FR2992502A1 - Method for linearizing power amplifier that is utilized in orthogonal frequency-division multiplexing-type transmitter in digital communication field, involves determining vector of estimation co-efficients using conditioning matrix - Google Patents

Abstract

The method involves pre-correcting a modulated signal (21) from correction coefficients, and supplying a corrected signal to a power amplifier. The corrected signal is amplified (22). An inverse response of the amplifier is estimated (23) from the amplified signal. Estimation co-efficients are delivered as the correction coefficients. A vector of the estimation co-efficients is determined from a vector of the correction coefficients using a conditioning matrix having a Toeplitz structure of vectors that correspond to combination of elements from a same row of the matrix. Independent claims are also included for the following: (1) a device for linearizing a power amplifier (2) a computer program comprising a set of instructions for executing a method for linearizing a power amplifier.

Description

Method and device for linearization of a power amplifier, corresponding computer program. FIELD OF THE DISCLOSURE The field of the invention is that of digital communications.

More specifically, the invention relates to the linearization of power amplifiers within a signal transmitter. The invention applies to any type of transmitter, in particular transmitters implementing a multicarrier modulation technique, such as OFDM modulation (Orthogonal Frequency Division Multiplex, for "orthogonal frequency division multiplexing") by example. 2. PRIOR ART Power amplifiers are conventionally used in transmission systems in order to increase the power of the signal, in particular for long-distance communications.

These amplifiers have non-linear characteristics generally leading to distortions of the transmitted signal: spectral rise of the level of the side lobes, generation of harmonics, creation of interferences between non-linear symbols, creation of interferences between carriers, etc. Thus, these distortions lead in particular to transmission errors and a degradation of the bit error rate (BER).

Therefore, to prevent or at least reduce these distortions, it is necessary to find a way to "linearize" the effect of the power amplifier. A classical technique of linearization of power amplifiers relies on linearization with adaptation by indirect learning. This linearization technique of the prior art is illustrated in particular by FIG. 1 and consists in inserting a pre-corrector 12 between a modulator 11 and a power amplifier (AP) 13. The pre-corrector 12 makes it possible to linearize the effect of the power amplifier 13. Indeed, the pre-corrector applies a set of pre-correction coefficients C [n] representative of the inverse of the characteristic of the power amplifier to the signal u [n] coming from the modulator 11. The pre-corrector 12 delivers a corrected signal yd [n] at the input of the power amplifier 13. Thus, the concatenation "pre-corrector-power amplifier" makes it possible to apply a quasi-linear operation on the signal from the modulation u [n] for example. The pre-corrector thus makes it possible to limit or even compensate for the distortions brought by the power amplifier 13 on the signal to be transmitted. The coefficients of the pre-corrector 12, dynamically adapted to compensate for the non-linearities of the power amplifier, are determined by indirect learning.

In other words, a module 14, implementing an estimation algorithm, is used so as to determine the coefficients of an estimator whose function is to approach at best the inverse of the characteristic of the amplifier. 13. Periodically, the coefficients of the estimator are used for updating the coefficients of the pre-corrector.

However, the inventors have detected that this technique suffers from a major disadvantage, namely the calculation time of the pre-correction coefficients. Indeed, currently, the time required to obtain a pre-corrector 12 to effectively fight against the non-linear effects of the power amplifier is very long, of the order of ten minutes.

There is therefore a need for a new technique of linearization of a power amplifier making it possible to significantly reduce the calculation time of the pre-correction coefficients in order to improve the dynamic correction reactivity of the pre-corrector. 3. DISCLOSURE OF THE INVENTION The invention proposes a new solution which does not have all of these drawbacks of the prior art, in the form of a method of linearization of a power amplifier using at least an iteration of the following steps: - pre-correction of a modulated signal, from a set of pre-correction coefficients, delivering a corrected signal input of the power amplifier, - amplification of the corrected signal, delivering a amplified signal, - estimation, from the amplified signal, of an inverse response of the power amplifier, delivering a set of estimation coefficients intended to be used as pre-correction coefficients during the step of pre -correction of at least one next iteration.

According to the invention, the estimation step determines a vector of the estimation coefficients, from a vector of the pre-correction coefficients, by using a conditioning matrix having a vector Toeplitz structure, where a vector corresponds to a grouping of successive elements of the same line of the conditioning matrix.

Thus, the invention proposes a new technique for optimizing the determination of the dynamic pre-correction applied at the input of the power amplifier. Indeed, the estimation step according to the invention is accelerated by the use of a conditioning matrix specific to the linearization process according to the invention. The specificity of the matrix used is based on its "vector" Toeplitz structure. In other words, vectors belonging to the conditioning matrix according to the invention have Toeplitz properties. As a reminder, a "classical" Toeplitz matrix is a matrix with constant diagonals, that is to say of which all the elements of each diagonal are identical. For example, the document "Toeplitz and Circulating Matrices: A Review" (RMGray, Foundations and Trends® in Communications and Information Theory Vol 2, No. 3 (2006) 155-239 0 2006 RM Gray) describes more particularly the theory related to classic Toeplitz matrices.

The conditioning matrix used in the process according to the invention differs from the conventional Toeplitz matrix in that it has constant vector diagonals, that is to say that the same vector is reproduced diagonally in the conditioning matrix. A vector corresponds to a grouping or g-tuple (with g an integer denoting the number of grouped elements) of successive elements of the same line of the conditioning matrix. As detailed below, the implementation of this conditioning matrix makes it possible to considerably accelerate the dynamic determination of the pre-correction coefficients. As a result, the pre-corrector convergence time is improved without significant degradation of system performance. Consequently, a transmitter incorporating the pre-corrector and power amplifier assembly according to the invention will have an increased reactivity to emit for example a modulated, amplified and quasi-linear OFDM signal. According to one particular aspect of the invention, the linearization method comprises a preliminary step of constructing the conditioning matrix from a specific block formed of a plurality of vectors organized in successive lines, the prior stage of construction at least one iteration of the following sub-steps: - repetition of the specific block delivering a repeated specific block, - shift of a line of the vectors in said repeated specific block, - addition of a new vector in place of the placed vector in the first line in the repeated specific block, - deletion of the vector corresponding to the vector placed in the last line in the specific block, these substeps delivering a new specific block used at the next iteration. In other words, the invention makes it possible to reduce the time for determining pre-corrector pre-correction coefficients because of the specific construction of such a conditioning matrix having Toeplitz properties, based on iterations comprising steps that are not very complex with regard to the conventional operations necessary for determining the pre-correction coefficients. According to another characteristic of the invention, the estimation step implements a multiplication of the conditioning matrix by the vector of pre-correction coefficients, such that: Y [n] = W (2) [] ( 2) [n], with: -> (2) C [n] the vector of pre-correction coefficients at iteration n; Y- [n] the vector of the estimation coefficients at the iteration n; W2 [n] the conditioning matrix at iteration n.

In particular, when the estimation step is implemented in an estimator having a polynomial structure with memory, we have: vo [ni vok-11 vo [n-K +1] K +1] Win] vo n L -1] v, _i [n + L-1] vo [n + L-2] L-21 vo [n + L-11 L-K] -> (2) C [n] = [C00, c1.0, - "CK-1,0, c01, c11, -, CK-11, - - -, C01-1, C11-1, -, CK-1,1-1 K an integer corresponding to the memory depth of the estimator , I an integer corresponding to the order of non-linearity of the estimator, L an integer corresponding to the number of rows of the conditioning matrix W2 [n]; v, [n], x [n] Ix [n] I for 0 i / -1, n an integer corresponding to an iteration index Among the estimators having a polynomial structure with memory, one can cite for example the estimators according to the Wiener model as described in the document "Linearisation of broadband power amplifiers by adaptive predistortion in baseband "(E. Cottais, Ph.D. thesis, University of Nantes, 2005). As a feature of the invention, the linearization method implements a step of updating the pre-correction coefficients from the estimation coefficients estimated during the estimation step. This update step is for example performed during a current iteration, after the estimation step, or according to another example performed during a next iteration, before the pre-correction step.

According to another characteristic of the invention, the updating step implements a "Damped-Newton" type algorithm such that: - (2) C [n + 1] = -C (2) [n] + ju [w (2) H [n] w (2 [n]] - 1 w (2) H - [n] e [n] with: - (2) C [n] the pre-correction coefficients used during the pre-correction step of a current iteration, - (2) C [n + 1] the pre-correction coefficients used during the pre-correction step of a next iteration; a damping constant, and -e [n] = 17> d [ni-i with Yd [n] = yd [n], ..., yd [n + 1], ..., yd [n + L -1] 1T and yd [n] the corrected signal at iteration n The "Damped-Newton" type algorithm is described in particular in the document "A Generalized Memory Polynomial Model for Digital Predistortion of RF Power Amplifiers" ( DR Morgan, Z. Ma, Kim J., MG Zierdt, and J. Pastalan, IEEE Transactions on Signal Processing Vol 54, No. 10 October 2006. This algorithm has the advantages of being simple to implement. work and to offer satisfactory performances. Advantageously, the updating step according to the invention implements calculation operations in several components in parallel. The paralleling of the different calculation operations on different components in parallel makes it possible to increase the reduction in the determination time of the pre-correction coefficients.

According to a first particular embodiment, the updating step implements the following steps, to determine an intermediate matrix equal to the matrix product W (2) 1I [n] W (2) [n]: - determination of a first diagonal element B [m, m] of the intermediate matrix such that: L-1 B [M, M] = [n-m + I] STP-m + 1] for 0 m / -1 with S [ n] = [vo [n], ..., v [n] ,. - determination of the set of diagonal elements of the intermediate matrix from the following recurrence equation: B [m + 1, m + 1] = B [m, m] -? [n-m + L-1 ], e> [n-m + L-1] +? [nml] ST [nm-1] - determination of a set of elements of the intermediate matrix located only below or only above the diagonal elements - Obtaining the rest of the elements of the intermediate matrix by applying a Hermitian symmetry to the set of elements.

Indeed, the matrix product W (2) H [n] W (2) [n] is a square intermediate matrix of size KIxKI and thus comprises K2 square matrix elements B [m, q] with 0 m I -1 and 0 q I-1, a "matrix element" B [m, m] corresponding to a square block placed on the diagonal of the intermediate matrix, that is to say that this element corresponds to a part of the diagonal.

According to a second embodiment of the implementation of the updating step, the number of lines L of the conditioning matrix W2 [n] is equal to an integer multiple a of the number of columns K * I. According to this second embodiment, the updating step implements the following steps, to determine the matrix product W (2) 11 [n] W (2) [n]: - cutting of the conditioning matrix W2 [n] in square sub-blocks W./(2) [n], a line of a square sub-block corresponding to a line of the conditioning matrix; determination of intermediate matrices Mi such that M = W (2) H [n] [n], for j ranging from 0 to a-1, - summation of the intermediate matrices Mi, such that: -1 W2 '[n'II 7 (2) [n] = re = w (2) H nlw (2) 1- niM. According to this second embodiment, the step of determining the intermediate matrices implements the following substeps, for an intermediate matrix: determination of the diagonal elements of the intermediate matrix from the following recurrence relation: M [m + 1, m + 1] = M [m, m] -? [n-m + L-1] ST [n-m + L-1] +? [nme [nm -1] L-1 with Mi [m, m] = [n- m + 1] ST [n - m +1] for 0 m / - 1 1 _, [n] lT and, - determination of a set of elements of the intermediate matrix located only below or just above the elements - obtaining the rest of the elements of the intermediate matrix by applying Hermitian symmetry to the set of elements. In another embodiment, the invention relates to a device for linearizing a power amplifier comprising the following means, activated during at least one iteration: a pre-corrector of a modulated signal, pre-correcting the modulated signal from a set of pre-correction coefficients, delivering a corrected signal at the input of the power amplifier, - a corrected signal power amplifier, delivering an amplified signal, - a estimator estimating, from of the amplified signal, an inverse response of the power amplifier, providing a set of estimation coefficients for use as pre-correction coefficients by the pre-corrector during at least one subsequent iteration.

According to the invention, the estimator of such a linearization device determines a vector of the estimation coefficients from a vector of the pre-correction coefficients by using a conditioning matrix having a vector Toeplitz structure, where a vector corresponds to a grouping of successive elements of the same line of the conditioning matrix.

Such a linearization device is particularly suitable for implementing the linearization method described above. This is for example a device implemented in discrete time, and therefore implantable on dedicated electronic cards (FPGA, DSP). It may of course include the various features relating to the linearization process according to the invention. Thus, the characteristics and advantages of this device are the same as those of the linearization method according to the invention, and are not detailed further. The invention furthermore relates to one or more computer programs comprising instructions for implementing a linearization method according to the invention when this or these programs are executed by a processor.

The invention can thus be implemented in various ways, in particular in hardware ("hardware") or software ("software") form. 4. List of Figures Other features and advantages of the invention will appear more clearly on reading the following description of a particular embodiment, given as a simple illustrative and non-limiting example, and the accompanying drawings, among which: - Figure 1, described in relation to the prior art, shows a linearization scheme of a power amplifier; FIG. 2 illustrates one embodiment of the linearization method according to the invention; FIG. 3 represents a numerical example of a conditioning matrix according to the invention; FIGS. 4A and 4B show two variants of the steps of updating the pre-correction coefficients; FIG. 5 represents the performances of the method according to one embodiment of the invention; - Figure 6 shows the structure of a linearization device according to one embodiment of the invention. 5. Description of an embodiment of the invention 5.1 General principle The general principle of the invention is based on an optimization of the reconfiguration of a pre-corrector for linearizing a power amplifier. In particular, the optimization according to the invention is based on an acceleration of the determination of the estimation coefficients and an acceleration of the updating of the pre-correction coefficients by means of the previously obtained estimation coefficients. The "double acceleration" of dynamic pre-correction according to the invention is obtained by using a specifically constructed conditioning matrix, in particular so as to exploit the properties of Toeplitz. Indeed, the conditioning matrix used in the process according to the invention differs from the conventional Toeplitz matrix in that it has constant vector diagonals whose size is for example equal to the order of non-linearity of the system (power amplifier, pre-corrector and estimator), that is to say that the same vector is reproduced diagonally in the conditioning matrix. The construction of such a conditioning matrix implements iterations comprising stages that are not very complex and faster to implement (namely repetition, addition and vector offset), with regard to the conventional operations necessary for determination of the pre-correction coefficients.

On the other hand, the invention proposes two embodiments making it possible to accelerate the updating of the pre-correction coefficients while also taking advantage of the structure of the specific conditioning matrix according to the invention. As a result, an effective reduction of the time required to optimize the pre-corrector is obtained.

A method of linearization of a power amplifier according to one embodiment of the invention is described below. 5.2 Example of Implementation In relation to FIG. 2, the main steps implemented by a method of linearization of a power amplifier according to one embodiment of the invention are presented. These different steps are for example implemented within a linearization device, which can in particular be integrated within an OFDM transmitter. To this effect, it is recalled that OFDM modulation is increasingly used for digital transmissions, in particular on multipath transmission channels. This multicarrier modulation technique notably makes it possible to overcome the inter-symbol interference generally observed when using a single-carrier modulation on a multipath channel. The linearization method according to this embodiment of the invention is an iterative method. Indeed, the linearization process is of the "indirect learning" type. In other words, since the power amplifier is non-linear "permanently", the pre-corrector, "transparent" during initialization of the method according to the invention becomes non-linear over the iterations so that the set "pre-corrector + power amplifier" becomes linear over the iterations.

We denote n the index or iteration number. Since it is a process based on indirect learning, some notations of FIG. 1, in particular relating to the inputs / outputs of the various elements of the linearization device, are repeated in order to clarify the description of the linearization process. of a power amplifier according to the invention.

According to one embodiment of the invention, the linearization method implements at least one iteration of a set of steps shown in relation to FIG. 2. During a first step 21, a pre-correction of a modulated signal, from a set of pre-correction coefficients, is implemented and delivers a corrected signal yd [n] at the input of the power amplifier. It should be noted that during an initialization iteration not shown, the set of pre-correction coefficients ü> (2) [n], comprising for example N coefficients, is initialized, the first coefficient of this set for example 1 and the other coefficients being zero.

Thus, as indicated above, the pre-corrector is "transparent", in other words devoid of pre-correction effect during the initialization iteration. During a second step 22, the corrected signal from the pre-corrector is amplified by the power amplifier which outputs an amplified signal x [n]. According to this embodiment, the values of the amplified signals x [n] obtained at each iteration are recorded in a buffer (or "buffer") of the estimator. From each value x [n], we determine a vector y, [n] = x [n] x [n] I 'for 0 i 1 -1, corresponding to an I-tuplet, with I the order of non-linearity of the system (power amplifier, pre-corrector and estimator), used subsequently for the construction of the conditioning matrix according to the invention. Furthermore, in order to construct a packaging matrix comprising L rows and KxI columns, K + L values of the amplified signals x [n] are recorded according to this embodiment, namely the values ranging from x [n - K +1]. at x [n + L -1].

Then, the linearization method according to the invention implements an estimation step 23, from the amplified signal, of an inverse response of the power amplifier, delivering a set of estimation coefficients intended to be used. as pre-correction coefficients during the pre-correction step of at least one subsequent iteration. According to the embodiment presented, the structure of the estimator is chosen as being polynomial with memory and in particular able to memorize the amplified signals coming from the power amplifier. Among the estimators having a polynomial structure with memory, one can cite for example the estimators according to the Wiener model as described in the document "Linearisation of broadband power amplifiers by adaptive predistortion in baseband" (E. Cottais, PhD thesis, University of Nantes, 2005). The estimation coefficients y [n] are obtained in particular according to the following equation, by taking the notations of FIG. 1: 1-1 K-1 Vn, y [n] = ck, ix [n-k] lx [ n - k] li i = ok = o with I the order of non-linearity and K the depth of memory of the estimator. The coefficients ck, i are the estimation coefficients to be estimated, in particular by an estimation algorithm. The estimation step of the invention differs from that of the prior art in that it uses a conditioning matrix W (2) [n], to determine a vector of the estimation coefficients -E [n] from a vector of the pre- - (2) correction coefficients C [n], such that Yln] = W (2) [n] C (2) [n]. In particular, the packaging matrix W2 [n] used according to the invention has a vector Toeplitz structure, a vector corresponding to a grouping of successive elements of the same line of the conditioning matrix.

An exemplary packaging matrix according to the invention is particularly represented in FIG. 3. According to this embodiment of the invention, the packaging matrix W2 [n] having a Toeplitz structure by vectors is obtained in particular by means of a construction step 25.

The construction of the conditioning matrix W2 [n], the example of which is shown in FIG. 3, is detailed below. The values of the elements of the conditioning matrix W2 [n] are obtained from the values of the amplified signals output from the power amplifier recorded in the memory of the polynomial memory estimator. In particular, the values of the amplified signals x [n] to x [n-K +1] are used to obtain the elements of the first row of the matrix, and the values of the amplified signals x [n] to x [n + L -1] with L the number of samples of an OFDM symbol are used to form a first column of vectors of the conditioning matrix W (2) [n]. More precisely, the values of the amplified signals x [n] being in the form of vectors each corresponding to a I-tuple of samples of the amplified signal obtained during an iteration, a matrix comprising L rows and KxI columns is obtained. In the simplified example represented in FIG. 3, it is considered that the parameters K, I and L respectively have the following values K = 3, 1 = 3 and L = 9. Here, it should be noted that the value of L is relatively small compared to what is actually implemented according to the invention. Indeed, Figure 3 is only intended to give a merely illustrative example of the specific conditioning matrix of the invention. For applications in the field of transmissions employing OFDM modulation, the number of samples L of an OFDM symbol can be very large in front of KI, with for example K = 3, 1 = 7 and L = 40960. Thus, in the example illustrated in FIG. 3, the amplified signals x [n] are vectors corresponding to sets of three samples of the signal, and consequently, the conditioning matrix is formed of vectors corresponding to sets of three elements. of the matrix. In other words, the conditioning matrix has a vectorial granularity equal to 3. With regard to FIG. 3, each element of a vector, a vector consisting of three elements, is obtained by applying a function of the form. vi [r] = x [n] I x [ri] Ii for 0 i / -1, where i is an integer. Thus, the first vector 32 of the conditioning matrix W2 [n] located at the top left of the matrix comprises the three elements whose values are the following: v 0 [n] = 1.30, v1 [n] = 1.69 and v 2 [n] = 2.20. Similarly, the vector 33 located in the fifth line to the left of the conditioning matrix is obtained by applying the function of the form: vi [n + 4] = x [n + 4] 1 × [n + 4] I for 0 i / -1, and therefore includes the three elements whose values are as follows: vo [n + 4] = 3.5, vi [n + 4] = 12.25 and v2 [n] = 42.88.

The conditioning matrix may in particular be constructed from the following specific block (vo [n] v1_1 [n]): vo [n + L - 1] --- [n + L - 1] The specific block 31 is therefore formed of L vectors organized in successive lines, for example nine vectors according to the example shown in FIG. 3, each vector corresponding to a grouping of I successive elements of a line of the conditioning matrix, that is to say three elements according to this example. Specific block 31 thus groups nine vectors, whose first vector 32 is located in the first line and comprises the values vo [n] = 1.30, v1 [n] = 1.69 and y2 [n] = 2.20, and the last vector 34 is located on the last line and comprises the following values: vo [n + 8] = 5.10, v1 [n + 8] = 26.01 and v2 [n + 8] = 132.65.

From the specific block 31 previously described, the construction of the conditioning matrix W2 [n] uses, according to this example, at least one iteration of the following substeps: - repetition 251 of the specific block 31 delivering a repeated specific block, - Offset 252 of a line of the vectors in said repeated specific block, - 253 addition of a new vector 37 in the first line in the repeated specific block 36, - 254 deletion of the vector corresponding to the last vector 34 placed in the last line in said specific block. These substeps deliver a new specific block 36 used at the next iteration. Thus, with regard to FIG. 3, the specific block 31 is repeated on the right. For example, the vector corresponding to the last vector 34 in the specific block 31 is deleted in the specific repeated block. Then, all the vectors of the specific repeated block are shifted down one line, and the block is added in the first line. The vector 37 obtained from the amplified signal obtained at the iteration n-1, denoted x [n-1], comprising the three elements whose values are as follows: vo [n -1] = 1, 80, vi [n -1] = 3.24 and v2 [n -1] = 5.83.

The first vector 32 of the specific block previously located in the first line is therefore shifted to the second line, and the vectors of subsequent lines of the specific block are consequently also shifted by one line downwards. The last vector 34 of the specific block is consequently deleted in the repeated specific block 36.

A new specific block 36 is thus obtained. After a new iteration of the previously described substeps made from the new specific block 36, a new specific block 38 is obtained to the right of the specific block 36. In the first line of this new block 38, we add the vector 39 obtained from the amplified signal obtained at the iteration n-2, denoted x [n -2], comprising the three elements whose values are the following: v [n-2] = 2, 30, vi [n - 2] = 5.29 and y 2 [n - 2] = 12.17. As indicated above, the vectors are shifted by one line so that the first vector 32 of the starting specific block 31 is found in the third line in the new specific block 38 resulting from the second iteration. The last vector 35 of the specific block 36 is consequently deleted in the repeated specific block 38. Therefore, it can be seen from FIG. 3 that the conditioning matrix W2 [n] obtained is of the form: vo [ni] v vo [n-11 vo [n- K +1] K +1] 14.7 (21n> vo [n + L-1] v, _i [n + L-1] vo [n + L-2] L-21 vo [ n + L-K] L-K] y and has a Toeplitz structure by vector.

Indeed, as shown in FIG. 3, the first vector 32 of the specific block 31 is reproduced diagonally in the conditioning matrix because it is repeated in the second line of the specific block 36 and in the third line of the specific block 38. The vector diagonals are particularly emphasized in this illustration by a texture (hatched, non-hatched, cross, points) associated with each vector reproduced diagonally. It can therefore be seen that the conditioning matrix according to the invention is obtained by simple repetition, addition and offset operations which make it possible to increase the overall pre-correction reactivity of a method or device for linearizing an amplifier. of power according to the invention.

In order to compare the performances related to the use of the conditioning matrix W2 [n] according to the invention, the construction of a conditioning matrix A [n] conventionally used in linearization techniques with adaptation by indirect learning such as illustrated in Figure 1 is briefly recalled below. The classical matrix of conditioning A [n] is obtained in the following way: from the following vectors [x [n],, x [n-K + 11] T and [x [n],, x [n + L - li] T construction of the matrix Ai: x [n] x [n-1] --- x [n -.K +1] A, x [n]. *. x [N + L - 1] x [N + L - 2] - x [n L - K] where an element x [n] is a scalar. the function y [n] = x [n] Ix [n] I is then applied to each element of this matrix Ai to obtain finally / - 1 sub-matrices. finally, the classical matrix A [n] is the concatenation of these / matrices thus obtained: vo. [n] v0 [71 + 11 v1 [n] vi [n + 11 ::: v "[n] vi_i [n K + 1] A [n] = vo [n + L -11 --- vo [n + L - K] vi [n + L -11 --- vi [n + L - K] --- + L - 11 --- + L - K] It can thus be observed that the number of operations to obtain the conventional conditioning matrix is greater and that the operations are more complex than what is necessary to obtain the matrix of conditioning according to the invention.

A simulation and testing campaign carried out by the inventors could notably make it possible to demonstrate that the time required by the step of construction of the conditioning matrix W2 [n] of the linearization process according to the invention is in average 48% shorter compared to the time taken to build the classical conditioning matrix A [n].

In addition, because of the simplification of the construction of the conditioning matrix of the invention, it can be seen that the conditioning matrix W (2) [n] according to the invention comprises the same terms as the conventional conditioning matrix. A [n] in a different order, and in addition has properties of Toeplitz by vector.

Once the conditioning matrix is obtained at the end of the previously described construction step, it is then used by the estimator to determine a pre-correction coefficient vector C (2) [n], such as that Y [n] = 147 (2) [4 (2) [n], with, -> (2) 1 C [n] = [C0 0, c1.0 - - -, C K-1.0 , Coi C11, -, C K-11'- - - 'C 0 1-1, C11-1 "." C K-1.1-1 -> A step of updating 24 of the pre-corrector coefficients C (2) [n] can then be implemented, using a "Damped-Newton" type algorithm for example, such that: -> (2) -> (2) C [n + 1] = C [ n] + ju [w (2) H [n] w (2) [n] i147 - -1 (2) H [n] e [n] _ where y is a damping constant and e [n] = Yd [n] - Y- [n] with: -1T Yd [n] = [yd [n] ,. . . , y d [n + 1],. . . , y d [n + L -1] where d [n] is the corrected signal delivered by the pre-corrector input of the power amplifier. This update 24 is for example performed during a current iteration, after the estimation step 23, or according to another example performed during a next iteration, before the pre-correction step 21. Two variants of the updating step represented respectively in relation to FIGS. 4A and 4B are described below. 5.3 Variants for updating the pre-correction coefficients As indicated above, the invention also proposes to optimize, that is to say accelerate, the updating of the pre-correction coefficients by also drawing advantage of the structure of the specific packaging matrix W2 [n] according to the invention. Indeed, the inventors have established that contrary to the prejudices of the skilled person, it is not the matrix inversion in the update equation: -> (2) -> (2) -1 - ^ C [n + 1] = C [n] + 414 7 (2) 11 [n] 4 7 (2) [n]] w (2) H [n] e [n] which is the most greedy in time of calculation but the determination of the matrix product The inventors therefore propose two variants for the update step. 5.3.1 First variant According to a first variant shown in relation to FIG. 4A, the updating step 24 implements the following steps, to determine an intermediate matrix equal to the matrix product W (2) H [n ] W (2) [n]: - determination 2411 of a first diagonal element B [m, in] of the intermediate matrix W ") H [n] W (2) [n] such that: L-1 B [ M, M] = IS * PM ± en-M + 11 1 = 0 with S [n] = [vo [n], ..., v, [n], ..., v i_l [n] l - determination 2412 of the set of diagonal elements of the intermediate matrix from the following recurrence equation: B [m + 1, m + 1] = B [m, m] -? [n-m + Le [n -m + L-1] +? [nm-1] ST [nm-11 - determination of a set of elements 2413 of the intermediate matrix located only below or only above the diagonal elements, - obtaining 2414 from the rest of the elements of the intermediate matrix by applying a hermitian symmetry to the set of elements. -IT In other words, by noting S [n] = [ y o [n], ..., y, [n], ..., v 1_1 [n] _1, we can write w2 [n] in the following form: i Frn] S rn. - 1] ... FIT '- K + 11 \ w (2) [ni = Pe rn + 11 S'. [n] ::: F rn -K + 21 \ Frn + L - 11F rn + L - 2] - -FIT '- K + L1 1 It is then possible to identify, in the expression of the matrix product W ( 2) 11 [n] W (2) [n], sub-blocks, denoted by B [m, m], presenting by nature a Hermitian symmetry, and which are obtained by the block matrix product: L-1 B [ m, m] = Ir [n-m + T [n-m + 1] 1-13 We can then apply the recurrence relation mentioned above to determine the sub-blocks B [m + 1, m + 1 ]. In order to illustrate the performances of this variant of updating of the pre-correction coefficients according to the invention, the inventors have carried out a complexity study which made it possible to highlight that the gain in complexity (which is the ratio between the number of operations to obtain W (2) 11 [n] W (2) [n] by direct calculation and the number of operations to obtain this same matrix by exploiting the Hermitian character and the relations between the diagonal blocks of the matrix according to the invention) is given by the expression: 2K 2 G (K) K 2 -K + 2 The performance curve shown in FIG. 5 is obtained. According to this curve, the maximum gain of the order of 2 , 3 is obtained for K = 4. We thus obtain a reduction of the calculation time of the order of 56.5%. According to an advantageous aspect of the invention, the updating step implements calculation operations in several components in parallel. It is therefore possible to parallelize the calculations making it possible to obtain the matrix W (2) H [n] W (2) [n]. Indeed, the calculations are always the same, only the data differ.

Parallel calculations tests were undertaken using a dedicated processor using a "CUDA" type architecture (in English "Compute Unified Device Architecture"). Simulations on the Damped Newton algorithm have been able to highlight an increase of the gain of the order of 10% on the execution time by parallelizing the computation of W (2) H [n] W (2) [n] with CUDA. 5.3.2 Second variant According to a second variant shown in relation to FIG. 4B, to determine the matrix product W (2) H [n] W (2) [n], it is required that the number of lines L of the matrix of conditioning W2 [n] is equal to an integer multiple a of the number of columns K * I. The updating step 24 then implements the following steps: - cutting 2421 of said conditioning matrix W2 [n] into square sub-blocks W (2) [n], a line of a square sub-block corresponding to a line of the conditioning matrix, we thus obtain a square sub-blocks; determination 2422 of intermediate matrices Mi such that _ w., (2) 11 [n] w J2) [n], for j ranging from 0 to a-1, - summation 2423 of the intermediate matrices Mj, such that: W2 ' [n] = v a-1 = v a-1 W (21 r nlw (2) r il] i = 0 i = 0 L-1 / 1- More precisely, the step for determining an intermediate matrix Mi: determination 2424 of the diagonal elements of said intermediate matrix from the following recursion relation: Mi [m + 1, m + 1] = M i [m, m] -? [N-m + The [n-m + L-1] +? [Nme [nm-1] L-1 with Mi [m, m] S * [n - + l ] ST [n - + 1.0, v1 [n],, v _l [n]] T, and - determining 2425 a set of elements of said intermediate matrix located only below or only above said diagonal elements, - obtaining 2426 from the rest of the elements of said intermediate matrix by applying a Hermitian symmetry to said set of elements 5.4 Structure of a device Finally, in relation to FIG. 6, the simplified structure of a device for linearization of a power amplifier adapted to implement a method of linearization of a power amplifier according to one of the embodiments is presented. described above. Implemented within a transmitter of OFDM type for example, such a device comprises a memory 61 comprising a buffer memory, a processing unit 62, equipped for example with a microprocessor p.13, and driven by the program computer 63, implementing the method of linearization of a power amplifier according to one embodiment of the invention. At initialization, the code instructions of the computer program 63 are for example loaded into a RAM memory before being executed by the processor of the processing unit 62. The processing unit 62 receives as input a signal Sm, modulated for example according to an OFDM modulation, to be transmitted. The microprocessor of the processing unit 62 implements the steps of the method of linearization of a power amplifier described above, according to the instructions of the computer program 63, to "compensate" for the non-linearities of the amplifier of power. For this, the linearization device comprises, in addition to the buffer memory 61, a set 60 comprising a pre-corrector 64 of the modulated signal Sm, pre-correcting the modulated signal from a set of correction coefficients, delivering a corrected signal at the input of a power amplifier 65, the power amplifier 65 of the corrected signal, delivering an amplified signal, an estimator 66 estimating, from the amplified signal, an inverse response of the power amplifier 65, delivering a set estimation coefficients for use as correction coefficients by the pre-corrector during at least one iteration, the estimator determining a vector of the estimation coefficients from a vector of the correction coefficients using a packaging matrix having a vector Toeplitz structure, where a vector corresponds to a grouping of elements of a same line of the matrix of conditioning. The assembly 60 is driven by the microprocessor of the processing unit 62 and delivers an amplified signal, denoted SA, having a reduction of the distortions related to the power amplifier 65 because limited by the pre-correction implemented by the pre-corrector 64.

Claims (12)

REVENDICATIONS1. A method of linearization of a power amplifier implementing at least one iteration of the following steps: - pre-correction (21) of a modulated signal, from a set of correction coefficients, delivering a signal corrected in input said power amplifier, - amplifying (22) said corrected signal, delivering an amplified signal, - estimating (23), from said amplified signal, an inverse response of said power amplifier, delivering a set of estimation coefficients intended to to be used as correction coefficients during the pre-correction step of at least one subsequent iteration, characterized in that said estimating step determines a vector of said estimation coefficients from a vector of said coefficients correction using a packaging matrix having a vector Toeplitz structure, where a vector corresponds to a grouping of elements of a same line of said conditioning matrix. 2. A method of linearization of a power amplifier according to claim 1, characterized in that it comprises a preliminary step of construction (25) of said conditioning matrix W2 [n] from a specific block formed of a plurality of vectors organized in successive lines, said preliminary step of construction implementing at least one iteration of the following sub-steps: - offset (252) of a line of the vectors in said specific repeated block, - addition (253) of a new vector in place of the vector placed in the first line in said repeated specific block, - deletion (254) of the vector corresponding to the vector placed in the last line in said specific block, said substeps delivering a new specific block used at the next iteration. 3. A method for linearizing a power amplifier according to claim 1, wherein said estimating step implements a multiplication of said conditioning matrix by said vector of correction coefficients, such as that: Y [n] = 147 (2) [4 (2) [n] with, -> (2) C [n] said vector of pre-correction coefficients at iteration n; Y- [n] said vector of estimation coefficients at iteration n; W [n] said conditioning matrix at iteration n; and when the estimating step is carried out in an estimator having a polynomial structure with memory: Win] vo [ni vo [n-1] vo [n-K + 11 K + 11 vo [n + L-1] v, _i [n + L-1] vo [n + L-2] L-21 vo [n + L-K] L-K] -> (2) C [n] = [C00, cto,, CK_to, cop cil ,,,, C01_1, K an integer corresponding to a memory depth of said estimator, I an integer corresponding to a non-linear order of said estimator, L an integer corresponding to a number of rows of the conditioning matrix w (2) [n ]; v [] = x [n] lx [] 1 for 0 i / -1, n an integer corresponding to an iteration index. 4. A method of linearization of a power amplifier according to one of the preceding claims, characterized in that it implements a step of updating (24) said correction coefficients from the estimation coefficients estimated at during said estimation step. 5. A method of linearization of a power amplifier according to claim 4, characterized in that said updating step implements an algorithm of "Damped-Newton" type such that: -> (2) -> (2 ) -1 C [n + 1] = C [n] +, u [14 7 (2) H [n] W (2) [n]] W (2) 11 [n] e [n] with: - > (2) C [n] the correction coefficients used during the pre-correction step of a current iteration; -> (2) C [n + 1] the correction coefficients used during the pre-correction step of a next iteration; y a damping constant; summer [n] = Y d [n] - Y [n], with Y d [n] = [yd [n] ,. .., yd [n +., y d [n + L 1]] T. 6. A method of linearization of a power amplifier according to claim 5, characterized in that said updating step implements computation operations in several components in parallel. 7. A method of linearization of a power amplifier according to one of claims 5 or 6, characterized in that said updating step implements the following steps, to determine an intermediate matrix equal to the matrix product w (2 H [npy (2) [n] - determination of a first diagonal element B [ntin] of said intermediate matrix W (2) H [n] W (2) [n] such that: L-1 B [M] , M] = IS * PM ± lAn-M + 11 1 = 0 with S [n] = [vo [n], .. .., v - determination of the set of diagonal elements of said intermediate matrix from the following recurrence equation: B [m + 1, m + 1] = B [m, m] -? [n-m + L-1] ST [n-m + L-1] +? [nme [ nm-1] - determining a set of elements of said intermediate matrix situated only below or only above said diagonal elements, - obtaining the rest of the elements of said intermediate matrix by applying a hermitian symmetry to said set elements. 8. A method of linearization of a power amplifier according to one of claims 5 or 6, characterized in that in addition the number of lines L of said conditioning matrix W2 [n] is equal to an integer multiple of the number of columns K * I. 9. A method of linearization of a power amplifier according to claim 8, characterized in that said updating step implements the following steps, to determine the matrix product W (2) 11 [n] W (2) [n]: - cutting of said conditioning matrix W2 [n] into square sub-blocks W./(2)[n], a line of a square sub-block corresponding to a line of the conditioning matrix; intermediate matrices Mi such that M = wi (2) H [n] wi (2) [n] for j ranging from 0 to a-1, summation of said intermediate matrices Mj, such that: W2 '[n] 47 (2 ) [n] = N, this-1 m NI = w. (2) H Ln Ln 10. A method of linearization of a power amplifier according to claim 9, characterized in that said step of determining the intermediate matrices implements the following substeps, for an intermediate matrix Mi: - determination of the diagonal elements of said matrix intermediate from the following recursive relation: Mi [m + 1, m + 1] = Mi [m, m] -? [n-m + The [n-m + L-1] +? [nme [nm -1] L-1 with Mi [m, m] = [n-m + 1] ST [nm + 1] and 1 = 0 S [n] = [vo [n], ..., v 1 _, [ n] lT - determining a set of elements of said intermediate matrix located only below or only above said diagonal elements, - obtaining the rest of the elements of said intermediate matrix by applying a Hermitian symmetry to said set of elements. 11. Device for linearization of a power amplifier comprising the following means, activated during at least one iteration: a pre-corrector (64) of a modulated signal, pre-correcting said modulated signal from a set of correction coefficients, delivering a corrected signal at the input of said power amplifier, - a power amplifier (65) of said corrected signal, delivering an amplified signal, - an estimator (66) estimating, from said amplified signal, a inverse response of said power amplifier, delivering a set of estimation coefficients intended to be used as correction coefficients by the pre-corrector during at least one subsequent iteration, characterized in that said estimator determines a vector of said coefficients of estimation. estimation from a vector of said correction coefficients using a conditioning matrix having a Toeplitz structure by vect urs, where a vector corresponds to a grouping of successive elements of the same line of the conditioning scheduler. Computer program comprising instructions for carrying out a method according to one of claims 1 to 10 when said program is executed by a processor.