Physically Inspired Digital Predistortion for Dual Input Doherty

Power Amplifiers and Automatic in-Situ Identification

Giovanni Donati, Christian Musolff, Giuseppe Gottardo, Daniel Popp and Georg Fischer

Friedrich Alexander University of Erlangen-Nuremberg, Cauerstrasse 9, 91058 Erlangen, Germany

{giovanni.donati, christian.musolff, giuseppe.gottardo, daniel.popp, georg.fischer}@fau.de

Keywords: Digital Signal Processing, Digital Predistortion, Dual Input Doherty, Power Amplifiers

Abstract: A novel approach for the linearization of dual input Doherty power ampliﬁer (DPA) is derived by taking

inspiration from the operation of the device. A new point of view is evaluated and an automatic

identiﬁcation procedure is developed, reducing the complexity of the predistorter, improving linearity and

eciency at the same time and avoiding the usage of crest factor reduction (CFR). It is also emphasized the

importance of a power dependent phase relationship between the inputs of the dual input DPA. A validation

of the theory is performed by means of a MATLAB/ADS envelope co-simulation.

1 INTRODUCTION

Modern telecommunication systems are aiming for

very high performance demanding high linearity,

eciency and wide bandwidth. A key component of

the Base-Station (BS) operation is the power

ampliﬁer, which is the major contributor to the

whole power consumption of the system. The

signals used in order to improve the spectral

eciency have high peak to average power ratio

(PAPR) and are decisive in terms of the average

eciency of the whole system. For this reason

Doherty Power Ampliﬁers (DPA) are representing a

primary choice for BS applications. DPAs deliver an

extended eciency range and are perfect candidates

for ampliﬁcation of signals with a very high

dynamic range. Furthermore, the advances in the

design techniques led to new power ampliﬁer (PA)

architectures able to deliver high eciency over a

large bandwidth of operation. Class J and JF

realizations of the DPA are making use of harmonic

terminations to improve the bandwidth. It has

already been demonstrated that separating the input

branches and driving them separately is of huge

beneﬁt in terms of bandwidth and reconﬁguration of

the power added eciency (PAE) (Gustafsson,

Anderson and Fager, 2012; 2013). Also the concept

behind the algorithms for digital pre-distortion

(DPD) of dual input DPA were documented

(Cahuana et al., 2014), reporting very good

performance and showing the advantages of using

this architecture in BSs. The previous research has

demonstrated the advantage of driving MAIN and

PEAK ampliﬁers by means of a static splitter,

implemented in the digital domain, delivering the

optimal combinations of the inputs signals to the PA

in order to obtain high eciency (up to 42%).

Despite the improvements, the eect of the phase

dierence between the two input branches is still not

fully characterized yet. In this article we are showing

the importance of the power dependent phase

correction to be applied at the input of the dual input

DPA architecture, and we are presenting a way to

automatically identify the optimum combinations of

the inputs in-situ. We have reached an average

power eciency of 51%, and we developed a simple

physics-inspired algorithm for the pre-distortion that

we tested with a 5 MHz LTE signal. The results are

demonstrated and validated using envelope

simulations in Advanced Design System (ADS).

2 THEORY

In the work of Gustafsson, Anderson and Fager,

(2013) it was demonstrated how, the eciency in

power back-o (PBO) of a DPA could be improved

and maintained over a wide fractional bandwidth, by

introducing the back-o point εb as a design

parameter. All the control parameters of the device

Donati G., Musolff C., Gottardo G., Popp D. and Fischer G.

Physically Inspired Digital Predistortion for Dual Input Doherty Power Ampliﬁers and Automatic in-Situ Identiﬁcation.

DOI: 10.5220/0006227100530060

In Proceedings of the Fifth International Conference on Telecommunications and Remote Sensing (ICTRS 2016), pages 53-60

ISBN: 978-989-758-200-4

can be expressed as a function of the normalized

drive level ε, in particular the output power is

expressed as:































  









































(1)

where 



is the maximum current deliverable by

the MAIN PA, εb < ε < 1, θ is the phase dierence

between MAIN and PEAK ampliﬁer input, f is the

fractional bandwidth and k is the drive level of the

PEAK that sets the eciency bandwidth of the

DPA. In particular, as also demonstrated by the

work of Gustafsson, Anderson and Fager (2013), the

relationship determining the acceptable values for 



is:

 



  













(2)

Figure 1: Dependency of the DPA bandwidth on back off poin choice

Figure 1 is graphically showing how the choice

of 



is decisive for determining the eciency

bandwidth. In addition it was presented a closed

formula (Gustafsson, Anderson and Fager, 2013),

for the phase relationship between main and peak

power ampliﬁer (PA), where the dependency on the

fractional bandwidth and the drive level of the

PEAK is exploited (3):

















(3)

It is clear that the ability to control the input

signals of the DPA architecture makes it possible to

reach high eciency both at maximum power and

Fifth International Conference on Telecommunications and Remote Sensing

PBO, causing a active load modulation that assures

high performance on an extended frequency range.

The theory previously developed by Gustafsson,

Anderson and Fager (2013) states that improving the

eciency bandwidth of the DPA architecture leads

to a degree of freedom in the reconﬁguration of the

PA eciency, depending on the particular frequency

where a signal is residing. This is very important for

modern BS where we are continuously dealing with

multistandard signals and scenarios involving

multiband transmission. In Cahuana et al. (2014),

this theory was used to implement a digital power

splitter to get the maximum power eciency out of

the designed DPA

3 REVISION OF THE

IDENTIFICATION PROBLEM

The previous scientiﬁc work has opened a lot of

possibilities in terms of reconﬁguration and

bandwidth enlargement. Also if the articles in

literature are giving a very good insight of the

problem and deliver a solution, it is still unclear how

to identify the input combinations in a ﬂexible and

automatic way. If we imagine the problem as the

identiﬁcation of a drive function for the DPA, we

could depict it as the black box (Figure 2):

Figure 2: Block scheme for the identification of a drive

function.

where Pm, Pp and δϕ are respectively the values of

the input powers for MAIN and PEAK ampliﬁer,

and the phase relationship between them. At the

output of the model we have the power and the

power added eciency. Seen in this way, the

identiﬁcation of a single drive function can be

exploited as a multidimensional optimization

problem. Speciﬁcally if we could try all the possible

triplets (Pm, Pp, δϕ), we would end up discovering

that there is a theoretically inﬁnite number of

combinations leading to the same output power. The

challenge relies in identifying the triplets

maximizing the eciency for a speciﬁc power level

and frequency. In order to do so performed an

analysis on the model of a dual input DPA with 300

MHz of bandwidth (700 to 1000 MHz) and a

maximum output power of 100 W. A set of

measurements in ADS was obtained by means of

harmonic balance (HB) simulations, performing a

large power sweep over the possible combinations of

the input parameters at four frequency points. The

results of the simulations at 900 MHz are shown in

Figure 3:

Figure 3: Multidimensional identification dataset for drive

function.

where η is the power added eciency and ϕO is the

output absolute phase of the PA. The color is coding

the information about the eciency value assumed

by a speciﬁc point, with a resolution of about 2%.

Analyzing the results in ﬁgure 3 it becomes obvious

how several combinations of the inputs lead to the

same output power but not to the maximum

eciency. This appears much more evident in the

middle power region. The image was generated by

separating the data into bins in order to reduce

dimensionality of the dataset, which is otherwise

composed of more than 90.000.000.000 points.

Despite the separation into bins the data are quite

dense, so in order to better appreciate the magnitude

of the problem we should zoom in. Figure 4 presents

a closer view of the data. Using dierent triplets we

could generate 38 W at the output of the PA, but in a

very small range around it (4 mW) we could drop

the eciency to 30% or less by choosing a

suboptimal triplet.

Figure 4: Detail of the characterization space for Pm.

In (Cao et al, 2012) an algorithm for the DPD of

dual input power ampliﬁers was presented. From the

Physically Inspired Digital Predistortion for Dual Input Doherty

Power Amplifiers and Automatic in-Situ Identification

developed theory, it turns out that the knowledge of

an optimized signal for the peak power ampliﬁer is

necessary, together with the desired RF output

signal, in order to determine the shape of the

predistorter signal of the main PA. This technique

has an higher complexity than the classic approach,

but because the nonlinear order used was low it was

still considered acceptable. This algorithm shows a

good linearization performance and also tries to

optimize the eciency, but it seems that the

compromise between the two goals avoids obtaining

a very good eciency in PBO.

4 NOVEL LINEARIZATION

APPROACH

We can improve the identiﬁcation of the digital

static splitter by optimizing it for both eciency and

linearity. Below the compression point the response

of the system is depending only one the behavior of

the MAIN PA. Deﬁning the drive function in the

power domain, we can build a model for the

predistorter of the MAIN branch with a piecewise

lookup table (LUT).

Figure 5: Example of MAIN drive function.

Referring to Figure 5 we have three dierent

sections of the curve. The ﬁrst one is obtained by

turning the PEAK PA o and sending a power ramp

to the MAIN PA. We can determine its saturation

power and choose the back-o point. Interestingly

we are free to reconﬁgure the power eciency of the

dual input DPA by moving the back-o point. There

is a trade o between linearity and eciency when

choosing the back-o point. By deciding the

compression point of the MAIN PA we can allow a

certain amount of nonlinear eects included in the

system. The drawback observed is a decrease of the

back-o eciency. The third part of the curve is

linear because we don’t want to generate nonlinear

eects by predistorting.

The two curves could be directly blended but this

would generate problems in terms of bandwidth

expansion of the input signal. The knee between the

the two curves is a discontinuity in the ﬁrst order

derivative of the function and is responsible for the

generation of very high frequency components in the

spectrum. The bandwidth expansion generates issues

in the signal reconstruction path because the DAC

has a bandwidth limited by its sampling frequency

which is not inﬁnite. By using a Bezier interpolant

(Ping and Guozhao, 2011) to connect the two

curves, we are reducing the nonlinear eects of the

curve and improving the spectral eciency by

introducing G2 continuity at the blending points. By

deﬁning the behavior of the MAIN PA predistorter

we reduce the dimensionality of the identiﬁcation

problem and we detect the right value of output

power for the DPA in that point. Since we are trying

to linearize the device, we would like to have an

output characteristic which is linear in the amplitude

and possibly constant in phase. Using the

information about the output phase at the back-o

point, we can set a target for the algorithm

performing the identiﬁcation of the drive functions.

As in Cao et al. (2012), we can deﬁne a target output

power (equally spaced power points) with the

condition of constant output phase joined with a

LUT of powers to drive the MAIN PA. The ﬁrst

main dierence with the work of Ca, is that we are

not introducing any DPD mathematical model, we

are instead using a certain number of supports (for

instance 200) to extract the LUTs used later as

references to interpolate between the values. LUTs

can be considered less performing, especially in

terms of bandwidth expansion, when compared to

polynomials, butit is was already demonstrated

(Barradas et al., 2014) that they can be

reformulated in order to be as ecient as the

polynomial model. In order to identify the missing

predistorter functions, an intelligent algorithm can

be applied. We need to deﬁne a cost function and

minimize it in order to ﬁnd the value of the PEAK

and phase predistorted signals. A good candidate for

such function is the pure error vector module EVM

(not the classic EVM used for constellations), which

can be easily calculated as:









 









(4)

Fifth International Conference on Telecommunications and Remote Sensing

which is expressing the ratio between the error

vector and the original vector. The EVM also

accounts for the output phase, so by minimizing it

we are able to ﬁnd the correctly aligned output

vector with the wanted power and eciency. It

should be emphasized that the minimization problem

uses a mono dimensional cost function. The

eciency optimization is performed by choosing the

target output phase that we want to maintain at the

PA output. Gradient based algorithms such as the

ones used to train the classic DPD models could be

used to minimize a speciﬁc cost function, but they

have experimentally exhibited slow convergence on

this kind of problem. In addition they could

converge to global minima, preventing the discovery

of an absolute minimum. Particle Swarm

Optimization (Kennedy et al., 1995) is a very

attractive algorithm for this sort of application

because it is simple and allows control over the

power range swept at the input of the DPA. PSO is

really useful in a real application in order to avoid

damaging the devices due to wrong drive levels. In

the literature there are already documented uses of

PSO in the ﬁeld of DPD (Abdelhafiz et al., 2013) for

the computation of the coecients of DPD models.

Here we would use it for identifying the optimum

triplets directly. The idea behind PSO is very simple,

a single particle is described by a set of parameters:

 Position (X): described by the decision

variables

 Velocity (V): velocity of the particle

during its motion, deﬁnes also the direction

of search

 Local Best (L): local best met by the

particle, updated each time the local best is

improved during the search

 Global Best (G): global best found by the

whole swarm, this information is shared

between all the particles

Each particle is moving in the 2-dimensional space

updating its speed according to the social

interactions with the rest of the swarm. The formulas

to update the velocity and position are expressed as

in 5 and 6.









  

 



(5)













(6)

Table 1: PSO algorithm

The coecients appearing in the equation of the

velocity are controlling the ”memory” of the

particles to lead them towards the best solution that

has been found so far. Coecient c1 is controlling

the tendency of the particle to search in the direction

of its own best found solution, while c2 manages the

social interaction of the particle with the rest of the

swarm members to let its position drift towards the

global best found by the whole swarm. The ﬂow of

the optimization algorithm 1 is very simple to

implement and can be adapted to a large range of

problems by performing a proper sensitivity study of

Physically Inspired Digital Predistortion for Dual Input Doherty

Power Amplifiers and Automatic in-Situ Identification

the parameters. To make sure that the particle swarm

optimizer does not stop if no convergence is met, a

maximum number of iterations can be established.

This also sets the speed of the algorithm in the worst

case, when no optimum is found or when the cost

function does not reach the expected precision

5 APPLICATION OF PSO TO

STATIC DRIVE FUNCTION

IDENTIFICATION

In our approach, the PSO algorithm described above

was adapted to the problem of the identiﬁcation of a

single static drive function: Position X is a bi-

dimensional vector made of Pp (expressed in W) and

δΦ (expressed in degrees); a vector for the target

output power is generated by deﬁning 50 equally

spaced values; the target output phase is established

by using the procedure explained in the previous

section.

6 SIMULATION SETUP

In order to prove the concept, a co-simulation

MATLAB/ADS was performed. Signal generation,

baseband signal processing and analysis of the

results were performed in MATLAB while the

whole physical part of the simulation was performed

by ADS which was conﬁgured to perform circuit

envelop simulation. The workﬂow represented in

Figure 6 starts with a MATLAB script generating

the drive function for the MAIN PA with only 50

points, deﬁning the linear power target points and

identifying the back-o point in the same way

described in the previous sections.

Figure 6: Simulation setup interfacing MATLAB and

ADS.

When the algorithm reaches the back-o point it

reads the output phase of the PA and starts the

particle swarm optimizer to sequentially compute

the right pre-distorted phase and power for the peak

PA. Since we want to characterize the static

correction for the DPA, in MATLAB we are

generating constant power points of a duration

which avoids memory eects to be sensed at the

output. It was experimentally seen that the memory

eects of the PA model are visible just up to 300 ns.

For this reason we have set the duration of the power

pulses to 1 µs. The convergence of PSO is improved

by using more particles, but this also means a bigger

number of evaluations and slower results. We used

N = 20 particles as a good compromise between the

simulation time and the precision of the results. To

limit the maximum duration of the simulation we

have set the number of maximum iterations to 50.

The whole simulation takes about:









 



 



 



(7)

Unfortunately such simulation is time consuming

because of the calls to ADS made from MATLAB.

The simulation for one point takes about two

seconds, so the whole duration, in the worst case, is

about 27 hours. The solution is found after less than

10 iterations, so the simulation can be completed in

2 to 5 hours. We expect that by performing the

measurement in-situ using an FPGA system, the

time to measure each point can be reduced to the

limits of memory eects, resulting in a complete

identiﬁcation of the drive function in 15 ms. This

process can be applied around several carrier

frequencies, creating a raster of drive functions to

obtain a wideband model. This workﬂow generates a

LUT, which is used to evaluate the results by

running a simulation with an LTE signal. Results are

shown in the next section.

7 RESULTS

We have simulated the identification of the drive

function by setting the carrier frequency to 900

MHz. The identified drive function is shown in

Figure 7.

Looking at the phase relation between MAIN

and PEAK driving signals, we noticed that phase is

ranging from 200 degrees, at low output power, to

166 degrees at the maximum power. There are 34o

Fifth International Conference on Telecommunications and Remote Sensing

of total phase variation, which is not a negligible

quantity to account for. This shows the importance

of the relationship between Pp and , which is why

we should choose dual input DPAs for BS operation.

By correctly tweaking Pp we select a specific phase

relationship, at the input of the structure,

maximizing linearity and efficiency for a specific

carrier frequency.

Figure 7: Drive function for the DPA at 900 MHz.

Figure 8: Amplitude Input Output characteristic of

DPA + DF.

Looking at the phase relation between MAIN

and PEAK driving signals, we noticed that phase is

ranging from 200 degrees, at low output power, to

166 degrees at the maximum power. There are 34o

of total phase variation, which is not a negligible

quantity to account for. This shows the importance

of the relationship between Pp and δφ, which is why

we should choose dual input DPAs for BS operation.

By correctly tweaking Pp we select a specific phase

relationship, at the input of the structure,

maximizing linearity and efficiency for a specific

carrier frequency.

Using the drive function to pre-distort the DPA

driven by a 5 MHz LTE signal with a 10 dB PAPR

(no CFR was applied), we obtained a linear output

characteristic (Figure 8), where the dispersion

around the curve is due to the memory of the device.

As we can see in Figure 9, the whole system still

shows a non-linear phase characteristic

This is due to the fact that the identification

process is done on the two separated inputs of the

DPA. When applying a dynamic signal, the splitter

does not account for the phase difference between

the input of the DF and the output of the DPA.

Figure 9: Phase characteristic of DPA + DF

Figure 10: AM-AM and AM-PM characteristic of

DF + DPA after static phase correction

Physically Inspired Digital Predistortion for Dual Input Doherty

Power Amplifiers and Automatic in-Situ Identification

Such phase difference can be statically corrected

by a common identification technique. We can see

the effect of the phase linearization in Figure 10.

After applying the static phase correction (SPC)

we obtained a drastic improvement of the ACPR,

from 30 to 54 dBc (Figure 11) and an average power

added efficiency of 51:1%.

This represents a very good result, considering

that no CFR was applied to the input signal.

Figure 11: Resulting output spectra

8 CONCLUSIONS

In this article a novel approach for the linearization

of dual input DPAs was presented.

We showed how, taking inspiration from the device

operation, flexible reconfiguration of the efficiency

can be obtained by means of a digital drive function.

In addition to that, we developed an automatic

identification procedure eligible for FPGA

implementation, due to its simplicity.

The algorithm performs an optimization of the

input signals for the device and avoids a multi-object

approach delivering maximum efficiency by keeping

the linearity conditions at its output.

The procedure was validated by making use of a

MALTAB/ADS cosimulation environment and

testing the workflow on a 5 MHz LTE signal with a

10 dB PAPR. Results have demonstrated that very

good performance can be reached without

introducing CFR in the transmit chain.

Therefore this opens a huge number of

possibilities to adapt the performance to the signal's

probability density function and to future multiband

approaches for the linearization of this architecture.

Combined together, the identification of several

drive functions at different frequencies and, novel

techniques for the detection of the instantaneous

frequency of non-stationary signals, can lead to a

new wideband approach to the DPD.

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Gustafsson, D., Andersonn C.M. and Fager, C., 2013, “A

Modified Doherty Power Amplifier With Extended

Bandwidth and Reconfigurable Efficiency”, IEEE

Transactions on Microwave Theory and Techniques,

533-542.

Gustafsson, D., Andersonn C.M. and Fager, C., 2012, “A

Novel Wideband and Reconfigurable High Average

Efficiency Power Amplifier”, Microwave Symposium

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2014, “Linearization of Dual Input Doherty Power

Amplifiers”, IEEE Integrated Nonlinear Microwave

and Millimetre-wave Circuits (INMMic), 1-3.

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Fifth International Conference on Telecommunications and Remote Sensing