OFDM CLIPPING UP-SAMPLING AND EVM OPTIMIZATION SUCH THAT SPECTRAL INTERFERENCE IS CONCENTRATED OUTSIDE THE USED BAND The present invention relates to the field of wireless communication systems for transmitting digital multi-carrier signals. In particular, the invention relates to the reducing the Peak-to-Average-Power-Ratio (PAPR) for systems and methods using Orthogonal Frequency Division Multiplex (OFDM). A disadvantage in using transmission techniques like OFDM is the large PAPR of the transmitted signals, for it decreases the efficiency of the transmitter power amplifier. To reduce PAPR, normally the signals are clipped in the time domain combined with a filtering procedure, which compensates the spectrum impairments done by clipping. The spectrum impairments are a crucial point for OFDM signals, which are based on coding the data as spectrum lines in the frequency domain. Especially the higher modulations like 16 or 64 Quadrature Amplitude Modulation (QAM) are highly sensitive to adulterations of the spectrum lines. The technical problem is to find a clipping method, which produces for a predefined PAPR a minimum error for the spectrum lines. Clipping is a well-known method for reducing the PAPR in the digital transmit path of transmitters which use a data coding In the time domain like, for e.g., Wideband Code Division Multiple Access (WCDMA) systems. Several methods are known, see e.g. AWATER ET AL: Transmission system and method employing peak cancellation to reduce the peak-to-average power ratio. U.S. Patent No. 6,175,551 or DARTOIS, L.: Method for clipping a wideband radio signal and corresponding transmitter, as is European Patent Pub. No. 1 195 892 suggests to clip the signal peaks by subtracting a predefined clipping function when a given power threshold is exceeded. In order to ensure that clipping does not cause any out-of-band interference, a function is selected having approximately the same bandwidth as the transmitted signal. This is called soft-clipping. These methods are not optimal for OFDI\/l signals: In avoiding out-of-band interference they corrupt the spectral lines. Further methods to reduce PAPR are described in JAENECKE, PETER; STRAUSS, JENS AND DARTOIS, LUC: Method of scaling power amplitudes in a signal and corresponding transmitter/ Non-linear Method of Employing Peak Cancellation to Reduce Peak-to-Average Power Ratio. EP Patent Application No. 02360252.7, or FARNESE, DOMENICO: Techniques for Peak Power Reduction in OFDM Systems. Master Thesis Chalmer University of Technology, Academic Year 1997-1998. Coding schemes use known block codes In OFDM systems with constant-modulus constellations. The block code removes some constellation combinations. If those cdhibinations happen to produce large peaks, the coded system will have a smaller maximum peak than the uncoded version. These methods do not impair the signal quality; they are a desirable approach for systems with a small number of carriers. But as the number of carriers increases, coding schemes become intractable since the memory needed to store the code block and the CPU time needed to find the corresponding code word grows drastically with the number of carriers. Usually constellation points that lead to high-magnitude time signals are generated by correlated bit patterns, for example, a long string of ones or zeros. Therefore, by selective scrambling the input bit streams, may reduce the probability of large peaks generated by those bit patterns. The method is to form four code words in which the first two bits are 00,01,10 and 11 respectively. The message bits are first scrambled cyclically by four fixed equivalent m-sequences. Then the one with the lowest PAPR is selected and one of the pair of bits defined earlier is appended at the beginning of the selected sequence. At the receiver, these first two bits are used to select the suitable descrambler. PAPR is typically reduced to 2% of the maximum possible value while incurring negligible redundancy in a practical system. However, an error in the bits that encode the choice of scrambling sequence may lead to long propagation of decoding errors. For the tone reservation method a small subset of subcarriers are reserved for optimizing the PAPR. The objective is to find the time domain signal to be added to the original time domain signal x such that the PAPR is reduced. Let be X the Fourier transformation from jc, 1 is normally done with the following steps: (i) initialization ?7O') = 0; j = l,2 TJn); TJn) = u Un) i„"''n+Mm) = j„(m + l); »»i = 0,l Hn)-\, and, (ii) convolution of signal !„"'' with an appropriate interpolation filter fu, where the convoluted signal is given by jml and where NJ„ is preferably the (odd) length of the interpolation filter; ^/„/, = floor[Q.5*Nf„) is the "half" length. With we get the undipped up-sampled signal (7) <'"(",) = £/«(j)-4'*'(«/ -A^M + J'-I). «,■ = JV^, + l.yV^*+2 Assume that where Tcup is the aforementioned predefined clipping threshold. Then sjinj) must be reduced by a certain &, i.e. which leads to (8) d,r(nf) = &,r(nf)-Sa-fJN;,„ + l). where a„"'"'Uif) is given by the clipping condition (9) <"•(«,) = Zn,'^,ri"f) The centre of the filter is at j,„„„ = /v^„,,+i; in the convolution (8) the centre belongs to sample iV"'("/> • 'f we substitute in signal *„"'' at n^ sample s,"''(nf) by sample (10) :s„"'"(nf) = irO'r)- , ,^ ^,, /.(A^/./. -t-i) '— ^ ' we get because of equation (8) Clipping of the up-sampled interpolation level means, therefore, clipping of the unfiltered zero-padded level according to equation (11); because of and equation (10) Sa is given by (11) sa^.^^^:^ L(N.,,+l) r^__ , . I iT,7(/.,)ij The reduction defined in equation (11) can be done as hard clipping, or as soft clipping. In case of hard clipping, only the sample at n^ is modified; in case of soft clipping, the sample at n^ and samples around it are modified according of a predefined clipping function fc. One aspect of the present invention is that if the need of a clipping procedure on the up-sampled interpolation level appears, then clipping can be performed on the unfiltered zero-padded level in such a way that the clipping condition is fulfilled at HJ after interpolation. This is achieved e.g. by using equation (11). In order to simplify the representation it is assumed that y,(/v^i,/,+i) = i and that the clipping function fc and the interpolation filter fu have the same length, i.e., From equation (8) we get y=-'Vy, with +7V It follows that (12) a,r(r,y)=^&;''(n,)-K„Ss, where Equating the clipping condition (10) with equation (13) one gets or S.=^d„"nn,) 1 — \d:''(nj) 10 Sample nt was clipped before interpolation filtering, i.e., it was corrected according to equation (11). Normally, a re-filtering is required for the soft clipped part of all those *„"'', which were already interpolated. In order to avoid a re-flltering, & is determined in such a way that for the interpolated sample nf holds \d„">"'(nj)\=T,i^. It is only necessary to compute the correction for all other already interpolated samples, which are situated in the clipping filter range n^ - NJ, Hf +o, i.e., a„"i'Un,~k) for *=0,..„ + N^,. Soft clipping of the already interpolated samples is preferred. For the already interpolated samples a soft clipping of the signal .?/ is pretended, i.e., it is not really clipped, rather, the implications are simulated to the interpolated signal in case signal .?„•"' would have been clipped. In using equation (8) we get for l< = 1 ^'"■(nf -1)= 2]/«0')'5„'"'("/ -Nfl, + J-2) = Sample sj(nf-Hf^,,-\) is out of the clipping range which starts at nf-N^,; i.e., C,rinf-Nj„-\)^d,r(r,,.-Nfl,-\). Thus, d:(nf-\) = JJ\)JJnf-Nfl,-\)+ + 1] fJNj„+\ + j){j„(nf+j-\)-Ss-f,(Nfl,+j)] 7—Wfl+l or, a/Utf -1) = ffjnf - \)'Ss 2 fJNj^ + 1 + j)f,(Nfl, + ;) 11 The general solution is a,;""{n,-k) = &„"i'{nf~k)-Ss *4A or where +A', (14) «•*= 2] fJNfl,+\ + j)fJNfl,+j-k + l). k = {U A^^. All samples which fall into the clipping range, but which are not interpolated can be clipped as usual by a convolution i„'""(H^ +fc) = V"'("/ +k)-Ss'f,(N„,+k + \)- k = l2 Nfl,. An example for the output of part 1 is given in Fig. 6 and Fig. 7. Part 2 EVM Optimization and Second Clipping Identifying an optimum clipping is treated as a minimum problem under constraints. - Minimum Condition The minimum condition requires that the occupied subcarriers should be disturbed as less as possible, whereas the non-occupied subcarriers do not underlie any restriction. A preferred minimum condition follows from the properties of the Fourier transformation (the index n for Indicating the symbol number is omitted in the following description): The Fourier transformation S(1),.... Silm) from signal s(1) sik) can be calculated by means of the Fourier Matrix f according to where ' *' denotes the matrix multiplication. Let be (15) rj = ^"'''u)-sU); ;=i.2 ig, li where s"'''(j) is the/^ sample of the output from the up-sampling and first clipping unit for any OFDM symbol, and where s(y) is the f^ sample of the inverse Fourier transformation about the sub-carriers, i.e., y^ y,^ is the error vector in the time domain (Fig. 8, Fig. 9). The Fourier transformation of it (Fig. 10, Fig. 11) yields the error vector in the frequency domain, which is responsible for the EVM. In optimizing EVM, the contributions in this vector must be minimized. The function is used as a preferred measure for minimizing the errors produced by clipping and filtering; A^ is the number of the first occupied sub-carrier, and X^ the number of the last sub-carrier. From ffi ^Yk // = 0 it follows Yk = Tk" -~-~~ 2^ Yj" 2^ fjj • f^ respectively, (16) n = n old ■hr'j^^ j= k = l,2,..J ff' where X, '-(*) .t", '^* " ^a\ Zi-^" -^^ . and K*)* Jl^f 1=-^ It holds imag(l,,,)«0 (s,k=l,2,...,lffl)^ and (17) V^=rotateiv^,k-l), k=l,2 /^ , where (18) v,=[r„,r„ r,,^], 13 so that Instead of the matrix t the vector vi can be used. In a preferred implementation, the vector vi is shortened additionally, in order to reduce the computational complexity, i.e. that the required computational effort is limited. Optional extensions: (i) Optionally, a development of the y^ can be used. It is calculated in applying equation (16) iteratively. As an example, the second step of the development is calculated as follows: Given is the result of the first step. The second step is defined by equation (16) as Inserting in this equation the first step result y/" yields immediately y^^-', etc. (ii) Imitation of the tone reservation approach (WIMAX). In equation (16) the sum 2] can be replaced by J] , where A is the index set for the occupied sub-carrier. I.e., on demand, all sub-carriers can be omitted in the sum, which are resen/ed (according the WIMAX standard) for the tone reservation. (ill) Alternatively, a constraint condition can be introduced in such a way that EVMik)^r,,^; A =1.2 /^, for each symbol, where y'a^ is a predefined threshold, which restricts EVM of sample k to the limit of TEV-,^ %. Constraints There arie three types of constraints concerning clipping tliresliold, spectrum masl< requirement, and continuation condition: 14 Clipping Constraint: It is assumed that the mean power is normalized to a pre¬defined value. The clipping constraint says that \l\l)\