CN106453172A - Memory polynomial digital pre-distortion method based on piecewise linear function - Google Patents

Abstract

The invention relates to the technology of digital pre-distortion, provides a novel digital pre-distortion structure, and achieves a good effect in the linearization of a power amplifier. According to the technical scheme, a memory polynomial digital pre-distortion method based on a piecewise linear function includes: the input of a pre-distortion module is y(n)/G, and the output is the conjugate of z(n), and G is the gain of the power amplifier. An input signal is x(n), the input signal passes through a structure which is the same with the pre-distortion module to generate an output signal z(n), e(n)=z(n)-the conjugate of z(n), e(n) is minimized by employing the recursive least squares algorithm iteration, and the signal is linearly amplified. The method is mainly applied to linearization occasions of the power amplifiers.

Description

Memory polynomial digital pre-distortion method based on piecewise linear function

Technical field

The present invention relates to digital pre-distortion technology, more specifically, relate to the memory polynomial number based on piecewise linear function Word pre-distortion method.

Background technology

Power amplifier plays very important role in a wireless communication system, but it is but main in transmitting procedure The nonlinear source wanted.People abandon a part of non-linear generally for the efficiency of transmission improving signal.Therefore modern communications system The efficient modulation system of many employings in system, such as QAM, OFDM, LTE, but this kind of signal has higher peak-to-average force ratio, is easily passing Spread spectrum and distortion inside and outside band is produced during defeated.Therefore, the linearisation of power amplifier becomes key therein.Number Word pre-distortion technology is high due to its flexibility, and uniformity is good, and applicability is strong, facilitates the features such as realization, becomes Recent study Popular and most popular technology.Polynomial Method in digital pre-distortion technology is mainly studied by the present invention.

Abroad, Lei Ding et al. proposed a kind of memory polynomial model, Dennis R.Morgan et al. in 2004 Proposed a kind of memory polynomial model comprising before and after's intermodulation item in 2006, the characteristic of power amplifier can be carried out more preferably Modeling, thus reach more preferable predistortion effect.2015, Anding Zhu proposed a kind of based on piecewise linear function Vector predistortion model, but phase information need to be extracted, it is therefore not easy to hardware and implement.Domestic, 2009, Liu Feng proposed Young waiter in a wineshop or an inn's multiplication algorithm is applied in the middle of the research of digital pre-distortion.2011, Wang Min proposed a kind of number based on QRD-RLS algorithm Word predistortion model.2015, Liu Yue proposed a kind of digital pre-distortion model based on dynamic rational function.

Content of the invention

For overcoming the deficiencies in the prior art, by the study to existing digital pre-distortion technology, it is contemplated that propose one Plant novel digital pre-distortion structure, and in terms of power amplifier linearization, obtain good effect.The present invention uses Technical scheme is, based on the memory polynomial digital pre-distortion method of piecewise linear function, the input of predistortion module be y (n)/ G, is output asG is the gain of power amplifier.Input signal is x (n), and input signal is passed through identical with predistortion module Structure produce output signal be z (n),Make e (n) by using recursive least squares iteration Reach to minimize, so that signal reaches Linear Amplifer.

Predistortion module uses General Memory multinomial model, and structure is as follows：

Wherein：N is not in the same time, a_kl,b_klm,c_klmIt is respectively memory polynomial, front intermodulation item, rear intermodulation item model system Number, K_a,K_b,K_cIt is respectively memory polynomial, front intermodulation item, the polynomial order of rear intermodulation item, L_a,L_b,L_cIt is respectively memory many Item formula, front intermodulation item, the memory depth of rear intermodulation item, M_b,M_cFor the degree of depth of front and back's intermodulation item, x (n) and y_GMPN () is respectively many The input and output signal of item formula model；

Wherein, the higher order term in General Memory multinomial model can be converted to the sum term of piecewise linear function, segmentation Linear function is defined as follows：

Wherein Χ (n)=[x (n), x (n-1) ..., x (n-N+1)]^TFor input vector, b and α_iFor N-dimensional weight vector, a, c_iFor scalar parameter, i=1 ..., σ, if piecewise linear function for representing a continuous non-thread with memory effect Sexual system, then above formula is converted to：

Wherein x_r(n) and y_rN () is real-valued input and output signal, K is piecewise interval, β_kFor fragmentation threshold, L is memory The degree of depth, a_l,c_k,a_klBeing respectively each polynomial coefficient, b is constant value.

Piecewise linear function is expressed and is converted to such as minor function：

?：

Be converted to：

Wherein x_rN () is real-valued signal, x (n) is multinomial model input signal, and is complex valued signals, and comprises phase place Information.

Adding the impact of intermodulation item in piecewise linear function, piecewise linearity multinomial model is as follows：

Wherein, β_kFor threshold value, x (n) and y_PWL-MPN () is input signal and output signal.

Being described as follows of RLS algorithm：

To each moment n, calculate

π (n)=P (n-1) u (n)

E (n)=d (n)-w^H(n-1)u(n)

W (n)=w (n-1)+k (n) e^*(n)

P (n)=λ^-1P(n-1)-λ^-1k(n)u^H(n)P(n-1)

Wherein, π (n) is intermediate quantity, and P (n) is inverse correlation matrix, and u (n) is input vector, and k (n) is gain vector, e (n) For error, d (n) is desired output, w (n) weight vectors, and λ is step factor, RLS algorithm is applied in predistortion architecture, then U (n)=v (n) is the input vector of predistortion module, and d (n)=z (n) is expectation output signal,For The output signal of predistortion module, makes e (n) ≈ 0 by iteration, so that power amplifier reaches linear convergent rate.

The feature of the present invention and providing the benefit that：

Emulated on computers by matlab software, it can be deduced that the spectrogram of input/output signal, accompanying drawing 2. The Adjacent Channel Power Ratio of Traditional GM P predistortion model is-52.7181dBc, and the multinomial mould of piecewise linear function that the present invention proposes The Adjacent Channel Power Ratio of type is-53.8404dBc, and Adjacent Channel Power Ratio is compared conventional model and about improve 1dB.Traditional GM P mould The normalized mean squared error of type is-29.1648dB, and the normalized mean squared error that the present invention proposes model is-36.9255dB, Its performance is significantly larger than conventional model.

Brief description：

Fig. 1 indirect predistortion architecture figure.

The input and output spectrogram of Fig. 2 predistortion model.

Detailed description of the invention

The present invention is by the research to prior art, it is proposed that a kind of multinomial numeral based on piecewise linear function is pre-to be lost True behavior model, and pass through matlab software emulation, achieve good effect.

Digital pre-distortion technology is high due to flexibility, and applicability is strong, is always people in terms of power amplifier line linearisation Focus of attention.The digital pre-distortion model that the present invention proposes is at Adjacent Channel Power Ratio (ACPR) and normalized mean squared error (NMSE) aspect all achieves good effect.Technical solution of the present invention is as follows：

1. first the digital pre-distortion structure of power amplifier is illustrated, accompanying drawing 1.This figure is indirect predistortion architecture Schematic diagram.The input of predistortion module is y (n)/G, is output asG is the gain of power amplifier.Input signal is x (n), the output signal that input signal produces through the structure identical with predistortion module is z (n), ideally, it is believed that y (n)= Gx (n), thereforeSo thatNonlinear effect due to power amplifier E (n) is made to be not zero.Therefore e (n) should be made to reach to minimize by iteration, so that signal reaches Linear Amplifer.The present invention's Predistortion iterative algorithm uses recursive least squares (RLS).

2. the explanation of pair predistortion module.Traditional predistortion module is in the majority with multinomial model, popular in recent years Stronger with applicability for General Memory multinomial (GMP), its polynomial construction is as follows：

Wherein：N is not in the same time, a_kl,b_klm,c_klmIt is respectively memory polynomial, front intermodulation item, rear intermodulation item model system Number, K_a,K_b,K_cIt is respectively memory polynomial, front intermodulation item, the polynomial order of rear intermodulation item, L_a,L_b,L_cIt is respectively memory many Item formula, front intermodulation item, the memory depth of rear intermodulation item, M_b,M_cFor the degree of depth of front and back's intermodulation item, x (n) and y_GMPN () is respectively many The input and output signal of item formula model.It is good that General Memory multinomial model is considered as power amplifier linearization aspect A kind of behavior model, because it had both contained the non-linear of power amplifier and memory effect, contains again before and after's intermodulation item right The impact of signal transmission.But owing to adaptive algorithm needs more parameter, there is unstability etc. and lack in the high-order item that is multiplied itself Point makes this model be unfavorable for that hardware is implemented.

3. the present invention introduces digital pre-distortion technology typical case's piecewise linear function (CPWL), and this structure can represent a kind of and connect Continuous nonlinear function and there is very high precision.Higher order term in General Memory multinomial model can be converted to segmented line Property function sum term, therefore make this model more flexibly and be easy to hardware to implement.Piecewise linear function is defined as follows：

Wherein Χ (n)=[x (n), x (n-1) ..., x (n-N+1)]^TFor input vector, b and α_i(i=1 ..., σ) it is N Dimensional weight vector, a, c_i(i=1 ..., σ) it is scalar parameter.If piecewise linear function is used for representing that has a memory The Continuous Nonlinear Systems of effect, then above formula can be converted to：

Wherein x_r(n) and y_rN () is real-valued input and output signal, K is piecewise interval, β_kFor fragmentation threshold, L is memory The degree of depth, a_l,c_k,a_klBeing respectively each polynomial coefficient, b is constant value.

Although piecewise linear function can represent the nonlinear model with memory effect, but there are two problems.The One, owing to the threshold value of piecewise linear function isThe nonlinear power amplifier model that can be changed into of threshold value provides Very big flexibility, but the parameter of recursive least squares is to be iterated according to the output of power amplifier, so this table Reach formula and be unfavorable for the extraction of parameter, therefore this expression can be converted to such as minor function：

This structure is conducive to recursive algorithm to the iteration of parameter and process.Second, due to the applicable territory of piecewise linear function For real number field, and in power amplifier, the signal of transmission is complex signal, and therefore we can be：

Be converted to：

Wherein x_rN () is real-valued signal, x (n) is complex valued signals, and comprises phase information.

5., in order to improve the accuracy of predistortion model, piecewise linear function adds the impact of intermodulation item.Therefore Whole piecewise linearity multinomial model (PWL-MP) is as follows：

Wherein, β_kFor threshold value, x (n) and y_PWL-MPN () is input signal and output signal.Multinomial with traditional General Memory Formula model is compared, and piecewise linear function model is more flexible and accurate, and higher order term is converted to sum term, therefore at hardware During enforcement more stable.

6. the adaptive algorithm of traditional classical has LMS and RLS two kinds, and RLS algorithm is due to its fast convergence rate, good stability Become the first-selection of predistortion.Being described as follows of RLS algorithm：

To each moment, n=1,2 ... calculate

π (n)=P (n-1) u (n)

E (n)=d (n)-w^H(n-1)u(n)

W (n)=w (n-1)+k (n) e^*(n)

P (n)=λ^-1P(n-1)-λ^-1k(n)u^H(n)P(n-1)

Wherein, π (n) is intermediate quantity, and P (n) is inverse correlation matrix, and u (n) is input vector, and k (n) is gain vector, e (n) For error, d (n) is desired output, w (n) weight vectors, and λ is step factor.We RLS algorithm be applied to shown in Fig. 1 pre- In distortion configuration, then u (n)=v (n) is the input vector of predistortion module, and d (n)=z (n) is expectation output signal,For the output signal of predistortion module, make e (n) ≈ 0 by iteration, so that power amplifier reaches linear Output.

The present invention uses indirect digital pre-distortion structure to carry out simulating, verifying, and indirect digital pre-distortion structure is as shown in Figure 1. Input signal uses 16QAM modulation, 10 sampling rates, and by the raised cosine filter that lifting factor is 0.5, signal enters pre- It is first normalized before distorter.Owing to the behavior model of power amplifier can also serve as predistorter model, therefore in advance Distorter uses piecewise linearity multinomial model, and power amplifier uses memory polynomial model, and adaptive algorithm uses RLS algorithm.As Fig. 2 show the output spectrum figure of different predistorter model.

Claims (5)

1. the memory polynomial digital pre-distortion method based on piecewise linear function, is characterized in that, predistortion module defeated Enter for y (n)/G, be output asG is the gain of power amplifier.Input signal is x (n), and input signal is passed through and predistortion The output signal that the identical structure of module produces is z (n),Changed by using recursive least squares In generation, makes e (n) reach to minimize, so that signal reaches Linear Amplifer.

2. the memory polynomial digital pre-distortion method based on piecewise linear function as claimed in claim 1, is characterized in that, in advance Distortion module uses General Memory multinomial model, and structure is as follows：

$\begin{array}{c}{y}_{GMP}\left(n\right)=\underset{k=0}{\overset{K_a-1}{\mathrm{\Σ}}}\underset{l=0}{\overset{L_a-1}{\mathrm{\Σ}}}{a}_{kl}x\left(n-l\right)|x\left(n-l\right){|}^k\\ +\underset{k=1}{\overset{K_b}{\mathrm{\Σ}}}\underset{l=0}{\overset{L_b-1}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_b}{\mathrm{\Σ}}}{b}_{klm}x\left(n-l\right)|x\left(n-l-m\right){|}^k\\ +\underset{k=1}{\overset{K_c}{\mathrm{\Σ}}}\underset{l=0}{\overset{L_c-1}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_c}{\mathrm{\Σ}}}{c}_{klm}x\left(n-l\right)|x\left(n-l+m\right){|}^k\end{array}$

Wherein：N is not in the same time, a_kl,b_klm,c_klmIt is respectively memory polynomial, front intermodulation item, rear intermodulation item model coefficient, K_a, K_b,K_cIt is respectively memory polynomial, front intermodulation item, the polynomial order of rear intermodulation item, L_a,L_b,L_cIt is respectively memory polynomial, front Intermodulation item, the memory depth of rear intermodulation item, M_b,M_cFor the degree of depth of front and back's intermodulation item, x (n) and y_GMPN () is respectively multinomial model Input and output signal；

Wherein, the higher order term in General Memory multinomial model can be converted to the sum term of piecewise linear function, piecewise linearity Function is defined as follows：

$f\left(X\right(n\left)\right)=a+b^{T}X\left(n\right)+\underset{i=1}{\overset{\mathrm{\σ}}{\Σ}}{c}_i|{{\mathrm{\α}}_i}^{T}X\left(n\right)-1|$

Wherein Χ (n)=[x (n), x (n-1) ..., x (n-N+1)]^TFor input vector, b and α_iFor N-dimensional weight vector, a, c_iFor Scalar parameter, i=1 ..., σ, if being used for piecewise linear function to represent a Continuous Nonlinear system with memory effect System, then above formula is converted to：

$y_r\left(n\right)=\underset{l=0}{\overset{L}{\Σ}}{a}_l{x}_r(n-l)+b+\underset{k=1}{\overset{K}{\Σ}}{c}_k|\underset{l=0}{\overset{L}{\Σ}}{a}_{kl}{x}_r(n-l)-{\mathrm{\β}}_k|$

Wherein x_r(n) and y_rN () is real-valued input and output signal, K is piecewise interval, β_kFor fragmentation threshold, L is memory depth, a_l,c_k,a_klBeing respectively each polynomial coefficient, b is constant value.

3. the memory polynomial digital pre-distortion method based on piecewise linear function as claimed in claim 2, is characterized in that, Piecewise linear function is expressed and is converted to such as minor function：

$y_r\left(n\right)=\underset{l=0}{\overset{L}{\Σ}}{a}_l{x}_r(n-l)+b+\underset{k=1}{\overset{K}{\Σ}}\underset{l=0}{\overset{L}{\Σ}}{c}_{kl}|x_r(n-l)-{\mathrm{\β}}_k|$

?：

$\underset{k=1}{\overset{K}{\Σ}}\underset{l=0}{\overset{L}{\Σ}}{c}_{kl}|x_r(n-l)-{\mathrm{\β}}_k|$

Be converted to：

$\underset{k=1}{\overset{K}{\Σ}}\underset{l=0}{\overset{L}{\Σ}}{c}_{kl}x(n-l)|x(n-l)-{\mathrm{\β}}_k|$

Wherein x_rN () is real-valued signal, x (n) is multinomial model input signal, and is complex valued signals, and comprises phase information.

4. the memory polynomial digital pre-distortion method based on piecewise linear function as claimed in claim 2, is characterized in that, Adding the impact of intermodulation item in piecewise linear function, piecewise linearity multinomial model is as follows：

$\begin{array}{c}{y}_{PWL-MP}\left(n\right)=\underset{l=0}{\overset{L_a-1}{\mathrm{\Σ}}}{a}_{l}x\left(n-l\right)\\ +\underset{k=1}{\overset{K_b}{\mathrm{\Σ}}}\underset{l=0}{\overset{L_b-1}{\mathrm{\Σ}}}{b}_{kl}x\left(n-l\right)\left|\right|x\left(n-l\right)|-{\mathrm{\β}}_k|\\ +\underset{k=1}{\overset{K_c}{\mathrm{\Σ}}}\underset{l=0}{\overset{L_c-1}{\mathrm{\Σ}}}\underset{m=1}{\overset{M_c}{\mathrm{\Σ}}}{c}_{klm}x\left(n-l\right)\left|\right|x\left(n-l-m\right)|-{\mathrm{\β}}_k|\end{array}$

Wherein, β_kFor threshold value, x (n) and y_PWL-MPN () is input signal and output signal.

5. the memory polynomial digital pre-distortion method based on piecewise linear function as claimed in claim 1, is characterized in that, Being described as follows of RLS algorithm：To each moment n, calculate

π (n)=P (n-1) u (n)

$k\left(n\right)=\frac{\mathrm{\π}\left(n\right)}{\mathrm{\λ}+u^H\left(n\right)\mathrm{\π}\left(n\right)}$

E (n)=d (n)-w^H(n-1)u(n)

W (n)=w (n-1)+k (n) e* (n)

P (n)=λ^-1P(n-1)-λ^-1k(n)u^H(n)P(n-1)

Wherein, π (n) is intermediate quantity, and P (n) is inverse correlation matrix, and u (n) is input vector, and k (n) is gain vector, and e (n) is for by mistake Difference, d (n) is desired output, w (n) weight vectors, and λ is step factor, RLS algorithm is applied in predistortion architecture, then u (n) =v (n) is the input vector of predistortion module, and d (n)=z (n) is expectation output signal,Lose for pre- The output signal of true module, makes e (n) ≈ 0 by iteration, so that power amplifier reaches linear convergent rate.