Method of pre-distorting input signal to compensate for effects of non-linear transfer function of power amplifier, and computer program product and apparatus therefor

Abstract

The invention relates to a method for pre-distorting an input signal in order to compensate for the effect of a non-linear transfer function of a power amplifier configured to amplify a radio frequency signal on a radio frequency signal generated by the input signal. The method comprises:-performing a Walsh transform (E300) on an M-term sequence dependent on time-domain sampling of the input signal, generating M sequential components of the corresponding transformed sequence; -calculating (E310) a sum of a plurality of operands resulting from a product of data dependent on at least one element of the transformed sequence and the corresponding predistortion coefficient, generating a corresponding sequential component of the predistorted transformed input signal. The sum follows the structure of the voltra series converted to the Walsh domain; -performing an inverse Walsh transform (E320) on the sequential components of the pre-distorted transformed input signal, generating an output signal for producing the radio frequency signal.

Description

Technical Field

[0001] The present invention relates to the field of data transmission by using radio frequency signals.

[0002] More particularly, the present invention relates to a method for predistorting an input signal to compensate for the effects of a non-linear transfer function of a power amplifier configured to amplify such radio frequency signals.

[0003] Therefore, the application fields of the present invention are, in particular but not limited to, the field of mobile phones (for example 4G or 5G networks defined by 3GPP (abbreviation for “3rd Generation Partnership Project” in English)), WLAN wireless local area network (abbreviation for “Wireless Local Area Network” in English, for example using WiFi), digital broadcasting systems (DVB-T (abbreviation for “Digital Video Broadcasting – Terrestrial” in English, ISDB-T (abbreviation for “Integrated Services Digital Broadcasting-Terrestrial” in English), DAB (abbreviation for “Digital Audio Broadcasting” in English)), high-speed wireless Internet access (WiMAX), asymmetric digital lines (xDSL), point-to-point links, etc. Prior art

[0004] Communication technologies such as OFDM (Orthogonal Frequency Division Multiplex) or WCDMA (Wideband Code Division Multiple Access) allow to significantly increase the spectral efficiency of digital communication systems in response to their exponential growth. However, the waveforms implemented in the context of these technologies have a high Peak-to-Average Power Ratio, or PAPR (Peak-to-Average Power Ratio). As a result, these waveforms are very sensitive to nonlinearities introduced by the power amplifier (PA). In particular, such nonlinearities distort the amplitude and, where appropriate, also the phase of the wanted RF signal. This leads to interference in adjacent communication channels and to a degradation of the amplitude of the Error Vector Magnitude (EVM, or Error Vector Magnitude).

[0005] To avoid these problems, one possibility is to utilize the linear amplification region of the PA. However, when the PA operates at near saturation power, the amplification efficiency in the linear region decreases significantly compared to the efficiency in the nonlinear region.

[0006] Alternatively, digital predistortion (DPD) compensates for the distortion caused by the nonlinear transfer function of the PA so as to utilize the high energy efficiency of the nonlinear region of the PA transfer function while correctly transmitting the modulated signal. According to the DPD method, as described, for example, in the article "The evolution of PA linearization: From classic feedforward and feedback throughanalog and digital predistortion" by A. Katz, J. Wood, and D. Chokola, IEEE Microwave Magazine, vol. 17, no. 2, pp. 32-40, 2016, a predistortion module is implemented in the digital domain upstream of the PA in the transmitter (i.e., an inverse model of the PA transfer function is implemented) so that the entire system behaves as a linear system.

[0007] Furthermore, due to the changing behavior of the PA over time (e.g. PA parameters drift with temperature, aging, etc.), the model parameters implemented in the predistortion module need to be updated over time. Figure 1 A typical DPD architecture is shown. The samples x[n] of the input signal x, here a baseband signal, are generated digitally according to the communication standard used (bit rate, coding, modulation scheme, etc.).

[0008] More specifically, the samples x[n] are processed by the predistortion module 110, which outputs predistorted samples z[n], which are converted to analog signals by a DAC (Digital-to-Analog Converter) 120. The analog signal is up-converted to radio frequency by a mixer 130 driven by a local oscillator 140. The radio frequency signal is filtered by a filter 150 to suppress its image. Subsequently, the obtained signal is amplified by a PA 160 and then radiated by an antenna. In addition, in order to track the behavior of the PA 160 over time, a coupler 170 is added at the output of the PA 160 to extract a representative signal of the radio frequency signal amplified by the PA 160. The representative signal is down-converted to a low frequency by a mixer 130 also driven by the local oscillator 140. The signal thus down-converted is filtered by an anti-aliasing filter 180 and then sampled by an ADC (Analog-to-Digital Converter) 180. Therefore, the samples y[n] output by ADC 180 are used by predistortion module 110 to update its model. More specifically, the model implemented in predistortion module 110 is calculated so that the spectral regrowth added to the predistorted samples z[n] compensates for the spectral regrowth associated with the nonlinearity of PA 160. In practice, the transfer function of predistortion module 110 preemphasizes the highest level of sample x[n] ( Figure 1a ) to compensate for the saturation of the transfer function of PA 160 ( Figure 1b When the transfer function of the predistortion module 110 corresponds to the transfer function of the PA 160, the entire system has a linearized transfer function ( Figure 1c ).

[0009] Furthermore, DPD techniques are usually divided into three categories based on the frequency scheme considered:

[0010] - Baseband pre-distortion;

[0011] - IF predistortion; and

[0012] - RF pre-distortion.

[0013] The most widely used technique is baseband predistortion, which works at the lowest sampling frequency compared to the other two techniques mentioned above. Therefore, it is possible to consider implementing the predistortion according to known baseband methods on a DSP (Digital Signal Processor) or an FPGA (Field-programmable gate array). However, the cost of this known method in terms of digital resources makes it difficult to implement it in intermediate frequencies or radio frequencies. In addition, finding the model implemented in the predistortion module 110 involves an iterative algorithm with a relatively high computational complexity.

[0014] Therefore, there is a need for a predistortion technique which has a lower computational load compared to known techniques, for example being able to be implemented in baseband, intermediate frequency or even directly in radio frequency. Summary of the invention

[0015] In one embodiment of the present invention, a method for predistorting an input signal is provided to compensate for the effect of a nonlinear transfer function of a power amplifier configured to amplify a radio frequency signal on a radio frequency signal generated by the input signal. According to this method, an electronic device performs:

[0016] - performing a Walsh transform (WT) on at least one sequence of M items of M time-domain samples dependent on at least one input signal to generate at least one M sequential components of a corresponding transformed sequence;

[0017] - for at least one given sequential component in the Walsh domain, calculating at least one sum of a plurality of operands resulting from the product of, on the one hand, data dependent on at least one element of the transform sequence corresponding to said given sequential component and, on the other hand, corresponding predistortion coefficients, producing a sequential component of the predistorted transformed input signal. At least one data dependent on at least one binary convolution between two elements corresponding to said given sequential component, each element belonging to a transform sequence, and / or dependent on at least one binary self-convolution of an element of the transform sequence corresponding to said given sequential component. Said sum follows a structure dependent on a Volterra series of time domain samples of the input signal and converted to the Walsh domain. Said predistortion coefficients are determined to compensate for the influence of the transfer function of the power amplifier. Said calculation is repeated for M sequential components in the Walsh domain, producing M sequential components of the predistorted transformed input signal;

[0018] - Performing an inverse Walsh transform (IWT) on the M sequential components of the predistortion transformed input signal to generate an output signal for generating a radio frequency signal.

[0019] The present invention therefore provides a new and inventive solution for compensating for the effects of a non-linear transfer function of a power amplifier.

[0020] More specifically, the invention proposes to implement the predistortion model in the Walsh domain. Indeed, the binary structure of the Walsh sequence and the structure of the digital calculations resulting therefrom in the Walsh domain make it possible to reduce the computational load compared to known techniques. In particular, this approach enables the predistortion model to be implemented in baseband, intermediate frequency or even directly in radio frequency.

[0021] More specifically, this model is based on the evaluation of sums, each sum corresponding to an order component of the Voltra series transformed into the Walsh domain.

[0022] In some embodiments, the Walsh transform is applied to a plurality of M sequences of M time domain samples dependent on at least one input signal to generate a plurality of M sequential components of the corresponding transformed sequences. The at least one data is dependent on:

[0023] - at least one binary convolution between two elements corresponding to said given sequential component, each element belonging to one of a plurality of transformed sequences; and / or

[0024] - at least one binary self-convolution of an element of the transform sequence corresponding to the given ordered component.

[0025] The sum follows the structure of a Voltaic series that depends on a sequence of multiple M time-domain samples of the input signal and is converted to the Walsh domain.

[0026] In some embodiments, at least one of the M-term sequences includes at least one term dependent on:

[0027] - the product between two time domain samples of the input signal; and / or

[0028] - An integer power of at least one time-domain sample of the input signal.

[0029] Therefore, all or part of the multiplication operation of the input signal samples is performed in the time domain.

[0030] In some embodiments, the Walsh transform is applied to a plurality of M sequences of M time-domain samples of the input signal to generate a plurality of M sequential components of the corresponding transformed sequences. The at least one data is dependent on at least one binary self-convolution of an element in the transformed sequence corresponding to the given sequential component.

[0031] In some embodiments, at least one sequence of M terms includes at least one term dependent on an integer power of at least one time-domain sample of the input signal.

[0032] In some embodiments, the Walsh transform is applied to a sequence of M items corresponding to a given sequence of M time-domain samples of the input signal, generating M sequential components of the corresponding transformed sequence. The calculation includes calculating the sum of M operands, the i-th operand (i is an integer from 1 to M) being obtained by multiplying, on the one hand, the data obtained by the i-th order binary self-convolution of an element in the transformed sequence corresponding to the given sequential component, and on the other hand, the corresponding predistortion coefficient.

[0033] Therefore, the predistortion model is based on a simplified Volta series, called the MP (Memory Polynomial) model.

[0034] In some embodiments, the method comprises determining the predistortion coefficients based on minimization of an error signal representing a difference between the input signal on the one hand and a modulation signal of the amplified radio frequency signal on the other hand.

[0035] In some embodiments, the method comprises determining predistortion coefficients based on minimization of an error signal representing a difference between the input signal on the one hand and a second output signal generated by applying a predistortion method to the modulated input signal representing the amplified radio frequency signal on the other hand.

[0036] Therefore, the coefficients of the predistortion model are determined directly.

[0037] In some embodiments, the method comprises determining predistortion coefficients based on minimization of an error signal representing a difference between, on the one hand, a modulation signal of a second radio frequency signal generated by a non-predistorted input signal and amplified by the power amplifier and, on the other hand, the output signal.

[0038] Therefore, the coefficients of the model are first determined to model the power amplifier.Thus, the predistortion coefficients are determined from the coefficients for modeling the power amplifier (eg, by inverting a matrix containing the coefficients for modeling the power amplifier).

[0039] In some embodiments, the determining of a technique to be employed to achieve the minimization belongs to the group consisting of:

[0040] - Least squares method;

[0041] - Normalized least squares method;

[0042] - Gauss-Newton algorithm; or

[0043] - Recursive least squares method.

[0044] In some embodiments, the techniques are implemented in the Walsh domain based on a signal constituting an error signal converted in the Walsh domain.

[0045] Thus, the computational load of the determination of the predistortion coefficients is reduced.

[0046] In some embodiments, the determining is performed periodically.

[0047] Therefore, changes in the characteristics of the power amplifier (e.g., temperature or aging) are taken into account in the model.

[0048] The present invention also relates to a computer program, comprising program code instructions for implementing any one of the above-mentioned pre-distortion methods when executed on a computer.

[0049] In one embodiment of the present invention, a predistortion electronic device is provided, which includes a reprogrammable computer or a dedicated computer configured to implement the steps of the predistortion method of the present invention (according to any of the different embodiments described above). Therefore, the features and advantages of the device are the same as the corresponding steps of the aforementioned predistortion method. Therefore, it will not be described in detail.

[0050] The present invention also relates to a radio frequency transmitter, comprising the above-mentioned predistortion electronic device (according to any one of the above-mentioned different embodiments). BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Other objects, features and advantages of the present invention will become more apparent by reading the following description in conjunction with the accompanying drawings, in which:

[0052] Figure 1 In the discussion of the “Prior Art” section, a radio frequency transmitter implementing a digital predistortion module according to known techniques is presented;

[0053] Figure 1a In the “Prior Art” section, it is discussed that Figure 1 The transfer function of the digital pre-distortion module;

[0054] Figure 1b In the “Prior Art” section, it is discussed that Figure 1 The transfer function of the PA;

[0055] Figure 1c In the “Prior Art” section, it is discussed that the Figure 1 The overall transfer function of the combination of the digital predistortion module and the transfer function of the PA;

[0056] Figure 2 A radio frequency transmitter implementing a digital predistortion module according to an embodiment of the present invention is shown;

[0057] Figure 3 The steps of a predistortion method according to an embodiment of the present invention are shown;

[0058] Figure 4 An embodiment of the present invention is shown for implementing Figure 3 An example of a device structure for some steps of a predistortion method. DETAILED DESCRIPTION

[0059] Now combine Figure 2 The radio frequency transmitter 200 implementing the digital pre-distortion module 210 according to one embodiment of the present invention is described.

[0060] About Combination Figure 1 The known architecture described above, the transmitter 100 includes a pre-distortion module 210, which implements the following combination Figure 3A predistortion method is described in detail. This method is based on implementing a digital predistortion model based on Voltra series in the Walsh domain. More specifically, the binary structure of the Walsh sequence and the structure of the digital calculations generated therefrom in the Walsh domain enable a reduced computational load compared to known techniques.

[0061] In particular, this approach enables the predistortion model to be implemented in baseband, IF or even directly in RF. Figure 2 In the embodiment of the present invention, the predistortion module 210 directly processes the RF signal so that it is amplified by the PA 160 before being radiated by the antenna.

[0062] However, in other embodiments, the predistortion module 210 processes a baseband or intermediate frequency input signal. In this case, the signal output by the predistortion module 210 is, for example, based on a signal similar to Figure 1 The architecture of is up-converted to radio frequency by a mixer 130 driven by a local oscillator 140. In this case, the mixer 130, also driven by the local oscillator 140, can be used in a feedback loop to generate a signal used by the predistortion module 210 to update its model.

[0063] In other embodiments, we exploit the binary nature of the Walsh sequence to implement the inverse Walsh transform in a semi-analog manner. More specifically, the predistorted output signal Each sequential component of , controlled by the inverse Walsh sequence amplitude corresponding to the order component under consideration, is converted into an analog signal by a 1-bit DAC (e.g. buffer type). The outputs of the different 1-bit DACs are added in the analog domain to obtain the output signal The continuous-time version of .

[0064] Now combine Figure 3 The steps of a predistortion method according to an embodiment of the present invention are described.

[0065] 1. Step E300:

[0066] During a step E300 , a Walsh transformation is performed on at least one sequence of M items of M time-domain samples x[n] dependent on an input signal, generating M sequential components of at least one corresponding transformed sequence.

[0067] 1.1 General:

[0068] More specifically, the predistortion model considered here is based on the Voltaic series transformed into the Walsh domain. It should be noted that such a model is applicable both to the modeling of the transfer function of the PA 160 and to the predistortion of the input signal x[n] itself. Only the coefficients involved differ in the two cases, as described below in connection with step E330. Returning to step E300, we consider the following formula of the Voltaic series in the time domain:

[0069] [Formula 1]

[0070]

[0071] in is the sample with index n in the output of module 210, and:

[0072] [Formula 2]

[0073]

[0074] is a voltaic nucleus; and

[0075] It is a Volta wave.

[0076] In order to be able to apply the discrete Walsh transform, the Volta waveform is split into a sequence of M waveforms, here organized in vector form.

[0077] Therefore, for a linear waveform, the following vector is obtained:

[0078] [Formula 3]

[0079]

[0080] For quadratic waveforms:

[0081] [Formula 4]

[0082]

[0083] In general, for a q-order waveform:

[0084] [Formula 5]

[0085]

[0086] Therefore, by performing a discrete Walsh transform on the above sequence, we get the vector:

[0087] [Formula 6]

[0088] =

[0089] in is a Walsh matrix of order M (as defined, for example, in the article by J. Johnson and M. Puschel, “In search of the optimal Walsh-Hadamard transform”, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100), vol. 6, 2000, pp. 3347–3350 vol.6).

[0090] By using an equivalent partitioning of the Volta kernel, after performing the M-dimensional discrete Walsh transform, we obtain the vector:

[0091] [Formula 7]

[0092] =

[0093] Therefore, the Voltra series given by Equation 1 is converted to the Walsh domain corresponding to the M-dimensional Walsh transform in the form:

[0094] [Formula 8]

[0095]

[0096] in is the output signal of module 210 The value of the sequential component indexed by n in the Walsh field, where n is an integer from 0 to M-1.

[0097] 1.2 MP case:

[0098] To further reduce the computational load implemented in the predistortion module 210, a simplified model based on the Voltaic series is implemented in some embodiments.

[0099] Among the commonly used models, there is the MP model (abbreviation for "Memory Polynomial" in English). In this case, , Formula 8 is simplified to:

[0100] [Formula 9]

[0101]

[0102] in:

[0103] [Formula 10]

[0104]

[0105] and:

[0106] [Formula 11]

[0107]

[0108] 1.3 Multiplication and Binary Convolution:

[0109] Reconsidering the general expression Equation 5 or the simplified expression Equation 11 for the MP model, it can be observed that the Walsh transform of some order of the Voltaic waveform involves one or more sequences of Walsh transforms, one or more of which depends on:

[0110] - the product between two time domain samples x[n] of the input signal; and / or

[0111] - An integer power of at least one time-domain sample of the input signal x[n].

[0112] However, as described, for example, in the article "Journal of electrical engineering" by MZ Anna Usakovah and Jana Kotuliakova, vol. 53, no. 9-10. Cambridge, LA: MIT Press, 1958, pp. 285-288, the Walsh transform of a product is equal to the binary convolution of the Walsh transforms of the operands of the product. In other words:

[0113] [Formula 12]

[0114]

[0115] in represents a binary convolution. This implementation is very efficient in terms of computational load. In fact, and The binary convolution expression is:

[0116] [Formula 13]

[0117]

[0118] in is the binary sum of p and n. Such a binary sum, when p and n are two positive integers, is expressed as:

[0119] [Formula 14]

[0120]

[0121] in , as shown in the expression:

[0122] [Formula 15]

[0123]

[0124] Thus, according to the embodiment considered, the Walsh transform of certain orders of the Voltaic waveform achieves:

[0125] - corresponding to at least one binary convolution between two elements of said given sequential components, corresponding to the Walsh transform of two time-domain sampling sequences of the input signal x[n]; and / or

[0126] - at least one binary self-convolution of an element of the transform sequence corresponding to the given ordered component.

[0127] 1.4 Conclusion of step E300:

[0128] According to the embodiment described above in conjunction with step E300, in order to evaluate the Walsh transformation of the Voltaic waveform, the following different configurations may be encountered:

[0129] - the Walsh transform is applied to a plurality of M sequences of M time-domain samples that are dependent on one or more corresponding input signals x[n]: for example corresponding to the general case of formula 5, when all or some of the multiplications (or exponentiations, still interpreted as multiplication calculations) are implemented in the time domain before applying the Walsh transform to the sequence under consideration, and other multiplications (or exponentiations, still interpreted as multiplication calculations) are implemented in the Walsh domain in the form of binary convolutions (or binary self-convolutions, if applicable) of the elements of some of the transformed sequences;

[0130] - the Walsh transform is applied to multiple M sequences of M time-domain samples that depend on a single input signal x[n]: for example, it corresponds to the MP case of formula 11, when all or some of the exponentiations (still interpreted as multiplication calculations) are realized in the time domain before applying the Walsh transform to the sequence under consideration, and other exponentiations are realized in the Walsh domain in the form of binary self-convolutions of the elements of some of the transformed sequences;

[0131] - The Walsh transform is applied to a single sequence of M terms of M time-domain samples that depends on a single input signal x[n]: i.e. the MP case corresponding to equation 11, when the exponentiation (still interpreted as a multiplication calculation) is implemented in the Walsh domain as a binary self-convolution of the elements of the transformed sequence, the order of which corresponds to the exponentiation considered.

[0132] Regardless of the embodiment considered, a given sequence of M items depending on at least one M time-domain samples of the input signal x[n] is Walsh transformed to obtain M sequential components of the corresponding transformed sequence.

[0133] 2. Step E310:

[0134] During step E310, for at least one given sequential component in the Walsh domain, at least one sum of a plurality of operands is calculated, said operand resulting from the product of, on the one hand, data dependent on at least one element of the transformed sequence X corresponding to said given sequential component and, on the other hand, the corresponding predistortion coefficient H, producing a sequential component of the predistorted transformed input signal .

[0135] More specifically, referring to Equation 8 and Equation 9, the summation operand appears to be weighting a piece of data by a coefficient h (an element of the matrix H), which depends on:

[0136] - transforming the data of a single element of the sequence X: this is the case when the multiplication (or exponentiation, still interpreted as a multiplication calculation) is implemented in the time domain before applying the Walsh transform to the sequence under consideration;

[0137] - one or more binary convolutions corresponding to two elements of said given sequential components, each element belonging to a transformed sequence X: corresponding for example to the general case of formula 5, when all or some of the multiplications are implemented in the time domain before applying the Walsh transform to the sequence under consideration, the other multiplications being implemented in the Walsh domain in the form of binary convolutions of elements of certain transformed sequences; and / or

[0138] - One or more binary self-convolutions of an element of the transform sequence X corresponding to the given sequential component: For example, corresponding to the MP case of formula 11, when all or part of the exponentiation (still interpreted as a multiplication calculation) is implemented in the Walsh domain in the form of binary self-convolutions. For example, in the case of optimization related to the computational load, for the MP model, the sum is the sum of M operands. The i-th operand (i is an integer from 1 to M) is obtained by the product of: on the one hand, the data obtained by the i-th order binary self-convolution of an element of the transform sequence X corresponding to the given sequential component, and on the other hand, the corresponding predistortion coefficient. Therefore, only binary self-convolutions are implemented, thereby reducing the computational load.

[0139] Returning to step E310, the calculation is repeated for the M sequential components of the Walsh domain to obtain the M sequential components of the predistortion transformed input signal. , n is an integer from 0 to M-1, as shown in Formula 8 and Formula 9.

[0140] 3. Step E320:

[0141] During a step E320, the M sequential components of the predistortion transformed input signal are Perform an inverse Walsh transform to obtain the output signal used to generate the RF signal In other words, the RF signal is the output signal generate, itself depends on the input signal x[n].

[0142] As above combined Figure 2 As mentioned above, according to the embodiment under consideration, the input signal processed by the predistortion module 210 can be in baseband, in an intermediate frequency or directly on the radio frequency carrier concerned. In the latter case, the output signal generated in step E320 Directly the RF signal (such as Figure 2 In the embodiment shown in the figure), in the embodiment where the input signal is baseband or intermediate frequency, the RF signal is output as Generated by frequency conversion as described above.

[0143] Furthermore, according to the embodiment considered, the inverse Walsh transform is implemented in a purely digital manner (e.g. Figure 2 ), or by utilizing the binary nature of the Walsh sequence to combine Figure 2 The semi-analog approach described implements the inverse Walsh transform.

[0144] 4. Step E330:

[0145] The predistortion coefficients H implemented in step E310 are determined to compensate for the influence of the transfer function of the PA 160. For example, the PA 160 is calibrated during production and a set of one (or more, for example depending on temperature or aging of components) predistortion coefficients H is thus determined.

[0146] Alternatively, the predistortion coefficient H is obtained by the predistortion module 210 via Figure 2 Such a determination is performed, for example, upon initialization of transmitter 200, or periodically during transmission to account for changes in the characteristics of the power amplifier during transmission of the RF signal.

[0147] More specifically, three different variations of determining the predistortion coefficients H by the predistortion module 210 are described below.

[0148] 4.1 Variant 1:

[0149] In the first variant, according to Figure 2 In the architecture of the transmitter 200, the determination of the predistortion coefficient H is based on minimization of an error signal, the error signal being expressed as:

[0150] - input signal x[n]; and

[0151] - a signal y[n] representing the modulation of the amplified radio frequency signal;

[0152] The difference between.

[0153] In other words, it is sought here to minimize the difference between the modulation of the amplified RF signal (ie, the distortion experienced by the PA 160) and the input signal delivering an undistorted modulation.

[0154] According to an embodiment, such minimization-implemented techniques belong to the following group:

[0155] - Least squares method;

[0156] - Normalized least squares method;

[0157] - Gauss-Newton algorithm; or

[0158] - Recursive least squares method.

[0159] Preferably, such minimization techniques are implemented in the Walsh domain based on signals constituting an error signal converted in the Walsh domain. In this example, the error signal in the Walsh domain is of the form:

[0160] [Formula 16]

[0161]

[0162] For example, the application of the least squares algorithm as described in detail in N. Wiener's book "Nonlinear Problems in Random Theory", Cambridge, LA: MIT Press, 1958, results in the following update formula for the predistortion coefficients:

[0163] [Formula 17]

[0164]

[0165] in is the adaptation step size, in the case of a general Voltra series:

[0166] [Formula 18]

[0167]

[0168] and:

[0169] [Formula 19]

[0170]

[0171] Each H coefficient is updated once for each new data block X (e.g., fed at a predefined refresh rate). The estimated gradient is calculated as an average of the data, rather than as an instantaneous value as in the time domain method. Therefore, it more accurately reflects the actual gradient, thereby accelerating the convergence of the algorithm. For example, in the case of the MP model, each iteration requires Q+1 Walsh transforms (i.e., M×log2(M) additions and / or subtractions in the so-called "fast" Walsh transform implementation), (Q×M) multiplications and / or additions for model adaptation, and (Q×M) multiplications and / or additions for coefficient updates. Therefore, the computational complexity of the algorithm is O(2×N1×Q×M + (Q+1)×M×log2(M)).

[0172] 4.2 Variant 2:

[0173] In a second variant, the determination of the predistortion coefficients H is based on the minimization of an error signal representing:

[0174] - input signal x[n]; and

[0175] - a second output signal generated by applying the current predistortion method to an input signal equal to the signal y[n] representing the modulation of the amplified radio frequency signal;

[0176] In other words, it is sought here to directly obtain the compensation of the distortion caused by the predistortion module 210 to the PA 160 by feeding at the input of the module 210 under consideration a signal y[n] representing the modulation of the amplified RF signal and comparing the output of the module 210 with the input signal x[n].

[0177] According to an embodiment, such minimization implements one of the techniques mentioned in variant 1 above.

[0178] Preferably, such minimization techniques are implemented in the Walsh domain based on signals constituting an error signal converted in the Walsh domain. In this example, the error signal in the Walsh domain is of the form:

[0179] [Formula 20]

[0180]

[0181] in is the second output signal generated by applying the present predistortion method to an input signal equal to the signal y[n] representing the modulation of the amplified RF signal, converted in the Walsh domain. Thus, in the case of a general Voltaic series:

[0182] [Formula 21]

[0183]

[0184] For example, by applying the least squares algorithm mentioned in the above variant 1, the following update formula for the predistortion coefficient is obtained:

[0185] [Formula 22]

[0186]

[0187] When implementing Variant 2, the same advantages discussed in Variant 1 apply.

[0188] 4.3 Variant 3:

[0189] In a third variant, the determination of the predistortion coefficients H is based on the minimization of an error signal representing:

[0190] - a modulation signal of a second radio frequency signal generated from the non-predistorted input signal x[n] and amplified by the PA 160; and

[0191] - Output signal ;

[0192] In other words, it is sought here, in a first step, to obtain the coefficients H that allow modeling of the PA 160 PA , so that the coefficients of the model converge so as to obtain at the output of the module 210 a mapping signal of the second radio frequency signal obtained at the output of the PA 160. Therefore, in the present variant, the signal output by the model, in the case of a general Voltaic series, is of the form:

[0193] [Formula 23]

[0194]

[0195] The predistortion coefficients H are obtained from the coefficients used to model the power amplifier, for example according to the method proposed by Yu and E. Zhu in the article "A comparative study of learning architecture for digital predistortion", 2015Asia-Pacific Microwave Conference (APMC), 2015, pp. 1-3, by the following formula:

[0196] [Formula 24]

[0197]

[0198] According to an embodiment, the minimization of the error signal implements one of the techniques mentioned in variant 1 above.

[0199] Preferably, such minimization techniques are implemented in the Walsh domain based on signals constituting an error signal converted in the Walsh domain. In this example, the error signal in the Walsh domain is of the form:

[0200] [Formula 25]

[0201]

[0202] in is a modulated signal of the second RF signal generated from the non-predistorted input signal x[n] and amplified by the PA 160 .

[0203] For example, in the case of a general Voltaic series, applying the least squares algorithm mentioned in the above variant 1, the following update formula for the model coefficients implemented in module 210 is obtained:

[0204] [Formula 26]

[0205]

[0206] When implementing Variant 3, the same advantages discussed in Variant 1 apply.

[0207] Now combine Figure 4 Describe an embodiment of the present invention for implementing Figure 3 An example of the structure of the device 210 for performing all or part of the steps of the predistortion method.

[0208] The device 210 comprises different means, such as a random access memory 403 (e.g. a RAM memory), a processing unit 402 (e.g. equipped with a processor), and is controlled by a computer program stored in a read-only memory 401 (e.g. a ROM memory or a hard disk). At initialization, the code instructions of the computer program are loaded into the random access memory 403, for example, and then executed by the processor of the processing unit 402.

[0209] Figure 4 Only the device 210 is shown to execute Figure 3 All or part of the steps of the predistortion method (according to the above combination Figure 3 In fact, these steps can be performed indifferently on a reprogrammable computer (PC computer, DSP processor or microcontroller) executing a program comprising a sequence of instructions, or on a dedicated computer (such as a set of logic gates such as FPGA or ASIC, or any other hardware module).

[0210] If the device 210 is implemented by a reprogrammable computer, the corresponding program (i.e., sequence of instructions) may be stored in a removable (e.g., CD-ROM, DVD-ROM, USB key) or non-removable storage medium, which may be partially or fully read by a computer or processor.

[0211] In some embodiments, the device 210 further includes a Figure 2 The semi-analog method for implementing the inverse Walsh transform device. For example, such a device includes:

[0212] - a plurality of 1-bit DACs (e.g., buffer type), each DAC being controlled by an inverse Walsh sequence amplitude corresponding to the sequential component considered in the inverse transform; and

[0213] - An analog summer for adding the outputs of the different 1-bit DACs to generate an analog quantity (voltage or current) representing the inverse Walsh transform of the predistorted transformed input signal to generate the output signal.

[0214] Thus, in all embodiments, the device 210 includes a Figure 3 A device for performing all or part of the steps of the predistortion method (according to the above combination Figure 3 any of the embodiments and / or variations described herein).

[0215] In some embodiments, device 210 is implemented in radio frequency transmitter 200 .

Claims

1. A method for predistorting an input signal to compensate for the effect of a nonlinear transfer function of a power amplifier (160) on a radio frequency signal generated by the input signal, characterized in that An electronic device performs: - performing a Walsh transform (E300) on at least one sequence of M items depending on the M time domain samples of the input signal, generating at least one sequence of M sequential components corresponding to the transformed sequence; - for at least one given sequential component in the Walsh domain, calculating (E310) at least one sum of a plurality of operands resulting from the product of: on the one hand data dependent on at least one element of the transform sequence corresponding to said given sequential component and on the other hand corresponding predistortion coefficients, producing a sequential component of the predistorted transformed input signal, wherein at least one data depends on: at least one binary convolution between two elements corresponding to said given sequential component, each element belonging to a transform sequence and / or depends on at least one binary self-convolution of an element of the transform sequence corresponding to said given sequential component, The sum follows a structure that depends on a Voltaic series of time-domain sampling of the input signal and conversion to the Walsh domain, The predistortion coefficients are determined to compensate for the effects of the transfer function of the power amplifier, Repeating the calculation for the M sequential components of the Walsh domain to generate the M sequential components of the predistorted transformed input signal, - performing an inverse Walsh transform (E320) on the M sequential components of the predistorted transformed input signal to produce an output signal for generating the radio frequency signal.

2. The method according to claim 1, characterized in that The Walsh transform is applied to a plurality of M sequences of terms dependent on at least one sequence of M time-domain samples of the input signal, producing a plurality of M sequential components of corresponding transformed sequences, and wherein the at least one data is dependent on: - each transform sequence of the plurality of transform sequences corresponds to at least one binary convolution between two elements of the given sequential components; and / or - one of said plurality of transform sequences corresponds to at least one binary self-convolution of an element of said given sequential component, and wherein said sum follows the structure of a Voltaic series dependent on said plurality of M time-domain sample sequences and converted to the Walsh domain.

3. The method according to claim 2, characterized in that At least one sequence of M terms includes at least one term that depends on: - the product between two time domain samples of the input signal; and / or - an integer power of at least one time domain sample of the input signal.

4. The method according to claim 1, characterized in that: The Walsh transform is applied to a plurality of M sequences of items dependent on M time-domain sampling sequences of the input signal, producing a plurality of M sequential components of corresponding transformed sequences, and wherein the at least one data depends on at least one binary self-convolution of an element of a transformed sequence in the plurality of transformed sequences corresponding to the given sequential component.

5. The method according to claim 4, characterized in that At least one sequence of M terms includes at least one term dependent on an integer power of at least one time domain sample of the input signal.

6. The method according to claim 1, characterized in that The Walsh transform is applied to a sequence of M items corresponding to a given sequence of M time-domain samples of the input signal, producing M sequential components of a corresponding transform sequence, and wherein the calculation comprises calculating the sum of M operands, the i-th operand (i being an integer from 1 to M) being obtained by multiplying, on the one hand, the data obtained by the i-th order binary self-convolution of an element in the transform sequence corresponding to the given sequential component, and on the other hand, the corresponding predistortion coefficient.

7. A method according to any one of claims 1 to 6, comprising determining the predistortion coefficients based on minimization of an error signal representing the difference between the input signal on the one hand and a signal representing the modulation of the amplified radio frequency signal on the other hand.

8. A method according to any one of claims 1 to 6, comprising determining the predistortion coefficients based on minimization of an error signal representing the difference between the input signal on the one hand and a second output signal on the other hand, the second output signal being generated by applying the method to an input signal representing a modulation of the amplified radio frequency signal.

9. A method according to any one of claims 1 to 6, comprising determining the predistortion coefficients based on minimization of an error signal representing the difference between, on the one hand, a signal representing the modulation of a second radio frequency signal generated by the non-predistorted input signal and amplified by the power amplifier and, on the other hand, the output signal.

10. The method according to any one of claims 7 to 9, wherein said determining uses a technique belonging to the following group to achieve said minimization: - Least squares method; - Normalized least squares method; - Gauss-Newton algorithm; or - Recursive least squares method.

11. The method of claim 10, wherein the technique is implemented in the Walsh domain based on a signal consisting of an error signal converted in the Walsh domain.

12. The method according to any one of claims 7 to 11, wherein the determining is performed periodically.

13. A computer program product comprising program code instructions for implementing the method according to any one of claims 1 to 12 when said program is executed on a computer.

14. An electronic device (210) for predistorting an input signal to compensate for the effect of a nonlinear transfer function of a power amplifier (160) on a radio frequency signal generated by the input signal, characterized in that: It comprises a device (402) configured to implement the predistortion method according to any one of claims 1 to 12.

15. A radio frequency transmitter (200) comprising the device according to claim 14.

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