METHOD FOR THE DIGITAL COMPENSATION OF NONLINEARITIES IN A COMMUNICATION SYSTEM AND RECEIVER DEVICE

Abstract

Method for the digital compensation of nonlinearities in a communication system that includes a transmitter, a transmission channel and a receiver, comprising:

Description

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be better understood by reading the description of embodiments given purely by way of illustration and in no way limitative respectively with reference to the appended drawings in which:

FIG. 1 shows a time-based operation of a method for the digital compensation of nonlinearities in a communication system,

FIG. 2 shows real AM-AM and AM-PM characteristics of an amplifier and the approximation of the AM-AM and AM-PM characteristics obtained under the method for the digital compensation of nonlinearities,

FIG. 3 shows a Lagrange interpolating polynomial obtained under the method for the digital compensation of nonlinearities,

FIGS. 4A and 4B show results of a compensation simulation of AM-AM and AM-PM characteristics,

FIG. 5 shows the gain in terms of bit error rate obtained by the method for the digital compensation of nonlinearities,

FIG. 6 shows a communication system comprising a receiver device.

Identical, similar or equivalent parts of the different figures described hereinafter carry the same digital references so as to facilitate moving between one figure and the next.

DETAILED DISCLOSURE OF PARTICULAR EMBODIMENTS

Reference is made first of all to FIG. 1 which shows a time-based operation of a method for the digital compensation of non-linearities in a communication system 300 according to a particular embodiment, in combination with FIG. 6 showing the communication system 300 comprising a receiver device 100, such as a base station. In this embodiment, the method is applied to a wireless communication system 300 with OFDM type modulation between a mobile terminal 200 and a base station 100. But an embodiment of the invention may also apply to other systems of the single carrier or ultra broadband type, between any transmitter and any receiver.

In the example in FIGS. 1 and 6, a power amplifier 2 found at the mobile terminal end 200 is considered as the single source of nonlinearities in the whole communication system 300. But an embodiment of the invention allows other sources of nonlinearities to be compensated in the communication system 300, at the transmitter 200 and/or receiver 100 end, such as for example those due for example to a low noise amplifier, a variable gain amplifier, a mixer etc.

The signals considered here are complex and sampled in the time or frequency domain.

Let s be a signal intended to be amplified by the power amplifier 2 and emerging from the amplifier 2 in the form s1 before being transmitted in a transmission channel 4. In the time domain, we have:

s ₁(t)=g(∥s(t)∥).s(t)   (1)

where g is the amplifier gain.

g is a function of the amplitude of the input signal s. This gain g may modify the amplitude and/or the phase of the input signal s in a non-linear way, introducing nonlinearities into the communication system 300 when the AM-AM characteristic, in other words the curve of the output signal amplitude as a function of the input signal amplitude, and/or the AM-PM characteristic, in other words the curve of the output signal phase as a function of the input signal amplitude, of the gain element g, here the amplifier 2, is not linear.

In the frequency domain, S1 is the result of the convolution between the gain G of the amplifier 2 and the incoming signal S in the amplifier:

S ₁(f)=G(S(f))*S(f)   (2)

The amplified signal S1 is then transmitted by one or more antennae, and passes into the transmission channel 4. At the output of the transmission channel 4 a signal S2 is obtained such that:

S ₂(f)=H(f).S₁(f)+η(f)   (3)

where H stands for the transmission characteristic of the channel 4 in the frequency domain and η an additive white gaussian noise.

In this embodiment, prior to the transmission of the information signal S, at least one first learning sequence, or pilot, is used to estimate the characteristic of the channel 4. To do this, P1 follows the same transmission path as the information signals to be transmitted, in other words being firstly subject to an amplification stage by the power amplifier 2, then a passing through of the transmission channel 4. On reception, in other words at the output of the transmission channel 4, P1 is subject, in this embodiment, to a fast Fourier transform (FFT) (reference 6 in FIG. 1) so as to move P1 into the frequency domain. In FIG. 6, this FFT is implemented using fast Fourier transform means 102. This FFT is the example used where an OFDM system is involved, as is the case in this embodiment.

After this FFT, the characteristic of the channel 4 is then subject to estimation 8. This estimation is implemented using channel characteristic estimation means 104. The amplitude of P1 is chosen preferably to be substantially constant or of small dynamic, in other words having a low PAPR (Peak to Average Power Ratio). Only the P1 phase changes. In this way, the nonlinearities present in the communication system 300 do not bias the estimation of the channel 4, since in that way, they have no or little influence over P1. The channel 4 is estimated by measuring, frequency by frequency, the difference between the sequence received at the output of the channel 4 and the initial learning sequence P1. For example, in the case of an OFDM system, the characteristic of the channel 4 is obtained directly from the ratio between the received sequence and the initial learning sequence P1, this sequence being for example an alternate set of symbols of values +1 and −1.

The nonlinearities present in the communication system 300 are subject to estimation 10, after the channel 4 estimation is obtained. In the example in FIGS. 1 and 6, the estimated nonlinearities are those of the power amplifier 2. This estimation 10 of nonlinearities consists in determining interpolation points of the AM-AM characteristic and/or of the AM-PM characteristic of the amplifier 2.

To do this, at least one pilot P2 is first amplified by the power amplifier 2 then sent through the transmission channel 4. Given that the communication system is of the OFDM type, the pilot P2 is subject to an FFT 6 by the FFT means 102, as previously for P1 during the estimation of the channel 4. This estimation 10 is implemented using nonlinearities estimation means 106.

To implement the estimation 10 of the nonlinearities, an orthonormal base of projection polynomials {p₀,p₁, . . . ,p_n} is first calculated. This base is obtained from moments of the amplitude of the learning sequences or pilots transmitted, in other words from moments of the amplitude of initial P2 before it is sent through the power amplifier 2 and the channel 4.

After P2 has been subject to the FFT 6, coefficients {cA₀,cA₁, . . . ,cA_n} of the AM-AM characteristic and/or coefficients {cφ₀,cφ₁, . . . ,cφ_n} of the AM-PM characteristic can be determined by projecting P2 on the orthonormal base {p₀,p₁, . . . ,p_n}. These coefficients allow nonlinearities approximation to be obtained such that:

ĝ(∥x∥)=(cA₀p₀(∥x∥)+cA₁p₁(∥x∥)+. . . cA_np_n(∥x∥)exp(j*(cφ₀p₀(∥x∥)+cφ₁p₁(∥x∥)+ . . . cφ_np_n(∥x∥)))   (4)

This projection allows a good estimation of the whole nonlinearities characteristic to be obtained despite the presence of noise in the channel 4.

Lastly, from this approximation, the interpolation points of coordinates b_i=ĝ(a_i) of the nonlinearities characteristic ĝ are calculated.

The different amplitudes of the symbols forming the learning sequence P2 will be selected so as to cover as far as possible the whole dynamic of the amplitude of the signals transmitted subsequently by the communication system 300, so as to take into account all the nonlinearities sustained by the signals transmitted through the communication system 300.

The estimation of the AM-AM characteristic will now be specified.

Prior to calculating the orthonormal base of projection polynomials {p₀,p₁,p_n}, it is appropriate to define a scalar product adapted to the vector space formed by this orthonormal base.

In the time domain, the scalar product associated with this orthonormalisation is the expected product over a certain observation time T, such that:

U,V =E[u(t)v(t)]_ε[0,T]  (5)

For a system sampled at

$T_e=\frac{T}{N}\text{:}$

$\begin{array}{cc}〈u,v〉=\sum _{k=0}^Nu\left(k\right)v\left(k\right)& \left(6\right)\end{array}$

In the frequency domain, the scalar product associated with this orthonormalisation is the expected convolution product over a certain observation frequency band B, such that:

U,V =E[U(f)*V(f)*V(f)]_fε[0,B]  (7)

For a system sampled at F_e=F*N:

$\begin{array}{cc}〈U,V〉=\sum _{k=0}^NU\left(k\right)V\left(k\right)& \left(8\right)\end{array}$

This scalar product selected is in fact a bilinear, symmetrical and defined positive function.

An orthonormal base of projection polynomials {p₀,p₁, . . . ,p_n} can be obtained by the Gram-Schmidt method for the orthonormalisation of a base {1,x,x²,x³, . . . ,xⁿ}.

Here for example are the first three polynomials obtained for the orthonormal base in the time domain:

$p_0\left(x\right)=1$ $p_1\left(x\right)=\frac{x-〈p_0,p〉p_0\left(x\right)}{x-〈p_0,p〉p_0\left(x\right)}=\frac{x-{\chi }_1}{\sqrt{{\chi }_2-{\chi }_1}}$ $\begin{array}{c}{p}_2\left(x\right)=\frac{x^2-〈p_0,p^2〉p_0\left(x\right)-〈p_1,p^2〉p_1\left(x\right)}{x^2-〈p_0,p^2〉p_0\left(x\right)-〈p_1,p^2〉p_1\left(x\right)}\\ =\frac{x^2-\left({\chi }_3-{\chi }_2{\chi }_1\right)x+\left(\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_1-{\chi }_2\right)}{\begin{array}{c}\sqrt{{\chi }_4+{\left({\chi }_3-{\chi }_2{\chi }_1\right)}^2}+\\ {\left(\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_1-{\chi }_2\right)}^2-\\ 2\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_2+2{\chi }_2\left(\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_1-{\chi }_2\right)-\\ 2\left(\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_1-{\chi }_2\right)\left({\chi }_3-{\chi }_2{\chi }_1\right){\chi }_1\end{array}}\end{array}$

With χ₁=E[p], χ₂=E[p²], χ₃=E[p³], χ₄=E[p⁴] the moments of p, in other words the moments of the amplitude of initial P2 before it is sent through the amplifier 2.

For an estimation in the frequency domain, an orhonormal base is constructed in the same way taking the formulas (7) and (8) for the scalar product calculations.

The number of polynomials forming this orthonormal base is selected as a function of the precision required in respect of estimating nonlinearities, and of the complexity of the algorithm generated by a large number of polynomials.

The channel estimation 8 implemented previously is then used to obtain y(t), the amplitude of P2 corrected by the effects of the transmission channel 4. In this way, an amplitude y(t) of the pilot P2 affected solely by the nonlinearities of the amplifier 2 is obtained.

The nonlinearities characteristic is then estimated by projecting y(t) on the orthonormal time or frequency base, previously calculated. The coefficients {cA₀,cA₁, . . . ,cA_n} of the AM-AM characteristic are obtained by:

cA_k=∥y∥,p_k  (9)

The calculation of the nonlinearities approximation for the AM-AM characteristic may therefore be:

$\begin{array}{cc}g\widehat{\left(s\right)}=\sum _{k=0}^n〈y,p_k〉p_k\left(s\right)=\sum _{k=0}^n{\mathrm{cA}}_kp_k\left(s\right)& \left(10\right)\end{array}$

In order to be able to use this approximation, a certain number of interpolation points of the nonlinearities characteristic ĝ is calculated. 5 interpolation points may for example be selected.

Let {a₁,a₂, . . . ,a_m} be the abscissas and {b₁,b₂, . . . ,b_m} the ordinates of the interpolation points of the AM-AM characteristic.

In order to obtain a good description of the nonlinearities of the power amplifier 2, the a_i may be chosen so as to have a majority of the interpolation points corresponding to the low amplitudes of the AM-AM characteristic, for example by distributing them exponentially.

In this embodiment, the ordinates of these interpolation points are given by the equation:

$\begin{array}{cc}{b}_i=\widehat{g\left(a_i\right)}=\sum _{k=0}^n{\mathrm{cA}}_kp_k\left(a_i\right)=\sum _{k=0}^n〈y,p_k〉p_k\left(a_i\right)& \left(11\right)\end{array}$

The P_k(x) and P_k(a_i) may be calculated previously from the pilot P2 used, and the abscissas of the interpolation points a_i, a multiplication-accumulation then allowing the b_i to be obtained.

The interpolation points are therefore obtained at the cost of low complexity. This projection makes it possible to use all available samples of y(t), thereby obtaining a robust to noise estimation of nonlinearities.

In order to obtain an estimation of the AM-PM characteristic, by choosing the same orthonormal time base, the phase difference φ(t) is projected between the learning sequences, or pilots, received and transmitted, on this orthonormal base.

In a way similar to the AM-AM characteristic, the calculation of the nonlinearities approximation for the AM-PM characteristic may therefore be:

$\begin{array}{cc}\mathrm{angle}\left(\hat{g}\left(s\right)\right)=\sum _{k=0}^n〈\varphi ,p_k〉p_k\left(s\right)=\sum _{k=0}^nc{\varphi }_kp_k\left(s\right)& \left(12\right)\end{array}$

Let {c₁,c₂, . . . ,c_n} be the abscissas and {d₁,d₂, . . . ,d_n} the ordinates of the interpolation points of the AM-PM characteristic.

In this embodiment, the ordinates of these interpolation points are given by the equation:

$\begin{array}{cc}{d}_i=\mathrm{angle}\left(\hat{g}\left(c_i\right)\right)=\sum _{k=0}^nc{\varphi }_kp_k\left(c_i\right)=\sum _{k=0}^n〈\varphi ,p_k〉p_k\left(c_i\right)& \left(13\right)\end{array}$

In order to obtain a good description of the nonlinearities of the power amplifier, the abscissas c_i of the in-phase characteristic may also be chosen so as to have more points for the low amplitudes, for example by distributing them exponentially.

To obtain both the AM-AM and AM-PM characteristics, it is possible either to project amplitude and phase of the received pilot successively according to the equations (10) and (12) or to use an orthonormal base of the space of the complex polynomials for the norm considered.

According to this variant, the Gram-Schmidt orthonormalisation is then carried out from a base {1,x,x*,x²,xx*, . . . }. The complex pilot received can then be projected directly on this base.

The nonlinearities approximation is therefore in this case:

$\begin{array}{cc}\begin{array}{c}\widehat{g\left(s\right)}=\widehat{g\left(s\right)}\exp \left(j·\mathrm{angle}\left(\widehat{g\left(s\right)}\right)\right)\\ =\sum _{k=0}^n〈y.\exp \left(\mathrm{j\varphi }\right),p_k\left(s\right)〉p_k\left(s\right)\end{array}\widehat{g\left(s\right)}=\left(\sum _{k=0}^n{\mathrm{cA}}_kp_k\left(s\right)\right)\exp \left(j*\left(\sum _{k=0}^nc{\varphi }_kp_k\left(s\right)\right)\right)& \left(14\right)\end{array}$

The interpolation points obtained are then also complex.

FIG. 2 shows the approximation of the AM-AM and AM-PM characteristics ordained by projection on an orthonormal base of three polynomials of a learning sequence of 64 time samples distorted at transmission by a Solid State Power Amplifier (SSPA). The curve 1 shows the real AM-AM characteristic. From 4 interpolation points 3a to 3d, the approximation of the AM-AM characteristic shown by the curve 5 is obtained. In FIG. 2 it can be seen that the approximation of the AM-AM characteristic 5 is almost superimposed over the real AM-AM characteristic 1. A similar result is obtained for the AM-PM characteristic, the curve 7 representing the real AM-PM characteristic and the curve 11 representing the approximation of the AM-PM characteristic obtained by the interpolation points 9a to 9d. The approximation of the AM-PM characteristic 11 obtained is almost superimposed over the real AM-PM characteristic 7.

Since the nonlinearities are estimated, it is now possible to implement compensation 12 for the nonlinearities sustained by an information signal s transmitted in the communications system 300.

The nonlinearities can be compensated immediately after the analogue-to-digital conversion of the signal in the communication system 300, after the transmission of signal s in the channel 4. This signal is denoted s₂(t) in FIG. 1. In FIG. 6, the signal received is sent to nonlinearities compensation means 108.

It is possible to implement a compensation for the AM-AM characteristic, and then a compensation for the AM-PM characteristic.

In this case, an interpolating polynomial, for example a Lagrange polynomial, is calculated, using the interpolation points (a_i,b_i) to invert characteristic in amplitude of the amplifier 2. The following signal is then obtained:

$\begin{array}{cc}{s}_3^{\prime }\left(t\right)=\sum _{j=1}^ma_j\prod _{i\ne j}\frac{s_2\left(t\right)}{b_j-b_i}\exp \left(j·\mathrm{angle}\left(s_2\left(t\right)\right)\right)& \left(15\right)\end{array}$

The abscissas and ordinates of the interpolation points have been inverted. In this way the inverse nonlinearities characteristic is directly interpolated from inverse abscissa b_i and ordinate a_i interpolation points. The Lagrange polynomials are advantageous on account of their reliability in describing a bijective amplifier characteristic and their adapted implementation. Other interpolating polynomials, other than those of Lagrange, can also be selected (splines, Newton, etc.).

Using this compensation method, it is not necessary to have a high order Lagrange polynomial in order to get effective compensation for nonlinearities.

FIG. 3 shows a Lagrange interpolating polynomial 15, showing the inverse AM-AM characteristic, obtained from 4 interpolation points 13a to 13d, the abscissas and ordinates of which have been inverted.

Since the AM-AM characteristic is compensated, phase distortion is then evaluated as a function of the amplitude by the equation:

$\begin{array}{cc}\mathrm{angle}\left(\widehat{g\left(s_3^{\prime }\right)}\right)=\sum _{k=0}^n〈\varphi ,p_k〉p_k\left(s_3^{\prime }\right)& \left(16\right)\end{array}$

This phase then just needs to be subtracted from the signal phase to correct the AM-PM characteristic and obtain at the output some compensation 12 of nonlinearities:

s ₃(t)=s₃′(t).exp(−j*angle(ĝ(∥s₃′∥)))   (17)

FIG. 4A shows results of compensation simulation of the AM-AM characteristic. The set of points 17 show the AM-AM characteristic obtained at output with no compensation method. The set of points 19 shows the AM-AM characteristic obtained with the compensation method, with a learning sequence of 64 symbols and in the presence of noise on the transmission channel. It can be seen that the compensation method makes it possible to obtain a compensated signal almost similar to a linear signal. In the same way, FIG. 4B shows results of compensation simulation of the AM-PM characteristic. The set of points 21 shows the AM-PM characteristic obtained at output with no compensation method. The set of points 23 shows the AM-PM characteristic obtained with the compensation method, with a learning sequence of 64 symbols and in the presence of noise on the transmission channel. There again, it can be seen that the compensation method allows a compensated signal to be obtained that is almost similar to a linear signal.

Instead of firstly compensating the AM-AM characteristic and then the AM-PM characteristic, it is also possible to implement a joint compensation of the AM-AM and AM-PM characteristics.

In this case, a complex Lagrange polynomial is used to interpolate the in amplitude and in phase characteristic of the amplifier:

$\begin{array}{cc}{s}_3\left(t\right)=\sum _{j=1}^ma_j\prod _{i\ne j}^{}\frac{s_2\left(t\right)-b_i}{b_j-b_i}& \left(18\right)\end{array}$

where the pairs (a_i,b_i) are obtained after projection on a base of complex polynomials.

The gain in terms of bit error rate is shown in FIG. 5. In this figure, the curves represent the bit error rate (BER) as a function of the signal to-noise ratio (SNR) for an OFDM system comprising an amplifier of the travelling wave tube (TWT) type. The curves 25, 27 and 29 show respectively the case of an ideal signal, an uncompensated signal, and a signal compensated by the compensation method.

The signal whereof the nonlinearities have been compensated can then be passed into the frequency domain by an FFT 6 (FIG. 1) implemented by FFT means 110 in FIG. 6, for example in the case of a communication system of the OFDM type. This signal may then pass through an equalisation phase 14 in order to compensate the noise of the channel 4. This equalisation phase may be implemented by equalisation means 112. This equalisation 14 may be obtained by subtracting the channel estimation 8 implemented previously by means 104 for estimating the channel characteristic of the signal received. Lastly, after the equalisation phase, the signal may pass through a decision phase 16 demodulating and decoding for example the signal, implemented by means 114 in FIG. 6.

One embodiment of the invention is compatible with a method for restricting or clipping the power to be transmitted upstream of the power amplifier 2, and a method for compensating the distortions caused by such clipping at the receiver end. To do this, the maximum amplitude of the learning sequence or pilot is defined as being lower than the clipping level.

The method according to one embodiment of the invention can for example be implemented in communication systems of the OFDM, WCDMA, EDGE type, or more generally in all radio, wire, optical communication systems etc.

Claims

1. Method for the digital compensation of nonlinearities in a communication system that includes a transmitter, a transmission channel and a receiver, comprising: at least one stage of estimating the nonlinearities induced by the transmitter and/or the receiver, from at least one learning sequence received at the receiver end and distorted by said nonlinearities,at least one stage of compensating for said nonlinearities distorting a signal received at the receiver end from the previous estimation of nonlinearities.

2. Method according to claim 1, the nonlinearities being estimated through stages of: calculating an orthonormal base of projection polynomials {p0,p1, . . . ,pn},calculating the nonlinearities approximation g({circumflex over (∥)}x∥) for an AM-AM characteristic and/or an AM-PM characteristic of a gain element g to which all communication system nonlinearities are reduced, as a function respectively of the equation:

3. Method according to claim 2, the orthonormal base being obtained by a Gram-Schmidt orthonormalisation of a base {1,x,x2,x3, . . . ,xn}.

4. Method according to claim 2, the coefficients {cA0,cA1, . . . ,cAn} of the AM-AM characteristic and/or the coefficients {cφ0,cφ1, . . . ,cφn} of the AM-PM characteristic being calculated by projection of the learning sequence on the orthonormal base.

5. Method according to claim 2, the abscissa ai and ordinate bi interpolation points for the AM-AM characteristic being calculated according to the equation:

6. Method according to claim 2, the orthonormal base being obtained by a Gram-Schmidt orthonormalisation of a base {1,x,x*,x2,xx*, . . . } and the nonlinearities approximation being calculated according to the equation:

7. Method according to claim 1, the nonlinearities being compensated by: a stage of compensating the AM-AM characteristic from an interpolating polynomial obtained from inverse abscissa bi and ordinate ai interpolation points calculated previously, and/ora stage of compensating the AM-PM characteristic by subtracting a phase distortion evaluated at the received signal phase.

8. Method according to claim 7, the AM-AM characteristic being compensated by calculating the signal:

9. Method according to claim 1, the nonlinearities being compensated by a joint compensation of the AM-AM and AM-PM characteristics from a complex interpolating polynomial by calculating the signal:

10. Method according to claim 1, comprising before the nonlinearities estimation stage, a stage of estimating the transmission channel characteristic from at least one other learning sequence transmitted through the transmission channel.

11. Method according to claim 10, the amplitude of the other learning sequence being chosen substantially constant.

12. Method according to claim 10, the estimated channel characteristic being taken into account for estimating the nonlinearities.

13. Method according to claim 10, comprising after the nonlinearities compensation stage, an equalisation stage compensating for the channel noise present in the signal received from the estimation of the transmission channel characteristic.

14. Method according to claim 1, comprising after the nonlinearities compensation stage, a demodulation and/or decoding stage.

15. Method according to claim 1, the signals and/or learning sequences received being subject to a fast Fourier transform.

16. Method according to claim 1, the learning sequence received at the receiver end for estimating the nonlinearities being transmitted from the transmitter or the receiver.

17. Receiver device intended to receive signals transmitted by a transmitter through a transmission channel, comprising at least one digital nonlinearities compensator that includes at least: an estimator of the nonlinearities induced by the transmitter and/or the receiver from at least one learning sequence received and distorted by said nonlinearities,a compensator of said nonlinearities distorting a signal received from the previous estimation of the nonlinearities.

18. Device according to claim 17, the estimator of nonlinearities comprising at least: a calculator of an orthonormal base of projection polynomials {p0,p1, . . . ,pn},a calculator of the nonlinearities approximation g({circumflex over (∥)}x∥) for an AM-AM characteristic and/or an AM-PM characteristic of a gain element g to which all communication system nonlinearities are reduced, as a function respectively of the equation:

19. Device according to claim 18, the calculator of the orthonormal base implementing a Gram-Schmidt orthonormalisation of a base {1,x,x2,x3,xn}.

20. Device according to claim 18, the calculator of the coefficients {cA0,cA1, . . . ,cAn} of the AM-AM characteristic and/or of the coefficients {cφ0,cφ1, . . . ,cφn} of the AM-PM characteristic implementing a projection of the learning sequence on the orthonormal base.

21. Device according to claim 18, the calculator of abscissa ai and ordinate bi interpolation points for the AM-AM characteristic resolving the equation:

22. Device according to claim 18, the calculator of the orthonormal base implementing a Gram-Schmidt orthonormalisation of a base {1,x,x*,x2,xx*, . . . } and the calculator of the nonlinearities approximation resolving the equation:

23. Device according to claim 17, the compensator of nonlinearities comprising at least: a compensator of the AM-AM characteristic from an interpolating polynomial obtained from abscissa ai and ordinate bi interpolation points calculated previously, and/ora compensator of the AM-PM characteristic by subtracting a phase distortion evaluated at the received signal phase.

24. Device according to claim 23, the compensator of the AM-AM characteristic calculating the signal:

25. Method according to claim 17, the compensator of the nonlinearities implementing a joint compensation of the AM-AM and AM-PM characteristics from a complex interpolating polynomial by calculating the signal:

26. Device according to claim 17, comprising at least one transmission channel characteristic estimator from at least one other learning sequence transmitted through the transmission channel.

27. Device according to claim 26, the estimated channel characteristic being taken into account by the nonlinearities estimator.

28. Device according to claim 26, comprising at least one equaliser compensating for the channel noise present in the received signal from the estimation of the transmission channel characteristic.

29. Device according to claim 17, comprising at least one demodulator and/or one decoder.

30. Device according to claim 17, comprising a fast Fourier transform (FFT) implementing an FFT on the signals and/or learning sequences received.

31. Device according to claim 17, said receiver device being a wireless base station.