The invention is based on a priority application EP 04293042.0 which is hereby incorporated by reference.
The present invention relates to a method of coding data, wherein a coding signal is used for coding data symbols, said coding signal comprising an orthogonal component and an error component, wherein a transmission signal depending on said data symbols and said coding signal is obtained by said coding, wherein the transmission signal is preferably obtained according to the equation
wherein ψn(ƒ) is the coding signal and N is the number of data symbols (d1, d2, . . . , dN) to be coded.
The present invention also relates to a transmitter comprising means for coding data symbols in order to obtain a transmission signal depending on said data symbols and a coding signal.
Coding methods of the aforementioned kind are applied in contemporary data transmission systems, and orthogonality conditions relating to the coding signal are used for decoding data previously so coded.
More specifically, such coding methods are for instance used within orthogonal code division multiplexing (OCDM) systems and orthogonal frequency division multiplexing (OFDM) systems.
When implementing the above coding methods on computer systems, an undesired error component is introduced to the coding signal due to the finite precision of computer systems leading to a wrong data representation of values of the coding signal. This error component can e.g. be represented by an addend to the solely desired orthogonal component of the coding signal and leads to a violation of the orthogonality conditions, as far as the aggregate coding signal, i.e. the sum of the orthogonal component and the error component is concerned. I.e., the aggregate coding signal does no longer satisfy said orthogonality conditions.
The coding signal may e.g. be represented as
ψn(ƒ)=ψn0(ƒ)+Δψn(ƒ),
wherein ψn0(ƒ) denotes the orthogonal component and Δψn(ƒ) denotes the error component of said coding signal.
Using such a prior art coding method and signal within transmission and/or communication systems leads to inter-symbol interference (abbr.: ISI), wherein the absolute value of the ISI corresponds to the degree of violation of the respective orthogonality conditions.
In view of these disadvantages of contemporary coding methods, it is an object of the present invention to provide an improved method of coding data that avoids ISI.
According to the present invention, this object is solved for a coding method of the above mentioned type by determining a correction function and by applying said correction function to said transmission signal in order to obtain a corrected transmission signal.
Thus it is possible to reduce or even eliminate ISI which reduces errors when decoding the inventive corrected transmission signal.
According to an advantageous embodiment of the present invention, said step of applying the correction function is preferably performed by adding and/or subtracting said correction function to/from said transmission signal, which requires only few computational resources and which does not introduce further unnecessary e.g. numerical errors. It is also possible to apply the correction function to the transmission signal by multiplication. However, in this case, an approach of determining the correction function might be more complicated as compared to an approach of adding the correction function to the transmission signal.
A further advantageous embodiment of the present invention is characterized by determining said correction function depending on the coding signal, in particular depending on the error component (Δψn(ƒ)) of the coding signal (ψn(ƒ)).
According to another advantageous embodiment of the present invention, said method is characterized in that said correction function is determined depending on an ISI-term corresponding to an inter-symbol interference (ISI) that occurs when coding said data symbols. Preferably, said correction function is determined so as to minimize the ISI-term.
Yet another advantageous embodiment of the present invention is characterized in that said orthogonal component ψn0(ƒ) of said coding signal ψn(ƒ) satisfies an orthogonality condition, in particular the orthoquality condition
wherein k,n=1, . . . , N, wherein Hk(ƒ) is the Hermite polynomial of k-th order, χk is a known constant, and wherein δnk is the Kronecker symbol.
The Hermite polynomial may be written as
Instead of using Hermite polynomials, according to a further advantageous embodiment of the present invention any other set of orthogonal functions may also be employed to define the coding signal, or its orthogonal component, respectively. In this case, of course, a corresponding orthogonality condition must be used that fits to the respective coding signal.
According to a further advantageous embodiment of the present invention, the ISI-term εk is obtained according to the equation
wherein Hk(ƒ) is the Hermite polynomial of k-th order, Δψn(ƒ) is said error component, and wherein
constitutes said correction function.
A further solution to the object of the present invention is given by a transmitter comprising means for coding data symbols (d1, d2, . . . , dN) in order to obtain a transmission signal (S(ƒ)) depending on said data symbols (d1, d2, . . . , dN) and a coding signal (ψn(ƒ)), characterized by further comprising predistortion means capable of determining a correction function (ξ(ƒ)) and of applying said correction function (ξ(ƒ)) to said transmission signal (S(ƒ)) in order to obtain a corrected transmission signal (Spd(ƒ)).
Further applications, features and advantages of the present invention are described in the following detailed description with reference to the drawings, in which
a depicts results corresponding to the inventive coding method,
b depicts further results corresponding to the inventive coding method, and
According to a first embodiment of the present invention, a coding signal
ψn(ƒ)=ψn0(ƒ)+Δψn(ƒ), (equation 1)
is used for coding data, wherein ψn0(ƒ) denotes an orthogonal component and Δψn(ƒ) denotes an error component of said coding signal ψn(ƒ).
The orthogonal component ψn0(ƒ) satisfies the orthogonality condition
wherein k,n=1, . . . , N, wherein Hk(ƒ) is the Hermite polynomial of k-th order, χk is a known constant, and wherein δnk is the Kronecker symbol.
The error component Δψn(ƒ) symbolizes a deviation of the coding signal ψn(ƒ) from an ideal coding signal ψn,ideal(ƒ), which solely comprises an orthogonal component:
ψn,ideal(ƒ)=ψn0(ƒ).
Said error component Δψn(ƒ) of the coding signal ψn(ƒ)=ψn0(ƒ)+Δψn(ƒ) is e.g. due to a data representation of said ideal coding signal ψn,ideal(ƒ) by means of data types such as used within a computer system or a digital signal processor (DSP), respectively, which offer finite precision.
The data to be coded is provided in form of data symbols d1, d2, . . . , dN, each of which comprises a data word length of e.g. 18 bit, and a transmission signal S(ƒ) according to
is obtained by said coding. Said transmission signal S(ƒ) is given in the frequency domain in the present example and depends on said data symbols d1, d2, . . . , dN as well as on said coding signal ψn(ƒ).
In order to obtain the coded data symbols e.g. withina receiver, the already above described orthogonality condition
of equation 2 is used, wherein decoded symbols Tk, k=1, . . . , N, are obtained according to the following equation:
In the ideal case, i.e. when using the ideal coding signal
ψn,ideal(ƒ)=ψn0(ƒ),
an ideal transmission signal
and thus ideally decoded data symbols Tk,ideal, k=1, . . . , N, under ideal conditions of infinite precision may be obtained:
wherein χk=const. and k=1, . . . , N I.e., in the ideal case with a vanishing error component Δψn(ƒ)=0, a perfect reconstruction by decoding said ideal transmission signal Sideal(ƒ) in the above way is possible:
Within real applications, there is usually a nonvanishing error component Δψn(ƒ) which leads to the following term when coding/decoding according to prior art methods:
In difference to the ideal case, wherein the decoded symbols can be obtained with the equation
in the real case there is an unwanted term εk according to equation 5, which is denoted as a so-called ISI-term εk for the further description, since it symbolizes an unwanted inter-symbol interference that is occurring in the real case when using prior art coding methods.
Said ISI-term εk is particularly disadvantageous when using modulation schemes of higher order and impairs a correct decoding of data symbols.
Accordingly, the coding method of the present invention comprises determining a correction function ξ(ƒ) which is applied to the transmission signal S(ƒ) and which effects a predistortion of the transmission signal S(ƒ) whereby a corrected transmission signal Spd(ƒ) is obtained:
Said inventive correction function ξ(ƒ) is determined in order to reduce or even eliminate said unwanted ISI-term εk thus enabling a correct decoding of coded data symbols.
For determining the inventive correction function ξ(ƒ), the following approach is adopted:
The decoding of a corrected transmission signal Spd(f) leads to decoded data
k=1, . . . , N, which, as in the ideal case, does not comprise an ISI-term εk.
As a consequence of using the inventive corrected transmission signal Spd(f), it is thus obtained
which leads to
by using equation 4 which is described above.
Consequently, for the ISI-term εk it is found that:
if Tk,pd=χk dk as demanded for a decoding without an influence of the ISI-term εk.
When comparing equation 5 with equation 6,
it can be seen that
i.e. said inventive correction function ξ(ƒ) depends on the data symbols dn and the error component Δψn(ƒ).
For calculating the inventive correction function ξ(ƒ), equations 4 and 6 are used:
wherein by means of discrete integration the equation
is obtained which leads to the equation system:
Hk(ƒ1)ξ(ƒ1)+Hk(ƒ2)ξ(ƒ2)+ . . . +Hk(ƒL)ξ(ƒL)=γk, k=1,2, . . . , N (equation 8)
with
The discrete integration used to obtain equation 7 generally enables to replace the integral term
comprising a function u(f) by the term
as long as u(f) is nonzero only within a certain range −ƒg≦ƒ≦+ƒg and u(f) is only defined for discrete values of the variable f, wherein Δƒ=ƒl+1−ƒl=const. for l=1, . . . , L−1, which in the present example holds true for Hk(f) ξ(f).
Since there are L many unknowns ξ(ƒ1), . . . , ξ(ƒL) within equation system 8, L equations are required for solving the equation system. However, as can be seen from equation 7, there are only N many unknowns to be dealt with because of k=1, . . . , N; thus it is sufficient to consider only N many unknowns, e.g. the N first unknowns ξ(ƒ1), . . . , ξ(ƒN), of equation system 8. The remaining unknowns ξ(ƒN+1), . . . , ξ(ƒL) can be set to zero. Accordingly, a simplified equation system is obtained:
Hk(f1)ξ(f1)+Hk(f2)ξ(f2)+ . . . +Hk(fn−1)ξ(fN−1)+Hk(fN)ξ(fN)=γk (equation 9)
After solving the above equation system, the values ξ(ƒ1), . . . , ξ(ƒN) of the correction function ξ(ƒ) are known and can be used to correct the transmission signal S(f) according to:
Consequently, by using the corrected transmission signal, the ISI-term εk can be minimized, cf. equation 6.
A further embodiment of the present invention is characterized by a coding signal
Ψn(ƒ)=Hn(ƒ)·e−ƒ
i.e. ψn0(ƒ)=Hn(ƒ)e−ƒ
The present embodiment is further characterized by said transmission Signal S(f) comprising two sub-signals I(f) and Q(f), which may e.g. represent an in-phase component I(f) of the transmission signal S(f) and a quadrature component Q(f), respectively:
S(ƒ)=I(ƒ)+iQ(ƒ), (equation 10)
wherein said sub-signals I(f) and Q(f) are defined within a frequency range f=μ[−ƒg,−ƒg+Δƒ,−ƒg+2Δƒ,−ƒg+3Δƒ, . . . , 0,Δƒ, . . . , +ƒg], ƒg=2.5 MHz, wherein μ constitutes a parameter that may be re-calculated.
Said frequency range f may also be denoted as f={ƒ1, ƒ2, . . . ƒL}, wherein L may e.g. be 16 or 32. The sub-signal I(f) is determined by data symbols and Hermite polynomials having an odd index:
whereas the sub-signal Q(f) is determined by data symbols and Hermite polynomials having an even index:
In order to decode the data symbols dn, n=1,3, . . . Nodd and dn, n=2,4, . . . , Neven, respectively, the following equations must be considered for I(f) and Q(f), respectively:
Thus, for the correction functions ξI(ƒ), ξQ(ƒ) is found:
and consequently, after solving the respective equation system for ξI(ƒ1), . . . , ξI(ƒN) and ξQ(ƒ1), . . . , ξQ(ƒN), which can be accomplished in analogy to solving equation system 8 as described above, corrected sub-signals I(f) and Q(f) and thus the corrected transmission signal Spd(ƒ) can be obtained:
Spd(ƒ)=S(ƒ)−ξ(ƒ)=I(ƒ)+iQ(ƒ)−ξI(ƒ)−iξQ(ƒ)
a depicts results corresponding to the inventive coding method applied to the sub-signal I(f) as used in the aforedescribed embodiment of the present invention in comparison with results achieved by prior art. The results are given in form of a table which contains in its first column an index number i ranging from 1 to 10 and denoting one of ten specific data symbols d1 to d10, which are presented in the second column denoted “di” of said table.
The third column of the table shown in
Even for data symbol values of zero, i.e. for d5 to d10 according to column 2 of
When coding the data symbols of column 2 according to the inventive method, i.e. by applying the inventive correction function ξI(ƒ), the decoding yields data symbol values as given in column 4 of
Column 5 shows the data symbol values of column 4 rounded to zero decimals, which are equal to the respective values of column 2. Notably, even for the data symbols d5 to d10, having a value of zero, the corresponding values of column 4 or 5 show no deviation, which is due to the inventive suppression of inter-symbol interference by using the correction function ξI(ƒ).
Similar to
A graphical representation of the results according to the table of
The present invention is not limited to using Hermite polynomials. Instead of using Hermite polynomials, according to a further advantageous embodiment of the present invention any other set of orthogonal functions may also be employed to define the coding signal, or its orthogonal component, respectively. In this case, of course, a corresponding orthogonality condition must be used that fits to the respective coding signal.
According to another embodiment of the present invention, it is also possible to define an in-phase component I(f) of the transmission signal S(f) and a quadrature component Q(f) according to
wherein 2*N many data symbols dnI, n=1, . . . , N, dnQ, n=1, . . . , N may be coded which leads to the transmission signal
S(ƒ)=I(ƒ)+iQ(ƒ).
Coding said 2*N many data symbols in the above described manner, i.e. particularly by using the same coding signal Ψn(ƒ) for each sub-signal I(f), Q(f) can be performed since said in-phase component I(f) and said quadrature component Q(f) do not influence each other when forming said transmission signal S(f), because I(f) constitutes the real part of the transmission signal S(f) and Q(f) constitutes the imaginary part of the transmission signal S(f), and said real part and said imaginary part may be considered separately as far as coding by using the inventive method is concerned.
Number | Date | Country | Kind |
---|---|---|---|
04293042.0 | Dec 2004 | EP | regional |