CN101615890B - Method and device for processing digital pre-distortion - Google Patents

Abstract

The invention discloses a method and a device for processing digital pre-distortion. The method comprises the following steps: according to output signals of a radio-frequency power amplifier and a pre-distortion coefficient intermediate transformation matrix acquired by calculation, acquiring elements of previous M rows of a pre-distortion coefficient second matrix in turn, initializing a pre-distortion coefficient third matrix, and acquiring elements of previous K rows above a diagonal in the pre-distortion coefficient third matrix according to the elements of the previous M rows of the pre-distortion coefficient second matrix; acquiring elements of other rows except the previous K rows above the diagonal in the pre-distortion coefficient third matrix according to a second property formula, and acquiring the elements under the diagonal in the pre-distortion coefficient third matrix according to a first property formula; and carrying out Cholesky decomposition for the pre-distortion coefficient third matrix to acquire a pre-distortion coefficient matrix, and carrying out pre-distortion processing for input signals. The method and the device greatly reduce the computing times, complexity and required storage space of the pre-distortion coefficient third matrix, save computing resources, and improve the computing efficiency.

Description

A kind of digital pre-distortion processing method and device

Technical field

The present invention relates to predistortion (Pre-Distorter) technology, particularly a kind of digital pre-distortion (DPD, Digital Pre-Distorter) processing method and device.

Background technology

In electronic circuit, when can making it that input signal is amplified, the nonlinear distortion of radio-frequency power amplifier (PA, Power Amplifier) produces new frequency (harmonic wave) component, disturb the signal of emission or the signal of other channel.In order to improve the nonlinear distortion of PA, prior art generally adopts the DPD technology.The DPD technology is used for the signal that is input to PA is originally carried out pre-distortion earlier by increase a nonlinear network at the PA front end, and then that predistortion is later signal is input to PA.The design of nonlinear network need be satisfied: the signal through nonlinear network and PA can be by linear amplification.That is: the nonlinear distortion of nonlinear network has just in time remedied the nonlinear distortion of PA, and the system that nonlinear network and PA are constituted is equivalent to linear amplifier.

Fig. 1 is an apparatus structure schematic diagram of realizing DPD in the prior art.Referring to Fig. 1, this device comprises pre-distortion unit, PA, error signal calculation unit, pre-distortion coefficients computing unit and signal normalization unit, and among the figure, dotted arrow represents that pre-distortion unit and pre-distortion coefficients computing unit adjust synchronously, wherein

The pre-distortion unit is used for the pre-distortion coefficients according to the generation of pre-distortion coefficients computing unit, input signal x (n) is carried out pre-distortion, output signal z (n);

PA is used to receive the signal z (n) of pre-distortion unit output, carries out output signal y (n) after the processing and amplifying;

The error signal calculation unit is used for the estimated value with the signal z (n) of pre-distortion coefficients computing unit generation with signal z (n)

Subtract computing, output error signal e (n) is used for the pre-distortion coefficients computing unit is adjusted;

The pre-distortion coefficients computing unit is used for the signal according to the output of signal normalization unit, and the error signal e (n) of error signal calculation unit output, calculates and generate pre-distortion coefficients, to the estimated value of error calculation unit output z (n)

And, the signal x (n) that imports the pre-distortion unit is adjusted synchronously according to the pre-distortion coefficients of obtaining;

The signal normalization unit is used for the signal y (n) of PA output is carried out normalized, exports the pre-distortion coefficients computing unit to.

Below the concise and to the point operation principle that realizes the DPD algorithm in the prior art of describing:

If external input signal is x (n), the pre-distortion element output signal is z (n), and the PA output signal is y (n), and input signal x (n) is through after the pre-distortion cell processing, and the signal z (n) that is input to PA with the pass of the output signal of PA is:

$z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}---\left(1\right)$

In the formula (1), l, k, n are natural number, the maximum l of l _MaxBe memory length, l _Max=L-1; K is an exponent number; N is a sample number; a _KlBe pre-distortion coefficients.

In formula (1), if obtain a _Kl, then can carry out pre-distortion to the feedback signal y (n) of input signal x (n) and radio-frequency power amplifier output, output signal z (n) is input to PA, can improve the nonlinear distortion of PA output signal y (n).

In the prior art, in order to obtain pre-distortion coefficients a _Kl, carry out with down conversion.

If $u_{\mathrm{kl}}\left(n\right)=\frac{y(n-l)}{G}{\left|\frac{y(n-l)}{G}\right|}^{k-1}---\left(2\right)$

In the formula (2), G is a normalization coefficient.

Calculate u respectively _Kl(n), the result that formula (2) is calculated forms column matrix u _Kl, promptly

u _kl＝[u _kl(0)，u _kl(1)，...，u _kl(N-1)] ^T (3)

The column matrix u that will obtain by formula (3) again _KlForm pre-distortion coefficients first matrix U;

U＝[u ₁₀，u ₂₀，...，u _K0，......，u _1(L-1)，u _2(L-1)，...，u _K(L-1)] (4)

If $\stackrel{\→}{z}=U\stackrel{\→}{a}---\left(5\right)$

In the formula (5), vector

Column vector for pre-distortion element output signal z (n) formation:

$\stackrel{\→}{z}={[z\left(0\right),z\left(1\right),......,z(N-1)]}^T---\left(6\right)$

Vector

For by pre-distortion coefficients a _KlThe column vector that constitutes:

$\stackrel{\→}{a}={[a_{10},a_{20},...,a_{K0},......,a_{1(L-1)},,a_{2(L-1)},...,a_{K(L-1)}]}^T---\left(7\right)$

Utilize least square solution formula (5), can get vectorial

Estimated value

:

$\hat{a}{\left(U^{H}U\right)}^{-1}{U}^H\stackrel{\→}{Z}---\left(8\right)$

In the formula, () ^HThe conjugate transpose of expression ().

To import the pre-distortion unit by the pre-distortion coefficients that formula (8) obtain, input signal will be carried out pre-distortion, output signal $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}$ As the input of PA, improved the nonlinear distortion of PA, make PA output signal y (n) for linear.

In actual applications, generally use orthogonal polynomial to optimize above-mentioned DPD algorithm, thereby make and to find the solution the pre-distortion coefficients that obtains more accurately and stable.Below optimized Algorithm is carried out brief description.

Optimized Algorithm of the prior art is with the pre-distortion element output signal $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}$ Carry out conversion.

Order $W_{\mathrm{jk}}=\frac{{(-1)}^{j+k}(k+j)!}{(j-1)!(j+1)!(k-j)!}---\left(9\right)$

The W that formula (9) is obtained _JkThe capable k column element of j as W is formed upper triangular matrix W, and W is the pre-distortion coefficients intermediate transform matrices, and wherein, k, j are natural number, 1≤k≤K, 1≤j≤k.Other establishes,

${\mathrm{\ψ}}_k\left(x\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{W}_{\mathrm{jk}}x{\left|x\right|}^{j-1}---\left(10\right)$

Formula (1) then $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}$ Variable being changed to:

$z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}{\mathrm{\ψ}}_k\left(x(n-l)\right)---\left(11\right)$

Composite type (9)～formula (11) can be with formula (5) $\stackrel{\→}{z}=U\stackrel{\→}{a}$ Be transformed to,

$\stackrel{\→}{z}=F\stackrel{\→}{b}---\left(12\right)$

In the formula, pre-distortion coefficients second matrix F=[U ₀W ..., U _L-1W] (13)

Here, U _l=[u _1l, u _2l..., u _Kl], l=0,1 ..., L-1.

Equally, utilize least square solution formula (12), can solve the form of similarly separating, be i.e. vector with formula (7), formula (8)

Estimated value

:

$\hat{b}={\left(F^{H}F\right)}^{-1}{F}^H\stackrel{\→}{Z}---\left(14\right)$

By formula (8), formula (13) and formula (14), can obtain the pre-distortion coefficients estimated value

:

$\hat{a}=W\hat{b}---\left(15\right)$

Detailed process to the DPD algorithm optimized describes below.

Suppose that input PA and the signal training sequence that obtains from PA output are respectively z (n) and y (n), wherein, the sample number of supposing two sequences all is N, and wherein, N 〉=KL+L-1 describes in detail below and obtains the pre-distortion coefficients estimated value by z (n) and y (n)

Process.

Fig. 2 is the schematic flow sheet of DPD algorithm in the prior art.Referring to Fig. 2, this flow process comprises:

Step 201 is carried out Digital Down Convert and filtering with signal training sequence y (n).

In this step, calculate y (n) cos (2 π f _IF* t), and with result of calculation by 180 tap finite impulse filters (FIR, Finite Impulse Response), obtain homophase (Inphase) signal, i.e. I signal I (n).Here, f _IFCarrier frequency during for Digital Down Convert.

Calculate y (n) sin (2 π f _IF* t), and with result of calculation by 180 tap FIR filtering, obtain quadrature (Quadrature) signal, i.e. Q signal Q (n).If:

y′(n)＝(I(n)+j×Q(n))/2 (16)

Step 202, with y ' (n) and z (n) carry out the normalizing digitized processing.

The normalization formula of signal z (n) is:

$z\left(n\right)=\frac{z\left(n\right)}{\left|\right|z\left|\right|},n=1,...,N---\left(17\right)$

In the formula,

$\left|\right|z\left|\right|=\sqrt{\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|z\left(n\right)\left|\right|}^2}{N}}---\left(18\right)$

Similarly, y ' normalization formula (n) is:

$y^{\′}\left(n\right)=\frac{y\left(n\right)}{\left|\right|y^{\′}\left|\right|},n=1,...,N---\left(19\right)$

$\left|\right|y^{\′}\left|\right|=\sqrt{\frac{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\left|\right|y^{\′}\left(n\right)\left|\right|}^2}{N}}---\left(20\right)$

Step 203, by the y ' after the normalization (n) and z (n) calculate the channel response ch of DPD loop, carry out channel estimating.

The computing formula of channel response ch is:

ch＝z(n) ^Hy′(n)/N (21)

Step 204 according to the y ' after the normalization (n) and channel response ch, calculates y " (n).

In this step, order

y″(n)＝y′(n)·ch ^* (22)

y″(n)＝[y″(1)，y″(2)，y″(3)，...，y″(N)] (23)

In the formula, ch ^*Conjugation for ch." (n) form pre-distortion coefficients first matrix U by y.

Step 205 generates vector

In this step, vector $\stackrel{\→}{z}={[z\left(L\right),z(L+1),......,z\left(N\right)]}^T,$ Expression is input to the data vector of PA, wherein, preceding (L-1) individual data sample z (1), z (2) ..., z (L-1) is used for first of generator matrix F and goes.

Step 206 is calculated W _JkAnd by W _JkGenerator matrix W.

In this step, $W_{\mathrm{jk}}=\frac{{(-1)}^{j+k}(k+j)!}{(j-1)!(j+1)!(k-j)!}$

The W that following formula is obtained _JkForm upper triangular matrix W, and will be by W _JkThe upper triangular matrix W that generates stores or nonzero element among the W is stored, and in the follow-up flow process, reads data among the upper triangular matrix W if desired, then directly reads from the data of preserving.

For instance, if K=7, then upper triangular matrix W can be expressed as:

$W=\left[\begin{array}{ccccccc}{W}_{11}& W_{12}& W_{13}& W_{14}& W_{15}& W_{16}& W_{17}\\ 0& W_{22}& W_{23}& W_{24}& W_{25}& W_{26}& W_{27}\\ 0& 0& W_{33}& W_{34}& W_{35}& W_{36}& W_{37}\\ 0& 0& 0& W_{44}& W_{45}& W_{46}& W_{47}\\ 0& 0& 0& 0& W_{55}& W_{56}& W_{57}\\ 0& 0& 0& 0& 0& W_{66}& W_{67}\\ 0& 0& 0& 0& 0& 0& W_{77}\end{array}\right]=\left[\begin{array}{ccccccc}1& -3& 6& -10& 15& -21& 28\\ 0& 4& -20& 60& -140& 280& -504\\ 0& 0& 15& -105& 420& -1260& 3150\\ 0& 0& 0& 56& -504& 2520& -9240\\ 0& 0& 0& 0& 210& -2310& 13860\\ 0& 0& 0& 0& 0& 792& -10296\\ 0& 0& 0& 0& 0& 0& 3003\end{array}\right]$

Step 207 generates and stores matrix F ^HF and

Wherein, F ^HF is pre-distortion coefficients the 3rd matrix.

In this step, establish ${\mathrm{\ψ}}_k\left(x\right)=\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{W}_{\mathrm{jk}}x{\left|x\right|}^{j-1}$

Formula (1) is transformed to: $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{l=0}{\overset{L-1}{\mathrm{\Σ}}}{a}_{\mathrm{kl}}{\mathrm{\ψ}}_k\left(x(n-l)\right)$

Utilize following formula, with formula (5) $\stackrel{\→}{z}=U\stackrel{\→}{a}$ Be transformed to: $\stackrel{\→}{z}=F\stackrel{\→}{b}$

In the formula, F=[U ₀W ..., U _L-1W]

According to the F generator matrix F that obtains ^HF and

And storage.

Step 208 is to matrix F ^HF carries out Qiao Lisiji (Cholesky) and decomposes, and obtains matrix G and G ^H

Qiao Lisiji decomposition algorithm formula is:

F ^HF＝GG ^H (24)

In the formula, G is (the rank lower triangular matrix of KL * KL).

Step 209 is carried out the back substitution first time.If

$\stackrel{\→}{z}=F\stackrel{\→}{b}---\left(25\right)$

Both members is with taking advantage of F ^H,

$F^H\stackrel{\→}{z}=F^{H}F\stackrel{\→}{b}={\mathrm{GG}}^H\stackrel{\→}{b}\⇒G^{-1}{F}^H\stackrel{\→}{z}=G^H\stackrel{\→}{b}---\left(26\right)$

If $F^H\stackrel{\→}{z}=\stackrel{\→}{d},$ Wherein,

The vector of capable 1 row of expression KL is the intermediate vector variable, and then formula (26) can be changed into.

$G^{-1}\stackrel{\→}{d}=G^H\stackrel{\→}{b}---\left(27\right)$

If $G^{-1}\stackrel{\→}{d}=\stackrel{\→}{h}---\left(28\right)$

Then, can derive by formula (27) and formula (28): $G\stackrel{\→}{h}=\stackrel{\→}{d},$ Just

By following conversion, can obtain matrix h.

$G\&CenterDot;\stackrel{\&RightArrow;}{h}=\stackrel{\&RightArrow;}{d}\&DoubleRightArrow;{\mathrm{<figure-callout\; id="1"\; label="h"\; filenames="S2008101157014E00031.png"\; state="\{\{state\}\}">h</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="S2008101157014E00031.png"\; state="\{\{state\}\}">d</figure-callout>}}_1/g_{11}$

$h_i=\frac{1}{g_{i,j}}(d_i-\underset{k=1}{\overset{i-1}{\mathrm{\&Sigma;}}}{g}_{i,k}{h}_k),i=\mathrm{2,3},...,\mathrm{KL}---\left(30\right)$

Step 210 is carried out the back substitution second time, according to the matrix h and the G that obtain ^HCalculate matrix b.

By formula (27) and formula (28), can get:

$G^H\&CenterDot;\stackrel{\&RightArrow;}{b}=\stackrel{\&RightArrow;}{h},$ Just

Formula (31) is carried out conversion, obtains matrix b,

$G^H\&CenterDot;\stackrel{\&RightArrow;}{b}=\stackrel{\&RightArrow;}{h}\&DoubleRightArrow;b_{\mathrm{KL}}=h_{\mathrm{KL}}/g_{\mathrm{KL},\mathrm{KL}}^{*}$

$b_i=\frac{1}{g_{i,i}^{*}}(h_i-\underset{k=1}{\overset{i-1}{\mathrm{\&Sigma;}}}{g}_{i+k,i}^{*}{b}_{i+k}),i=\mathrm{KL},\mathrm{KL}-1,....,1---\left(32\right)$

Step 211 generates pre-distortion coefficients matrix a.

By formula (15), can get:

$a=\left[\begin{array}{cccc}W& 0& ...& 0\\ 0& W& ...& 0\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ 0& 0& ...& W\end{array}\right]b$

Wherein,

$a=\left[\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="WB"\; filenames="S2008101157014E00031.png"\; state="\{\{state\}\}">WB</figure-callout>}}_1\\ {\mathrm{WB}}_2\\ .\\ .\\ .\\ {\mathrm{WB}}_L\end{array}\right],$ $b=\left[\begin{array}{c}{B}_1\\ B_2\\ .\\ .\\ .\\ B_L\end{array}\right],$ $B_i=\left[\begin{array}{c}{b}_{K(i-1)+1}\\ b_{K(i-1)+2}\\ .\\ .\\ .\\ b_{\mathrm{Ki}}\end{array}\right]---\left(33\right)$

Obtained pre-distortion coefficients matrix a, the pre-distortion unit just can carry out pre-distortion according to pre-distortion coefficients matrix a to input signal x (n), output signal z (n).

Therefore the DPD algorithm of optimizing in the prior art utilizes orthogonal polynomial structural matrix W, improves accuracy and stability that pre-distortion coefficients is calculated.Particularly, by matrix W structural matrix F, and to matrix F ^HF carries out Cholesky and decomposes, and obtains lower triangular matrix G and upper triangular matrix G ^HUtilize matrix G and G ^HObtain the value of matrix b, obtain pre-distortion coefficients a by upper triangular matrix W again, make the pre-distortion coefficients a that obtains more accurately with stable.By the pre-distortion coefficients matrix that calculates, input signal x (n) is carried out importing PA again after the pre-distortion, can effectively handle the nonlinear distortion of PA.

But the DPD algorithm that should optimize, the required memory space of its computing is very big.For example, in step 207, storage matrix F ^HF and

Need take a large amount of system resource, for instance, be used for the required space size of storage matrix and be: K*L*N.Wherein, K 〉=7, L 〉=4, N＞4000; And computing is complicated, need carry out a large amount of multiplication and add operation.Cause its relevant hardware cost height, to having relatively high expectations of hardware platform.

Summary of the invention

In view of this, the invention provides a kind of digital pre-distortion processing method, can reduce the complexity of computing significantly, reduce the required space of storage.

The present invention also provides a kind of digital predistortion process apparatus, can reduce the complexity of computing, reduces the required space of storage.

A kind of digital pre-distortion processing method provided by the invention comprises:

Obtain the preceding M row element of pre-distortion coefficients second matrix successively according to the output signal of radio-frequency power amplifier and the pre-distortion coefficients intermediate transform matrices that calculates, and initialization pre-distortion coefficients the 3rd matrix, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the preceding M row element of described pre-distortion coefficients second matrix, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of described output signal;

Obtain other row element except that K row element before described more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in described pre-distortion coefficients the 3rd matrix according to the first characteristic formula;

Described pre-distortion coefficients the 3rd matrix is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix, input signal is carried out pre-distortion according to the described pre-distortion coefficients matrix that obtains.

Described according to radio-frequency power amplifier output signal and the pre-distortion coefficients intermediate transform matrices that the calculates preceding M row element that obtains pre-distortion coefficients second matrix successively and obtain according to the preceding M row element of described pre-distortion coefficients second matrix that the preceding K row element more than the diagonal comprises in described pre-distortion coefficients the 3rd matrix:

Generate the proper polynomial matrix U (n) of pre-distortion coefficients first matrix U by the output signal y (n) of radio-frequency power amplifier;

Polynomial matrix U (n) and pre-distortion coefficients intermediate transform matrices W multiplied each other obtain matrix F (n): F (n)=U (n) W;

Preceding K row element more than the diagonal in pre-distortion coefficients the 3rd matrix is initialized as zero, obtain the preceding M row element of pre-distortion coefficients second matrix successively according to matrix F (n), and after obtaining every row element, the row vector F that constitutes according to the current line element of pre-distortion coefficients second matrix _i, upgrade the above preceding K row element of diagonal in current pre-distortion coefficients the 3rd matrix.

The mode of obtaining the i row element of pre-distortion coefficients second matrix F is: F _i=[F (L+i), F (L+i-1) ..., F (i)], 1≤i≤M.

The described mode of obtaining the i row element of pre-distortion coefficients second matrix F comprises:

When i=1, the matrix F (L) that n in the matrix F (n) is equaled the L correspondence equals all elements sequence arrangement of the matrix F (1) of 1 correspondence to n, as the 1st row element F of pre-distortion coefficients second matrix F ₁=[F (L), F (L-1) ..., F (1)];

When i＞1, with capable K the element that move to right of i-1 of pre-distortion coefficients second matrix F, replace a leftmost K element with matrix F (L+i-1), the i that obtains pre-distortion coefficients second matrix F is capable: F _i=[F (L+i-1), F (L+i-2), F (L+i-3) ..., F (i)].

Described generating feature polynomial matrix U (n) comprising: according to described output signal evaluator u _k(n), and with multinomial u _k(n) for vector generates described polynomial matrix U (n), wherein, U (n)=[u ₁(n) u ₂(n) ... u _K(n)], u ₁(n)=and y (n), u _k(n)=u _K-1(n) | y (n) |, 1≤k≤K.

The described row vector that constitutes according to the current line element of pre-distortion coefficients second matrix upgrades F _iThe above preceding K row element of diagonal comprises in described current pre-distortion coefficients the 3rd matrix:

To described row vector F _i, calculate F _i ^HF _iThe above preceding K row element of middle diagonal, and result of calculation is added in current described pre-distortion coefficients the 3rd matrix on the preceding K row element more than the diagonal according to the element position correspondence, form the above preceding K row element of diagonal in new current pre-distortion coefficients the 3rd matrix.

The described second characteristic formula is:

F ^HF(m，n)＝F ^HF(m-K，n-K)+F*(1，m)·F(1，n)-F*(N-L+1，m-K)·F(N-L+1，n-K)；

The described first characteristic formula is: F ^HF (n, m)=(F ^HF (m, n)) ^*

Calculate $W_{\mathrm{jk}}=\frac{{(-1)}^{j+k}(k+j)!}{(j-1)!(j+1)!(k-j)!},$ And with the W that calculates _JkAs the capable k column element of j of described pre-distortion coefficients intermediate transform matrices W, wherein, k, j are natural number, 1≤k≤K, 1≤j≤k.

The described pre-distortion coefficients matrix that described basis is obtained carries out pre-distortion to input signal and comprises:

After according to the pre-distortion coefficients matrix that obtains the feedback signal y (n) of input signal x (n) and radio-frequency power amplifier output being handled, the signal z (n) after handling is input to radio-frequency power amplifier, wherein, $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}.$

A kind of digital predistortion process apparatus, this device comprises: pre-distortion unit, radio-frequency power amplifier and pre-distortion coefficients computing unit, wherein,

The pre-distortion unit is used for the pre-distortion coefficients matrix according to the generation of pre-distortion coefficients computing unit, input signal x (n) is carried out pre-distortion, to radio-frequency power amplifier output signal z (n);

Radio-frequency power amplifier is used to receive the signal z (n) of pre-distortion unit output, carry out power amplification and handle the back to external output signal y (n), simultaneously with the signal feedback of output to the pre-distortion coefficients computing unit;

The pre-distortion coefficients computing unit, be used for obtaining successively the preceding M row element of pre-distortion coefficients second matrix according to the output signal of radio-frequency power amplifier and the pre-distortion coefficients intermediate transform matrices that calculates, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the preceding M row element of described pre-distortion coefficients second matrix, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of described output signal;

Obtain other row element except that K row element before described more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in described pre-distortion coefficients the 3rd matrix according to the first characteristic formula;

Described pre-distortion coefficients the 3rd matrix is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix.

As seen from the above technical solution, obtain the preceding M row element of pre-distortion coefficients second matrix successively according to the output signal of radio-frequency power amplifier and the pre-distortion coefficients intermediate transform matrices that calculates, and initialization pre-distortion coefficients the 3rd matrix, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the preceding M row element of described pre-distortion coefficients second matrix, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of described output signal; Obtain other row element except that K row element before described more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in described pre-distortion coefficients the 3rd matrix according to the first characteristic formula; Described pre-distortion coefficients the 3rd matrix is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix, input signal is carried out pre-distortion according to the described pre-distortion coefficients matrix that obtains.Greatly reduce number of times, complexity and the required memory space of pre-distortion coefficients the 3rd matrix operation, saved calculation resources, improved operation efficiency.

Description of drawings

Fig. 1 is an apparatus structure schematic diagram of realizing DPD in the prior art.

Fig. 2 is the schematic flow sheet of DPD algorithm in the prior art.

Fig. 3 is the schematic flow sheet of generator matrix FHF of the present invention.

Fig. 4 realizes the apparatus structure schematic diagram of DPD for the present invention.

Embodiment

For making purpose of the present invention, technical scheme and advantage clearer, below with reference to the accompanying drawing embodiment that develops simultaneously, the present invention is further elaborated.

In the embodiment of the invention, the DPD algorithm is improved,, utilize matrix F according to proper polynomial matrix U (n) and upper triangular matrix W generator matrix F ^HTwo characteristics of F are carried out computing, can reduce to calculate and obtain matrix F ^HThe complexity of F reduces and calculates the required resource and the requirement of memory space.

The present invention mainly is to reduce and calculates and storage matrix F ^HThe system resource that F is required is described in detail below.For other flow process of obtaining pre-distortion coefficients, same as the prior art, do not repeat them here.

Ability and those of ordinary skill pass through matrix F ^HThe analysis of F can be derived matrix F ^HF has two following characteristics:

First characteristic formula: the F ^HF (n, m)=(F ^HF (m, n)) ^*(34)

The second characteristic formula:

F ^HF(m，n)＝F ^HF(m-K，n-K)+F*(1，m)·F(1，n)-F*(N-L+1，m-K)·F(N-L+1，n-K) (35)

In formula (34) and the formula (35), m 〉=K, n 〉=K, n 〉=m.F ^HF (m, n) representing matrix F ^HThe element of the capable n row of m among the F, F (m, n) element of the capable n row of m among the representing matrix F.

By formula (34) and formula (35) as can be known, for matrix F ^HF only needs to be positioned in the compute matrix the above preceding K row element of diagonal, and being positioned at other above row element of diagonal can calculate according to formula (35); And for the element below the diagonal in the matrix, can carry out conversion and calculate and can obtain according to formula (34).

Among the present invention, establish F _mThe m row element of representing matrix F, then matrix F ^HF can be expressed as:

$F^{H}F=\left[\begin{array}{cccc}{F}_1^H& F_2^H& ...& F_{N-L-1}^H\end{array}\right]\left[\begin{array}{c}{F}_1\\ F_2\\ .\\ .\\ .\\ F_{N-\mathrm{<figure-callout\; id="1"\; label="L\; +"\; filenames="S2008101157014E00031.png"\; state="\{\{state\}\}">L</figure-callout>}+1}\end{array}\right]=\underset{i=1}{\overset{N-L+1}{\mathrm{\&Sigma;}}}{F}_i^H{F}_i---\left(37\right)$

For different i, matrix F _i ^HF _iWith matrix F ^HF has identical line number and columns.

If obtained F _i, for matrix F ^IHF _i, then can be from known matrix F _iIn obtain being positioned at preceding K row element on the diagonal, then, according to formula $F^{H}F=\underset{i=1}{\overset{N-L+1}{\mathrm{\&Sigma;}}}{F}_i^H{F}_i$ Can obtain matrix F ^HF is positioned at the preceding K row element on the diagonal.

Therefore, utilize formula $F^{H}F=\underset{i=1}{\overset{N-L+1}{\mathrm{\&Sigma;}}}{F}_i^H{F}_i,$ Can not need calculating and storage to be used for generator matrix F ^HAll ranks of the matrix F of F, and only need the row element of compute matrix F, and store, be used for compute matrix F _i ^HF _iThe required memory space of a row element of storage matrix F is KL, and the required memory space of the existing whole matrix F of storage is KLN, wherein, and K 〉=7, L 〉=4, N 〉=4000.Thereby, with respect to prior art, greatly reduce the required space of storage and the complexity of calculating.

Fig. 3 is generator matrix F of the present invention ^HThe schematic flow sheet of F.Referring to Fig. 3, this flow process comprises:

First row element of matrix F is calculated and obtained to step 301, and the individual element of the first row Far Left K (L-1) of matrix F is stored, and is used for the calculating of subsequent step 306.

In this step, the step of obtaining first row element of matrix F is:

1), calculates the absolute value v (n) of y (n).Promptly

v(n)＝|y(n)| (38)

2), generator polynomial u _k(n).

Single order multinomial u ₁(n), u ₁(n)=y (n); (39)

Second order polynomial u ₂(n), u ₂(n)=u ₁(n) v (n); (40)

Three rank multinomial u ₃(n), u ₃(n)=u ₂(n) v (n); (41)

...；

K rank multinomial u _K(n), u _K(n)=u _K-1(n) v (n) (42)

3), generating feature polynomial matrix U (n).

According to formula (39)～formula (42),

U(n)＝[u ₁(n)?u ₂(n)...u _K(n)] (43)

4), according to formula (13), generator matrix F (n),

F(n)＝U(n)·W (44)

5),, obtain first row of matrix F by formula (44).

F ₁＝[F(L)，F(L-1)，...，F(1)] (45)

In the formula, F (L), behind first row of generator matrix F stores the individual element of the first row Far Left K (L-1) of matrix F for the matrix that n in the matrix F (n) equals the L correspondence.

Step 302 makes i=1, with A representing matrix F ^HF, i.e. pre-distortion coefficients the 3rd matrix, and initialization matrix F ^HF is A=F ^HF=0.That is: for 1 all≤m, n≤KL, initialization A (m, n)=0, A (m, n) the capable n column element of m among the representing matrix A here.Also can be that the preceding K row element more than the diagonal in pre-distortion coefficients the 3rd matrix is initialized as zero.

Step 303, compute matrix $A=A+F_i^H{F}_i.$

In this step, only need compute matrix F _i ^HF _iWith the preceding K row element more than the diagonal in the matrix A, with matrix A and matrix F _i ^HF _iAddition and revest A.

Specifically, before this step, determined the i row element of pre-distortion coefficients second matrix F, in this step the row vector F of this i row element formation _i, upgrade the above preceding K row element of diagonal in current pre-distortion coefficients the 3rd matrix.

For 1≤m≤K and m≤n, utilize following assignment algorithmic formula compute matrix A:

A(m，n)＝A(m，n)+F*(i，m)·F(i，n) (46)

Formula (46) expression F* (i, m) with F (i, n) multiply each other gained long-pending again with A (m, n) after the addition gained and revest A (m, n), wherein, F (i, n) expression F _iIn n element, F* (i, n) expression F (i, conjugation n).

Step 304, if i＜N-L+1 makes i=i+1, execution in step 305 then; Otherwise, execution in step 306.

The also available following code segment realization of this step,

Ifi＜N-L+1

{

i＝i+1；

goto?step?305.

}

Else

{

Goto?step?306

}

Step 305, the i row element of generator matrix F returns execution in step 303 then.

At first, before this step, obtain the i-1 row element of matrix F:

F _i-1＝[F(L+i-2)，F(L+i-3)，...，F(i-1)] (47)

Secondly, calculate F (L+i-1).

Computational methods with reference to U that provides in the step 301 (n) and F (n) calculate U (L+i-1) earlier, calculate F (L+i-1)=U (L+i-1) W then.

Then, with capable K the element that move to right of i-1 of matrix F, and then replace a leftmost K element with F (L+i-1), the i that obtains matrix F is capable:

F _i＝[F(L+i-1)，F(L+i-2)，F(L+i-3)，...，F(i)] (48)

To row vector F _i, calculate F _i ^HF _iThe above preceding K row element of middle diagonal, and result of calculation is added in current pre-distortion coefficients the 3rd matrix A on the preceding K row element more than the diagonal according to the element position correspondence, form the above preceding K row element of diagonal in new current pre-distortion coefficients the 3rd matrix A.

Step 306 obtains matrix F according to formula (35) ^HOther element of the above ranks of F diagonal.

Concrete computing formula is as follows:

A(m，n)＝A(m-K，n-K)+F*(1，m)·F(1，n)-F*(N-L+1，m-K)·F(N-L+1，n-K)

(49)

In the formula, mn 〉=K, n 〉=K and n 〉=m.

Step 307 obtains matrix F according to formula (34) ^HThe element that the F diagonal is following.

That is: A (n, m)=(A (m, n)) *

So far, flow process finishes, and the matrix A that step 307 obtains is exactly a matrix F ^HF.

The process of obtaining pre-distortion coefficients in follow-up is same as the prior art, does not repeat them here.

Fig. 4 realizes the apparatus structure schematic diagram of DPD for the present invention.Referring to Fig. 4, this device comprises pre-distortion unit, PA and pre-distortion coefficients computing unit, wherein,

The pre-distortion unit is used for the pre-distortion coefficients according to the generation of pre-distortion coefficients computing unit, input signal x (n) is carried out pre-distortion, output signal z (n);

PA is used to receive the signal z (n) of pre-distortion unit output, carry out power amplification and handle the back to external output signal y (n), simultaneously with the signal feedback of output to the pre-distortion coefficients computing unit;

The pre-distortion coefficients computing unit, be used for signal y (n) that exports according to PA and the pre-distortion coefficients intermediate transform matrices W that calculates and obtain the preceding M row element of pre-distortion coefficients second matrix F successively, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix A according to the preceding M row element of pre-distortion coefficients second matrix F, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of output signal;

Obtain other row element except that preceding K row element more than the diagonal in pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in pre-distortion coefficients the 3rd matrix A according to the first characteristic formula;

Pre-distortion coefficients the 3rd matrix A is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix.

In the practical application, the pre-distortion coefficients computing unit calculates $W_{\mathrm{jk}}=\frac{{(-1)}^{j+k}(k+j)!}{(j-1)!(j+1)!(k-j)!},$ And with the W that calculates _JkForm upper triangular matrix W; Calculate the first row element F of matrix F by the y (n) of PA output ₁And storage; Initialization F ^HF=0; Compute matrix $F^{H}F=F^{H}F+F_1^{\mathrm{<figure-callout\; id="1"\; label="H\; F"\; filenames="S2008101157014E00031.png"\; state="\{\{state\}\}">H</figure-callout>}}{F}_{}{}_1$ The above preceding K row element of middle diagonal.Then, calculate the second row element F of matrix F by the y (n) of PA output ₂, and calculate $F^{H}F=F^{H}F+F_2^H{F}_2$ The above preceding K row element of middle diagonal.According to mode like this, carry out the processing of follow-up each row according to this, OK until (N-L+1).That is: capable to i, 2＜i≤N-L+1 is calculated the i row element F of matrix F by the y (n) of PA output _i, and calculate $F^{H}F=F^{H}F+F_i^H{F}_i$ The above preceding K row element of middle diagonal.Until i=N-L+1.

Obtain matrix F according to formula (35) ^HAbove other row element except that preceding K row element of diagonal among the F; Calculate matrix F according to formula (34) again ^HThe following element of diagonal among the F is at last to matrix F ^HF carries out Cholesky and decomposes, and obtains lower triangular matrix G and upper triangular matrix G ^H, utilize Cholesky to decompose lower triangular matrix G and the upper triangular matrix G that obtains ^HObtain the pre-distortion coefficients matrix.And utilize G and G ^HIt is similar to obtain pre-distortion coefficients matrix and prior art, does not repeat them here.

Table 1 is the comparison of complexity and required memory space in the algorithm simplified of prior art algorithm and the present invention.

Table 1

	Multiplication operand	The add operation number	Memory space
				Prior art F HF	6496000	6495188	KLN＝7*4*4000
F of the present invention HF	2856924	2857491	KL＝7*4＝28
				The complexity reduction	43.98％	43.99％	99.99％

As seen from the above-described embodiment, the DPD algorithm of the simplification that the present invention proposes greatly reduces the complexity of matrix operation and required memory space, has saved calculation resources, has improved operation efficiency.Be compared to the DPD algorithm of prior art, improved DPD algorithm can reduce compute matrix F ^HThe F complexity reaches 43.98%, storage matrix F ^HThe required space size of F is reduced to 0.01% especially.Because F ^HThe computational complexity of F accounts for 85% of whole existing DPD algorithm, and to matrix F ^HThe memory space of F almost is more than 95% of whole existing DPD algorithm stores amount, thereby shortcut calculation is by reducing F significantly ^HThe computational complexity of F and memory space lower the complexity of whole DPD algorithm greatly, and memory space is reduced to almost negligible degree.

The above is preferred embodiment of the present invention only, is not to be used to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of being done, be equal to and replace and improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. a digital pre-distortion processing method is characterized in that, this method comprises:

Obtain the preceding M row element of pre-distortion coefficients second matrix successively according to the output signal of radio-frequency power amplifier and the pre-distortion coefficients intermediate transform matrices that calculates, and initialization pre-distortion coefficients the 3rd matrix, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the preceding M row element of described pre-distortion coefficients second matrix, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of described output signal;

Obtain other row element except that K row element before described more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in described pre-distortion coefficients the 3rd matrix according to the first characteristic formula;

Described pre-distortion coefficients the 3rd matrix is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix, input signal is carried out pre-distortion according to the described pre-distortion coefficients matrix that obtains; Wherein,

Described according to radio-frequency power amplifier output signal and the pre-distortion coefficients intermediate transform matrices that the calculates preceding M row element that obtains pre-distortion coefficients second matrix successively and obtain according to the preceding M row element of described pre-distortion coefficients second matrix that the preceding K row element more than the diagonal comprises in described pre-distortion coefficients the 3rd matrix:

Generate the proper polynomial matrix U (n) of pre-distortion coefficients first matrix U by the output signal y (n) of radio-frequency power amplifier;

Polynomial matrix U (n) and pre-distortion coefficients intermediate transform matrices W multiplied each other obtain matrix F (n): F (n)=U (n) W; Calculate

And with the W that calculates _JkAs the capable k column element of j of described pre-distortion coefficients intermediate transform matrices W, wherein, k, j are natural number, 1≤k≤K, 1≤j≤k;

Preceding K row element more than the diagonal in pre-distortion coefficients the 3rd matrix is initialized as zero, obtain the preceding M row element of pre-distortion coefficients second matrix successively according to matrix F (n), and after obtaining every row element, the row vector F that constitutes according to the current line element of pre-distortion coefficients second matrix _i, upgrade the above preceding K row element of diagonal in current pre-distortion coefficients the 3rd matrix;

The described second characteristic formula is:

F ^HF(m，n)＝F ^HF(m-K，n-K)+F ^*(1，m)·F(1，n)-F ^*(N-L+1，m-K)·F(N-L+1，n-K)；

The described first characteristic formula is: F ^HF (n, m)=(F ^HF (m, n)) ^*

2. the method for claim 1 is characterized in that, the mode of obtaining the i row element of pre-distortion coefficients second matrix F is: F _i=[F (L+i), F (L+i-1) ..., F (i)], 1≤i≤M.

3. method as claimed in claim 2 is characterized in that, the described mode of obtaining the i row element of pre-distortion coefficients second matrix F comprises:

When i=1, the matrix F (L) that n in the matrix F (n) is equaled the L correspondence equals all elements sequence arrangement of the matrix F (1) of 1 correspondence to n, as the 1st row element F of pre-distortion coefficients second matrix F ₁=[F (L), F (L-1) ..., F (1)];

When i＞1, with capable K the element that move to right of i-1 of pre-distortion coefficients second matrix F, replace a leftmost K element with matrix F (L+i-1), the i that obtains pre-distortion coefficients second matrix F is capable: F _i=[F (L+i-1), F (L+i-2), F (L+i-3) ..., F (i)].

4. the method for claim 1 is characterized in that, described generating feature polynomial matrix U (n) comprising: according to described output signal evaluator u _k(n), and with multinomial u _k(n) for vector generates described polynomial matrix U (n), wherein, U (n)=[u ₁(n) u ₂(n) ... u _K(n)], u ₁(n)=and y (n), u _k(n)=u _K-1(n) | y (n) |, 1≤k≤K.

5. the method for claim 1 is characterized in that, the described row vector that constitutes according to the current line element of pre-distortion coefficients second matrix upgrades F _iThe above preceding K row element of diagonal comprises in described current pre-distortion coefficients the 3rd matrix:

To described row vector F _i, calculate

F _iThe above preceding K row element of middle diagonal, and result of calculation is added in current described pre-distortion coefficients the 3rd matrix on the preceding K row element more than the diagonal according to the element position correspondence, form the above preceding K row element of diagonal in new current pre-distortion coefficients the 3rd matrix.

6. the method for claim 1 is characterized in that, the described pre-distortion coefficients matrix that described basis is obtained carries out pre-distortion to input signal and comprises:

After according to the pre-distortion coefficients matrix that obtains the feedback signal y (n) of input signal x (n) and radio-frequency power amplifier output being handled, the signal z (n) after handling is input to radio-frequency power amplifier, wherein, $z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}\underset{l=0}{\overset{L-1}{\mathrm{\&Sigma;}}}{a}_{\mathrm{kl}}y(n-l){\left|y(n-l)\right|}^{k-1}.$

7. a digital predistortion process apparatus is characterized in that, this device comprises: pre-distortion unit, radio-frequency power amplifier and pre-distortion coefficients computing unit, wherein,

The pre-distortion unit is used for the pre-distortion coefficients matrix according to the generation of pre-distortion coefficients computing unit, input signal x (n) is carried out pre-distortion, to radio-frequency power amplifier output signal z (n);

Radio-frequency power amplifier is used to receive the signal z (n) of pre-distortion unit output, carry out power amplification and handle the back to external output signal y (n), simultaneously with the signal feedback of output to the pre-distortion coefficients computing unit;

The pre-distortion coefficients computing unit, be used for obtaining successively the preceding M row element of pre-distortion coefficients second matrix according to the output signal of radio-frequency power amplifier and the pre-distortion coefficients intermediate transform matrices that calculates, and obtain the preceding K row element more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the preceding M row element of described pre-distortion coefficients second matrix, wherein, the size of M equals the poor of the sample number of output signal and memory length, and the size of K equals the exponent number of described output signal; Comprise: the proper polynomial matrix U (n) that generates pre-distortion coefficients first matrix U by the output signal y (n) of radio-frequency power amplifier; Polynomial matrix U (n) and pre-distortion coefficients intermediate transform matrices W multiplied each other obtain matrix F (n): F (n)=U (n) W; Preceding K row element more than the diagonal in pre-distortion coefficients the 3rd matrix is initialized as zero, obtain the preceding M row element of pre-distortion coefficients second matrix successively according to matrix F (n), and after obtaining every row element, the row vector F that constitutes according to the current line element of pre-distortion coefficients second matrix _i, upgrade the above preceding K row element of diagonal in current pre-distortion coefficients the 3rd matrix; Calculate

And with the W that calculates _JkAs the capable k column element of j of described pre-distortion coefficients intermediate transform matrices W, wherein, k, j are natural number, 1≤k≤K, 1≤j≤k;

Obtain other row element except that K row element before described more than the diagonal in described pre-distortion coefficients the 3rd matrix according to the second characteristic formula, and obtain the element below the diagonal in described pre-distortion coefficients the 3rd matrix according to the first characteristic formula; The described second characteristic formula is:

F ^HF(m，n)＝F ^HF(m-K，n-K)+F ^*(1，m)·F(1，n)-F ^*(N-L+1，m-K)·F(N-L+1，n-K)；

The described first characteristic formula is: F ^HF (n, m)=(F ^HF (m, n)) ^*

Described pre-distortion coefficients the 3rd matrix is carried out Cholesky decompose, decompose the matrix that obtains according to Cholesky and obtain the pre-distortion coefficients matrix.

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