the present invention is based essentially comprises determining only the position and the approximate magnitude or height of the maximum value of the signal after the interpolation device  15 . In this way, only estimated values of the signal maximum are calculated with little complexity, instead of having to calculate these values exactly for each iteration. This estimation process is preferably carried out using shortened filter simulations, which model the original filter impulse responses. 
     The present invention solves the initially mentioned problem in particular by providing a method for reducing the crest factor of a multicarrier signal having the following steps: (a) transformation of a signal using an IFT device; (b) interpolation and filtering of the output signal using an interpolation device which has a filter device; (c) determination of an estimated value of a signal maximum of the interpolated and filtered output signal, from which a correction variable is derived; (d) correction of the output signal from the IFT device using the correction variable ( 32 ) which is derived from the determined estimated value of the signal maximum; and (e) iterative repetition of the two last-mentioned steps until a predetermined number of iterations is reached, and/or a predetermined crest factor is achieved. 
     According to one preferred development, the output signal from the IFT device is filtered using a filter device, between method steps (a) and (c). 
     According to a further preferred development, during the process of determining the correction variable from the estimated value of the signal maximum of the interpolated and filtered output signal, the output signal from the IFT device or, possibly, the corrected output signal, once one iteration has been carried out, is temporarily stored in a memory device of a PAR reduction device. 
     According to a further preferred development, during the process of determining the correction variable from the estimated value of the signal maximum of the interpolated and filtered output signal, the output signal from the IFT device or, possibly, the corrected output signal once one iteration has been carried out under the influence of the filter device and of the interpolation device, which has a filter device, on the output signal from the IFT device or on the corrected signal is estimated in a simulation device, in order to produce a simulation signal in the PAR reduction device. 
     According to a further preferred development, the correction variable is determined from the estimated value of the signal maximum from the simulation signal in a detection device of the PAR reduction device, and this correction variable is multiplied by a normalized signal, which is similar to a Dirac, with the sampling positions synchronized, and with the multiplication result being added to the signal which is temporarily stored in the memory device. 
     According to a further preferred development, two or more correction variables are determined from the estimated value of the signal maximum in one iteration step, and are added to the signal which is temporarily stored in the memory device. 
     According to a further preferred development, during the process of determining the estimated value in the PAR reduction device, the bit width and hence the resolution of the output signal from the IFT device are reduced. 
     According to a further preferred development, only half of the sample values of the simulated signal are stored in the detection device in order to determine the correction variable from the estimated value of the signal maximum. 
     According to a further preferred development, during the process of determining the correction variable from the estimated value of the signal maximum, the sampling point and the estimated amplitude of the signal maximum are calculated. 
     According to a further preferred development, the simulation signal is calculated from a convolution of a shortened impulse response of the first filter device and of a reduced impulse response of the interpolation device, which has a second filter device, using the output signal from the IFT device or the corrected signal, once one iteration has been carried out. 
     According to a further preferred development, the first 20% of the sample values of the impulse response of the first filter device and the central 60% of the sample values of the impulse response of the interpolation device with the second filter device are used for the convolution. 
     According to a further preferred development, the output signal from the second filter device is converted in a D/A converter and is filtered in a further filter device before being supplied to an amplifier device. 
     According to a further preferred development, a high-pass filter is used as the first filter device, a low-pass filter is used as the second filter device and a low-pass filter is likewise used as the further filter device. 
     According to a further preferred development, a fourth order IIR high-pass filter is used as the first filter device, and an FIR interpolation filter is used as the second filter device. 
     According to a further preferred development, the signal is a DMT or OFDM signal. 
     One exemplary embodiment of the invention will be explained in more detail in the following description and is illustrated in the drawings, in which: 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  shows a schematic block diagram to explain one embodiment of the present invention; 
         FIGS. 2   a, b  show two schematic functional diagrams to explain the method of operation of one embodiment of the present invention, with  FIG. 2   a  showing the impulse response of a fourth-order IIR high-pass filter, and  FIG. 2   b  showing the impulse response of an FIR interpolation filter; 
         FIG. 3  shows a schematic signal diagram to explain the method of operation of one embodiment of the present invention; and 
         FIG. 4  shows a block diagram to explain a known procedure. 
     
    
    
     Identical reference symbols in the figures denote identical or functionally identical components. 
     DETAILED DESCRIPTION 
     In the block diagram shown in  FIG. 1 , a datastream  10  is supplied to an IFT device  11  in which an inverse Fourier transformation is carried out, for example an inverse fast Fourier transformation of the signal  10 . The transformed output signal  12 , a multicarrier signal such as a DMT or OFDM signal, then has its crest factor, that is to say the ratio of the signal maximum value to the signal standard deviation, reduced in a PAR reduction device  20 . The PAR reduction device  20  is followed by a filter device  13 , which emits a filtered output signal  14 . This filtered output signal  14  is then interpolated in a first interpolation device  15 , for example an interpolation stage with a downstream low-pass filter, that is to say a predetermined number of zeros are inserted between successive sample values, with mirror-image sidebands that are produced in the process in the filtered signal  14  being suppressed in the integrated low-pass filter device. An interpolated and filtered signal  150  is thus generated at the output of the first interpolation device. 
     This is preferably followed by a second interpolation device  15 ′, in which the interpolated and filtered output signal  150  from the first interpolation device  15  is once again oversampled, with a second predetermined number of zeros being inserted between adjacent sample values of the already interpolated signal from the interpolation device  15 . Low-pass filtering to eliminate undesirable sidebands is also carried out in the second interpolation device  15 ′. More zeros are preferably inserted between adjacent sample values in the second interpolation device  15 ′ than in the first interpolation device  15 . The interpolated output signal  16  from the second interpolation device  15  is then converted to an analog signal, and is filtered, in a converter device  17  with a low-pass filter, thus producing a filtered analog output signal  18 , which is amplified in a downstream amplifier device (not shown) and can be transmitted via a transmission device (not shown). 
     In order now to reduce the crest factor of the analog output signal  18 , the transformed output signal  12  from the IFT device  11  is, according to the embodiment of the present invention illustrated in  FIG. 1 , supplied via a first control device  21  to a memory device  22 , where it is temporarily stored. The control device  21  is used together with a second control device  23  to carry out iterations via a connecting device  24  in the PAR reduction device  20  when a corrected output signal  25  is not yet below a predetermined crest factor. Furthermore, the control devices  21  and  23  can also be operated so as to pass on the corrected output signal  25  from the PAR reduction device  20  once a predetermined time period has elapsed. 
     The transformed output signal  12  from the IFT device  11  or, if one iteration has been carried out, the signal  25  whose crest factor has been corrected, is supplied to an interpolation device  15 ″. The same predetermined number of zeros are inserted between adjacent sample values in this interpolation device  15 ″ as in the interpolation device  15 , although no low-pass filtering is carried out. A signal  26  which is produced in this way from the signals  12  and  25  is then supplied to a filter simulation or filter estimation device  27 . This filter estimation device is used to estimate both the influence of the first filter device  13  and that of the second filter device in the interpolation device  15 . 
     However, this is not done by including a detailed simulation of the impulse response of the first and second filter devices  13 ,  15  that are involved, but by merely using approximations of the corresponding impulse responses in the filter estimation device  27 , in order to reduce the computation complexity. In order to make it possible to estimate the influence of the first and second filter devices in the high-pass filter  13  and in the low-pass filter in the interpolation device  15  on the transformed signal  12  and on the corrected signal  25 , a convolution process, for example, is carried out using a shortened impulse response of the corresponding first and second filter devices with the interpolated signal  26 , that is to say with the signal  26  provided with additional zeros between adjacent sample values.  FIGS. 2   a  and  2   b , which illustrate examples of two impulse responses, will now be used as a reference to explain the filter approximation process. 
       FIG. 2   a  shows an example of a sampled impulse response of the first filter device  13 , for example of a fourth-order IIP high-pass filter, in which it can be seen that subsequent maximum values are determined only by the first of the coefficients  40  of the filter. Furthermore, the bit width of the coefficients  40  and of the input signal as well can be reduced in order to reduce the computation complexity in the filter estimation device  27  as shown in  FIG. 1 . In the example shown in  FIG. 2   a , it is sufficient to use the first four coefficients with reduced resolution for estimation of the output maximum value. 
     A similar situation also applies to the second filter device in the interpolation device  15  shown in  FIG. 1 .  FIG. 2   b  shows an example of the impulse response of this second filter device, for example an FIR interpolation filter. In this case, the coefficients  40  in the center of the filter are essentially required, that is to say approximately the first 15 coefficients  40 , and the last 15 coefficients  40  are redundant. If shortened impulse responses such as these are used for approximation, then only a lower level of computation complexity is now required and it is correspondingly possible to calculate more iterations for each data frame. 
     Referring now once again to  FIG. 1 , an output signal  28  or simulation signal from the filter estimation device  27 , which contains the approximated influence of the filters  13 ,  15  on the transformed signal  12  or on the corrected signal  25 , is supplied to a detection device  29 . In order to determine the maximum value of the signal  28 , the only signal values which are considered in the detection device  29  are those which are above a predetermined amplitude, that is to say above a predetermined threshold value. The corresponding sample values are determined successively from these signal values which are above the threshold value, for example starting with the highest signal value. The position, that is to say the specific sample value with the greatest amplitude, is in each case detected in the detection device  29 . This sampling position or these sampling positions, that is to say in each case the precise position of the respective sample value in the data frame of the signal  28 , is/are passed via the connection  30  to a Dirac function memory device  31 . A function which is similar to a Dirac function is stored, normalized with respect to the maximum amplitude  1 , in this Dirac function memory device  31 . 
     One or more correction variables  32  which have been determined in the detection device  29  and have been derived from the signal maxima (possibly modified such that the estimated signal maximum is reduced by a threshold value and is multiplied by a factor of between 0 and 1) are then multiplied by the function  33  which is similar to a Dirac function and is normalized with respect to the maximum amplitude  1 , and are then subtracted from the signal which is stored in the memory device  22 , that is to say either from the transformed signal  12  or, once one iteration loop has been carried out, from the already corrected signal  25 . In this way, the crest factor (that is to say the ratio of the signal maximum to the signal standard deviation) is reduced in the PAR device  20 , and a corrected signal  25  is produced, with a reduced crest factor. 
     The corrected signal  25  can now once again be passed through a reduction process (iteration) via the control device  23 , the connecting device  24  and the control device  21 , as has already been described in the text above with reference to the transformed signal  12 . In order to reduce the computation complexity in the PAR device  20 , according to the invention, a signal maximum with only an estimated amplitude, approximated by the blocks  15 ″ and  27  after passing through the filters  13  and  15  on the basis of the filter approximation in each iteration process, is subtracted from the original signal  12  or from the already corrected signal  25 . 
       FIG. 3  shows an example of a sampled signal with an impulse  41  similar to a Dirac function, normalized with respect to the amplitude  1 . In order to reduce the hardware complexity, it is also possible, for example, to make use of the symmetry of the signal as shown in  FIG. 3  in order, for example, to store only half of the sample values. 
     Although the present invention has been described above with reference to a DMT or OFDM transmission device, it is not restricted to this and can, in principle, be applied to any multicarrier signals in order to reduce the crest factor or the peak-to-average ratio. 
     An interpolation device  15  and, in consequence, also the interpolation simulation  15 ″ are preferably used to carry out as little oversampling as possible, for example two or four times, in order to optimize the computation time. The influence of the second interpolation device  15 ′ with a corresponding low-pass filter as well as the D/A converter unit  17  with a low-pass filter have not been included in the PAR reduction process since their influence is only minor although, in principle, this is likewise possible with approximated filter impulse responses in the PAR reduction device  20 .