Multi-carrier amplifier linearization system and method

ES 2 393 538 T3

DESCRIPTION

Multicarrier amplifier linearization system and procedure.

Technical field

The present invention relates, in general, to multifrequency communication systems with non-linearities in the transmission and, more particularly, it relates to a method and a circuit for pre-compensating the non-linear distortions experienced by a signal multiplexed in frequency in said systems.

Background of the invention

Many communication systems have elements or sub-systems that introduce unwanted non-linear distortions in the signals they transmit. For example, radio signal transmitters of wireless communication signals typically include power amplifiers (APs) at their output, which often have non-linear input-output characteristics and therefore introduce non-linear distortions. linear in the output wireless signal. The linearization of an AP has been a complex problem, especially for multi-carrier communication systems. A key issue in such linearization is to characterize the non-linear distortion of the multicarrier signal, caused by the non-linearity of the AP. Once the effect of the non-linearity of the AP on the signal is adequately characterized, the signal entering the AP can be pre-distorted in a way that pre-compensates for the non-linearity of the AP, reducing the non-linear distortion of the output signal at an appropriately low level.

US Patent 6,885,241, which has common inventors with the present application and was assigned to the assignee of the present application, discloses a type-based approach to generate a baseband pre-distortion function to pre-compensate for signals from single frequency before they enter the AP. Although the method disclosed in the patent 6,885,241 can be configured for use with multi-frequency signals in which the number of multiplexed frequency channels is small, it does not provide a good estimate of the required phase compensation when the signal contains a large number. of multiplexed asynchronous carriers.

An object of the present invention is to provide a method and circuit for compensating for non-linear distortions of frequency multiplexed signals in multi-carrier communication systems.

Summary of the invention

Consequently, the present invention relates to a method for compensating for non-linear distortion of a frequency multiplexed signal (MF) in an amplifier, comprising the following steps: a) pre-distorting the MF signal before passing it through the amplifier according to one or more adjustable pre-distortion parameters; b) passing the MF signal through the amplifier to obtain an output MF signal; c) sampling at least a part of the output MF signal to obtain a sampled signal comprising a sequence of signal samples; d) calculating a signal correlation matrix of size NxN for the sampled signal, where N is an integer greater than a number K of frequency channels in the MF signal, where K> 1; e) estimating a signal-to-distortion (RSD) ratio, or a value related thereto, based on the signal correlation matrix; and f) iteratively repeating steps a) to e) while varying the one or more adjustable pre-distortion parameters to increase RSD.

According to one aspect of the procedure, the RSD is estimated based on a relationship of eigenvalues ​​of the correlation matrix. In one embodiment, the method comprises computing a ratio of one or more larger eigenvalues ​​to one or more smaller eigenvalues. In one embodiment, the method comprises computing a ratio of a sum of the largest K eigenvalues ​​and a sum of the smallest (NK) eigenvalues. In one embodiment, the step of calculating the correlation matrix comprises calculating N different autocorrelation coefficients of the sampled signal.

Another aspect of the present invention refers to a circuit comprising an amplifier having an input port to receive an input frequency multiplexed signal (MF) comprising K frequency channels, and an output port to output an MF signal. output signal, in which the amplifier introduces non-linear distortions to the input MF signal while forming the output MF signal from it. The circuit further comprises a predistorter, coupled to the input port of the non-linear circuit, to pre-distort the input MF signal according to one or more adjustable pre-distortion parameters before passing it through the amplifier, a signal sampler, coupled to the output port of the amplifier, to sample at least a part of the output MF signal to get a sampled output signal, and a driver, operatively coupled between the signal sampler and the pre-distortion circuit, to receive the sampled output signal and to iteratively generate the one or more adjustable predistortion parameters. The controller further comprises a correlation calculation module for calculating a correlation matrix of size NxN for the sampled output signal, where N is an integer greater than K, an RSD calculation module, operatively coupled to the correlation calculation module. , to calculate a signal-to-distortion (RSD) ratio based on the correlation matrix, and a pre-distortion generator, operatively coupled to the RSD calculation module, to generate the one or more pre-distortion parameters depending on the RSD.

ES 2 393 538 T3

Brief description of the drawings

The invention will be described in greater detail with reference to the accompanying drawings, which represent preferred embodiments thereof, in which like elements are indicated by like reference numerals, and in which:

Fig. 1 is a schematic block diagram of a non-linear distortion pre-compensation circuit in accordance with the present invention;

Fig. 2 is a schematic block diagram of a first implementation of a quadrature multicarrier transmitter with non-linear distortion pre-compensation and vector downconversion in a feedback circuit;

Fig. 3 is a schematic block diagram of a second implementation of a quadrature multicarrier transmitter with non-linear distortion pre-compensation and scalar downconversion in the feedback circuit;

FIG. 4 is a schematic block diagram of an exemplary pre-distorter controller in accordance with one embodiment of the present invention;

Fig. 5 is a schematic block diagram of a correlation matrix computing module according to an embodiment of the present invention;

FIG. 6 is a graph showing non-linear output amplitude (upper panel) and phase (lower panel) plots characteristic of a No. 1 AP (traveling wave tube amplifier);

Fig. 7 is a graph showing non-linear output amplitude (upper panel) and phase (lower panel) plots characteristic of a No. 2 AP (solid state power amplifier);

Fig. 8 is a graphic illustration of the distribution of eigenvalues ​​according to the simulations;

Fig. 9 is a graph showing enlarged parts of the eigenvalue distribution of Fig. 8;

Fig. 10 is a graph showing the output characteristics of AP No. 1 (point curves), the corresponding predistortion functions generated in the simulations by the 1^to implementation (Fig. 2) of the present invention (dashed curves), and the resulting compensated characteristics (solid curves) for the amplitude (upper panel) and phase (lower panel) of the output signal;

Fig. 11 is a graph showing simulated graphs of the output spectrum of AP No. 1 with and without linearization according to the 1st implementation (Fig. 2) of the present invention;

Fig. 12 is a graph showing the simulated constellations of the output signal of AP No. 1 with and without linearization according to the 1st application (Fig. 2);

Fig. 13 is a graph showing the output characteristics of AP No. 2 (dotted curves), the corresponding predistortion functions generated in simulations by the 1st implementation (Fig. 2) of the present invention (dashed curves) , and the resulting compensated characteristics (solid curves) for the amplitude (upper panel) and phase (lower panel) of the output signal;

Fig. 14 is a graph showing simulated graphs of the output spectrum of AP No. 2 with and without linearization according to the 1st implementation (Fig. 2) of the present invention;

Fig. 15 is a graph showing the simulated constellations of the output signal of AP No. 2 with and without the linearization according to the 1st implementation (Fig. 2);

Fig. 16 is a graph showing the output characteristics of AP No. 1 (dotted curves), the corresponding predistortion functions generated in simulations by the 2nd implementation (Fig. 3) of the present invention (dotted curves) , and the resulting compensated characteristics (solid curves) for the amplitude (upper panel) and phase (lower panel) of the output signal;

Fig. 17 is a graph showing simulated graphs of the output spectrum of AP No. 1 with and without the linearization according to the 2nd implementation (Fig. 3) of the present invention;

Fig. 18 is a graph showing the simulated constellations of the output signal of AP No. 1 with and without the linearization according to the 2nd implementation (Fig. 3);

Fig. 19 is a graph showing the output characteristics of AP No. 1 (dotted curves), the corresponding predistortion functions generated in simulations by the 1st implementation (Fig. 2) of the present invention (curves

ES 2 393 538 T3 dashed), and the resulting compensated characteristics (solid curves) for the amplitude (upper panel) and phase (lower panel) of the output signal;

Fig. 20 is a graph showing simulated graphs of the output spectrum of AP No. 2 with and without linearization according to 2^to implementation (Fig. 3) of the present invention;

Fig. 21 is a graph showing simulated constellations of the output signal of AP No. 2 with and without the linearization according to the 2nd implementation (Fig. 3);

Fig. 22 is a graph showing the measured output spectra of an AP with and without linearization according to the 1st implementation (Fig. 2) of the present invention;

Fig. 23 is a graph showing the measured output spectra of an AP with and without linearization according to the 2nd implementation (Fig. 3) of the present invention.

Detailed description

In the following detailed description, numerous specific details are set forth in order to provide a complete understanding of the invention. However, those of ordinary skill in the art will understand that the present invention can be practiced without these specific details. In other cases, well-known methods, procedures, components, and circuits have not been described in detail so as not to obscure the present invention.

Some parts of the detailed description, below, are presented in terms of algorithms and symbolic representations of operations on data bits or binary digital signals within a computer memory. These representations and algorithmic descriptions can be the techniques used by people with knowledge of the subject to convey the essence of their work to other people with knowledge of the subject.

Unless otherwise specified, as is evident from the following statements, it is appreciated that in all specification descriptions that use terms such as processing, computation, calculation, determination, or the like, they refer to the action and / or the procedures of a computer or computer system, or similar electronic computing device, that manipulates and / or transforms the data represented as physical, such as electronic quantities within the records and / or memories of the computer system in other data similarly represented as physical quantities in the memories, records of the computer system or other similar information storage, transmission or display devices.

Furthermore, the term circuit, in the context of the present specification, means a single component or a multiplicity of components, active and / or passive, that are arranged to cooperate with each other to provide a desired function, and may be implemented, at least partially, in firmware and / or software.

The term "signal" means at least an RF signal, a current signal, a voltage signal, or a data signal, and can mean a complex signal, such as a signal composed of quadrature I and Q signals.

The term "modulated signal" as used herein includes modulated carrier AC signals having a non-zero carrier frequency, and having their frequency, phase, and / or amplitude modulated in accordance with a predetermined modulation format with a sequence of information symbols, and modulation signals that have a DC carrier, such as binary or multilevel data signals, used to modulate one of the parameters of a DC carrier signal. The terms modulation format and modulation scheme are used in memory interchangeably.

Exemplary embodiments of a circuit for compensating for distortions experienced by a multicarrier signal in a non-linear circuit will now be described, in detail, with reference to the block diagrams shown in Figs. 1 to 4, in which like elements are indicated by like reference numerals. Each block in the diagrams shown in Figs. 1 a 4 is a functional unit of the circuit, and is adopted to perform one or more steps of the method of the present invention to compensate for non-linear distortions of the multicarrier signal in an embodiment thereof; These steps will also be described later herein in conjunction with the description of the corresponding functional blocks of the circuit.

Referring firstly to Fig. 1, there is shown a simplified block diagram of an apparatus 1 with compensation for non-linear distortions of an input multi-carrier, frequency multiplexed (MF) signal according to an embodiment of the present invention. Apparatus 1, also referred to herein as circuit 1, includes a non-linear circuit (CNL) 37 for performing a desired function on the MF signal passing through it. The CNL 37 has an input port 7 for receiving the MF signal 3, and an output port 9 for outputting the MF signal after it passes through it. Hereinafter, the MF signal before entering the CNL 37 is referred to as the input MF signal 3, and after passing the CNL 37 as the output MF signal 5. CNL 37 is preceded

ES 2 393 538 T3 operatively by a pre-distorter (PD) 33, which is coupled to the input port 7 of the CNL 37 to predistort the MF signal 3 to pre-compensate the non-linear distortions in the CNL 37, as described in detail below. A feedback circuit 99 is coupled between the output port 9 of the CNL 37 and a control port 22 of the pre-distorter 33; its function is to control the operation of the pre-distorter 33 as a function of the MF 5 output signal at the output port 9 of the CNL 37. In operation, the feedback circuit 99 receives the output MF signal 5 from the output port 9, or at least a part of it derived from the output port 9 using a bypass coupler 45, and estimates the non-linear distortion which is present in the output MF signal 5 of the CNL 37, to allow the pre-distorter 33 to pre-compensate it. The feedback circuit 99 can operate iteratively, repeatedly adjusting a pre-distortion function applied to the input MF signal 3 by the pre-distorter 33 until the non-linear distortion, measured by the feedback circuit 99, is sufficiently reduced.

The feedback circuit 99 includes a sampling circuit 65, also referred to herein as sampler 65, which is operatively followed by a controller 88 to control the pre-distorter 33. Controller 88 includes various functional blocks, such as a correlation calculation module 11, also referred to herein as a correlation matrix calculator (CMC), an RSD calculation module 14, which hereinafter also referred to as an RSD calculator, and a pre-distortion generator (GPD) 17, where the abbreviation 'RSD' refers to signal-to-distortion ratio. The CMC 11, RSD calculator 14, and GPD 17 can be embodied as software or firmware modules defined within a single processor or multiple processors, or with dedicated hardware logic.

In accordance with embodiments of the present invention, controller 88 uses a novel technique to estimate nonlinear distortions of a signal in a transmission chain of a multi-carrier communication system. The technique is based on the understanding that a multicarrier signal composed of K modulated carriers can be characterized in an N-dimensional space, with N> K, and that this N-dimensional space can be decomposed into a signal subspace, of dimension K, and an orthogonal noise subspace of dimension (NK). In the absence of non-linearity, the signal subspace contains all or almost all of the signal energy, while the noise subspace is a space with little or no signal energy. However, in the presence of non-linearity, the inter-modulation and intra-modulation products cause energy to propagate to the 'noise' subspace in the form of distortion energy, thus reducing the energy ratio of the signal subspace with respect to the energy of the noise subspace. The reduction in the ratio is generally proportional to the non-linearity in the transmission chain, the effect of which on the MF signal can be reduced using a pre-distortion function, or a set of predistortion parameters, that maximize the energy ratio of the signal with respect to distortion energy (RSD). This novel technique is described below in detail with reference to exemplary embodiments of the method and circuit of the present invention.

To aid in description hereinafter, the following notations and definitions will be used. The input MF signal 3 is assumed to be composed of a plurality of independent frequency channels, with an integer K> 1 indicating the number of frequency channels that are present in the MF signal. The terms multicarrier and frequency multiplexed are used herein interchangeably to refer to signals made up of multicarrier signals having different carrier frequencies. The term frequency channel refers to a modulated carrier signal s_k(t) that has a carrier frequency D_k = 2mf_k which is specific to the frequency channel; here, k = 1, ..., K is an integer channel index. Mathematically, the kth carrier signal can be described by equation (1):

(1) in which a_k(t) indicates an amplitude and <J>_k(t) indicates a phase of the k-th channel signal, and t indicates the time.

In one embodiment, the K frequency channels are multiplexed by summing their respective baseband signals. A baseband representation of the MF signal at CNL 37 input port 7, indicated here as x (t), can be expressed mathematically with the following equation (2):

(2)

1:=1

In operation, the non-linear circuit 37 introduces unwanted non-linear distortions to the MF signal; a baseband representation of the output MF signal 5 produced by the CNL 37 at its output port 9 will be indicated as y (t). The term non-linear circuit is used here to refer to a circuit that, after receiving an input signal at its input port, outputs an output signal that is related, non-linearly, to the input signal, from so that, for example, an output power of the circuit is scaled, non-linearly, with an input power to the circuit.

ES 2 393 538 T3

Exemplary embodiments of the present invention, described herein, relate to non-linear circuits 37, which output a signal y (t) that has both a desired linear component with respect to the input signal x (t), and an unwanted non-linear component with respect to the input signal x (t), with the unwanted non-linear component also referred to as non-linear distortion. By way of example, the non-linear circuit 37 may be an amplifier having a coefficient g₁ linear gain, in which case the output MF signal can be expressed as follows:

+ O)

Here D_x(t) indicates the non-linear distortion introduced by the non-linear circuit 37; d_x(t) is a non-linear function of the input signal x (t) MF and is defined by the non-linear characteristics of the amplifier 37. To simplify the description that follows, hereinafter, it will be assumed that the coefficient of linear gain g₁ = 1; however, it will be appreciated that the procedure described herein remains valid for any value of the linear gain coefficient.

In many practical applications, the presence of this non-linear distortion in the output MF signal is undesirable. Accordingly, the function of the feedback circuit 99 is to first estimate the non-linear distortion of the output MF signal and then, based on this estimate, to select a suitable pre-distortion function for the pre-distorter. 33 to minimize, or at least reduce, non-linear distortion in the output MF signal to a suitably low level.

The operation of the feedback circuit 99 can generally be described as follows. First, the output MF signal 5, or a fraction thereof according to a bypass ratio of the bypass coupler 45, is received by the sampler 65. The sampler 65 samples, that is, measures the output MF signal 5 at a sampling frequency r_s which satisfies the Nyquist sampling theorem to cover the entire frequency band encompassed by the K frequency channels. Indicating the total frequency bandwidth occupied by the K channels as B_K, this corresponds to a requirement of γ,> 2Βκ. (4)

The sampler 65 outputs an MF signal 128 sampled in the form of a sequence y (n) of signal samples, where the discrete index n = 1, 2, ... indicates consecutive signal samples. Using equations (1) to (3) and the discrete time index n, the signal samples at the output of sampler 65 can be described as

X ») = + (5)

The sampled signal y (n) is provided to the CMC 11, which calculates, from it, a correlation matrix R of a size NxN, where N indicates the number of columns and the number of rows of the matrix R; N is greater than K and is referred to here as the order of the matrix. In the context of the present specification, the computation of a matrix is ​​understood as the computation of all the elements of the matrix necessary to define the matrix, and store them in a computer-readable memory, in an ordered way, so that any element R (¡, j) of the matrix can be accessed when necessary, where the indices i and j indicate columns and rows of the matrix, respectively. The order N of the matrix can be any value greater than the number K of carriers. If K is known, a convenient choice is N = 2K, so that both the signal subspace and the noise subspace have approximately the same dimension. If K is unknown, it can be estimated from the measurement, for example, using an information theoretical criterion, such as Akaike's theoretical information criterion (AIC) or the minimum description length criterion (MDL), which are known in the art, or based on the distribution of eigenvalues, as described below.

Based on the calculated correlation matrix or, more particularly, a ratio of its eigenvalues ​​corresponding to the signal and noise sub-spaces, the RSD calculator 14 generates an estimate of the RSD, or a value related thereto. , this estimate provides a convenient measure of the non-linear distortion in the MF signal at the output of the CNL 37.

Repeating this RSD measurement procedure, that is, sampling the output signal, calculating the correlation matrix and estimating, from it, the RSD, while varying a pre-distortion function that the predistorter 33 applies to the input MF 3 signal, a suitable pre-distortion function that precompensates for the non-linear distortion can be found in the CNL 37, to increase the RSD to a sufficiently high level.

The procedure of RSD measurement based on the received MF signal can be further understood by analyzing the properties of the correlation matrix of the sampled output MF signal 128.

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The correlation matrix R of size NxN can be expressed mathematically using vector notations, as explained below

R = £ {yy} (7) in which the superscript H indicates the complex conjugate and the transpose of a matrix or vector, EQ indicates an average of a set, and y is a vector composed of N consecutive signal samples and (n +1) ay (n + N); represents a subsection of the sampled signal 128 of length N beginning with sample y (n + 1) and consisting of a sequence of N signal samples:

(X ·) 1

W

In equation (8) the discrete time index n is eliminated since the average E {} in equation (7) is carried out over a wide range of indices n of the starting sample.

The correlation matrix R of a sampled signal is a symmetric matrix, whose input i, j, R (i, j) is an auto-correlation coefficient of the sampled signal with a discrete time delay (ij), that is, an average value of a product of a first signal sample y (ni) by a second signal sample y (nj) that lags behind the first signal sample by (ij) samples, 1 <i, j <N :

(6) in which the superscript indicates the complex conjugate of a complex number. The set average E {} in equation (6) can be approximated by an average over a sufficiently long section of the sampled signal 128, preferably containing more than one, and more preferably many, for example 100 or more, symbol periods of each of the carriers s_k(t) modulated. For a stationary signal, that is, a signal whose statistical properties do not depend on time, equation (6) can be rewritten as:

- ** (M) = r & fr (* ») where the delay of discrete samples | ij | varies between 0 and N-1, and r (rj) = r * (ji). Accordingly, in one embodiment, the calculation of the correlation matrix R may involve calculating at least N different autocorrelation coefficients r (p) of the sampled signal, corresponding to the sample delay p-values ​​between 0 and N-1, and saving them in a computer readable memory for use as elements of the correlation matrix R according to R (i, j) = r (rj) in further processing. In one embodiment, each of the at least N different auto-correlation coefficients r (p) is calculated by accumulating, for a section of the sampled signal 128 spanning multiple modulation periods of each of the frequency channels, products of pairs of the signal samples y (n). and * (np) that have the same delay p between samples, where p is an integer in the interval from 0 to (N-1), and calculating an average value of them.

Although the nonlinear distortion d_x(t) depends on the input signal x (t), which is not linearly correlated with the input signal, that is, (9)

From equations (9), (7) and (5), it follows that the correlation matrix R can be represented as a sum of a correlation matrix Ri of the input signal MF x (t), and a matrix R_d correlation of component d_x(t) of non-linear distortion, that is:

R = Ri + Rj (10) where

ES 2 393 538 T3

R_w»I '{d * d}, *

¿OTj (U)

Component d_x(t) Nonlinear distortion is composed of multiple intermodulation products between the K input carrier signals, as well as their intra-modulation products. The stronger the non-linearity of CNL 37, the greater the relative strength of the inter-modulation and intra-modulation products.

Next, the correlation matrix R will be indicated in the absence of non-linear distortion, that is, when d_x(n) = 0, as Ri, and in the presence of nonlinear distortion as R₂. It can be shown that Ri has a range that does not exceed the number K of independent carriers, provided the following conditions are met: i) high sampling frequency: the bandwidth B of each signal s_k(t) carrier is much less than the sampling frequency r_s, that is, B «r_s, so that the amplitude and phase of each of the carriers s_k(t) modulated remains substantially constant over every N consecutive sampling points, and ii) independent channels: the carriers s_k(t) are modulated by uncorrelated signals and are therefore statistically independent. Under these conditions, the correlation matrix Ri has only K positive eigenvalues, and the remaining (NK) eigenvalues ​​are all zero.

Consequently, indicating the K nonzero eigenvalues ​​by yi, and₂, ... Y_K arranged in descending order, Ri can be expressed as

0 / in which U is a unit matrix NxN whose columns are N eigenvectors, and which satisfies the equation U '¹ = U^H.

Based on this property of Ri, the N-dimensional space encompassed by the N eigenvectors can be decomposed into two subspaces: the one-dimensional signal subspace K, which is encompassed by K eigenvectors associated with the K eigenvalues, bigger, and, and₂, ... Y_k, and the orthogonal subspace, of dimension (NK), which is encompassed by the remaining eigenvectors associated with the (NK) null eigenvalues ​​γ_1κ+ ι, Yn, and referred to herein as the noise subspace or the distortion subspace. With this decomposition of the signal into subspaces, the largest K eigenvalues ​​represent the total energy in the signal subspace, while the noise subspace, in the absence of non-linear distortion, does not contain energy, that is, all eigenvalues noise γ-ικ + 1, ... Yn are zero.

In the presence of nonlinear distortion, Ra has nonzero elements and is typically a positive definite matrix when d_x(t) contains many high-order inter-modulation and intra-modulation products. This is true as long as the number of inter-modulation and intra-modulation products is greater than the dimension of R_d, which is typically true as long as N is not very large, for example, N ~ 2K. Consequently, all the N eigenvalues ​​of the matrix R are positive, or at least not negative.

Consequently, if the number of substantially nonzero eigenvalues ​​exceeds K, this indicates that the signal energy is propagated to the noise subspace rather than being contained in the Kdimensional signal subspace, as in the case of linear amplification. In other words, due to non-linear distortion, part of the signal energy is converted into noise-like components residing in the noise subspace, thereby reducing the signal energy in the signal subspace. In a general case, with the correlation matrix of the MF signal in the presence of the non-linear distortion indicates as R₂, the eigenvalue decomposition of the correlation matrix takes the form

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Λ₂ - KA_toV = V

<img file="ES2393538T3_D0001.tif" />

(13) in which V is the matrix of eigenvectors of the matrix R₂ correlation, and A, λ₂, λ_Ν are eigenvalues ​​of the matrix R₂ of correlation arranged in descending order. Then the K largest eigenvalues ​​1M2. ····. λ_κrepresent the energy in the signal subspace, while the smallest (NK) eigenvalues ​​λ · ι_{+ κ}, ...., λ_Νrepresent the energy in the noise subspace.

Therefore, the signal-to-distortion ratio (RSD), which characterizes the quality of the MF signal in the presence of non-linear signal distortion, can be estimated based on a relationship of the eigenvalues ​​corresponding to the subspaces of signal and noise, respectively. In particular, the RSD can be estimated as a ratio of a sum of the K largest eigenvalues ​​λ |, λ₂, ...., λ_κ with respect to a sum of the smallest (NK) eigenvalues ​​of the matrix R₂ correlation:

SOR = go

Σ * .iieI

Σ ^ (14)

The higher the RSD, the better the signal quality or the lower the effect of non-linear distortion on the signal. In the ideal case without non-linearity and in the high sampling frequency approximation, -ιλκ = λ₂+ κ ⁼ = λ_Ν = 0, and the RSD is infinite.

To reduce non-linear distortion of the output MF signal 5, the input MF signal 3 is pre-distorted by predistorter 33, using an adjustable pre-distortion function, before the signal passes through CNL 37. The pre-distortion function should have non-linear characteristics inverse to the non-linear characteristics of CNL 37, so that when the pre-distorted signal passes through the AP, the non-linear effect is canceled at the AP output.

This pre-distortion function, or one or more adjustable parameters that define it, is generated by the predistortion generator 17 depending on the RSD value calculated by the RSD calculator 14, or an objective function value related thereto, to increase the RSD. Different procedures can be used to find a suitable pre-distortion function that maximizes RSD; For example, controller 88 may be programmed to search through a plurality of values ​​of the one or more adjustable parameters that define the pre-distortion function, at each stage measuring and saving the corresponding RSD values, and then selecting those values ​​of the adjustable parameters that provide a higher RSD. Such an exemplary algorithm is provided below.

Accordingly, the compensation procedure for the non-linear distortion of the MF signal passing through the CNL 37 can be described as follows:

a) the input MF signal is pre-distorted before passing it through the non-linear circuit according to one or more adjustable pre-distortion parameters using the pre-distortion 33;

b) after passing through CNL 37, the MF signal, or at least a part thereof, is received by feedback circuit 99 as a received output MF signal;

c) in the feedback circuit 99, the received output MF signal is sampled by the sampler 65 to obtain a sampled signal 128 comprising a sequence of samples y (n) of signal;

d) based on the sampled signal 128, the CMC 11 calculates a signal correlation matrix of size NxN, where N&gt; K;

e) Next, this correlation matrix is ​​used by RSD calculator 14 to generate an RSD estimate.

Next, steps a) to e) can be repeated iteratively while varying the one or more adjustable predistortion parameters so as to increase the RSD.

Now, exemplary embodiments of the invention will be described in more detail, with reference to a transmitter

ES 2 393 538 T3 quadrature multicarrier (QMC) employing a power amplifier (AP) having a non-linear input / output characteristic, which is compensated for using the technique generally described above.

Referring first to FIG. 2, there is shown a simplified block diagram of a QMC transmitter circuit 100, hereinafter referred to simply as a transmitter 100. The transmitter 100 has a digital circuit part and an analog circuit part which are indicated by a dotted line 44 between them. Transmitter 100 can be viewed as an embodiment of circuit 1, in which CNL 37 is in the form of a power amplifier (AP); accordingly, in this embodiment and other embodiments of the CNL 37, it will be referred to as the AP 37. According to an arrangement known in the art, the AP 37 receives the input MF signal 3 'from a vector modulator 30. In this embodiment, the 3 'MF signal that is passed through the AP 37 is generated from K discrete modulated quadrature channel signals s_k(m), k = 1, 2, ..., K. These discrete channel signals are summed together using a digital signal multiplexer 15, with a pre-assigned frequency assignment to respective carrier frequencies Ω-ι, Ω₂, ..., Ω_κ, listed in ascending order for convenience of description. This frequency assignment is relative to a frequency D_RF RF carrier that is generated by a local oscillator (OL) 35, as is known in the art. To distinguish from the frequency!_RF RF carrier, frequencies Ω_κCarriers will also be referred to in this embodiment as subcarrier frequencies.

The K signals s_kDiscrete channel (m) can be described mathematically using equation (1), substituting the discrete time, or symbol period, the index m in place of the continuous time variable t, where a_k(m) and &lt;P_k(m) the amplitude and phase, respectively, of the k-th signal of the discrete channel. The discrete time index m can indicate time intervals of consecutive information symbols with which the subcarrier frequencies D_k, k = 1, 2, ..., K, are modulated. These K discrete channel signals are assumed to be_k(m) are statistically independent of each other, and that their individual bandwidths B are small relative to the total bandwidth B_K occupying after multiplexing, and in relation to the frequency r_s used in feedback circuit 199.

In the digital multiplexer 15, the summed signal is divided into a component l (m) in phase and a component Q (m) in quadrature, which are then converted to analog waveforms, indicated by l (t) and Q (t), respectively, by two digital-to-analog (D / A) converters 20 after passing through a pre-distorter 133. The in-phase and quadrature analog components l (t) and Q (t) are then passed to the vector modulator 30, where they are used to modulate an amplitude and a phase of the RF carrier signal generated by the OL 35. The resulting analog 3 'MF signal, whose baseband representation is indicated as x (t), is amplified by the AP 37, and is output from it in the form of the output MF signal 5, whose band representation base is indicated as y (t).

The AP 37 is a non-linear device, and its output signal y (t) can be described mathematically with equation (3), with the term d_x non-linear distortion dependent on the non-linear characteristics of the AP 37 and the input signal x (t). To compensate for this non-linearity, the transmitter 100 includes the pre-distorter (PD) 133 and a feedback circuit 199, which generally have the same functionality as the PD 33 and the feedback circuit 99, respectively, described above with reference to the circuit. 1 of Fig. 1.

More specifically, the pre-distorter 133 operates in the digital domain, applying a non-linear pre-distortion function to the received digital I and Q signals to generate a pre-distorted digital MF signal in the form of two signal components I and Q. in quadrature, which will be indicated as l_D(m) and Q_D(m), respectively. In one embodiment, the pre-distortion function is a function of complex values ​​of the amplitude a of the MF signal at the input of predistorter 33; indicating it as D (a | c- |, c₂), this pre-distortion function can generally be described with the following equation:

2} (ii | ci, c3), 4 (

In this equation, c₁ = (c ^, c₁₂, ..., c_1L) is a vector of L parameters for an amplitude pre-distortion function A (a | c- |), c₂ = (c₂₁, c₂₂, ..., C_2J) is a vector of J parameters for a phase pre-distortion function ip (a $. The amplitude pre-distortion function A (a | c- |) is useful to cancel the AM-PM conversion of the AP, and the function4J (a | c ₂phase distortion) is useful to cancel the AP's AM-PM conversion. The integers L and J define the number of adjustable parameters used by the pre-distorter 33 and, generally, they can each be equal to or greater than zero, but they cannot both be equal to zero, so there is at least minus one load pre-distortion parameter that can be varied to adjust the pre-distortion function. In operation, these parameters are generated and / or varied by the pre-distortion generator 17 in the controller 88.

By way of example, the pre-distorter 133 can generate the signals l_D(m) and Q_D(m) pre-distorted from the input MF signals l (m) and Q (m) in quadrature according to the following equations:

<img file="ES2393538T3_D0002.tif" />

ES 2 393 538 T3 (16) in which _fl = 7/^) + 0³^) (17) is the amplitude of the input MF signal at pre-distorter 33.

In one embodiment, the amplitude and phase distortion functions are polynomial functions of the amplitude a of the MF signal, and are defined as follows:

A (a, c,) = c,, íT +. + c ^ a '(18) and

^(0,05) = ^(2+^(2¹ + ... + Cjjdf ·⁷. (19)

In other embodiments, other forms of the pre-distortion function may be used, including, but not limited to, Volterra series, Fourier series, and rational functions.

Feedback circuit 199 includes controller 88 for controlling pre-distorter 133, and sampler 65 embodied herein with two analog-to-digital (A / D) converters. In addition, the feedback circuit 199 includes a vector mixer 55 followed by two low pass filters 60 (FPB) connected between the mixer 55 and the A / D converters 65. In operation, a fraction of the MF signal y (t) from the output of the AP 37 is directed by the bypass coupler 45 to the vector mixer 55. The mixer 55 downconverts the received fraction of the output MF signal 5 to the baseband by mixing it with the RF carrier signal supplied by the OL 35, and outputs the received downconverted MF signal as components u ( t) and v (t) of in-phase and quadrature signals, which then are subjected to low-pass filtering by FPBs 60 and are sampled by sampler 65 to generate signal 128 sampled in the form of u (n) and v (n) l / Q signals with discrete real values, where y (n ) = u (n) + jv (n), which are supplied to controller 88. Next, controller 88 computes the matrix R₂ correlation, and calculates the eigenvalues ​​of R₂ o estimates a ratio thereof for the signal and noise sub-spaces to obtain an estimate of RSD, and updates the pre-distortion parameters as a function of the estimated RSD, as described, in general, above and , as described below, more specifically, with reference to a specific exemplary embodiment. Controller 88 can be implemented using a digital signal processor (DSP), as indicated by way of example in the figure. A person skilled in the art would appreciate that other processing means can be used to implement controller 88, such as, but not limited to: a general purpose processor, a specialized microprocessor, an FPGA (Field Programmable Gate Array), an ASIC (application specific IC) or a combination of the above. In some embodiments, controller 88 and PD 133 can be implemented using a single processor, such as a single FPGA.

Once the input MF signal is pre-distorted with the pre-distortion function Díalc-ic ^), the output MF signal of the AP 37 becomes dependent on the pre-distortion function. Consequently, the matrix R₂ correlation and therefore the corresponding RSD calculated by controller 88 depend on the parameter sets C1 and c₂adjustable, i.e. RSD = RSD (ci, c₂). The pre-distortion function, or a set of parameters that define it, such as elements of C1 and / or c₂, is loaded to pre-distorter 133 to pre-distort the input signal of the AP, for example, according to equation (16). The procedure is iterative, and controller 88 can continually make adjustments to pre-distorter 133 to maximize the RSD of the MF signal 5 at the output of AP 37.

The use of the vector mixer 55 in the feedback circuit 199 of the transmitter 100 allows to capture substantially all the information about the signal MF y (t) at the output of the AP, and use it to estimate the RSD and optimize the pre-distortion function. . However, use of the vector mixer 55 can introduce unwanted gain and phase imbalances between the I and Q output signals u (t) and v (t), which can provide inaccurate RSD estimates and degrade compensation performance. distortion, unless corrective action is taken. In addition, the vector down-conversion scheme of Fig. 2 requires two low pass filters 60 and two A / D converters 65 in the feedback circuit 199.

Now, referring to FIG. 3, a QMC transmitter circuit 200 is illustrated, which can be viewed as an embodiment of transmitter 100 with a simplified feedback circuit 299 that implements scalar down-conversion and sampling. In this implementation, referred to hereinafter as implementation No. 2, to distinguish it from that of Fig. 2, referred to as implementation No. 1, a

ES 2 393 538 T3 single scalar mixer 155 and consequently a single FPB 60 and a single A / D converter 65 to perform a downconversion of the output MF signal 5 to baseband to form the received output MF signal, which is now scalar, that is, represented by a single waveform with real values, and to sample a signal u (t) scalar, downconverted, resulting at the sampling frequency r to obtain a signal u (n) sampled. The bandwidth requirements of the FPB and the frequency r_s sampling remain the same as for the implementation of Figs. 1 and 2.

The scalar signal sampled in the form of a sequence of signal samples u (n) is used by controller 88 to directly construct the correlation matrix R. In this embodiment, the correlation matrix R has real values, as opposed to the R with complex values ​​in the embodiment of Fig. 2, which is used, in turn, to estimate the RSD based on a relationship of the values own of the correlation matrix. Since the scalar sequence, that is, with real values, of the signal samples u (n) contains non-linear distortion information, it can be used to derive the pre-distortion function. Statistically, however, there may be some performance degradation due to the fact that only half of the samples are actually used. This loss of performance can be mitigated by increasing the length of the sample sequence that is used to calculate the correlation matrix R. The hardware savings in this scalar implementation of the feedback circuit is evident, and gain / phase imbalances due to the vector mixer are advantageously avoided.

Referring to FIG. 4, a functional block diagram of controller 88 is shown in one embodiment thereof. The controller 88 in this embodiment includes in its input the CMC 110, which is operatively followed by an eigenvalue calculator 120 (CVP), which, in turn, is followed by an eigenvalue classifier 130 (EVS), which, in turn, it is connected to an RSD calculator 140. An output of RSD calculator 140 is coupled to RSD memory 150 to store RSD values ​​or OR values._Sdr of objective function related to it. An RSD comparator 160 is operatively coupled between the RSD calculator 140 and a pre-distortion generator (GPD) 170, and is further coupled to RSD memory 150 to compare the values ​​stored therein with a current RSD value. obtained from RSD calculator 140. An output of pre-distortion generator 170 is coupled to predistorter 133 (PD).

In operation, the CMC 110 receives the sampled signal 128, and generates, from it, the correlation matrix R or, equivalently, all the different elements thereof; Since the correlation matrix is ​​symmetric, it has a maximum of N * (N-1) / 2 different elements, and it can have only N different elements corresponding to N autocorrelation coefficients, being able to obtain all the other elements of the matrix obtainable at from these. The operation of the CMC 110 has been generally described above, and is described in more detail below, with reference to FIG. 5 for an exemplary embodiment.

The CVP 120 obtains from the CMC 110 all the necessary elements C (i, j) of the matrix, and calculates the eigenvalues ​​A, of them using procedures known in the art, such as the transformation of the correlation matrix R to a diagonal form using an eigenvalue decomposition of the form represented by equation (13). The EVS 130 receives the eigenvalues ​​from the CVP 120, sorts them in ascending or descending order to identify one or more, and even K, larger signal-related eigenvalues, and passes them to the RSD calculator 140 to calculate the RSD or an O value_SDR objective related to it.

In one embodiment, the RSD calculator uses equation (14) to calculate the RSD as a ratio of a sum of the largest K eigenvalues ​​to a sum of the remaining eigenvalues, that is, the (NK) values own smaller ones.

In another embodiment, the EVS 130 and CVP 120 can be omitted, and the RSD calculator obtains the coefficients of the correlation matrix R from the CMC 110 to estimate the RSD directly, without first finding the eigenvalues. In such an embodiment, the RSD calculator estimates the RSD based on a condition number of the correlation matrix R, which is a ratio of the eigenvalue λ₁ larger with respect to a smaller eigenvalue, that is, according to the equation

SDR = -. (2Í1)

The condition number of a matrix can be roughly calculated using procedures known in the art, without separately calculating the major and minor eigenvalues. Using the RSD defined by equation (20) as a feedback signal in optimizing the pre-distortion function can be advantageous when the ratio of the carrier bandwidth to the sampling frequency r is relatively large, to cause that signal energy propagates from the signal subspace to the noise subspace. This energy propagation is mainly concentrated in the boundary region between the signal subspace and the noise subspace and thus would less affect the largest and smallest eigenvalues. By using the ratio of the largest eigenvalue to the smallest eigenvalue as an estimate of the RSD, the propagation effect of the approximation can be alleviated

ES 2 393 538 T3 narrow band signal.

In other embodiments, the RSD calculator 140 may implement an intermediate approximation between those defined by equations (14) and (20), and may take two or more larger eigenvalues ​​into account when estimating the signal contribution, and / or two or more smaller eigenvalues ​​when estimating the distortion contribution. Consequently, the RSD calculator can generate and estimate the RSD according to an equation

<img file="ES2393538T3_D0003.tif" />

(21) in which K-ι can be between 1 and K, and K₂ it can be between K and N-1. Accordingly, the RSD can be calculated, in general, as a ratio of one or more of the largest K eigenvalues ​​relative to one or more of the smallest (NK) eigenvalues. The numerator and denominator in the RSD definition can also be calculated as linear combinations of the eigenvalues ​​corresponding to the signal and noise sub-spaces, respectively. Which of the calculated eigenvalues ​​belongs to the signal subspace and noise subspace, and the number K of multiplexed carriers, can be determined in some embodiments by comparing the eigenvalues ​​with a threshold value, and determining the number of eigenvalues ​​that exceed threshold.

The calculated RSD is provided to RSD comparator 160, which compares it to an RSD value from a previous iteration stored in RSD memory 150; the RSD memory 160 is then updated with the current RSD value for use as a reference in a next iteration. Pre-distortion generator 170 increases or decreases the one or more adjustable pre-distortion parameters c, as a function of an output from comparator 160.

In one embodiment, the pre-distortion generator 170 provides the updated values ​​of the one or more adjustable pre-distortion parameters to the pre-distortion 133, which then generates the pre-distortion function D (a | c. |, C2) and applies it to the input MF signal (l (m), Q (m)}, for example, as described above with reference to equation (16). In another embodiment, the function D (a | c₁, c₂) pre-distortion is generated by predistortion generator 170 for a plurality of values ​​of the amplitude a of the MF signal and is then provided to pre-distortion generator 133 in the form of a distortion look-up table. in which the values ​​of the pre-distortion function are stored depending on the amplitude a, or the intensity at² input MF signal. This look-up table is stored in pre-distorter 133 and is used to pre-distort the input MF signal until the next iteration.

The pre-distorter 133 calculates the amplitude ^to + 2 j_and |_{to 5}θη₃| mf d_and input (l (m), Q (m)} for each received data symbol, and uses the distortion look-up table to generate the pre-distorted MF signal, which is then passed through CNL 37. Note that in embodiments where both controller 88 and PD 133 are implemented in hardware using a single digital processor, such as a single FPGA or ASIC, in which case the distortion look-up table generation functionality can be attributed to either PD 133 or GPD 170.

In a subsequent iteration, the procedure described above to sample the output signal MF 5 of the CNL 37, calculate the correlation matrix, estimate the RSD based on a relation of its eigenvalues ​​and update the pre-distortion function, is repeated then to determine an optimized pr e-distortion function that corresponds to a maximum RSD value, or increases the RSD value to a desired degree.

It will be appreciated that instead of using the RSD values ​​obtained as defined by any of equations (14), (20) or (21) as a feedback parameter in consecutive iterations of the procedure of determining the optimal values ​​of the pre-distortion parameters, you can choose to use an alternative objective function as said feedback parameter. For example, in one embodiment, the RSD calculator 140 generates an objective function value that is inversely proportional to the RSD, OR_Sdr = A / RSD, where A is a constant parameter, and this objective function value is then stored in RSD memory 150 for comparison with an objective function value obtained in a next iteration. In this embodiment, controller 88 would be programmed to search for a set of pre-distortion parameters that minimize or reduce the value of the objective function, thereby maximizing or increasing RSD. In other embodiments, other functions of the RSD can be calculated and used as the objective function whose value is being minimized or maximized in the iterations.

It will further be appreciated that a variety of optimization algorithms can be used to iteratively determine optimal values ​​of the pre-distortion parameters that maximize, or at least adequately increase, the RSD value. By way of example, an alternative one-dimensional search algorithm to find an optimal set of pre-distortion parameters is described below; Other algorithms can also be used, such as the maximum descent procedure.

ES 2 393 538 T3

Alternative 1-dimensional search algorithm

In the following description of the alternative 1-dimensional search algorithm, it is convenient to introduce a single set of pre-distortion parameters c ξ c₁Uc₂ ξ (c₁, c₂) of length (L + J) composed of the two sets c₁, c₂separate for the amplitude and phase pre-distortion functions given by equation (18) and (19); Here, the elements of the set c are given as ci = c1i for i = 1, .., L, and ci = c2 (iL) for i = L + 1, .., L + J. In these notations, the pre-distortion function D (a | c. |, C₂) ξ D (alc), The alternative 1-dimensional search algorithm can then be described as a sequence of the following steps.

A) Initialization

A1) Select dimension N of the correlation matrix, a search step of size δ;

A2) Set the pre-distortion parameters to their default value, such as for example c = (1,0, .., 0);

A3) Calculate the pre-distortion function D (alc), and load it into the pre-distortion circuit, if only one of the amplitude and phase pre-distortion functions has changed, only that function can be updated and loaded;

A4) Acquire a sequence of signal samples from the output of the AP 37;

A5) Calculate the correlation matrix R2, and determine its own values ​​or its condition number;

A6) Calculate the RSD based on the eigenvalues ​​or the condition number or an objective function value related to it;

A7) Store RSD, or objective function value related to it, in RSD memory;

B) Iterations:

B1) Select a first pre-distortion parameter ct, l = 1;

B2) Increase c_l at δ, that is, set c_l = c₁ + δ

B3) Carry out steps A3) to A6)

B4) Compare the RSD, or the objective function value related to it, with a value stored in the RSD memory;

B5) If the RSD / objective function value changes in a desired direction, change to a next pre-distortion parameter with l = l +1, and return to step B2); if not, decrease c_1l in 2δ, that is, c_1l = c_1l - 2δ, and performs steps B3) and B4);

B6) If the value of the objective function changes in the desired direction, change to a next pre-distortion parameter with l = l +1 and go back to stage B2), if not, set c_l = c₁ + 2δ, and continues;

B7) If l &lt;L + J, set l = l + 1, and go back to stage B2; if not, continue;

If a preset performance requirement is satisfied, the algorithm stops; if not, it goes to step (B1) for the next iteration.

The recursive update procedure in the alternative 1-dimensional search can be repeated whenever necessary, for both amplitude and phase pre-distortion functions or for one of them. A variable step size can be used in the search to speed up convergence during the initial stage, and to achieve better performance when a steady state is reached.

Now, referring to FIG. 5, there is shown a schematic block diagram of the correlation matrix calculator 110 in accordance with one embodiment of the invention. In this embodiment, the correlation matrix R is calculated from a section of the sampled signal 128 of length M, that is, consisting of a sequence of M signal samples, [y (n)]. This section of the sampled signal 128 of length M is referred to herein as a measurement sequence of signal samples, a measurement section of the sampled signal, or simply as a measurement sequence. To simplify the notations, it is assumed that the sample index n counts the signal samples from the beginning of the measurement sequence, that is, n = 1, 2, ..., M, and the measurement sequence is represented in the form [y (n)] ξ [y (1), y (2), ..., y (M)]. If the length M of the measurement sequence is greater than N, the correlation matrix R can be estimated from the measurement sequence according to equation (22) below:

ES 2 393 538 T3

<td></td><td>rxn</td><td>X2) </td><td> , 0. · -, ν + Γή</td><td>peo</td><td>and (2) ··.</td>

<td>R- ¹</td><td>and &lt;2)</td><td>X3)</td><td></td><td></td><td>X3)</td>

<td>MN</td><td></td><td></td><td></td><td> +</td><td></td>

<td></td><td>[and (AND</td><td>XAf + 1) </td><td></td><td></td><td>X * + D - XM) J</td>

(22)

The actual calculation of the correlation matrix R can be performed by the CMC 110, recursively, to eliminate the need to store all M samples in the measurement sequence. The functional block diagram in Fig. 5 schematically shows an embodiment of the CMC 110 that implements a recursive calculation of the correlation matrix R. In this embodiment, the sampled signal 128 is received by a derived delay line (TDL) 205 of length N, such as a series-to-parallel shift register. The TDL 205 has N shunts 230 coupled to an arithmetic / memory block 220, where each shunt 210 is followed by a storage element 210 to store the signal samples y (n), y (n-1),. .., and (n-N + 1) successive, with all the N storage elements 210 and shunts 230 activated by the same clock. The arithmetic / memory block 220 has memory, referred to herein as the auto-correlation memory, for storing the auto-correlation coefficients rj of the sampled signal 128. The following recursive formula (23) can be used in block 220 to calculate the autocorrelation coefficients and update the content of the autocorrelation memory:

= - [&lt;«- W- or + M +¹ - +1 - /)] (23)

Π in which i, j = 1,2, ..., N, n = 1, ..., M, the superscript indicates the complex conjugate of a complex number, and r¡j (n) indicates a value calculated for the r, auto-correlation coefficient or, equivalently, the element R (i, j) of the correlation matrix, when an mth sample of the measurement sequence is received by the CMC 110.

In one embodiment, only N autocorrelation coefficients corresponding to N different values ​​of the sample relative delay p = 0.1, ..., N-1 are recursively calculated.

Once every M samples, the auto-correlation memory is sampled in block 220, and its content is assigned to the elements R (i, j) of the correlation matrix R, R (i, j) = r, j (M), after which it can be re-initialized to allow the next measurement cycle.

Simulation results

The estimation of non-linearity described above and the linearization technique in the context of applying AP linearization in multicarrier transmitters has been verified using computer simulations. In the simulations, four carrier signals are generated with different modulation schemes according to the configurations in Table 1, and then they are frequency multiplexed, to produce the input MF signal with the number of modulated carriers, or independent frequency channels. , k = 4.

Table 1: Signal settings for simulations

<td>Carrier No.</td><td> 1</td><td> 2</td><td> 3</td><td> 4</td>

<td>Modulation:</td><td>QPSK</td><td>8-PSK</td><td>QPSK</td><td>16-QAM</td>

<td>Symbol rate:</td><td>1 MHz</td><td>1 MHz</td><td>1 MHz</td><td>1 MHz</td>

<td>Fall factor:</td><td> 0,25</td><td> 0,25</td><td> 0,35</td><td> 0,35</td>

<td>Carrier frequency</td><td>0 MHz</td><td>2 MHz</td><td>4 MHz</td><td>6 MHz</td>

<td colspan="5">Sampling frequency = 16 MHz</td>

The measured characteristics of a traveling wave tube amplifier (TWTA) and a solid state power amplifier (SSPA) differing in their non-linearities, were used in the simulations to test the ability of the technique.

Two real-valued coefficient polynomials are used to implement the pre-distortion: one for the amplitude pre-distortion that has an order of L = 8, and the other for the phase pre-distortion that has an order of J = 12. The reason the higher order is chosen for the phase pre-distortion polynomial is because the AM-PM conversion tends to have

ES 2 393 538 T3 greater variation. Figs. 6 to 8 summarize the characteristics of the AP, the distributions of the eigenvalues ​​and the performance of the linearization of the AP.

Figs. 6 and 7 show the characteristics of the APs used in the simulations. In the figures, the points represent the measured characteristics, and the solid red lines represent the characteristics fitted by the polynomial models of order 5 used in the simulations to represent the transfer functions of the AP. Although the amplitude characteristics of these two APs appear similar, however, their phase characteristics are quite different, and both are correctly described by polynomial functions.

Eigenvalue distributions

To illustrate the decomposition of the signal space and the distribution of the eigenvalues ​​over the subspaces, an 8x8 correlation matrix is ​​calculated from the signal generated according to Table 1. Here, the dimension N = 2K = 8 of the correlation matrix, so that the signal subspace and the noise subspace have the same dimension, although any dimension N greater than K, ie greater than 4, can be used in this example. In each case, a 10,000 symbol measurement sequence is generated, and the resulting signal waveform is used in the calculation of the correlation matrix. In this example, the first AP (TWTA) is used.

The eigenvalues ​​calculated from the respective correlation matrix without and with AP are shown in Table 2. The corresponding RSDs are also shown in the Table. All eigenvalues ​​are normalized to the largest for ease of comparison. The corresponding distributions of the eigenvalues ​​are also plotted in Fig. 8, with the parts enlarged in more detail shown in Fig. 9.

Table 2. Distribution of eigenvalues ​​in different scenarios

<td rowspan="2"></td><td colspan="8">Own values</td><td rowspan="2">RSD</td>

<td colspan="4">Signal eigenvalues</td><td colspan="4">Noise eigenvalues</td>

<td>Without AP</td><td> 1,0000</td><td> 0,9983</td><td> 0,9898</td><td> 0,9085</td><td> 0,0908</td><td> 0,0089</td><td> 0,0002</td><td> 0,0000</td><td> 39,00</td>

<td>With AP</td><td> 1,0000</td><td> 0,9965</td><td> 0,9797</td><td> 0,9024</td><td> 0,1029</td><td> 0,0240</td><td> 0,0128</td><td> 0,0106</td><td> 25,80</td>

The following observations can be made:

i) There is a clear distinction between the four largest eigenvalues, which are the signal eigenvalues, and the four smallest eigenvalues, which are the noise eigenvalues, provided there are four signals. This distinction helps to define and identify the signal subspace and the noise subspace.

ii) When the exact number of carriers is unknown, the distinction between the two groups of eigenvalues ​​can be used to determine the number of carriers.

iii) The existence of the non-linearity of the AP causes the reduction in the energy of the signal subspace and the increase in the energy of the noise subspace, as illustrated in Fig. 9, thus considerably increasing the values noise, which, in turn, reduces RSD, as shown by the RSD values ​​in the last column of Table 2.

iv) In the absence of AP non-linearity, not all noise eigenvalues ​​are zero, due to the inaccuracy of the approximation that the signal envelopes remain constant for N = 8 consecutive sampling periods. The duration of the 8 sample periods is half of a symbol period, during which the envelopes of the signal can actually change a lot. However, the noise eigenvalues ​​are still very small compared to the signal eigenvalues, validating the narrowband signal approximation and allowing the procedure to work properly.

Figs. 10 to 12 and 13 to 15 show the results of linearization of AP No. 1 (TWTA) and AP No. 2 (SSPA), respectively, using the embodiment of Fig. 2, hereinafter referred to as memory, Implementation No.

1. In Figs. 10 and 13, the characteristics of the AP, the pre-distorter (PD) and the respective cascaded PD and AP (Total) systems are shown. The resulting combined characteristics are seen to be essentially linear after the iterative linearization described above. In Figs. 11 and 14, the spectra of the output MF signals without and with linearization are shown, together with the spectra of the ideal signal without non-linear distortions. In addition to the four modulated carrier signals, the strong spectral regrowth exists without linearization. With linearization, spectral sprouting is greatly reduced.

As a final illustration of system performance, Figs. 12 and 15 show the four-channel constellations without and with linearization. It can be clearly seen that the non-linearity of the AP severely degrades performance, and that the AP linearization technique provides an accurate pre-distortion function that effectively linearizes the AP and

ES 2 393 538 T3 essentially restores the signal constellations.

Figs. 16 to 18 and 19 to 21 show the results of linearization of PA1 and PA2 using the simplified embodiment of Fig. 3, hereinafter referred to as Implementation No. 2. As with the embodiment of Fig. 2, it is noted that you can achieve considerable linearization performance using this simplified implementation, although slight degradation may be observed, compared to the results of the Fig. 2 embodiment.

Summarizing the simulation results, Table 3 shows the levels of spectral regrowth due to the non-linearity of the AP and the improvement attributed to the linearization of the AP using the pre-distorter derived by the proposed estimation technique. It is observed that without linearization, both APs generate an out-of-band spectral flare greater than -20 dB, and that the linearization technique achieves at least a 20 dB improvement in spectral flare suppression in all cases, with the realization of Fig. 2 slightly exceeding that of of Fig. 3.

Table 3: Summary of Spectral Regrowth Suppression Performance

<td rowspan="2"></td><td rowspan="2">Without PD</td><td colspan="2">With PD</td>

<td>Implementation N ° 1</td><td>Implementation N ° 2</td>

<td>AP N ° 1</td><td>-19 dB</td><td>-45 dB</td><td>-44 dB</td>

<td>AP N ° 2</td><td>-18 dB</td><td>-40 dB</td><td>-38 dB</td>

As an additional measure of system performance, the error vector magnitude (EVM) is calculated in each case, and is summarized in Table 4. It is observed that for AP No. 1, linearization improves EVM performance from approximately 10% to less than 1%, while for AP No. 2, it improves EVM performance from about 10% to about 1%.

Table 4: Summary of EVM performance improvement

<td rowspan="2">Carrier No.</td><td colspan="3">AP N ° 1</td><td colspan="3">AP N ° 2</td>

<td>Without PD</td><td>Implementation N ° 1</td><td>Implementation N ° 2</td><td>Without PD</td><td>Implementation N ° 1</td><td>Implementation N ° 2</td>

<td> 1</td><td> 8,97%</td><td> 0,51%</td><td> 0,61%</td><td> 9,67%</td><td> 0,91%</td><td> 1,08%</td>

<td> 2</td><td> 11.07%</td><td> 0,47%</td><td> 0,63%</td><td> 11,92%</td><td> 1,02%</td><td> 1,20%</td>

<td> 3</td><td> 11.09%</td><td> 0,52%</td><td> 0,67%</td><td> 11,66%</td><td> 0,90%</td><td> 1,08%</td>

<td> 4</td><td> 8,71%</td><td> 0,58%</td><td> 0,96%</td><td> 9,73%</td><td> 1,14%</td><td> 1,24%</td>

The linearization performance for AP # 1 is slightly better than for AP # 2, which has a more complex phase variation than AP # 1.

Another observation is that although much simpler in the measurement circuit, Implementation No. 2 experiences a slight performance degradation under the ideal simulation condition, compared to Implementation No. 1. This is understandable and expected, since the The number of samples used to calculate the correlation matrix in Implementation No. 2 is effectively half of the samples used in Implementation No. 1. On the other hand, Implementation # 1 has to use a vector mixer in the feedback circuit, which in practice experiences some degradation due to its gain / phase imbalances, even if a gain / phase imbalance calibration is implemented. Therefore, both implementations can lead to the same linearization performance in practice, with Implementation # 2 being more attractive in some applications due to its simplicity.

Experimental results

The AP linearization technique described above is used to derive the pre-distortion functions for multicarrier AP linearization in an existing 20 GHz 4-carrier experimental setup. Due to the bandwidth limitation of the reconstruction filter in this configuration, the symbol rate and the carrier frequency assignment of the four signals are reduced from those used for the simulations in Table 1 to the values ​​in Table 5. The frequency assignment is relative to the RF OL frequency of 20 GHz. The sampling frequency is also reduced.

Table 5: Signal settings for the experimental setup

ES 2 393 538 T3

<td>Carrier number:</td><td> 1</td><td> 2</td><td> 3</td><td> 4</td>

<td>Modulation:</td><td>QPSK</td><td>8-PSK</td><td>QPSK</td><td>16-QAM</td>

<td>Symbol rate:</td><td colspan="4">39.0625 khZ</td>

<td>Fall factor:</td><td> 0,25</td><td> 0,25</td><td> 0,35</td><td> 0,35</td>

<td>Carrier frequency</td><td>-117.1875 KHz</td><td>-39.0625 KHz</td><td>39.0625 KHz</td><td>117.1875 KHz</td>

<td>Sampling rate</td><td colspan="4">5 MHz</td>

The four channel signals are generated in a computer according to the parameters in Table 5, and summed with the appropriate carrier frequency assignment. The I and Q waveforms of the summed signal are converted to analog by means of a PCI-based digital-to-analog conversion card. Analog waveforms are filtered with a low pass filter before being fed to a 20 GHz vector modulator. The RF carrier modulated signal from the vector modulator is supplied to a 0.25W SSPA, the output of which is downconverted to a low IF of 1 MHz. The IF signal is then digitized by an analog conversion card. -a-digital, PCI-based, at 5 MHz. The digitized signal is subsampled by a factor of 8 before being used to derive the pre-distortion functions.

The correlation matrix R is estimated from M = 8,000 samples. An 8-order polynomial and a 12-order polynomial are used to represent the amplitude and phase pre-distortion functions, respectively. Both implementations of Fig. 2 and Fig. 3 are tested in the experiment. The results are shown in Figs. 22 and 23. It is observed that the new linearization technique obtains a precise pre-distorter that eliminates the effect of the non-linearity of the AP and reduces the spectral flare from approximately -20 dBc to approximately -40 dBc. It should also be noted that the two implementations achieve essentially the same linearization performance.

Advantageously, the method of the present invention, described above, to linearize an amplifier in a multicarrier transmission system based on a correlation matrix of the output signal can be used during the normal operation of the circuit, thus allowing way, that adapts to changing conditions without service interruptions. As a further advantage, no prior knowledge of the number K of multiplexed frequency channels is required, which can be estimated during operation within the procedure itself, although knowledge, in advance, of the number of K channels simplifies implementations.

It should be noted that the various embodiments described herein may utilize features of the other embodiments, and many variants thereof will be apparent to a reader skilled in the art. Of course, many other embodiments can be devised without departing from the scope of the invention. For example, controller 88 may use alternative optimization techniques to determine an optimal pre-distortion function that appropriately maximizes or increases the estimated RSD. In addition, other methods could be used to calculate the eigenvalues ​​of the correlation matrix, or directly estimate a ratio thereof for the signal and noise sub-spaces in embodiments of the present invention. Furthermore, the method of the present invention can be carried out in a calibration step, rather than during operation, in which case the bypass coupler 45 can be omitted and all of the output signal 5 can be directed to the feedback circuit. Furthermore, although the specific details of the method and circuit of the present invention have been described above with reference to a power amplifier of a quadrature multicarrier transmitter, the present invention is not limited in this sense, but can be used to linearize other types of amplifiers, such as, but not limited to, input and intermediate stage amplifiers, as well as other non-linear circuits that exhibit unwanted non-linearities in multicarrier systems.