DE102009021417B4 - Method and apparatus for nonlinear transformation and envelope scaling of OFDM signals - Google Patents

Abstract

Method for non-linear transformation and envelope scaling of an OFDM symbol consisting of NF sinusoidal subcarriers of bandwidth B, the data content of which is given with the cardinality M of the modulation alphabet by a possible realization of the data vector, the NF components of which represent the data symbols to be transmitted and the complex amplitudes of the NF Subcarriers, characterized in that with a matrix S (s) to be selected from a set {S (1) ... S (S)} of S different mapping matrices of the dimension NF × NF from the data vector d (r) according to (A2 ) the mapped data vector is formed, it is transformed into the vector with the Fourier matrix, the time-continuous signal ũ (r, s) (t) is formed from u (r, s) according to (A4) by D / A conversion, this with an the range (0, ∞) selected and designated as the preclipping factor is multiplied, the resulting signal gũ (r, s) (t) is clipped according to u ( r, s, g) cl (t) according to (A5) the signal u (r, s, g) cl, LP (t) is generated by removing the spectral components outside the OFDM bandwidth B by means of low-pass filtering, and from this finally with a selected envelope maximum A, the complex envelope of the OFDM symbol to be transmitted is formed, with that mapping matrix S (s) selected from the set {S (1) ... S (S)} after the preclipping factor g has been selected and in ( A3) is used, which minimizes the PAPR of the OFDM symbol with the complex envelope u (r, s, g, A) (t) according to (A6).

Description

1 state of the art

In the development of today's and in the design of future mobile systems, the channel access method OFDM (Orthogonal Frequency Division Multiplex) plays an important role. OFDM is also used in wireless local area networks (WLAN). The basic principles as well as the advantages and disadvantages of the OFDM technique are described in detail in the standard work R. van Nee, R. Prasad, "OFDM for multimedia communications", Artech House, 2000. As explained on pages 119 through 123 of this book, the ratio of peak to average power ratio (PAPR) for OFDM signals can be very high. When using power-efficient transmit amplifiers, which are typically non-linear, a high PAPR leads to signal distortions and is therefore a serious disadvantage of the OFDM method. To mitigate this disadvantage of the OFDM transmission technique, a number of methods for PAPR reduction of OFDM signals have been proposed in the literature. Most of these methods originate from the two worlds of clipping and data spreading, which until now have been considered as completely disjoint and not in synergetic combinations. This may be due to the fact that clipping is a well-known method even from the days of analog radio transmission technology, while the data spread in OFDM transmission systems is to be assigned to the modern field of digital signal processing. The data spreading is based on not modulating the individual data symbols in each case to a single OFDM subcarrier, but to spread across several or all OFDM subcarriers.

The clipping as a non-linear process has the disadvantage that initially also spectral components outside the frequency band provided for the OFDM transmission arise (out of band power), which must then be eliminated by filtering again, which disadvantage as 1, the desired envelope limitation in part again is nullified (amplitude regrowth) and disadvantage 2 depending on the data to be transmitted unpredictable Einhüllendenmaxima arise. So there is no envelope scaling, so you can not optimize the transmitter-side power amplifier for a fixed maximum amplitude; this goes hand in hand with its reduction in efficiency. In the US 2007/0121483 A1 a clipping method for PAPR reduction is proposed, which counteracts the two disadvantages mentioned, but in particular does not completely avoid the disadvantage 2.

The data spread has the disadvantage that the resulting envelope maxima as in clipping depend on the data to be transmitted, so that you can not optimize the transmitter-side power amplifier for a fixed maximum amplitude here. In the DE 103 17 193 A1 as well as in the US 2006/0067414 A1 A method of data spreading for PAPR reduction is proposed without, however, avoiding the just mentioned disadvantage.

• 1. Das nach der PAPR-Reduktion mit diesen Verfahren auftretende Einhüllendenmaximum des OFDM-Signals ist nicht a priori vorgebbar, sondern es ergibt sich a posteriori. Aufgrund dieses Nachteils ist es nicht möglich, Leistungsverstärker für die mit den bekannten Verfahren PAPR-reduzierten OFDM-Signale unter Vorgabe eines festen Einhüllendenmaximums auszulegen und zu optimieren.
• 2. Der Fokus der bekannten Verfahren liegt ausschließlich auf der PAPR-Reduktion als solcher, obwohl es sinnvoller wäre, die PAPR-Reduktion nicht als Selbstzweck, sondern lediglich als Zwischenstufe im Kontext einer Optimierung der Performanz des gesamten OFDM-Übertragungssystems anzusehen. Deswegen weisen die lediglich mit dem Ziel der PAPR-Minimierung konzipierten, bekannten OFDM-Übertragungsverfahren nicht die bestmögliche Übertragungsqualität auf, quantitativ beispielsweise beschreibbar durch die Detektionsfehlerwahrscheinlichkeit.

The article SH Han, JH Lee, "An overview of peak-to-average power ratio reduction techniques for multicarrier transmission", IEEE Wireless Communications, April 2005, p. 56-65, describes the PAPR reduction methods for OFDM known today. Table 2 of this Review lists these processes and characterizes their benefits and benefits. Not explicitly mentioned in the article two further disadvantages of the known methods for PAPR reduction:

• 1. The envelope maximum of the OFDM signal occurring after the PAPR reduction with these methods can not be predefined a priori, but results a posteriori. Because of this disadvantage, it is not possible to design and optimize power amplifiers for the PAPR-reduced OFDM signals using the known methods while specifying a fixed envelope maximum.
• 2. The focus of the known methods is exclusively on the PAPR reduction as such, although it would be more appropriate to view the PAPR reduction not as an end in itself but only as an intermediate in the context of optimizing the performance of the entire OFDM transmission system. Therefore, the known OFDM transmission methods designed only with the aim of minimizing PAPR do not have the best possible transmission quality, for example, quantitatively describable by the detection error probability.

2 problem and solution

In the following, vectors and matrices are indicated by bold and complex valence by underlining.

• • das es gestattet, das Einhüllendenmaximum des PAPR-reduzierten Signals a priori vorzugeben, und
• • bei dem die PAPR-Reduktion mit einer Optimierung der Performanz der gesamten OFDM-Übertragung einhergehen kann.

The present invention is based on the problem of combining the two methods of clipping and data spreading in a novel, synergistic manner and, by incorporating envelope scaling, predetermine a priori the envelope maximum of the signal subjected to clipping and data spreading in the interest of optimal amplifier design. The object of the invention is thus to reduce the PAPR of an OFDM signal by a method,

• • which allows to specify the envelope maximum of the PAPR reduced signal a priori, and
• • in which the PAPR reduction can be accompanied by an optimization of the performance of the entire OFDM transmission.

möglichen Realisierung

des Datenvektors gegeben ist. Die N_F Komponenten

des Vektors d ^{( r )} repräsentieren die zu übertragenden Daten und werden als Datensymbole bezeichnet; sie entsprechen den komplexen Amplituden der N_F OFDM-Subträger. Mit einer Abbildungsmatrix S ^(s) aus einem Vorrat von S unterschiedlichen, im allgemeinen komplexwertige Matrizen

wird aus dem Datenvektor d ^{( r )} nach (3) der abgebildete Datenvektor

erzeugt. Dieser wird mit der N_F×N_F-Fouriermatrix F in den Vektor

transformiert, aus dem durch D/A-Wandlung das zeitkontinuierliche Signal ũ ^(r,s)(t) entsteht. Dieses Signal wird mit einer aus dem Bereich (0, ∞) gewählten, als Preclipping-Faktor bezeichneten Größe g multipliziert, und das dabei resultierende Signal gũ ^(r,s)(t) wird gemäß

geclippt. Aus u (r,s,g) / cl (t) nach (7) entsteht durch Entfernen der spektralen Anteile außerhalb der OFDM-Bandbreite B nach (1) mittels Tiefpaßfilterung das Signal u (r,s,g) / cl,LP (t), und dieses wird schließlich durch Einhüllenden-Skalierung mit vorgegebenem Einhüllendenmaximum A gemäß

in die komplexe Einhüllende des zu übertragenden OFDM-Symbols umgewandelt. Dieses ergibt sich mit der Trägerfrequenz ƒ_o aus u ^(r,s,g,A)(t) nach (8) durch Tiefpaß-Bandpaß-Transformation als Bandpaßsignal a^(r,s,g,A)(t) = Re{u ^(r,s,g,A)(t)exp(j2πƒ_ot)} (9) This problem is solved by the method of non-linear transformation and envelope scaling specified in claims 1 and 2, and an OFDM symbol of bandwidth consisting of N _F sinusoidal subcarriers of duration T B = N _F / T (1) whose data content with the cardinality M of the modulation alphabet by one of

possible realization

given the data vector. The N _F components

of the vector d ^{( r )} represent the data to be transmitted and are referred to as data symbols; they correspond to the complex amplitudes of the N _F OFDM subcarriers. With an imaging matrix S ^(s) from a supply of S different, generally complex-valued matrices

becomes from the data vector d ^{( r )} to (3) the imaged data vector

generated. This becomes with the N _F × N _F -Fouriermatrix F in the vector

transformed, from which the time-continuous signal ũ ^{(r, s)} (t) is formed by D / A conversion. This signal is multiplied by a quantity g chosen from the range (0, ∞), called the pre-clipping factor, and the resulting signal g ũ ^{(r, s)} (t) is calculated according to

clipped. From u (r, s, g) / cl (t) according to (7), by removing the spectral components outside the OFDM bandwidth B according to (1) by means of low-pass filtering, the signal u (r, s, g) / cl, LP (t), and this is finally determined by envelope scaling with a given envelope maximum A according to

converted into the complex envelope of the OFDM symbol to be transmitted. This results with the carrier frequency ƒ _o from u ^{(r, s, g, A)} (t) according to (8) by low-pass bandpass transformation as a bandpass signal a ^{(r, s, g, A)} (t) = Re {u ^{(r, s, g, A)} (t) exp (j2πƒ _o t)} (9)

For the PAPR of the signal a ^{(r, s, g, A)} (t) according to (9) follows with u ^{(r, s, g, A)} (t) according to (8)

The described options with regard to the mapping matrix S ^{( s )} , the preclipping factor g and the envelope maximum A can be used according to claim 1 for PAPR minimization or according to claim 2 for minimizing the transmission error probability.

• • die Charakteristiken von Sendeverstärker und Sendefilter,
• • die Übertragungsfunktion des Übertragungskanals, der zum Beispiel ein frequenzselektiver Funkkanal sein kann, oder eine statistische Charakterisierung des Übertragungskanals in Form der Scattering Function, und
• • die Charakteristik der Störung, die zum Beispiel ein weißes Bandpaß-Gaußrauschen am Empfängereingang sein kann.

The OFDM signal a ^{(r, s, g, A)} (t) of (9) is sent over the transmission link to the receiver. The transmission path represents the generally interference-prone transmission channel, but also system components can be added to the transmission link. For influencing the signal a ^{(r, s, g, A)} (t) according to (9) through the transmission path, the channel operator Ƙ is introduced. For example, considered

• The characteristics of transmission amplifiers and transmission filters,
• The transmission function of the transmission channel, which may be, for example, a frequency-selective radio channel, or a statistical characterization of the transmission channel in the form of the scattering function, and
• The characteristic of the disturbance, which may be, for example, a white bandpass Gaussian noise at the receiver input.

The fed into the transmission line signal a ^{(r, s, g, A)} (t) according to (9) leads at the output to a signal of the complex envelope u (r, s, g, A, Ƙ) / Rx (t) = Ƙ ( u ^{(r, s, g, A)} (t)). (11)

kann man gemäß Patentanspruch 1 das PAPR minimieren.If the preclipping factor g is selected, the PAPR depends on (10) from the selected imaging matrix S ^{( s )} according to (4). By selecting the imaging matrix S ^{( s )} with the high index

can be minimized according to claim 1, the PAPR.

des gesendeten Datenvektors d ^{( r )} nach (3) mit möglichst geringer Detektionsfehlerwahrscheinlichkeit zu liefern. Im folgenden wird an einem Beispiel erläutert, wie der Empfänger zum Bilden einer solchen Schätzung vorgehen könnte. Es wird angenommen, daß alle R Datenvektoren d ^{( r )} nach (3) mit gleicher Wahrscheinlichkeit 1/R auftreten, und daß das wohlbekannte Maximum-Likelihood(ML)-Schätzverfahren angewandt wird. Nach diesem Verfahren ergibt sich der Hochindex des am wahrscheinlichsten gesendeten Datenvektors zu

The receiver generally has the task of knowing the signal of the complex envelope u (r, s, g, A, Ƙ) / Rx (t) after (11), which outputs the transmission path, an estimate

of the transmitted data vector d ^{( r )} according to (3) with the lowest possible detection error probability. The following is an example of how the receiver could proceed to make such an estimate. It is assumed that all R data vectors d ^{( r )} according to (3) occur with equal probability 1 / R, and that the well-known maximum likelihood (ML) estimation method is used. According to this method, the high index of the most likely sent data vector results

The content of the bracket on the left side of (13) expresses that r ^ depends on the choice of the mapping matrix S ^{( s )} , the preclipping factor g and the envelope maximum A, and the characteristics of the link represented by the channel operator ƙ. With r ^ ^{(s, g, A, Ƙ)} according to (13) one can express the probability of a detection error with transmitted data vector d ^{( r )} as P ^{(r, s, g, A, Ƙ)} = Prob (r ^ ^{(s, g, A, Ƙ)} ≠ r | d ^{(r) is} sent). (14)

kann man gemäß Patentanspruch 2 die Detektionsfehlerwahrscheinlichkeit minimieren.For selected quantities g and A and for a given channel operator Ƙ, P ^{(r, s, g, A, Ƙ)} depends on (14) the choice of the mapping matrix S ^{( s )} according to (4). By choice of the imaging matrix with the high index

can be minimized according to claim 2, the detection error probability.

gemäß

wobei eine jede Zeile und Spalte der Matrizen C^{( s )} eine einzige Eins und ansonsten Nullen enthält. Die nach (16) generierten Abbildungsmatrizen sind reell, und deshalb ist das Symbol S^{( s )} in (16) nicht unterstrichen.Claim 3 describes a simple procedure for forming the imaging matrices as a product of the N _F × N _F Walsh-Hadamard matrix W and in each case one of S different interchange matrices

according to

wherein each row and column of the matrices C ^{( s ) contains} a single one and otherwise zeros. The mapping matrices generated by (16) are real, and therefore the symbol S ^{( s )} in (16) is not underlined.

Particularly advantageous is the formation of the interchangeable matrices by cyclic permutation according to claim 4. Here one chooses S equal to N _F and writes

nach (16) und (17) ist neu und bietet die Vorteile, daß

• • lediglich der Hochindex (n_F) zum Empfänger signalisiert werden muß, um diesen über die verwendete Abbildungsmatrix
  
  zu informieren, und daß
• • die Abbildungsmatrizen
  
  im Empfänger nicht gespeichert werden müssen, sondern dort on-line auf einfache Weise anhand von (16) und (17) generiert werden können.

The generation of N _F image matrices

after (16) and (17) is new and offers the advantages that

• • Only the high index (n _F ) must be signaled to the receiver to this over the used imaging matrix
  
  to inform, and that
• • the image matrices
  
  need not be stored in the receiver, but can be generated there on-line in a simple manner using (16) and (17).

des Datenvektors d ^{( r )} nach (3) enthaltene Information wird über alle N_F Subträger gespreizt, was den schädlichen Einfluß der Frequenzselektivität der Radiokanäle auf die Systemperformanz mildert.The image matrices according to (16) to (17) are fully occupied. This results in an advantageous frequency diversity: that in each component

The information contained in the data vector d ^{( r )} according to (3) is spread over all N _F subcarriers, which mitigates the deleterious effect of frequency selectivity of the radio channels on system performance.

3 Device for applying the method according to the invention

3.1 Preliminary note

Claim 5 relates to a device for applying the method according to the invention, which is explained in more detail with reference to the transmission side and the transmission path of an OFDM transmission system. 1 shows the four-block structure under consideration in the equivalent low-pass range. The blocks 1 to three represent the transmitter, the block 4 the transmission path.

3.2 Selective data images 1

d ^{( r )} after (3) is placed in the block "Selective Data Mapping 1" whose task is to determine the imaged data vector d ^{( r, s )} according to (5).

3.3 Inverse Fourier Transformer and D / A Converter 2

How out 1 As can be seen, the imaged data vector d ^{( r, s )} after (5) in the block "inverse Fourier transformer and D / A converter 2 Entered. At its output, this delivers the low-pass equivalent ũ ^{( r, s )} (t) of the not yet non-linearly transformed and not yet enveloped scaled OFDM symbol from u ^{( r, s )} to (6) by D / A conversion corresponds to the imaged data vector d ^{( r, s )} .

3.4 low-pass limiter three

The internal structure of the block "Tiefpaßbegrenzer three "Covers how out 2 to see, three blocks. The block "Clipper 5 "Performs the operation (7). The block "low-pass filter 6 "Forms the above introduced signal u (r, s, g) / cl, LP (T). This is placed in the block "Encapsulation Scaler 7 At the output of which the signal u ^{( r, s, g, A )} (t) according to (8) is present.

3.5 transmission path 4

The block "Transmission line 4 "Represents the generally interference-prone transmission channel characterized by the operator Ƙ introduced above, but may additionally include, for example, the transmission amplifier and the transmission filter, and performs the operation (11).

Claims (6)

Method for non-linear transformation and envelope scaling of an OFDM symbol of bandwidth B consisting of N _F sinusoidal subcarriers, the data content of which is connected to the cardinality M of the modulation alphabet by one of the

possible realization

given the data vector whose N _F components

represent the data symbols to be transmitted and correspond to the complex amplitudes of the N _F subcarriers, characterized in that a matrix to be selected from a set { S ⁽¹⁾ ... S ^(S) } of S different mapping matrices of dimension N _F × N _F S ^{( s )} from the data vector d ^{( r )} to (A2) the imaged data vector

is formed, this with the Fourier matrix

in the vector

is transformed from u ^{(r, s)} to (A4) by D / A conversion, the time-continuous signal ũ ^{(r, s)} (t) is formed, this with a selected from the range (0, ∞), as a preclipping Factor g is multiplied, the resulting signal g ũ ^{(r, s)} (t) is clipped according to

from u (r, s, g) / cl (t) after (A5) by removing the spectral components outside the OFDM bandwidth B by means of low-pass filtering the signal u (r, s, g) / cl, LP (t) is generated, and from this finally with a selected envelope maximum A the complex envelope

is formed from the set { S ⁽¹⁾ ... S ^(S) } after the selection of the preclipping factor g that image matrix S ^{( s )} and in (A3) is used, the minimizes the PAPR of the OFDM symbol with the complex envelope u ^{(r, s, g, A)} (t) to (A6). Method for non-linear transformation and envelope scaling of an OFDM symbol of bandwidth B consisting of N _F sinusoidal subcarriers, the data content of which is connected to the cardinality M of the modulation alphabet by one of the

possible realization

given the data vector whose N _F components

represent the data symbols to be transmitted and correspond to the complex amplitudes of the N _F subcarriers, characterized in that a matrix to be selected from a set { S ⁽¹⁾ ... S ^(S) } of S different mapping matrices of dimension N _F × N _F S ^{( s )} from the data vector d ^(r) to (A8) the imaged data vector

is formed, this with the Fourier matrix

in the vector

is transformed from u ^{(r, s)} to (A10) by D / A conversion, the time-continuous signal ũ ^{(r, s)} (t) is formed, this with a selected from the range (0, ∞), as a preclipping Factor g is multiplied, the resulting signal g ũ ^{(r, s)} (t) is clipped according to

from u (r, s, g) / cl (t) after (All) by removing the spectral components outside the OFDM bandwidth B by means of low-pass filtering the signal u (r, s, g) / cl, LP (t) is generated, and from this finally with a selected envelope maximum A the complex envelope

is formed from the set { S ⁽¹⁾ ... S ^(S) } after the selection of the preclipping factor g that image matrix S ^{( s )} and in (A9) is used, the Minimum detection error probability results in the receiver-side detection of the OFDM symbol of the complex envelope fed into the transmission link u ^{(r, s, g, A)} (t) to (Al2). Method according to one of the claims 1 or 2, characterized in that the set of mapping matrices consists of S real matrices S ^{( s )} consisting of the N _F × N _F Walsh-Hadamard matrix W and one of S different commutation matrices

is formed according to

wherein each row and column of the matrices C ^{( s ) contains} a single one and otherwise zeros. Method according to Patent Claim 3, characterized in that the set of mapping matrices consists of N _F real matrices

and the interchange matrices according to

be formed. Apparatus for nonlinear transformation and envelope scaling of an OFDM symbol of bandwidth B consisting of N _F sinusoidal subcarriers, the data content of which is connected to the cardinality M of the modulation alphabet by one of the

possible realization

given the data vector whose N _F components

represent the data symbols to be transmitted and correspond to the complex amplitudes of the N _F subcarriers, characterized in that a block "Selective Data Mapping 1 With a matrix S ^{( s )} selected from a set { S ⁽¹⁾ ... S ^(S) } of S different mapping matrices of the dimension N _F × N _F from the data vector d ^(r) according to (A16) the imaged data vector

Form this into a block "Inverse Fourier Transformer and D / A Converter 2 "Is input, with the Fourier matrix

the vector d ^{(r, s)} to (A17) in the vector

transformed from u ^{(r, s)} to (A18) by D / A conversion, the time-continuous signal ũ ^{(r, s)} (t) forms and in a block "Tiefpaßbegrenzer three "Which multiplies the signal ũ ^{(r, s)} (t) by a variable g selected from the range (0, ∞), called a preclipping factor, the resulting signal g ũ ^{(r, s)} (t) clipped according to

from u (r, s, g) / cl (t) after (A19) by removing the spectral components outside the OFDM bandwidth B by means of low-pass filtering the signal u (r, s, g) / cl, LP (t), and from this finally with a selected envelope maximum A the complex envelope

forms and outputs the OFDM symbol to be transmitted, wherein from the set { S ⁽¹⁾ ... S ^(S) } after the selection of the preclipping factor g, that imaging matrix S ^{( s ) is} selected and used in (A17), which minimizes the PAPR of the OFDM symbol with the complex envelope u ^{(r, s, g, A)} (t) to (A20). Apparatus for nonlinear transformation and envelope scaling of an OFDM symbol of bandwidth B consisting of N _F sinusoidal subcarriers, the data content of which is connected to the cardinality M of the modulation alphabet by one of the

possible realization

given the data vector whose N _F components

represent the data symbols to be transmitted and correspond to the complex amplitudes of the N _F subcarriers, characterized in that a block "Selective Data Mapping 1 With a matrix S ^{( s )} selected from a set { S ⁽¹⁾ ... S ^(S) } of S different mapping matrices of the dimension N _F × N _F from the data vector d ^(r) according to (A22) the imaged data vector

Form this into a block "Inverse Fourier Transformer and D / A Converter 2 "Is input, with the Fourier matrix

the vector d ^{(r, s)} after (A23) in the vector

transformed from u ^{(r, s)} to (A24) by D / A conversion, the time-continuous signal ũ ^{(r, s)} (t) forms and in a block "Tiefpaßbegrenzer three ", Which multiplies the signal ũ ^{(r, s)} (t) by a quantity g selected from the range (0, ∞), referred to as the preclipping factor, and clips the resultant signal g ũ ^{(r, s)} (t) according to

from u (r, s, g) / cl (t) after (A25) by removing the spectral components outside the OFDM bandwidth B by means of low-pass filtering the signal u (r, s, g) / cl, LP (t), and from this finally with a selected envelope maximum A the complex envelope

forms and outputs the OFDM symbol to be transmitted, wherein from the set { S ⁽¹⁾ ... S ^(S) } after the selection of the preclipping factor g that image matrix S ^{(s) is} selected and used in (A23), the minimum detection error probability results in the receiver-side detection of the OFDM symbol of the complex envelope fed into the transmission link u ^{(r, s, g, A)} (t) according to (A26).

Images