CN104579188A - Discrete newton method based digital baseband adaptive predistortion algorithm - Google Patents

Abstract

The invention provides a discrete newton method based digital baseband adaptive predistortion algorithm. The adaptive algorithm is that a complex number equation is decomposed into an amplitude real number equation and a phase real number equation; the discrete newton method is performed for the iterative method of a binary nonlinear equation. According to the adaptive algorithm, the discrete newton method is used to replace the existing secant method, and one complex number equation is decomposed into two real number equations; the complex multiplication and addition are transformed into real number multiplication and addition, and therefore, the calculation load is greatly reduced, the convergence time is reduced, and the implementation is easy.

Description

A kind of Digital base-band pre-distortion adaptive algorithm based on discrete Newton method

Technical field

The present invention relates to a kind of Digital base-band pre-distortion adaptive algorithm, more particularly, the present invention relates to a kind of Digital base-band pre-distortion adaptive algorithm based on discrete Newton method.

Background technology

In power amplifier (PA, Power Amplifier) linearization technique, Digital base-band pre-distortion technology is one of current most widely used effective method.Pre-distortion technology (PD, Predistorter) arranges a predistorter before the power amplifier, and its characterisitic function is the inverse function of amplifier characteristic function.Like this, predistorter and the total action effect of amplifier linearly amplify.Digital base-band pre-distortion technology refers to settling signal predistortion in base band.Its operating frequency is low, does not relate to the radiofrequency signal of high frequency, applicable digital circuit, is convenient to apply DSP, is the pre-distortion technology having development most.

Digital base-band pre-distortion technology refers to, signal after baseband modulation is converted to digital signal by A/D, with DSP, pre-distortion is carried out to it, obtain digital predistortion signal, the pre-distorted signals of simulation is transformed to again through D/A, then be modulated on carrier frequency through radio-frequency modulator, and launch after carrying out power amplification by high power amplifier.Sub-fraction signal wherein feeds back to radio-frequency (RF) demodulator through coupler, and the signal demodulated is converted to digital signal by A/D again, is digital feedback signal, it is in adaptive algorithm, compare with echo signal, the look-up table of adjustment predistorter, makes it reach principal linear optimization effect.

Gain baseband predistortion is the one that Digital base-band pre-distortion is comparatively commonly used, by index entry, in the form of the look-up table finding input signal corresponding, the gain in form is multiplied with input signal, obtains pre-distorted signals, it is through the amplification of linear amplifier, draw output signal, then send feedback signal back to adaptation module, upgrade the gain in form table, so repeatedly, until the error in adaptation module is minimum value.

In gain baseband predistortion, need correct contrast original signal and feedback signal, therefore just very important to the compensation of loop time delay, existing method, in usual employing iterative method, secant method is as loop time delay evaluation method, but to there is convergence time long for secant method, the shortcomings such as amount of calculation is large.

A kind of adaptive algorithm of the Digital base-band pre-distortion technology based on quick Secant Method is disclosed in prior art, this method is by replacing the derivative term in Newton's formula by difference coefficient, to avoid Derivative Operation, therefore this algorithm is close to quadratic convergence, fast convergence rate, therefore use this algorithm speed higher, follow the tracks of more accurately simple and easy.

Summary of the invention

The invention provides a kind of Digital base-band pre-distortion adaptive algorithm based on discrete Newton method, compared to quick Secant Method, the iterative of complex nonlinear equation can be converted into the iterative problem of real Nonlinear System of Equations, can amount of calculation be reduced, convergence time is less, more easily realizes.

In order to realize above-mentioned technical purpose, provide a kind of Digital base-band pre-distortion adaptive algorithm based on discrete Newton method, in adaptive algorithm, a complex number equation formula is decomposed into amplitude and phase place two real number equations, and adopts discrete Newton method in the iterative solution method of Nonlinear System of Equations.

As preferably, described Digital base-band pre-distortion adaptive algorithm is specially gain baseband predistortion adaptive algorithm.

As preferably, described gain predistortion adaptive algorithm comprises the steps:

Step S1: find input signal v by index entry _if corresponding in the form of display look-up table (| v _i| ²) value;

Step S2: by find out in form described F (| v _i| ²) value be multiplied by v _i, export through predistorter and obtain pre-distorted signals v _d;

Step S3: by pre-distorted signals v _damplify through power amplifier, obtain outputing signal v ₀, and by described output signal v ₀form feedback signal v _ffeed back to adaptation module;

Step S4: described adaptation module is according to described input signal v _iwith described feedback signal v _fupgrade the gain in described display look-up table, so repeatedly, until the described input signal v in described adaptation module _iwith described feedback signal v _fbetween error be less than or equal to the minimum error values of in advance setting.

As preferably, described pre-distorted signals v _dv is outputed signal with described ₀relation v _o=v _dg (x), x=|v _d| ², wherein G (x) is the complex field characterisitic function of stating described power amplifier phase and magnitude characteristic.

As preferably, described input signal v _iwith pre-distorted signals v _dpass be v _d=v _if (y), y=|v _i| ², wherein F (y) is the complex field characterisitic function of statement predistorter phase and magnitude characteristic.

As preferably, if described predistorter and the total linear gain of described power amplifier are normal integer k, at described system input signal v _iwith system output signal v _opass is v _o=v _if (| v _i| ²) G (| v _if (| v _i| ²) | ²)=kv _i, through abbreviation transposition obtain complex number equation formula F (| v _i|) G (| v _i|| F (| v _i| ²) | ²)-k=0.

As preferably, by described complex number equation formula F (| v _i|) G (| v _i|| F (| v _i| ²) | ²)-k=0 is divided into amplitude and phase place two real number equations, with | () | represent the amplitude of plural number, represents plural phase place with ∠ (), then the amplitude characteristic function of described power amplifier is | v _o|=| v _d| G _a(| v _d| ²), phase function is ∠ v _o=G _p(| v _d| ²)+∠ v _d, the amplitude characteristic function of described predistorter is | v _d|=| v _i| F _a(| v _i| ²), phase function is ∠ v _d=F _p(| v _i| ²)+∠ v _i, the amplitude characteristic function of described predistorter and phase function are substituted into separately amplitude characteristic function and the phase function of described rate amplifier, obtain two real number equations, $\left\{\begin{array}{c}{F}_a\left({\left|v_i\right|}^2\right)G_a\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)-k=0\\ G_p\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)+F_p\left({\left|v_i\right|}^2\right)=0\end{array}\right.,$ Wherein F _a() and F _p() is amplitude and the phase gain of described display look-up table storage respectively, G _a() and G _p() is amplitude characteristic AM/AM function (the amplitude characteristic function between output signal and input signal) and phase characteristic AM/PM function (outputing signal the phase characteristic function between input signal) respectively.

As preferably, if nonlinear equation $F=\left\{\begin{array}{c}{f}_1(x_1,x_2)=0\\ f_2(x_1,x_2)=0\end{array}\right.,$ Nonsingular Jacobian matrix $J=\left(\begin{array}{cc}\frac{\∂f_1}{\∂x_1}& \frac{\∂f_1}{\∂x_2}\\ \frac{\∂f_2}{\∂x_1}& \frac{\∂f_2}{\∂x_2}\end{array}\right),$ Then Newton iterative method formula is X ^k+1=X ^k-J ^-1f.

As preferably, with non_derivative, described nonsingular Jacobian matrix is expressed as $M=\left(\begin{array}{cc}\frac{f_1(x_1^k,x_2^k)-f_1(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_1(x_1^k,x_2^k)-f_1(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\\ \frac{f_2(x_1^k,x_2^k)-f_2(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_2(x_1^k,x_x^k)-f_2(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\end{array}\right),$ Then X can be obtained ^k+1=X ^k-M ^-1f.

Compared with prior art, the invention has the beneficial effects as follows: in adaptive algorithm provided by the present invention, existing secant method is replaced with discrete Newton method, and a complex number equation formula dress is become two real number equation group, complex multiplication and addition are transformed into real multiplications and addition, substantially reducing amount of calculation, because this reducing convergence time, being more prone to realize.

attached body explanation

Fig. 1 is gain pre-distortion technology scheme schematic diagram provided by the invention;

Fig. 2 is the comparative result figure using Matlab to emulate secant method and discrete Newton method iterations.

In figure: 01-index entry, 02-show look-up table, 03-predistorter, 04-adaptation module, 05-power amplifier, 06-discrete Newton method, 07-secant method.

Embodiment

In order to make content of the present invention clearly with understandable, below in conjunction with specific embodiments and the drawings, content of the present invention is described in detail.

Please refer to Fig. 1, be mainly following four steps in gain pre-distortion technology scheme provided by the present invention:

Step 1: find input signal v by index entry 01 _if corresponding in the form of display look-up table 02 (| v _i| ²) value;

Step 2: by find out in form described F (| v _i| ²) value be multiplied by v _i, export pre-distorted signals v by predistorter 03 _d;

Step 3: by pre-distorted signals v _damplify through power amplifier 05, obtain outputing signal v ₀, and by described output signal v ₀form feedback signal v _ffeed back to adaptation module 04;

Step 4: described adaptation module 04 is according to described input signal v _iwith described feedback signal v _fand the gain upgraded in described display look-up table 02, so repeatedly, until the described input signal v in described adaptation module 04 _iwith described feedback signal v _fbetween error be less than or equal to the minimum error values of in advance setting.

Power amplifier 05 input signal provided by the invention is v _d, output signal as v _o, then

v _o＝v _dG(x)，x＝|v _d| ²(1)

Wherein G (x) is the complex field characterisitic function of stating described power amplifier phase and magnitude characteristic, due to the phase and magnitude only having the amplitude of input signal can affect output signal, so G (x) can regard the function of just input signal amplitude square as, and and the phase place of input signal have nothing to do.And G (x) is originally as the characterisitic function that power amplifier 05 is total, usually amplitude characteristic AM/AM function G can be divided into again _a(.) and phase characteristic AM/PM function G _p(.), amplitude and phase characteristic function are also all only square relevant with input signal amplitude, and the phase place of input signal is irrelevant.

Preferably, described power amplifier 05 adopts memoryless nonlinear model.

If the input signal of gain predistortion architecture is v _i, output signal as v _d, then

v _d＝v _iF(y)，y＝|v _i| ²(2)

Wherein F (y) is the complex field characterisitic function of statement predistorter phase and magnitude characteristic, only can regard as square relevant with input signal amplitude equally, and irrelevant with the phase place of input signal.F (y) itself is also the total characterisitic function of predistortion architecture, also can be divided into amplitude characteristic function F _a(.) and phase characteristic function F _p(.), amplitude and phase characteristic function are also all the function of input signal amplitude square, and the phase place of input signal has nothing to do.

(2) formula is substituted into (1) formula, if predistorter 03 and the total linear gain of power amplifier 05 are k.K is normal integer, and should be less than the intermediate-frequency gain of power amplifier 05.

v _o＝v _iF(|v _i| ²)G(|v _iF(|v _i| ²)| ²)＝kv _i(3)

Abbreviation is

F(|v _i| ²)G(|v _i| ²|F(|v _i|)| ²)＝k (4)

Transplant

F(|v _i|)G(|v _i||F(|v _i| ²)| ²)-k＝0 (5)

So find the process of the gain in optimum display look-up table 02, be just converted into the problem of unitary complex number equation rooting.

The present invention, by complex number equation (5) formula, is decomposed into amplitude and phase place two real number equations.With | (.) | represent the amplitude of plural number, represent the phase place of plural number with ∠ (.).

The amplitude characteristic function of power amplifier 05 is

|v _o|＝|v _d|G _a(|v _d| ²) (6.1)

Phase function is

∠v _o＝G _p(|v _d| ²)+∠v _d(6.2)

The amplitude characteristic function of predistorter 03 is

|v _d|＝|v _i|F _a(|v _i| ²) (7.1)

Phase function is

∠v _d＝F _p(|v _i| ²) ⁺∠v _i(7.2)

(7.1) formula is substituted into (6.1) formula, obtains

|v _o|＝|v _i|F _a(|v _i| ²)G _a(|v _i| ²|F _a(|v _i|)| ²) (8.1)

(7.2) are substituted into (6.2)

∠v _o＝G _p(|v _i| ²|F _a(|v _i| ²)| ²)+F _p(|v _i| ²)+∠v _i(8.2)

Because overall gain is k, namely amplitude gain is k, and phase place is changed to 0, then

|v _o|＝|v _i|F _a(|v _i| ²)G _a(|v _i| ²|F _a|(|v _i|) ²)＝k|v _i| (9.1)

∠v _o＝G _p(|v _i| ²|F _a(|v _i| ²)| ²)+F _p(|v _i| ²)+∠v _i＝∠v _i(9.2)

Abbreviation, and merge into equation group

$\left\{\begin{array}{c}{F}_a\left({\left|v_i\right|}^2\right)G_a\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)-k=0\\ G_p\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)+F_p\left({\left|v_i\right|}^2\right)=0\end{array}\right.---\left(10\right)$

F _a(.) and F _p(.) is amplitude and the phase gain of the storage of display look-up table 02, and the problem upgrading display look-up table 02 is just converted into the problem of binary real number Solving Nonlinear Systems of Equations.Due to F _a(.) and F _pthe derivative of (.) can not be asked, so can not use Newton method, but can adopt discrete Newton method, and thinking is the same with the Newton method improving nonlinear equation with secant method, the derivative difference coefficient in Newton iteration formula is replaced.

The iterative formula of the discrete Newton method of the equation group of derivation binary nonlinear below, if binary nonlinear equation group is

$F=\left\{\begin{array}{c}{f}_1(x_1,x_s)=0\\ f_2(x_1,x_2)=0\end{array}\right.---\left(11\right)$

Jacobian matrix is $J=\left(\begin{array}{cc}\frac{\∂f_1}{\∂x_1}& \frac{\∂f_1}{\∂x_2}\\ \frac{\∂f_2}{\∂x_1}& \frac{\∂f_2}{\∂x_2}\end{array}\right),$ As long as J is nonsingular matrix, then the iterative formula of Newton method is X ^k+1=X ^k-J ^-1f (12)

With non_derivative, then J can with matrix M instead of

$M=\left(\begin{array}{cc}\frac{f_1(x_1^k,x_2^k)-f_1(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_1(x_1^k,x_2^k)-f_1(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\\ \frac{f_2(x_1^k,x_2^k)-f_2(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_2(x_1^k,x_x^k)-f_2(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\end{array}\right)$

And, ask the inverse matrix of binary square formation to have short-cut method, if i.e., binary square formation $A=\left(\begin{array}{cc}{a}_{11}& a_{12}\\ a_{21}& a_{22}\end{array}\right),$ Then its inverse matrix is $A^{-1}=\frac{1}{a_{11}{a}_{22}-a_{12}{a}_{21}}\left(\begin{array}{cc}{a}_{22}& -a_{12}\\ -a_{21}& a_{11}\end{array}\right)$

Like this, the iterative formula of discrete Newton method can just be obtained

X ^k+1＝X ^k-M ^-1F (13)

Compare with the secant method of nonlinear equation as adaptive algorithm with the discrete Newton method of Nonlinear System of Equations, degree of convergence is the same, it is all superlinear convergence, the amount of calculation of discrete Newton method is fewer than secant method, secant method is owing to being solve Complex, and each iteration needs 2 complex addition and 4 complex multiplications, 2 complex division, namely 16 real multiplications, 12 real additions.The equation group of discrete Newton method is real number, so each iteration only needs 6 real multiplications and 16 real additions, visible, the number of multiplication is less than secant method.So just substantially reduce amount of calculation.

Please refer to Fig. 2, utilize Matlab to emulate self-adapted pre-distortion system, amplifier adopts travelling wave tube power amplifier, and baseband system is 16QAM-OFDM., back-off IBO=6dB, and signal source is 2 × 12.Simulation result shows, and discrete Newton method is fewer than secant iteration number of times, and discrete Newton method arrives stable at about 7 times.Like this, iterations is few, and each iterative computation amount is little, just can reduce convergence time.

Be understandable that, although the present invention with preferred embodiment disclose as above, but above-described embodiment and be not used to limit the present invention.For any those of ordinary skill in the art, do not departing under technical solution of the present invention ambit, the technology contents of above-mentioned announcement all can be utilized to make many possible variations and modification to technical solution of the present invention, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content not departing from technical solution of the present invention, according to technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all still belongs in the scope of technical solution of the present invention protection.

Claims (9)

1. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method, it is characterized in that, in adaptive algorithm, a complex number equation formula is decomposed into amplitude and phase place two real number equations, and adopts discrete Newton method in the iterative solution method of Nonlinear System of Equations.

2. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 1, is characterized in that, described Digital base-band pre-distortion adaptive algorithm is specially gain baseband predistortion adaptive algorithm.

3. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 2, is characterized in that, described gain predistortion adaptive algorithm comprises the steps:

Step (S1): find input signal v by index entry _if corresponding in the form of display look-up table (| v _i| ²) value;

Step (S2): by find out in form described F (| v _i| ²) value be multiplied by v _i, export through predistorter and obtain pre-distorted signals v _d;

Step (S3): by pre-distorted signals v _damplify through power amplifier, obtain outputing signal v ₀, and by described output signal v ₀form feedback signal v _ffeed back to adaptation module;

Step (S4): described adaptation module is according to described input signal v _iwith described feedback signal v _fupgrade the gain in described display look-up table, so repeatedly, until the described input signal v in described adaptation module _iwith described feedback signal v _fbetween error be less than or equal to the minimum error values of in advance setting.

4. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 3, is characterized in that, described pre-distorted signals v _dv is outputed signal with described ₀relation v _o=v _dg (x), x=|v _d| ², wherein G (x) is the complex field characterisitic function of stating described power amplifier phase and magnitude characteristic.

5. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 4, is characterized in that, described input signal v _iwith pre-distorted signals v _dpass be v _d=v _if (y), y=|v _i| ², wherein F (y) is the complex field characterisitic function of statement predistorter phase and magnitude characteristic.。

6. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 5, is characterized in that, if described predistorter and the total linear gain of described power amplifier are normal integer k, at described system input signal v _iwith system output signal v _opass is

V _o=v _if (| v _i| ²) G (| v _if (| v _i| ²) | ²)=kv _i, obtain complex number equation formula through abbreviation transposition

F(|v _i|)G(|v _i||F(|v _i| ²) ²)-k＝0。

7. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 6, is characterized in that, by described complex number equation formula F (| v _i|) G (| v _i|| F (| v _i| ²) ²)-k=0 is divided into amplitude and phase place two real number equations, with | () | represent the amplitude of plural number, represents plural phase place with ∠ (), then the amplitude characteristic function of described power amplifier is | v _o|=| v _d| G _a(| v _d| ²), phase function is ∠ v _o=G _p(| v _d| ²)+∠ v _d, the amplitude characteristic function of described predistorter is | v _d|=| v _i| F _a(| v _i| ²), phase function is ∠ v _d=F _p(| v _i| ²)+∠ v _i, the amplitude characteristic function of described predistorter and phase function are substituted into separately amplitude characteristic function and the phase function of described rate amplifier, obtain two real number equations,

$\left\{\begin{array}{c}{F}_a\left({\left|v_i\right|}^2\right)G_a\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)-k=0\\ G_p\left({\left|v_i\right|}^2{\left|F_a\left({\left|v_i\right|}^2\right)\right|}^2\right)+F_p\left({\left|v_i\right|}^2\right)=0\end{array}\right.,$ Wherein F _a() and F _p() is amplitude and the phase gain of described display look-up table storage respectively, G _a() and G _p() be respectively output signal with input signal between amplitude characteristic function and phase characteristic function.

8. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 7, is characterized in that, if nonlinear equation $F=\left\{\begin{array}{c}{f}_1(x_1,x_2)=0\\ f_2(x_1,x_2)=0\end{array}\right.,$ Nonsingular Jacobian matrix $J=\left(\begin{array}{cc}\frac{\∂f_1}{\∂x_1}& \frac{\∂f_1}{\∂x_2}\\ \frac{\∂f_2}{\∂x_1}& \frac{\∂f_2}{\∂x_2}\end{array}\right),$ Then Newton iterative method formula is X ^k+1=X ^k-J ^-1f.

9. the Digital base-band pre-distortion adaptive algorithm based on discrete Newton method according to claim 8, is characterized in that, with non_derivative, described nonsingular Jacobian matrix is expressed as $M=\left(\begin{array}{cc}\frac{f_1(x_1^k,x_2^k)-f_1(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_1(x_1^k,x_2^k)-f_1(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\\ \frac{f_2(x_1^k,x_2^k)-f_2(x_1^{k-1},x_2^k)}{x_1^k-x_1^{k-1}}& \frac{f_2(x_1^k,x_x^k)-f_2(x_1^k,x_2^{k-1})}{x_2^k-x_2^{k-1}}\end{array}\right),$ Then X can be obtained ^k+1=X ^k-M ^-1f.