CN103731106A - Segmented digital pre-distortion method of radio frequency power amplifier - Google Patents

Abstract

The invention provides a segmented digital pre-distortion method of a radio frequency power amplifier. According to the segmented digital pre-distortion method of the radio frequency power amplifier, a complete SCPWL segmented function is used for replacing traditional power series to construct a predistorter, and the limits of an existing method are broken through based on mathematical principles. According to the basic method, a characteristic curve of the predistorter is segmented into small sections, the nonlinear strength of each section is reduced, and therefore the order of each section is lowered. The segmented digital pre-distortion method of the radio frequency power amplifier is quite simple to achieve, only needs a simple subtracter, does not need comparative judgment operation, and can be achieved through the method of delaying first and segmentation second, and therefore the module of the entire predistorter can be standardized, has the potential of improving the effect of the predistorter and lowering hardware implementation difficulty.

Description

A kind of segmentation digital pre-distortion method of radio-frequency (RF) power amplification

Technical field

The present invention relates to a kind of segmentation digital pre-distortion method of radio-frequency (RF) power amplification.

Background technology

1, relevant digital predistorter

At radio and television, the fields such as communication, will amplify through power amplifier before signal transmitting.Power amplifier has natural nonlinear characteristic, if transmit signal power is larger, enters the non-linear more serious region of power amplifier, will the quality transmitting be caused to more serious impact.In order to alleviate nonlinear impact, existing way is the predistortion module of digital baseband part increase at front end, and the characteristic of this module is just in time contrary with power amplifier, can compensate the non-linear impact bringing of power amplifier, thereby improve transmission signal quality, as Fig. 1 shows.

Predistorter can be realized at radio frequency or base band.Along with the progress of digital technology, the signal processing of Modern Communication System has realized digitlization substantially, so predistorter is also used digital circuit.The position of base band digital predistortion device shows as Fig. 2.

2, existing technology and limitation thereof

2.1 power series memory multinomials

The function of digital predistorter is the nonlinear characteristic of using hardware circuit to approach predistorter.Therefore its essence be one with the nonlinear digital filter of memory characteristic.Current input is not only depended in the current output of power amplifier, and depends on input in the past.Therefore predistorter model need to have Memorability to carry out the memory characteristic of Contrary compensation power amplifier, makes the output of power amplifier only relevant with current input.The digital baseband predistorter Mathematical Modeling of existing practicality generally adopts the memory multinomial based on power function:

$z\left(n\right)=\underset{k=1}{\overset{K}{\mathrm{\Σ}}}\underset{q=0}{\overset{Q}{\mathrm{\Σ}}}{b}_{\mathrm{kq}}x(n-q){\left|x(n-q)\right|}^{k-1}---\left(1\right)$

(1) in formula, the exponent number of K representative polynomial (being the highest power of power function), Q represents memory depth.General k is got odd number 1,3,5 ..., therefore (1) formula only exists | x (n-q) | even power.

Existing predistorter be exactly use digital time delay, take advantage of, add, the computing circuit such as power realizes (1) formula, wherein b _kqbe coefficient undetermined, need to use supplementary structure to obtain, conventional structure is indirect learning structure at present, as shown in Figure 3.

Use the learner solution matrix equation in Fig. 3, just can obtain the coefficient b of predistorter _kq, copied in digital predistorter and asked for regard to having completed the parameter of predistorter.The parameter of predistorter is asked for general use software program and is realized.

The problem of 2.1 existing power series memory polynomial predistortion distorter

The unique method that promotes power series polynomial predistortion distortion effect is to improve the polynomial exponent number of (1) formula.Predistorter need to be used digital circuit and device to realize, and existing power series multinomial with reference to implementation method as shown in Figure 4.First signal must carry out power operation, then sends into FIR(finite impulse response digital filter) in.The subject matter of Fig. 4 is that the data that amplitude is less can be close to zero after the operation of high-order power, hardware circuit just cannot be differentiated these data more like this, so, the polynomial exponent number of existing power series generally can not surpass 5 rank, so the effect of predistortion also just has the limit that cannot break through.Cause the basic reason of this limit to originate from the mathematical principle of prior art, thereby the method that cannot implement by technology solve.

Power series polynomial predistortion distorter is applicable to the power amplifier of small nonlinearity, for strong nonlinearity power amplifier, requires very high power, and this power series polynomial predistortion distorter is just inapplicable.And the novel efficient power amplifiers such as envelope-tracking (ET) often have special AM-AM curve shape, and power series polynomial predistortion distorter is helpless for the nonlinear compensation of these special shapes.

Summary of the invention

The object of the present invention is to provide a kind of segmentation digital pre-distortion method of radio-frequency (RF) power amplification, do not change the study structure of existing predistortion, from mathematical principle, break through existing methodical restriction, promoted predistortion effect and reduced hardware and realized difficulty.

A segmentation digital pre-distortion method for radio-frequency (RF) power amplification, comprises the steps:

Step 1, construct complete SCPWL piecewise function:

Basic simple form standard linear segmented function, the mathematic(al) representation of SCPWL piecewise function i segment base function is:

${\mathrm{\&lambda;}}_i\left(x\right)=\left\{\begin{array}{c}\frac{1}{2}(x-{\mathrm{\&beta;}}_i+|x-{\mathrm{\&beta;}}_i\left|\right);x\&le;{\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">S</figure-callout>}}\\ \frac{1}{2}({\mathrm{\&beta;}}_S-{\mathrm{\&beta;}}_i+|{\mathrm{\&beta;}}_S-{\mathrm{\&beta;}}_i\left|\right);x>{\mathrm{\&beta;}}_S\end{array}\right.---\left(2\right)$

Wherein x is input signal, β _i, i=1,2 ..., S-1 is waypoint, need to pre-determine β _sget the maximum of signal amplitude;

By subtraction, operate acquisition (3) formula:

$\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{di}}\left(x\right)={\mathrm{\&lambda;}}_i\left(x\right)-{\mathrm{\&lambda;}}_{i+1}\left(x\right),i=\mathrm{1,2},...S-2\\ {\mathrm{\&lambda;}}_{d,S-1}\left(x\right)={\mathrm{\&lambda;}}_{S-1}\left(x\right)\end{array}---\left(3\right)$

M gets 1,2, and 4,6 ..., except λ _di(x) in addition, all the other only get λ _di(x) even power, carries out power operation and obtains (4) formula:

$\begin{array}{c}{\mathrm{\&psi;}}_i^m\left(x\right)={\mathrm{\&lambda;}}_{\mathrm{di}}^m\left(x\right),i=\mathrm{1,2},...S-2;m=\mathrm{1,2},...,M\\ {\mathrm{\&psi;}}_{S-1}^m\left(x\right)={\mathrm{\&lambda;}}_{d,S-1}^m\left(x\right)\end{array}---\left(4\right)$

Time delay is q, and the complete SCPWL function that power is m is:

$\left\{\begin{array}{c}{\mathrm{\&psi;}}_{\mathrm{iq}}^m\left(x(n-q)\right)={\mathrm{\&lambda;}}_{\mathrm{di},q}^m\left(\right|x(n-q)\left|\right)x(n-q),i=\mathrm{1,2},...,S-2;m=\mathrm{1,2},...,M\\ {\mathrm{\&psi;}}_{S-1,q}^m\left(x(n-q)\right)={\mathrm{\&lambda;}}_{d,S-1,q}^m\left(\right|x(n-q)\left|\right)x(n-q)\end{array}\right.---\left(5\right)$

In above formula,

m in represents λ _{di, q}the m power operation of (| x (n-q) |),

the data vector forming is

${\mathrm{\&psi;}}_q\left(x(n-q)\right)={[x(n-q),{\mathrm{\&psi;}}_{1q}^1\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{1q}^M\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{\mathrm{iq}}^1\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{\mathrm{iq}}^M\left(x(n-q)\right)]}^T---\left(6\right)$

If coefficient vector is $c_q={[c_{0\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,c_{1\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,c_{1\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^2,...c_{1q}^M,...c_{2\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,...,c_{S-1,q}^M]}^T,$ Wherein

represent the unit that time delay is q, the m time coefficient corresponding to basic function in i group, being always output as of complete SCPWL function predistorter:

$z\left(n\right)=\underset{q=0}{\overset{Q-1}{\mathrm{\&Sigma;}}}{c}_q^T{\mathrm{\&psi;}}_q\left(x(n-q)\right)---\left(7\right)$

Step 2, construct predistorter and obtain coefficient, and this coefficient is copied in predistorter:

(1) according to complete SCPWL construction of function predistorter:

First select a memory depth value Q, and use memory for digits unit that signal is carried out to q=0,1 ..., the delay process of Q-1, the later input signal of time delay is designated as x (n-q), is abbreviated as x _q(n).Predistorter has contained Q unit according to time delay degree of depth incremental package, and the structure of each unit is identical, and wherein the course of work of q unit is: x _q(n) after asking amplitude operation, obtain | x _q(n) |, then incite somebody to action | x _q(n) | with β _scompare operation, wherein β _sfor the maximum of preset signal amplitude, according to (2) formula, if | x _q(n) |≤β _s, use | x _q(n) | carry out follow-up computing, otherwise use β _scarry out follow-up computing.Signal enters S-1 expansion SCPWL basic function ψ subsequently _iq(x _q(n)), i=1,2 ... in S-1, i=1,2 ... ψ during S-2 _iq(x _q(n) deployed configuration) and ψ _{s-1, q}(x _q(n)) slightly different.Structure ψ _iq(x _q(n)) to first construct λ before _iq(| x _q(n) |), will | x _q(n) | with β _isubtract each other, suppose that poor is d _i=| x _q(n) |-β _i, ask for d _iabsolute value and initial value be added, ask for e _i=| d _i|+d _i, then will be multiplied by 0.5, obtain λ _iq(| x _q(n) |), i.e. λ _iq(| x _q(n) |)=0.5* (|| x _q(n) |-β _i|+| x _q(n) |-β _i), obtain λ _iq(| x _q(n) |) after, just can construct ψ _iq(x _q(n)); For i=1,2 ... S-2, first obtains λ _{di, q}(| x _q(n) |)=λ _{i+1, q}(| x _q(n) |)-λ _iq(| x _q(n) |), then by λ _{di, q}(| x _q(n) |) carry out power operation, ask for , m=1,2,4,6 ..., and will

respectively with corresponding coefficient multiply each other, be finally added, gained and again with x _q(n) multiply each other and just obtain ψ _iq(x _q(n)), ${\mathrm{\&psi;}}_{\mathrm{iq}}\left(x_q\left(n\right)\right)=x_q\left(n\right)\underset{m}{\mathrm{\&Sigma;}}{c}_{\mathrm{iq}}^m{({\mathrm{\&lambda;}}_{i+1,q}\left(\right|x_q\left(n\right)\left|\right)-{\mathrm{\&lambda;}}_{\mathrm{iq}}\left(\right|x_q\left(n\right)\left|\right))}^m,$ i=1,2,...S-2。During i=S-1, without subtracting each other, ${\mathrm{\&psi;}}_{S-1,q}\left(x_q\left(n\right)\right)=x_q\left(n\right)\underset{m}{\mathrm{\&Sigma;}}{c}_{\mathrm{iq}}^m{\mathrm{\&lambda;}}_{S-1,q}^m\left(\right|x_q\left(n\right)\left|\right);$ Original input signal and coefficient

multiply each other, gained and and ψ _iq(x _q(n)), i=1,2 ..., S-1 is added, and just obtains total output of predistorter q delay unit, $z(n-q)=x_q\left(n\right)c_{0\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1+\underset{i=1}{\overset{S-1}{\mathrm{\&Sigma;}}}{\mathrm{\&psi;}}_{\mathrm{iq}}\left(x_q\left(n\right)\right),$ The number of S is segments, be exactly total all time delays unit and the last output of predistorter

(2) obtain coefficient vector c, c copied into predistorter and stored:

Image data u (n) from the A/D converter of feedback path, then forms data vector according to the method for (6) formula, and forms data matrix Ψ according to the method for (8) formula _qand Ψ, last basis (9) formula dematrix Solving Equations obtains coefficient vector c, wherein

${\mathrm{\&Psi;}}_q=[0_{q\&times;r};{\mathrm{\&psi;}}_q^T\left(u\left(1\right)\right);{\mathrm{\&psi;}}_q^T\left(u\left(2\right)\right);...;{\mathrm{\&psi;}}_q^T\left(u(N-q)\right)]$

Ψ=[Ψ ₀Ψ ₁...Ψ _Q-1] （8）

c=[c ₀;c ₁;...;c _Q-1]

z=Ψc

c=(Ψ ^HΨ) ^-1Ψ ^Hz （9）

Utilize the long-pending breakpoint optimization of weighting curvature-chord length to be optimized waypoint:

Step 1, power amplifier feature measurement:

Measure the signal amplitude at the two ends of power amplifier, repeatedly measure and on average obtain input-input range relation of power amplifier, then the input-output amplitude of power amplifier is cut into N segment, obtain the coordinate { x of each section _i=(x _i, y _i) | i=1,2 ... N};

Step 2, according to (10) formula to (17) formula, calculate breakpoint location, and copy in predistorter and store, completed breakpoint optimization:

Above-mentioned consecutive points x _i-1, x _i, x _i+1between unit vector can be expressed as

${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\frac{x_{i-1}-x_i}{\left|\right|x_{i-1}-x_i\left|\right|},{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\frac{x_{i+1}-x_i}{\left|\right|x_{i+1}-x_i\left|\right|}---\left(10\right)$

Definition vector b ₁, b ₂:

$b_2=(b_{2x},b_{2y})=\frac{d_1+d_2}{\left|\right|d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\left|\right|},b_1=(b_{2y},-b_{2x})---\left(11\right)$

If x _i-1, x _i, x _i+1conllinear, definition

$b_1=(b_{1x},b_{1y})=\frac{x_{i+1}-x_i}{\left|\right|x_{i+1}-x_i\left|\right|},b_2=(-b_{1y},b_{1x})---\left(12\right)$

X now _i-1, x _i, x _i+1can be expressed as by local coordinate system system

x _i-1=x _i+ρb ₁+ηb ₂,x _i+1=x _i+ξb ₁+ζb ₂ （13）

Cross x _i-1, x _i, x _i+1make conic section f (t)=a ₀+ a ₁t+a ₂t ², by x _i-1, x _i, x _i+1coordinates restriction (ρ, η), (0,0), (ξ, ζ) can try to achieve a ₀, a ₁, a ₂, and then can try to achieve x _ithe curvature at place is

$c_i=\frac{f^{\&prime;\&prime;}\left(t\right)}{{(1+f^{\&prime;2}\left(t\right))}^{3/2}}{|}_{t=0}=\frac{2a_2}{{(1+a_1^2)}^{3/2}}---\left(14\right)$

Starting point x ₁curvature for through x ₁, x ₂, x ₃the curvature located in (ρ, η) of conic section, terminal x _ncurvature in like manner can obtain, so,

$c_1=\frac{{2a}_2}{{(1+{(a_1+{2a}_2\mathrm{\&rho;})}^2)}^{3/2}},c_N=\frac{{2a}_2}{{(1+{(a_1+{2a}_2\mathrm{\&xi;})}^2)}^{3/2}}---\left(15\right)$

If x _i, x _i+1between chord length be l _i, weighting curvature-chord length is amassed cl _ibe defined as

cl _i=0.5*(c _i+1+c _i) ^w*l _i （16）

(16) mistake! Do not find Reference source.In formula, w is weighted factor, gets the effect that w>1 can give prominence to curvature, while using SCPWL function approximation, only needs to determine the abscissa of breakpoint, if curve is divided into S-1 section, breakpoint is [β ₁β ₂... β _s], generally get β ₁=x ₁, β _s=x _n, by the long-pending summation of weighting curvature-chord length and in middle breakpoint place mean allocation, m=2,3 ..., S-2 breakpoint β _mfor

${\mathrm{\&beta;}}_m=x_{M+1},M=\underset{M_{}}{\mathrm{<figure-callout\; id="1"\; label="arg\; min\; M"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">arg</figure-callout>}\min }|\underset{i=1}{\overset{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}{\mathrm{\&Sigma;}}}{\mathrm{cl}}_i-(m-1)\frac{\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}{\mathrm{cl}}_i}{S-1}|---\left(17\right)$

Core content of the present invention is that the SCPWL piecewise function by completion replaces traditional power series and constructs predistorter, from mathematical principle, break through existing methodical restriction, its basic skills is to be segment by cutting apart the characteristic curve of predistorter, reduce the intensity of each piecewise nonlinear, thereby reduce the exponent number of each segmentation.This function segmentation method is simple, can promote by increasing the two-dimension method of segmentation and raising power the effect of predistorter.Utilize the predistorter of this construction of function can first time delay, rear segmentation realizes, and has standardized module.

Accompanying drawing explanation

Fig. 1 is predistorter principle schematic;

Fig. 2 is that Contemporary Digital base band predistortion device arranges schematic diagram;

Fig. 3 is the indirect learning structure of digital predistorter;

Fig. 4 is the implementation structure of existing digital predistorter;

Fig. 5 is the predistorter that the present invention uses standby SCPWL construction of function;

Fig. 6 is q the unit expanded view that the present invention uses standby SCPWL function predistorter;

Fig. 7 is that q i of unit basic function of the complete SCPWL function of the present invention predistorter realized schematic diagram;

Fig. 8 is λ of the present invention _iq| x (n) | the electrical block diagram of core cell;

Fig. 9 is the workflow diagram of segmentation digital predistorter of the present invention;

Figure 10 is the local coordinate system system schematic diagram in the present invention.

Below in conjunction with the drawings and specific embodiments, be described in further detail the present invention.

Embodiment

The segmentation digital pre-distortion method of a kind of radio-frequency (RF) power amplification of the present invention, specifically comprises the steps:

Step 1, construct complete SCPWL piecewise function;

Basic simple form standard linear segmented function (Simplicial canonical piecewise linear function, SCPWL) is the linear segmented function that utilizes absolute value, its i segment base function lambda _i(x) mathematic(al) representation is:

${\mathrm{\&lambda;}}_i\left(x\right)=\left\{\begin{array}{c}\frac{1}{2}(x-{\mathrm{\&beta;}}_i+|x-{\mathrm{\&beta;}}_i\left|\right);x\&le;{\mathrm{\&beta;}}_{\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">S</figure-callout>}}\\ \frac{1}{2}({\mathrm{\&beta;}}_S-{\mathrm{\&beta;}}_i+|{\mathrm{\&beta;}}_S-{\mathrm{\&beta;}}_i\left|\right);x>{\mathrm{\&beta;}}_S\end{array}\right.---\left(2\right)$

Wherein x is input signal; β _i, i=1,2 ..., S-1 is waypoint, need to pre-determine; β _sget the maximum of signal amplitude;

The subject matter of SCPWL function only has linear fundament function, and its approximation capability is limited, and the method for constructing complete SCPWL function is divided into two steps:

First the first step removes interdepending between SCPWL function, and this can realize by the subtraction operation of (3) formula:

$\begin{array}{c}{\mathrm{\&lambda;}}_{\mathrm{di}}\left(x\right)={\mathrm{\&lambda;}}_i\left(x\right)-{\mathrm{\&lambda;}}_{i+1}\left(x\right),i=\mathrm{1,2},...S-2\\ {\mathrm{\&lambda;}}_{d,S-1}\left(x\right)={\mathrm{\&lambda;}}_{S-1}\left(x\right)\end{array}---\left(3\right)$

Second step carries out power operation by the difference of the first step, and general m gets 1,2,4 ..., except λ _di(x) in addition, all the other only get λ _di(x) even power:

$\begin{array}{c}{\mathrm{\&psi;}}_i^m\left(x\right)={\mathrm{\&lambda;}}_{\mathrm{di}}^m\left(x\right),i=\mathrm{1,2},...S-2;m=\mathrm{1,2},...,M\\ {\mathrm{\&psi;}}_{S-1}^m\left(x\right)={\mathrm{\&lambda;}}_{d,S-1}^m\left(x\right)\end{array}---\left(4\right)$

Step 2, construct predistorter and obtain coefficient, and this coefficient is copied in predistorter;

(1) from step 1, time delay is q, and the complete SCPWL function that power is m is:

$\left\{\begin{array}{c}{\mathrm{\&psi;}}_{\mathrm{iq}}^m\left(x(n-q)\right)={\mathrm{\&lambda;}}_{\mathrm{di},q}^m\left(\right|x(n-q)\left|\right)x(n-q),i=\mathrm{1,2},...,S-2;m=\mathrm{1,2},...,M\\ {\mathrm{\&psi;}}_{S-1,q}^m\left(x(n-q)\right)={\mathrm{\&lambda;}}_{d,S-1,q}^m\left(\right|x(n-q)\left|\right)x(n-q)\end{array}\right.---\left(5\right)$

In above formula,

m in represents λ _{di, q}the m power operation of (| x (n-q) |), but not to ψ _iq(x (n-q)) asks m power,

the data vector forming is

${\mathrm{\&psi;}}_q\left(x(n-q)\right)={[x(n-q),{\mathrm{\&psi;}}_{1q}^1\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{1q}^M\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{\mathrm{iq}}^1\left(x(n-q)\right),...,{\mathrm{\&psi;}}_{\mathrm{iq}}^M\left(x(n-q)\right)]}^T---\left(6\right)$

If coefficient vector is $c_q={[c_{0\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,c_{1\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,c_{1\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^2,...c_{1q}^M,...c_{2\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">q</figure-callout>}}^1,...,c_{S-1,q}^M]}^T,$ Wherein

represent the unit that time delay is q, the m time coefficient corresponding to basic function in i group, being always output as of complete SCPWL function predistorter

$z\left(n\right)=\underset{q=0}{\overset{Q-1}{\mathrm{\&Sigma;}}}{c}_q^T{\mathrm{\&psi;}}_q\left(x(n-q)\right)---\left(7\right)$

The general structure of the predistorter that complete SCPWL function forms as shown in Figure 5, in figure, according to time delay (memory) degree of depth incremental package, contained Q unit, the structure of each unit is identical, wherein the expanded view of q unit as shown in Figure 6, the course of work of Fig. 6 can be specifically described as: the initial data x of input (n) is realized by memory for digits element through time delay q() after obtain x (n-q), be abbreviated as x _q(n), x _q(n) after asking amplitude operation, obtain | x _q(n) | (Fig. 6 a), then will | x _q(n) | with β _scompare operation (b of Fig. 6), wherein β _sfor the maximum of preset signal amplitude, according to (2) formula, if | x _q(n) |≤β _s, use | x _q(n) | carry out follow-up computing, otherwise use β _scarry out follow-up computing, signal enters S-1 expansion SCPWL basic function ψ subsequently _iq(x _q(n)), i=1,2 ... in S-1, i=1,2 ... ψ during S-2 _iq(x _q(n) deployed configuration) as shown in Figure 7, ψ _{s-1, q}(x _q(n) structure) is slightly different, without phase reducing, (is that a in Fig. 7 directly uses λ _s-1(x) replace).The number of S is segments, according to the effect of required predistortion, determines, S more predistortion effect is better, and complexity is higher, the uppermost x that branches in Fig. 6 _q(n) directly with

multiply each other, finally each branch summation output, total output of the unit that to have formed time delay be q get q=0,1 ..., during Q-1, according to the requirement of (7) formula, generated output $z\left(n\right)=\underset{q=0}{\overset{Q-1}{\mathrm{\&Sigma;}}}{c}_q^T{\mathrm{\&psi;}}_q\left(x(n-q)\right);$

ψ _q((6) formula is shown in the definition of x (n-q), wherein

requirement according to (3) formula to (5) formula generates, and concrete structure as shown in Figure 7.| x _q(n) | first according to shown in Fig. 8, generate λ _iq(| x _q(n) |) and λ _{i+1, q}(| x _q(n) |).λ wherein _iq(| x _q(n) |) by | x _q(n) | with β _isubtract each other, delivery, is added, and takes advantage of 0.5 etc. operation is later to obtain, subsequently λ _iq(| x _q(n) |) and λ _{i+1, q}(| x _q(n) |) subtract each other (last ψ _{s-1, q}(x _q(n)) without subtrator), then obtain according to the power operation of (5) formula

respectively with coefficient separately

multiply each other, be added, last and x _q(n) multiply each other, just obtained ψ _iq(x _q(n)), the m of Fig. 7 gets the 1,2, the 4th, the special case realizing.General change S and m can obtain different predistortion effects, can set flexibly as required.

Fig. 5-8 all adopt digital circuit, mainly use components and parts to have the modules such as mnemon (trigger), absolute value element, comparator, power operating unit and multiplier.

(2) predistorter coefficient obtains the indirect learning structure that still adopts Fig. 3, during use, predistorter and learner are embedded in the digital predistorter of Fig. 9, whole predistorter and the learner externally port of performance are x (n), z (n) and u (n), wherein x (n) and z (n) are respectively the input and output of predistorter, u (n) is the input of feedback path, predistorter is a hardware entities, by digital circuit, learner is not a hardware entities, by calculation procedure code, realized, in Fig. 3, marking learner block diagram is the operation principle for the ease of understanding system, after system is started working, by the control program weaving in advance image data u (n) from the A/D converter of feedback path, once can gather the data of several K, then according to the method for (6) formula, form data vector, and form data matrix Ψ according to the method for (8) formula _qand Ψ, last basis (9) formula dematrix Solving Equations obtains coefficient vector c, and c is copied into predistorter and stored, and completes the coefficient study and storage of predistorter, and predistorter just can normally have been worked, the work of predistorter and the study of coefficient are two independently processes, do not disturb mutually, predistorter is completed by circuit, work in fast state, because the characteristic variations of power amplifier is slow, the update cycle of predistorter coefficient can be very long, so the learning process of learner can be controlled slowly and be calculated by program code,

${\mathrm{\&Psi;}}_q=[0_{q\&times;r};{\mathrm{\&psi;}}_q^T\left(u\left(1\right)\right);{\mathrm{\&psi;}}_q^T\left(u\left(2\right)\right);...;{\mathrm{\&psi;}}_q^T\left(u(N-q)\right)]$

Ψ=[Ψ ₀Ψ ₁...Ψ _Q-1] （8）

c=[c ₀;c ₁;...;c _Q-1]

z=Ψc

c=(Ψ ^HΨ) ^-1Ψ ^Hz （9）

Step 3, utilize the long-pending breakpoint optimization of weighting curvature-chord length to be optimized waypoint;

Before optimizing, can adopt the method for even segmentation, be about to β ₁, β ₂..., β _sat [0, β _s] be uniformly distributed in interval.Breakpoint optimization can distribute more breakpoint in the larger place of power amplifier characteristic curve curvature, thereby improves the effect of predistortion.Because the curvature of characteristics Changing Pattern of power amplifier is identical with predistorter, so the optimization of breakpoint is carried out for power amplifier characteristic curve.

The estimated service life local coordinate system system method of estimation of curvature.First by curve segmentation and be expressed as the discrete point sequence { x of a sequence _i=(x _i, y _i) | i=1,2 ... N}, consecutive points x _i-1, x _i, x _i+1between unit vector can be expressed as,

${\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_1=\frac{x_{i-1}-x_i}{\left|\right|x_{i-1}-x_i\left|\right|},{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_2=\frac{x_{i+1}-x_i}{\left|\right|x_{i+1}-x_i\left|\right|}---\left(10\right)$

Definition vector b ₁, b ₂:

${\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">b</figure-callout>}}_2=(b_{2x},b_{2y})=\frac{{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="d"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">d</figure-callout>}}_2\left|\right|},{\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">b</figure-callout>}}_1=(b_{2y},-b_{2x})---\left(11\right)$

If x _i-1, x _i, x _i+1conllinear, definition,

${\mathrm{<figure-callout\; id="1"\; label="b"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">b</figure-callout>}}_1=(b_{1x},b_{1y})=\frac{x_{i+1}-x_i}{\left|\right|x_{i+1}-x_i\left|\right|},{\mathrm{<figure-callout\; id="2"\; label="b"\; filenames="140106171238.png,140106171252.png"\; state="\{\{state\}\}">b</figure-callout>}}_2=(-b_{1y},b_{1x})---\left(12\right)$

Now, x _i-1, x _i, x _i+1can be expressed as by the local coordinate system system shown in Figure 10:

x _i-1=x _i+ρb ₁+ηb ₂,x _i+1=x _i+ξb ₁+ζb ₂ (13)

Cross the x of Figure 10 _i-1, x _i, x _i+1make conic section f (t)=a ₀+ a ₁t+a ₂t ², by x _i-1, x _i, x _i+1coordinates restriction (ρ, η), (0,0), (ξ, ζ) can try to achieve a ₀, a ₁, a ₂, and then can try to achieve x _ithe curvature at place is

$c_i=\frac{f^{\&prime;\&prime;}\left(t\right)}{{(1+f^{\&prime;2}\left(t\right))}^{3/2}}{|}_{t=0}=\frac{2a_2}{{(1+a_1^2)}^{3/2}}---\left(14\right)$

Starting point x ₁curvature for through x ₁, x ₂, x ₃the curvature located in (ρ, η) of conic section, terminal x _ncurvature in like manner can obtain, so,

$c_1=\frac{{2a}_2}{{(1+{(a_1+{2a}_2\mathrm{\&rho;})}^2)}^{3/2}},c_N=\frac{{2a}_2}{{(1+{(a_1+{2a}_2\mathrm{\&xi;})}^2)}^{3/2}}---\left(15\right)$

If x _i, x _i+1between chord length be l _i, weighting curvature-chord length is amassed cl _ibe defined as:

cl _i=0.5*(c _i+1+c _i) ^w*l _i (16)

(16) mistake! Do not find Reference source.In formula, w is weighted factor, gets the effect that w>1 can give prominence to curvature, while using SCPWL function approximation, only needs to determine the abscissa of breakpoint.If curve is divided into S-1 section, breakpoint is [β ₁β ₂... β _s], generally get β ₁=x ₁, β _s=x _n.By the long-pending summation of weighting curvature-chord length and in middle breakpoint place mean allocation, m=2,3 ..., S-2 breakpoint β _mfor

${\mathrm{\&beta;}}_m=x_{M+1},M=\underset{M_{}}{\mathrm{<figure-callout\; id="1"\; label="arg\; min\; M"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">arg</figure-callout>}\min }|\underset{i=1}{\overset{{\mathrm{<figure-callout\; id="1"\; label="M"\; filenames="140106171249.png,140106171252.png"\; state="\{\{state\}\}">M</figure-callout>}}_1}{\mathrm{\&Sigma;}}}{\mathrm{cl}}_i-(m-1)\frac{\underset{i=1}{\overset{N-1}{\mathrm{\&Sigma;}}}{\mathrm{cl}}_i}{S-1}|---\left(17\right)$

The specific implementation method of step 3 divides power amplifier feature measurement and breakpoint location to calculate two steps.

(1) A in survey map 9, the signal amplitude of B 2 points (being the two ends of power amplifier), repeatedly measure and on average obtain input-input range relation of power amplifier, then the input-output amplitude of power amplifier is cut into N segment, obtain the coordinate { x of each section _i=(x _i, y _i) | i=1,2 ... N};

(2) according to (10) formula to (16) formula, calculate breakpoint location subsequently, and copy in predistorter and store, just completed breakpoint optimization.

(1) formula that prior art is used is a kind of power series, and top step number is that the 5 above circuit realizations in rank are just very difficult, thereby has limited the effect of predistorter.Basic ideas of the present invention are the piecewise functions that adopted a kind of uniqueness, use the method for segmentation, reduced the difficulty that realizes of each section, thereby without using higher-order function, general 3 rank of using just can arrive good effect, and effect can be improved along with the increase of segments, the method that segmentation of the present invention realizes is very simple, only need to use simple subtracter, without comparing decision operation, and can " first time delay, rear segmentation " realize, therefore the module of whole predistorter can be accomplished standardization.Thereby possessed, promote predistorter effect and reduce the potentiality that hardware is realized difficulty.Concrete advantage of the present invention comprises as follows:

(1) first the present invention enters to ask poor by SCPWL function, then carries out power operation, makes its double character that has possessed segmentation and power function, and coefficient still can once obtain by solution matrix equation (8) formula to the method for (9) formula.

(2) the present invention uses the predistorter of expansion SCPWL construction of function to have simple and standardized structure, the lifting of predistortion effect both can rely on increases segments (increasing the quantity of Fig. 7 unit), also can promote the power (power of m in Fig. 7) of each section, thereby there are the potentiality that potential reduction hardware is realized difficulty and promoted effect.

(3) realization of predistorter of the present invention is without special components and parts, and power is also without too high, generally, in 3 times, just can reach very high precision the highest 5 times, thereby be easy to hardware and realize, circuit all adopts digital device to realize, and mainly using components and parts is all conventional digital device, as mnemon (trigger), absolute value element, comparator, power operating unit, the modules such as multiplier.

(4) breakpoint location of predistorter of the present invention can the long-pending method of weighting curvature-chord length be optimized.Be particularly suitable for strong nonlinearity, the incompetent occasion of the tradition such as specific response characteristic memory polynomial predistortion distorter.

The above, it is only preferred embodiment of the present invention, not technical scope of the present invention is imposed any restrictions, therefore any trickle modification, equivalent variations and modification that every foundation technical spirit of the present invention is done above embodiment all still belong in the scope of technical solution of the present invention.

Claims (2)

1. a segmentation digital pre-distortion method for radio-frequency (RF) power amplification, is characterized in that comprising the steps:

Step 1, construct complete SCPWL piecewise function:

Basic simple form standard linear segmented function, the mathematic(al) representation of SCPWL piecewise function i segment base function is:

Wherein x is input signal, β _i, i=1,2 ..., S-1 is waypoint, need to pre-determine β _sget the maximum of signal amplitude;

By subtraction, operate acquisition (3) formula:

M gets 1,2, and 4,6 ..., except λ _di(x) in addition, all the other only get λ _di(x) even power, carries out power operation and obtains (4) formula:

Time delay is q, and the complete SCPWL function that power is m is:

In above formula, m in represents λ _{di, q}the m power operation of (| x (n-q) |),

the data vector forming is

If coefficient vector is

wherein

represent the unit that time delay is q, the m time coefficient corresponding to basic function in i group, being always output as of complete SCPWL function predistorter

Step 2, construct predistorter and obtain coefficient, and this coefficient is copied in predistorter:

(1) according to complete SCPWL construction of function predistorter:

First select a memory depth value Q, and use memory for digits unit that signal is carried out to q=0,1 ..., the delay process of Q-1, the later input signal of time delay is designated as x (n-q), is abbreviated as x _q(n), predistorter has contained Q unit according to time delay degree of depth incremental package, and the structure of each unit is identical, and wherein the course of work of q unit is: x _q(n) after asking amplitude operation, obtain | x _q(n) |, then incite somebody to action | x _q(n) | with β _scompare operation, wherein β _sfor the maximum of preset signal amplitude, according to (2) formula, if | x _q(n) |≤β _s, use | x _q(n) | carry out follow-up computing, otherwise use β _scarry out follow-up computing, signal enters S-1 expansion SCPWL basic function ψ subsequently _iq(x _q(n)), i=1,2 ... in S-1, i=1,2 ... ψ during S-2 _iq(x _q(n) deployed configuration) and ψ _{s-1, q}(x _q(n)) slightly different, structure ψ _iq(x _q(n)) to first construct λ before _iq(| x _q(n) |), will | x _q(n) | with β _isubtract each other, suppose that poor is d _i=| x _q(n) |-β _i, ask for d _iabsolute value and initial value be added, ask for e _i=| d _i|+d _i, then will be multiplied by 0.5, obtain λ _iq(| x _q(n) |), i.e. λ _iq(| x _q(n) |)=0.5* (|| x _q(n) |-β _i|+| x _q(n) |-β _i), obtain λ _iq(| x _q(n) |) after, just can construct ψ _iq(x _q(n)); For i=1,2 ... S-2, first obtains λ _{di, q}(| x _q(n) |)=λ _{i+1, q}(| x _q(n) |)-λ _iq(| x _q(n) |), then by λ _{di, q}(| x _q(n) |) carry out power operation, ask for

m=1,2,4,6 ..., and will

respectively with corresponding coefficient

multiply each other, be finally added, gained and again with x _q(n) multiply each other and just obtain ψ _iq(x _q(n)),

i=1,2 ... S-2.During i=S-1, without subtracting each other,

original input signal and coefficient

multiply each other, gained and and ψ _iq(x _q(n)), i=1,2 ..., S-1 is added, and just obtains total output of predistorter q delay unit,

the number of S is segments, be exactly total all time delays unit and the last output of predistorter

(2) obtain coefficient vector c, c copied into predistorter and stored:

Image data u (n) from the A/D converter of feedback path, then forms data vector according to the method for (6) formula, and forms data matrix Ψ according to the method for (8) formula _qand Ψ, last basis (9) formula dematrix Solving Equations obtains coefficient vector c, wherein

Ψ=[Ψ ₀Ψ ₁...Ψ _Q-1] （8）

c=[c ₀;c ₁;...;c _Q-1]

z=Ψc

c=(Ψ ^HΨ) ^-1Ψ ^Hz （9）。

2. the segmentation digital pre-distortion method of a kind of radio-frequency (RF) power amplification according to claim 1, is characterized in that utilizing the long-pending breakpoint optimization of weighting curvature-chord length to be optimized waypoint:

Step 1, power amplifier feature measurement:

Measure the signal amplitude at the two ends of power amplifier, repeatedly measure and on average obtain input-input range relation of power amplifier, then the input-output amplitude of power amplifier is cut into N segment, obtain the coordinate { x of each section _i=(x _i, y _i) | i=1,2 ... N};

Step 2, according to (10) formula to (17) formula, calculate breakpoint location, and copy in predistorter and store, completed breakpoint optimization:

Above-mentioned consecutive points x _i-1, x _i, x _i+1between unit vector can be expressed as

Definition vector b ₁, b ₂:

If x _i-1, x _i, x _i+1conllinear, definition

Now, x _i-1, x _i, x _i+1can be expressed as by local coordinate system system

x _i-1=x _i+ρb ₁+ηb ₂,x _i+1=x _i+ξb ₁+ζb ₂ （13）

Cross x _i-1, x _i, x _i+1make conic section f (t)=a ₀+ a ₁t+a ₂t ², by x _i-1, x _i, x _i+1coordinates restriction (ρ, η), (0,0), (ξ, ζ) can try to achieve a ₀, a ₁, a ₂, and then can try to achieve x _ithe curvature at place is

Starting point x ₁curvature for through x ₁, x ₂, x ₃the curvature located in (ρ, η) of conic section, terminal x _ncurvature in like manner can obtain, so,

If x _i, x _i+1between chord length be l _i, weighting curvature-chord length is amassed cl _ibe defined as

cl _i=0.5*(c _i+1+c _i) ^w*l _i （16）

(16) mistake! Do not find Reference source.In formula, w is weighted factor, gets the effect that w>1 can give prominence to curvature, while using SCPWL function approximation, only needs to determine the abscissa of breakpoint, if curve is divided into S-1 section, breakpoint is [β ₁β ₂... β _s], generally get β ₁=x ₁, β _s=x _n, by the long-pending summation of weighting curvature-chord length and in middle breakpoint place mean allocation, m=2,3 ..., S-2 breakpoint β _mfor

。

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