DE102006017636A1 - Transmitter signal`s spectral side lobe suppressing method for e.g. multi-carrier transmission system, involves obtaining algorithm specified in vector and matrix notation for determining weighting factors of cancellation subcarriers - Google Patents

Abstract

The method involves inserting determined subcarriers as cancellation subcarriers at edges of a related orthogonal frequency division multiplexing (OFDM)-transmitting signal spectrum in a frequency region of an OFDM transmission system, which carry no data information and contain special complex weighting factors instead of complex data symbols. An algorithm specified in a vector and matrix notation is obtained for determining weighting factors of the cancellation subcarriers.

Description

The present invention relates to a method for suppressing spectral sidelobes of the transmission signal in wireless or wireline OFDM (Orthogonal Frequency Division Multiplexing) transmission systems and in multi-carrier transmission systems using OFDM or based on OFDM, wherein in the frequency range of the transmission system at the two edges of the particular subcarriers are inserted as Auslöschungsunterträger C that carry no data information and instead of complex data symbols special, generally complex weighting factors g obtained according to an algorithm in compliance with a constraint || g || ² ≤ α, according to which the power of the weighted extinction subcarriers must not exceed a certain portion α of the total transmit power, it may be determined that the spectral sidelobes of the weighted extinction subcarriers substantially eliminate the spectral sidelobes of the original OFDM transmit signal by minimizing the superposition of the spectra Cg of the spectra suppressing weighted extinction subcarriers and the spectra Sb of all subcarriers modulated with data symbols b of the original transmit signal representing function Sb + Cg, where for vector g and b the vector notation and for C and S the matrix notation is chosen.

The Spectrum of an OFDM transmission signal is known to have strong sidelobes on. This means that in the case of OFDM transmission outside the transmission bandwidth considerable transmission powers are radiated.

to suppression Spectral sidelobes in OFDM are different according to the prior art Options.

Spectral Side lobes can be particularly filtered by means of measures suppress. Such measures mean for an additional Implementation effort and thus additional costs. On the other hand the transmission signal is influenced by the filtering process and it can disorders occur. In particular, the filtering becomes the OFDM symbol extended in the time domain, causing disturbing Symbol interference between consecutive OFDM symbols can arise.

A suppression spectral sidelobes leaves themselves in OFDM transmission systems also achieve that large guard bands to those in the frequency domain provided adjacent systems or subcarriers at the frequency domain edge OFDM system to be released. The procedure, subcarrier at the frequency domain edge release, i. For example, not using data symbols in the standards DAB ("Digital Audio Broadcasting ") and DVB-T ("Digital Video Broadcasting - Terrestrial ") known measures However, they are inefficient and waste valuable resources Spectrum. Is there only a small frequency range for transmission? to disposal, makes no sense, an OFDM transmission system in this frequency range, if large guard bands are to be provided or subbands released Need to become.

A suppression spectral sidelobe in OFDM transmission systems can also be done by pulse shaping. Instead of the rectangular pulse for the OFDM symbol in the time domain can other pulse shapes selected be a cheaper one Have spectrum, i. a spectrum whose sidelobes are faster subside. examples for such pulses are Nyquist pulses, such as the raised cosine pulse. However, other pulse shapes have as the rectangular pulse also quite disadvantages. It enlarges namely the temporal extent of the OFDM symbol, causing symbol interference can arise. Furthermore can for OFDM modulation and demodulation no longer the cost-effective implementation means DFT / IDFT ("Discrete Fourier Transformation "/" Inverse Discrete Fourier transformation ") or FFT / IFFT ("Fast Fourier Transformation "/" Inverse Fast Fourier Transformation") be used.

Of the The prior art suppression technique described above spectral side lobes in OFDM transmission systems is based For example, in the book by Proakis, J.G .: Digital Communications, New York: McGraw-Hill Inc., 1995 or in the book by van Nee, R .; Prasad, R .: "OFDM for Wireless Multimedia Communications ", Boston: Artech House, 2000 be looked up.

at some OFDM transmission systems there is a requirement to use small frequency ranges. These Demand is for example set in the design of OFDM-based "overlay" transmission systems. An "overlay" transmission system is a communication system, that in the spectrum of another transmission system work and the unused frequency ranges for transmission may use.

A the promising solutions for the suppression spectral sidelobe in transmission systems, based on OFDM, is the insertion of so-called cancellation bearers (Cancellation Carriers; CC). This technique is from the article by S. Brandes, I. Cosovic and M. Schnell: "Sidelobe suppression in OFDM systems by insertion of cancellation carriers ", Proceedings IEEE Vehicular Technology Conference (VTC'05 case), Sept. 2005. In this drive known to drive some so-called Auslöschungsunterträger on the left and right sides of the used OFDM spectrum inserted. This special subcarrier will not be for the data transmission but carry complex weighting factors that so determined be that the sidelobes of the transmit signal and the Auslöschungsuntererträger mutually extinguish.

In This article proposes an algorithm for determining the extinction carriers. which minimizes the sidelobes under a constraint which the for the extinction subcarrier spent performance limited so as not to consume too much of the transmission power for the extinction subcarriers. However, this algorithm requires that the extinction carrier coefficients for each new one Send sequence be recalculated. In addition, the algorithm contains for the determination of extinction subcarriers Root finding algorithm, e.g. the Newton algorithm, iterative is working. this leads to at a considerable computational effort and processing delays at the OFDM transmitter and therefore limited in practical OFDM systems the application of the extinction subcarrier algorithm proposed here.

to Determination of extinction subcarrier thus in this known method a significant computational effort required, the additional Costs and the question of the applicability of the proposed Algorithm in for the practice of suitable OFDM systems brings with it.

Of the The present invention is based on the object, spectral Sidelobe in OFDM transmission systems and multicarrier transmission systems, based on OFDM or using OFDM, suppress or at least significantly reduce without any additional Filter effort is required and the OFDM transmit signal by a to disturbances, especially symbol interference, leading filtering process affected becomes. In the side lobe suppression to be created by the invention about that In addition, the valuable resource spectrum without waste preferably fully exploited which is particularly important, if only a small frequency range for transmission available is. It should be used in a conventional manner Auslöschungsunterträger a simplified algorithm for determination developed by extinction subcarriers should be minimized by both the computational effort and the processing delay being held.

eingeführt wird, wobei D = –C^H(CC^H)^–1S gilt und unter der Voraussetzung ||Db||² ≤ α und durch Substituieren der Gleichungen D = –C^H(CC^H)^–1S und

in die Gleichung Sb + Cg = 0 die Gleichung Sb + Cg = Sb + CDb = Sb – CC^H(CC^H)^–1Sb = 0 erhalten wird.According to the present invention, which relates to a method for suppressing spectral sidelobes in OFDM transmission systems or OFDM based on the type mentioned above, this object is achieved in an advantageous manner that for determining the Auslöschungsuntererträger- Weighting factors here an algorithm also indicated in vector and matrix notation

where D = -C ^H (CC ^H ) ^-1 S, and assuming || Db || ² ≤ α and by substituting the equations D = -C ^H (CC ^H ) ^-1 S and

in the equation Sb + Cg = 0, the equation Sb + Cg = Sb + CDb = Sb - CC ^H (CC ^H ) ^-1 Sb = 0 is obtained.

The matrices D and S need only be computed once for all the data sequences of the transmission, and then they are expediently stored in a look-up table. To determine the extinction subcarrier weighting vector g, then only a matrix multiplication Db and the computation of || Db || ² performed.

The Determination of extinction subcontractors Side lobe suppression in OFDM systems and on OFDM multicarrier systems is therefore by Applying a simple algorithm that achieves a significant lower complexity as in the article by S. Brandes, I. Cosovic and M. Schnell: "Sidelobe suppression in OFDM systems by insertion of cancellation carriers ", Proceedings IEEE Vehicular Technology Conference (VTC'05 case), Sept. 2005, proposed Algorithm has. A slight disadvantage with this simplified Algorithm lies in a sidelobe suppression, which is slightly worse than is the one that is possible with the known algorithm.

The Invention thus has opposite The prior art has the considerable advantage that its simple algorithm a significantly lower computational complexity than previously proposed Algorithm unfolds, allowing him to apply in for practice suitable OFDM systems and their only one Disadvantage, in a slightly worse Side lobe suppression exists, far outweighs.

The Side lobe suppression in OFDM systems and multicarrier transmission systems based on OFDM is based on the present Invention thus by introduction of extinction subcontractors, that carry no information and instead of a complex data symbol special complex weighting factors obtained by means of a very advantageous algorithm can be determined so that the sidelobes of the OFDM transmission signal are minimized. The extinction subcarriers serve So to do so, the sidelobes, which through the other subcarriers of the OFDM transmission system be generated, extinguish or largely reduce.

The Process according to the present invention has over the other already acknowledged, usual Spectral sidelobe spectrometry has a number of advantages on. No symbol interference or other interference is generated. Only very small protective tapes are needed. DFT / IDFT or FFT / IFFT can continue to be used for OFDM modulation and demodulation.

Of the only drawback, the method of the present invention across from this conventional Method, is that the Auslöschungsunterträger not for data transfer to disposal which slightly reduces the transmission capacity.

advantageous Embodiments, developments and uses of the method according to the invention for suppression Spectral sidelobe of the transmission signal in wireless or wireless OFDM transmission systems and in multi-carrier transmission systems, using the OFDM or based on OFDM are in the immediate ones or indirectly to the claim 1 back dependent claims specified.

To the better understanding Below, the present invention is based on a relative simple example explained.

Consider an OFDM system with N subcarriers and 4QAM ("4 Quadrature Amplitude Modulation"). The duration of a 4QAM modulated symbol is denoted by T _s . Since an OFDM symbol simultaneously transmits N symbols modulated with 4QAM, the duration of an OFDM symbol is T = N * T _s . The subcarriers in an OFDM system are numbered from left to right, with the subcarrier on the left side denoted by 1 and its center frequency by f _t and the subcarrier on the right by N and its center frequency by f _N.

A single subcarrier s _n (x), n = 1, 2, ..., N is in the frequency domain as s n (x) = S (x - x n ), n = 1, 2, ..., N. (1) shown.

In equation (1), x is a through x = (f - f 0 ) T (2) given normalized frequency, where f denotes the frequency and f _{0 is} the center frequency. In addition, x _{n is} the nor-programmed frequency of the nth subcarrier. The function S (x) depends on the transmission window used, eg in the case of the rectangular time domain windowing for S (x)

If a different type of fenestration is used, e.g. the raised cosine windowing, must the equation (3) according to the Fourier transform of the chosen Window to be customized. The function S (x) is determined by the proposed Side lobe suppression methods won. As a result, the proposed method can be used with ease any transmission window be combined, since only S (x) are suitably modified got to. The following will be a common one rectangular window assumed on the transmitter.

Since the task is to suppress the sidelobes in a certain frequency range, s _n (x) is considered only in that range. Instead of observing continuous frequencies, M normalized discrete frequency samples y _m , m = 1, 2, ..., M, are observed, which are in the frequency range in which the optimization of sidelobes is performed. This reduces the equation (3) s n, m = s n (y m ) = S (y m - x n ), n = 1, 2, ..., N, m = 1, 2, ..., M. (4)

If s _{n, m} , m = 1, 2, ..., M are combined to form a vector, one obtains s _n = (s _{n, 1} , s _{n, 2} , ..., s _{n, M} ) ^T , n = 1, 2, ..., N. Finally, if the vectors s _n , n = 1, 2, ..., N, are combined into a matrix, we obtain S = (s 1 , s 2 , ..., s N ). (5)

The spectrum of the transmitted OFDM symbol is the superposition of the spectra of each subcarrier and is given by Sb (6), where b = (b ₁ , b ₂ , ..., b _N ) ^{T are} original symbols that modulates with 4QAM are.

To reduce sidelobes, M _l and M _r extinction subcarriers are inserted on the left and right sides of the OFDM spectrum used, respectively. As a result, the bandwidth of the OFDM spectrum is now N + M _r where M = M _l + M _r . The extinction subcarriers carry no data symbols and thus the spectrum of the mth extinction subcarrier is not multiplied by a complex data symbol but instead by 1:

The normalized center frequencies z _{m of} the M extinction subcarriers lie on the left and on the right side of the OFDM spectrum used.

formuliert, abhängig von ||g||2 ≤ α, (11)wobei g = (g₁, g₂, ..., g_M)^T und C = (c₁, c₂, ..., c_M). Die Nebenbedingung in (11) begrenzt die Leistung, die für die Auslöschungsunterträger aufgebracht wird, so dass nicht zu viel der Sendeleistung für die Auslöschungsunterträger aufgewandt wird. Die in dem genannten Beitrag angegebene Lösung dieses Problems beruht auf der Anwendung der Lagrange-Multiplikatoren-Methode, der Einzelwertzerlegung (SVD; Singular Value Decomposition) und der Verwendung eines Wurzelfindungsalgorithmus. Während die Einzelwertzerlegung (SVD) nur einmal ausgeführt werden muss, ist der Wurzelfindungsalgorithmus für jede neue Sendesequenz erneut anzuwenden.The samples of the spectrum of the extinction subcarriers C _{m, k} = C _m (y _k ) become a vector c m = (C m, 1 , C m 2 , ..., C m, K ) T , m = 1, 2, ..., M. (8) compiled. To suppress the sidelobes, each extinction subcarrier is multiplied by a complex weighting factor g _m , m = 1, ..., M. These complex weighting factors are determined so that the sidelobes of the weighted extinction subcarriers suppress the sidelobes of the original transmit signal. In other words, the superposition of the spectra of the weighted extinction subcarriers and the original transmission signal is accomplished Sb + Cg (9) and must be minimized. In the previously acknowledged paper by S. Brandes, I. Cosovic and M. Schnell: "Sidelobe suppression in OFDM systems by insertion of cancellation carriers", Proceedings IEEE Vehicular Technology Conference (VTC'05 case), Sept. 2005, this is Optimization as a linear least squares problem

formulated, depending on || g || 2 ≤ α, (11) where g = (g ₁ , g ₂ , ..., g _M ) ^T and C = (c ₁ , c ₂ , ..., c _M ). The constraint in (11) restricts the power applied to the extinction subcarriers so that too much of the transmission power is not used for the extinction subcarriers. The solution to this problem indicated in the said article is based on the application of the Lagrange multiplier method, Singular Value Decomposition (SVD) and the use of a root finding algorithm. While single value decomposition (SVD) has to be performed only once, the rooting algorithm must be reapplied for each new send sequence.

wobei D = –CH(CCH)–1S. (13) According to the present invention, to determine extinction subcarrier coefficients g, a much simpler algorithm is introduced which satisfies the constraint on function (11). The solution proposed by the invention is given by

in which D = -C H (CC H ) -1 P. (13)

It should be noted that, assuming || Db || ² ≦ α and by substituting equations (13) and (12) into equation (9) Sb + Cg = Sb + CDb = Sb - CC H (CC H ) -1 Sb = 0 (14) is obtained.

The matrices D and S only need to be computed once, are stored in a look-up table and used for each data sequence. Thus, to determine the cancellation subcarrier vector g, only a matrix multiplication (Db) and the computation of || Db || are used ² required.

The main idea behind the solution according to the equation (12) is to scale the vector Db in the case where its power is equal to or greater than α, so that the power effective at the extinction subcarrier vector g satisfies the constraint (11). With this approach, sidelobe suppression is reduced compared to the case where this scaling is not applied, and the resulting sidelobes (observed at the discrete frequency positions selected within the optimization range) are equal

erreicht.As a result, in this case, a reduction in the side-lobe performance of

reached.

It It should be noted that the proposed solution is in comparison to the one previously proposed solution in terms of Although the achievable spectral sidelobe suppression is suboptimal, but they have the computational complexity significantly reduced, as they use the application of root-finding algorithms avoids and requires a minimum number of bills to the extinction subcarrier vector g.

• – Das Verfahren gemäß der vorliegenden Erfindung ist nicht nur auf OFDM-Übertragungssysteme anwendbar, sondern auf alle Übertragungsverfahren, die auf OFDM beruhen, wie beispielsweise "Orthogonal Frequency-Division Multiple-Access" (OFDMA) und "Multi-Carrier Code-Division Multiple-Access" (MC-CDMA).
• – Das Verfahren gemäß der vorliegenden Erfindung ist auf OFDM-Systeme oder Mehrträger-Übertragungssysteme, die auf OFDM beruhen, mit beliebiger Unterträgeranzahl N anwendbar.
• – Das Verfahren gemäß der vorliegenden Erfindung ist nicht auf 4QAM beschränkt, sondern kann auf alle Modulationsverfahren erweitert werden, die in OFDM-Übertragungssystemen oder Mehrträger-Übertragungssystemen, die auf OFDM beruhen, verwendet werden.
• – Das Verfahren gemäß der vorliegenden Erfindung beschränkt sich nicht auf die Unterdrückung je eines Nebenzipfels an den beiden Rändern des Sendesignalspektrums. Vielmehr kann die Optimierung der Gewichtungsfaktoren auf eine beliebige Bandbreite ausgedehnt werden.
• – Das Verfahren gemäß der vorliegenden Erfindung ist nicht auf die Anwendung des Algorithmus auf alle verfügbaren Unterträger gemeinsam beschränkt. Die Unterträger können in bestimmter Weise in mehrere verschiedene Gruppen aufgeteilt werden und der Algorithmus kann auf diese Gruppen unabhängig angewandt werden. Überdies kann der Algorithmus auf nur einige der Gruppen von Unterträgern angewandt werden, während die anderen Gruppen von Unterträgern unverändert bleiben.
• – Das Verfahren gemäß der vorliegenden Erfindung lässt sich auf einfache Weise mit anderen Verfahren zur Nebenzipfelunterdrückung kombinieren, beispielsweise mit den drei einleitend beschriebenen Verfahren entsprechend dem Stand der Technik. Dies ist möglich, da das Verfahren gemäß der vorliegenden Erfindung keine prinzipiellen Änderungen am OFDM-Übertragungssystem oder dem auf OFDM basierenden Mehrträger-Übertragungssystem erfordert. Das resultierende Übertragungssystem mit Auslöschungsunterträgern bleibt ein OFDM-Übertragungssystem oder ein auf OFDM basierendes Mehrträger-Übertragungssystem.

The method according to the present invention is not on the example described above be but can be generalized to the following cases:

• The method according to the present invention is applicable not only to OFDM transmission systems, but to all transmission methods based on OFDM, such as "Orthogonal Frequency Division Multiple Access" (OFDMA) and "Multi-Carrier Code Division Multiple Access "(MC-CDMA).
• The method according to the present invention is applicable to OFDM systems or multi-carrier transmission systems based on OFDM with arbitrary subcarrier number N.
• The method according to the present invention is not limited to 4QAM but can be extended to all modulation methods used in OFDM transmission systems or multi-carrier transmission systems based on OFDM.
• The method according to the present invention is not limited to the suppression of each side lobe at the two edges of the transmission signal spectrum. Rather, optimizing the weighting factors can be extended to any bandwidth.
• The method according to the present invention is not limited to the application of the algorithm to all available subcarriers. The subcarriers can be divided into several distinct groups in a specific way and the algorithm can be applied independently to these groups. Moreover, the algorithm can be applied to only some of the subcarrier groups, while the other subcarrier groups remain unchanged.
• The method according to the present invention can be easily combined with other methods for sidelobe suppression, for example with the three prior art methods described in the introduction. This is possible because the method according to the present invention does not require any fundamental changes to the OFDM transmission system or the OFDM based multi-carrier transmission system. The resulting extender subcarrier transmission system remains an OFDM transmission system or an OFDM based multicarrier transmission system.

The Method according to the present invention can be applied to all OFDM based, wired multi-carrier transmission systems used be there to suppress there To achieve spectral sidelobes. Wired related Communication becomes OFDM frequently also called "Discrete Multi-Tone (DMT) modulation ". OFDM or DMT is often used in wired communication as Connection to the households ("last mile") used to digitally connect to the outside world to tie. The various transmission techniques available for this purpose are termed "Digital Subscriber Line "(DSL) summarized. DSL transmission technologies are for example HDSL ("High-Speed Digital Subscriber Line "), ADSL ("Asymmetric Digital Subscriber Line ") and SDSL ("Symmetric Digital Subscriber Line "). The DSL transmission techniques are examples of the scope of the inventive concept in the field of wired Communication. Further leaves the process of the invention for OFDM systems in the area "Power Line Communications ".

The Method according to the present invention Invention may also be applied to all OFDM based wireless transmission systems be used to there a suppression of spectral sidelobes to reach. The application here includes both already standardized, OFDM-based systems such as DAB, DVB-T or "High Performance Local Area Network 2 "(HIPERLRN / 2), as well as new systems, such as those based on OFDM MC-CDMA developments under the "Fourth Generation Mobile" (4G).

The Process according to the present invention is also in communication with so-called OFDM-based "overlay" systems of great interest. An "overlay" system is a transmission system (Filling system), that in the frequency band of another transmission system (main system) works and uses the currently idle frequency gaps there. Particularly suitable for "overlay" systems are systems based on OFDM, as these by switching off individual subcarrier groups Spaces in the spectrum can be spared, where the main system is currently broadcasting. Indeed would the strong sidelobes of a standard OFDM method either disturb the main system or make it necessary that large guard bands or steep-sided transmit filters must be used. First the sidelobe suppression according to the present Invention allows thus an efficient realization of "overlay" systems.

The method according to the present invention thus makes it possible to dispense with additional filtering or pulse shaping of the transmission signal and allows the use of smaller guard bands. The properties of the OFDM transmit signal are not adversely affected. The only, but not particularly relevant, disadvantage resulting from the use of the extinction subcarriers is a slightly smaller transmission capacity since the extinction subcarriers are not for data transmission can be attracted.

Further allows the method according to the present invention the realization of efficient, OFDM-based "overlay" systems that have recently been used in research be developed to better exploit the valuable resource Realize spectrum. The potential application for "overlay" systems ranges from the terrestrial radio transmission over the Aeronautical communication to satellite communication. Currently, e.g. in an EU project in the 6th Framework Program at the Development of an overlay system for the future ATC ("Air Traffic Control") communication in the VHF band worked.

Short is summarized in the method according to the present invention that is, in an OFDM system and in OFDM-based multicarrier systems, the extinction subcarrier to Using sidelobe reduction, an algorithm introduced that necessary to obtain suitable extinction subcarriers computational complexity keeps minimal.

This Algorithm aims at practical applications of extinction subcarriers OFDM systems in which the signal processing for each data sequence, i.e. For every OFDM symbol, should be kept minimal, since the well-known, in the article by S. Brandes, I. Cosovic and M. Schnell: "Sidelobe suppression in OFDM systems by insertion of cancellation carriers ", Proceedings IEEE Vehicular Technology Conference (VTC'05 case), Sept. 2005, algorithm a significant computational complexity for each data transfer sequence required. Compared to this existing algorithm for determination the extinction subcarrier is according to the invention the computational complexity significantly reduced.

Of the across from this considerable advantage as a subordinate price, the for this reduction in computational complexity has to be paid in a slight worse sidelobe suppression when using the mentioned known algorithm.

Claims (20)

A method for suppressing spectral sidelobes of the transmission signal in wireless or wireline OFDM (Orthogonal Frequency Division Multiplexing) transmission systems and in multi-carrier transmission systems using OFDM or based on OFDM, wherein in the frequency range of the transmission system at the two edges of the respective OFDM transmit signal spectrum Subcarriers are inserted as extinction subcarrier C, which carry no data information and instead of complex data symbols special, generally complex weighting factors g obtained according to an algorithm in compliance with a constraint || g || ² ≤α, according to which the power of the weighted extinction subcarriers must not exceed a certain portion α of the total transmit power, it may be determined that the spectral sidelobes of the weighted extinction subcarriers substantially cancel the spectral sidelobes of the original OFDM transmit signal by minimizing the superposition of the spectra Cg of the spectra weighted extinction subcarriers and the spectra Sb of all data carriers b modulated subcarriers of the original transmit signal representing the function Sb + Cg suppressing, here for g and b the vector notation and for C and S is selected the matrix notation, characterized in that for determining of the extinction subcarrier weighting factors is an algorithm, also shown in vector and template notation

where D = -C ^H (CC ^H ) ^-1 S, and assuming || Db || ² ≤ α and by substituting the equations D = -C ^H (CC ^H ) ^-1 S and

in the equation Sb + Cg = 0, the equation Sb + Cg = Sb + CDb = Sb - CC ^H (CC ^H ) ^-1 Sb = 0 is obtained. A method according to claim 1, characterized in that the matrices D and S for all data sequences Only one matrix multiplication Db and the calculation of || Db || for the determination of the extinction subcarrier weighting vector g are calculated once and stored in a look-up table ^{2 are} performed. Method according to one of the preceding claims, characterized through the use of a modulation scheme used in OFDM transmission systems or multi-carrier transmission systems which are based on OFDM or use OFDM. Method according to claim 3, characterized that 4QAM (4 quadrature amplitude modulation) as modulation method is used. Method according to one of the preceding claims, characterized characterized in that the algorithm is not limited to that constraint limited, which limits the transmission power of the extinction subcarriers, but that in addition any other constraints that meet the system requirements considered become. Method according to one of the preceding claims, characterized characterized in that the optimization of the weighting factors on each one Auslöschungsuntererträger to the both edges of the OFDM transmission signal spectrum. Method according to one of claims 1 to 5, characterized that the optimization of the weighting factors on extinction subcarriers is over arbitrary bandwidth at the two edges of the OFDM transmit signal spectrum extends. Method according to one of the preceding claims, characterized characterized in that the application of the algorithm is not at all available subcarrier limited together is, but that subcarrier be divided into several different groups in a certain way and the algorithm is applied to these groups independently. Method according to claim 8, characterized in that that the algorithm applies to only some of the subcarrier groups will, while the other groups of subcarriers unchanged stay. Method according to one of the preceding claims, characterized by a combination with one or more other methods for suppression Spectral sidelobe in the relevant OFDM transmission system or in the relevant A multi-carrier transmission system, the OFDM is used or based on OFDM. Use of the method according to one of the preceding claims in OFDM-based wired transmis sion systems to achieve a repression Spectral sidelobe. Use according to claim 11 in the context of a digital Connection of households ("last mile") to the outside world in accordance with the term "digital Subscriber Line "(DSL) summarized various transmission techniques. Use according to claim 11 in the context of an OFDM transmission system in the area "Power Line Communications ". Use of the method according to one of claims 1 to 10 in OFDM-based wireless transmission systems to achieve a repression Spectral sidelobe. Use according to claim 14 as part of an already standardized, OFDM-based transmission system, such as DAB, DVB-T or "High Performance Local Area Network 2 "(HIPERLAN / 2). Use according to claim 14 as part of a OFDM based MC-CDMA transmission system in the context of the Fourth Generation mobile radio "(4G). Use of the method according to one of claims 1 to 10 in conjunction with a so-called OFDM-based "overlay" transmission system, ie a transmission system which operates as a filling system in the frequency band of another, operated as a main system transmission system and the current there idle frequency gaps uses. Use according to claim 17 in the context of a terrestrial Radio transmission system. Use according to claim 17 in the context of an aeronautical Communication system. Use according to claim 17 in the context of a satellite communication system.