(1.Tsinghua University,Beijing 100084,China；2.RHP System Department,ZTE Corporation,Xi’an 710114,China)

Abstract: A robust digital predistortion (DPD) technique utilizing negative feedback itera?tion is introduced for linearizing power amplifiers(PAs)in long term evolution(LTE)/5G sys?tems.Different from the conventional direct learning and indirect learning structure,the pro?posed DPD suggests a two-step method to identify the predistortion.Firstly,a negative feed?back based iteration is used to estimate the optimal DPD signal.Then the corresponding DPD parameters are extracted by forward modeling with the input signal and optimal DPD signal.The iteration can be applied to both single-band and dual-band PAs,which will achieve superior linear performance than the conventional direct learning DPD while having a relatively low computational complexity.The measurement is carried out on a broadband Doherty PA (DPA) with a 200 MHz bandwidth LTE signal at 2.1 GHz,and on a 5G DPA with two 10 MHz LTE signals at 3.4/3.6 GHz for validation in dual-band scenarios.

Keywords: 5G;digital predistortion;power amplifiers;negative feedback iteration

1 Introduction

In order to accommodate the growing demands of massive applications,modern wireless communication systems must evolve to provide higher data capacity and bit rate,and support multiple subscribers simultaneously.These requirements motivate the application of broadband modulat?ed signals and concurrent multi-band transmission.In the forthcoming 5G era,the bandwidth requirements for transmis?sion signals in sub-6 GHz frequency band and millimeter wave band are up to 200 MHz and 800 MHz,respectively.

As one of the key devices in radio frequency (RF) transmit?ters,the power amplifiers (PAs) are characterized as the most power-hungry components and their performance will directly affect the efficiency of RF transmitters.In modern communica?tion system,high efficiency and linearity are two basic require?ments for PAs.In order to acquire higher efficiency,the PA should be operated close to the saturation region,inevitably leading to strong nonlinear distortion.In the 5G communica?tion system,the linearity requirements for the highly efficient PAs operated near the saturation region become even more stringent due to the application of broadband modulated band?width or concurrent multi-band transmission.Effective PA lin?earization techniques must be employed.

Digital predistortion (DPD) is the most popular PA linear?ization technique in the current 4G system.Based on accurate behavioral modeling,DPD can predict PA’s nonlinear behav?ior and eliminate them by adding a proper correction sig?nal[1–6].Due to the significant linearization performance and moderate hardware cost,the DPD technique is still one of the promising linearization solutions in 5G applications.

There are two common adaptive learning structures for DPD parameter extraction,that is,the direct learning (DL)architecture and the indirect learning (IDL) architecture[7–8].Fig.1 depicts the block diagrams of DL and IDL structures.The IDL estimates the post-inverse model of PA and copies it as the predistorter,thus,the linear performance is limited since the noise at PA’s output will be inevitably introduced in the parameter identification[9].Moreover,the IDL provides compromised linearization performance when the PA is high?ly compressed,and generates DPD signals with high peak-toaverage power ratio (PAPR) which might cause damage to the PAs.The DL algorithm,which is based on the pre-in?verse model of PA,is more robust and provides more precise parameter identification than IDL[10].However,since several iterations are needed before the DL algorithm converges to the optimal parameters,the DL estimation is more computa?tionally expensive and complex in structure.In the broad?band application scenario,the number of DPD parameters will be further increased in order to compensate the stronger nonlinear distortion,leading to the lower convergence speed and considerable calculation.

In Ref.[5],the concept of iterative learning control for the linearization of PAs is introduced,which provides a new per?spective for DPD parameter extraction.Ref.[11] proposes a negative feedback iteration based digital predistortion to lin?earize the broadband PAs.In this paper,we present a more ex?plicit investigation of the methodology and experimental re?sults of the negative feedback iteration based DPD,and ex?tend the technique to the multi-band scenario.The proposed DPD can realize superior linear performance in broadband ap?plication scenarios than conventional DL DPD while having a relatively low computational complexity.Furthermore,the pro?posed DPD can be prompted to the dual-band scenario.The measurements are performed on a broadband Doherty PA(DPA) with a 200 MHz bandwidth long term evolution (LTE)signal at 2.1 GHz,and on a DPA for 5G application with two 10 MHz LTE signals at 3.4/3.6 GHz carrier frequency to vali?date the performance of the proposed DPD technique.

2 Proposed DPD Technique Utilizing Nega?tive Feedback Iteration

The block diagram of negative feedback iteration based DPD technique in single band scenario is presented in Fig.2,where the proposed DPD method can be divided into two ma?jor steps.Firstly constructing a negative feedback iteration to obtain the optimal input signal of PA,which can be regarded as DPD signal,and then calculating the parameters of DPD module utilizing the original input signal and the optimal in?put signal obtained in the first step.

▲Figure 1.Indirect learning(IDL)and direct learning(DL)architectures.

2.1 Negative Feedback Iteration

According to the changes of output,the feedback can be di?vided into two categories:the positive feedback (which in?creases the output changes) and the negative feedback (which decreases the output changes).It is obvious that the output of PA will be more stable utilizing the negative feedback.

One of the simplest negative feedback structure is injecting the error between normalized output and input to the system as the new input.In the proposed method,the input signal in the previous iteration is considered,as presented in Fig.3,which indicates that the input in thek-th iteration as:

wherexk(n) and(n) denote the normalized input and output of PA in thek-th iteration,andu(n) is the original input sig?nal.λdenotes the feedback depth,andw0is a control factor used to adjust the convergence of negative feedback iteration.

According to Eq.(1),the input signal of PA will be modi?fied after each iteration.Since it is a negative feedback sys?tem,the changes of output signal will decrease during the iteration and even?tually tend to zero.However,due to the nonlinear behavior of PA,the out?put tends to be unchanged when the error between original input and out?put tends to be zero,that is,u(n) -λ-1(n) ≈0,which indicates that a linearized output will be obtained from the iteration format as in Eq.(1).At that time,the input signal of PA will also tend to be stable and have nonlin?ear relationship with the original input to produce the linear output.

2.2 DPD Parameter Extraction

The principle of DPD is to construct a nonlinear module cascaded before PA to linearize the output signal of PA.Therefore,the optimal input sig?nal obtained in the negative feedback iteration can be regarded as the DPD signal.The input and output signal of DPD module can be expressed utiliz?ing generalized memory polynomial(GMP)model[5],as shown in Eq.(2).

▲Figure 2.Structure of the negative feedback iteration based DPD technique in single-band scenario.

whereKa,b,candMa,b,cdenote the nonlinear order and memory depth,andLaandLbare the lagging and leading depth,respec?tively.

In DL DPD,the iteration format of DPD parameters b with least square(LS)algorithm can be written as:

where A is the basis function matrix composed of original in?put;uandydenote original input and PA output signal col?umn vector.Therefore,the DPD signal atk-th iteration has the form as:

Letλ=1,which indicates that the whole information of out?put signal is applied to the input,and thek-th DPD signal of proposed DPD can be written as:

▲Figure 3.Proposed negative feedback loop for iteration.

It appears that Eqs.(4)and (5)have the same iteration form under the case that the precise inverse matrix of A can be ob?tained.However,since the condition number of basis function matrix A increases dramatically with the increasing of parame?ters[12],the calculated inverse matrix is inaccurate which could enlarge the iteration error and the parameter accuracy would deteriorate in the next iteration.Therefore,the DPD signal ob?tained in the negative feedback iteration,which has eliminat?ed the numerical error,can be regarded as the optimal DPD signal.

Once the optimal DPD signal is identified,the parameters of DPD module can be estimated using LS algorithm with the original input and DPD signal,as in Eq.(6).

where bpdenotes the coefficients of the predistorter,and A is composed of the basis functions in Eq.(2)with the original in?put signalu(n).

Furthermore,another merit of the proposed DPD is the rela?tively low computational complexity.As it can be seen in Eq.(6),only once the parameter calculation is needed with the proposed DPD,while in the DL DPD the parameter calculation is needed in each iteration.Therefore,if the iteration times of both DPD schemes are equivalent,the computational complexity of the pro?posed DPD is less than the DL DPD.

2.3 Proposed DPD for Multi-Band PAs

In order to accommodate the growing demands of massive applications,the 5G and beyond 5G communication systems must evolve to support multiple standards at the same time.A diversity of wireless standards,along with the application of carrier aggregation (CA),present rigorous requirements for wireless transmitters.The increasing system complexity and fabrication cost are unaffordable and practically impossible.The concurrent multi-band transmitter is one of the most prom?ising solutions to this problem.Since multiple signals in differ?ent frequency bands are combined and transmitted in the same nonlinear transmit path,the interaction of concurrent sig?nals will produce complicated nonlinear distortions.In this case,numerous DPD techniques have been developed for multi-band transmitters[13–15].

The proposed digital predistortion can also be applied in multi-band scenarios.Take dual-band transmitter as an exam?ple.The input waveform is composed of dual-band signals,as in Eq.(7).

whereωis the angular frequency,Tsis the sampling interval of base band signal,andx1(n) andx2(n) are the baseband envelop signals at the lower band and upper band respective?ly.The nonlinear behavior of dual-band PA can still be ex?pressed as:

By substituting Eq.(7) into Eq.(8),it is obviously that the output signals at lower band and upper band are related to the input information in each band,and the input signal from the other band also contributes to the distortion.This behavior can be described using 2D-DPD model[13],as in Eq.(9).

wherey1(n)andy2(n)are the output signals at the lower band and upper band respectively.anddenote the model co?efficients.

The ideal output signals at lower and upper bands are lin?earized versions which only contain the input information in each band.Therefore,the negative feedback iteration format for dual-band PA has the similar form with that for single band scenario,as in Eq.(10).

Generally,in order to save the fabrication cost,the shared feedback path is adopted to observe the output information in both frequency bands.In this case,the negative feedback iter?ation is performed on the lower band and upper band by turns.For instance,when identifying the optimal DPD signal for the upper band,the input signal in the upper band is modified in each iteration while the input signal in the lower band remains the same.Fig.4 shows the block diagram of the proposed DPD applied in dual-band transmitters.

After estimating the optimal DPD signal in both transmit bands,the predistorters can be identified by forward modeling using the 2D-DPD model in Eq.(9).In this case,the optimal DPD signals(n)and(n)in each band are regarded as the model output,and the original input signalsu1(n) andu2(n) are the model input.Eq.(11) describes the coefficients extraction using LS algorithm.

where β1and β2are the coefficients of predistorters in upper and lower frequency band; A1and A2are the basis function matrixes composed ofu1(n)andu2(n),as in Eq.(9).

3 Experimental Results

In this section,we present experimental results on two broadband DPAs to validate the proposed DPD technique in both single-band and dual-band scenarios.Both PAs are driv?en in high-efficiency points near the saturation region in order to validate the proposed method’s performance and robust?ness under deep compression.

The experimental setups are depicted in Fig.5a.Within the transmitting chain,a two-channel-synchronized vector sig?nal generator (R&S SMW200A) was used to generate the broadband and dual-band RF signals from baseband samples.In the dual-band test,a wideband RF power combiner was re?sponsible for combining the multiple signals before feeding them to the driver amplifier and the PA.In the single-band test,an LTE signal stream with a 200 MHz bandwidth(2-carri?er) at 2.1 GHz and a 7.5 dB PAPR after crest factor reduction(CFR) were used as inputs in the experimental evaluations.The measurements were applied to a broadband (1.7 GHz–2.8 GHz) Lab-made Cree CGH40010p DPA.In the dual-band scenario,the evaluations were performed on a Lab-made Cree CGH40010p DPA which was designed for 5G applications with a bandwidth of 3.3–3.8 GHz.The test signals were two 7.5 dB PAPR uncorrelated LTE signals of 10 MHz bandwidth at carrier frequencies of 3.4 GHz and 3.6 GHz.Both the DPAs were operated in the saturation region to acquire high efficien?cy and obvious nonlinearity for the validation of the proposed DPD.Figs.5b and 5c show the schematic of Lab-made DPAs.

▲Figure 4.Structure of the negative feedback iteration based DPD technique in dual?band scenario.

On the feedback side,the broad and dual-band signals were coupled out from the PA output and thereafter converted to baseband samples by a spectrum analyzer (R&S FSW26).In the dual-band test,the upper band and lower band signals were captured by the wideband feedback path in each time slot,by turns.All algorithms and instrument control opera?tions were performed on the host per?sonal computer (PC) running Matlab.Adjacent channel power ratio (ACPR)was used to evaluate the nonlinear dis?tortions performance.

3.1 Evaluations on Broadband PA

In the DPD test,the conventional DL DPD and IDL DPD were per?formed as well as the proposed DPD for comparison.The feedback depthλand iteration stepwwere equal to 1 and 0.3 respectively.When the nega?tive feedback iteration is converged,the output signal of PA is greatly lin?earized,presenting with the ACPRs of the first adjacent channel ap?proaching-49 dBc.

▲Figure 5.Robust digital predistortion(DPD)test bench.

The parameters of DPD module were estimated utilizing GMP model withKa=Kb=Kc=11,Ma=Mb=Mc=8 andLa=Lb=6.Fig.6a shows the AM/AM and AM/PM curve with/without the proposed DPD.The nonlinear distortion,especially the memory effect,is obvious in the 200 MHz DPD test; however,the nonlinear characteristic has been improved significantly when applying the proposed DPD.Fig.6b presents the power spectrum density (PSD) with/without DPDs at the output of PA.With the proposed DPD,the output signal can achieve–45 dBc ACPR，which outperforms the DL DPD and IDL DPD by 1 dB and 4 dB respectively.Table 1 summarizes the linear performance of the PA’s output signals.

▲Figure 6.Measured AM/AM and AM/PM characteristics and PSDs.

▼Table 1.Measured performance in single band scenario

Fig.7a compares the converging speed between the nega?tive feedback iteration and DL DPD by calculating the normal?ized mean square error(NMSE)between the PA input and out?put signals after each iteration.Both the negative feedback it?eration and DL DPD converge after 5–6 iterations,while the negative feedback method shows a better NMSE performance.

Fig.7b shows the iteration speed and accuracy with differ?ent iteration steps.The converging speed increases with the larger steps,however,the optimal linear performance is get?ting poorer with the increasing of iteration steps.Furthermore,the linearity of the output signal even becomes worse after the NMSE in the iteration reaches the optimum.The measured re?sults indicate that the iteration step should be appropriately selected to balance the convergence speed and the linear per?formance.

▲Figure 7.Iterative convergence trend.

3.2 Evaluations on Dual-Band PA

The proposed DPD is validated on a broadband (3.3 GHz–3.8 GHz)DPA with the dual-band input signal.The dual-band signal is separated by 200 MHz at the carrier frequencies of 3.4 GHz and 3.6 GHz.Two uncorrelated 10 MHz LTE signals are applied in the dual-band measurements.The feedback depthλ1,λ2and literation stepsw1,w2are the same for both frequency bands,which are equal to 1 and 0.3 respectively.Similar with the single band test,the negative feedback itera?tions converge quickly after 5–6 times modification.When the iteration converges,the optimal DPD signals which im?prove the ACPRs of PA output signals at both bands to about-55 dBc are obtained.

The parameters of predistorters in lower and upper frequen?cy bands are extracted utilizing 2D-DPD model withK=7,andM=4.Fig.8 shows the AM/AM and AM/PM characteris?tics with/without the proposed DPD.The AM/AM and AM/PM curves in Fig.8 show notable dispersion,which can be attrib?uted to the intermodulation of the two uncorrelated signals at each frequency band.The nonlinear distortions and inter mod?ulations are compensated significantly with the proposed DPD,showing a more than 20 dB ACPR improvement at both frequency bands.Fig.8 depicts the observed PSDs of PA out?put signals at the lower band and upper band.Table 2 summa?rizes the above linear performance.

▲Figure 8.Measured PSDs and AM/AM,AM/PM characteristics at power amplifier(PA)’s output with/without the proposed DPD.

▼Table 2.Measured performance in dual-band scenario

4 Conclusions

In this paper,a negative feedback iteration based DPD tech?nique is proposed for linearizing power amplifiers in LTE/5G broadband and multi-band applications.The proposed DPD technique divides the conventional DPD process into two steps,which estimate the optimal DPD signal by negative feed?back iteration and then identify the predistorter by forward modeling.Benefited from the iteration,the proposed DPD can achieve a better linearization performance than conventional DL DPD while having a lower computational complexity.The validations are carried on a broadband DPA with a 2-carrier 200 MHz bandwidth LTE signal at 2.1 GHz,and on a dualband scenario with two 10 MHz LTE signals at 3.4 GHz and 3.6 GHz.The measurements provide potential application val?ue of the proposed DPD in LTE/5G systems.