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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 7, JULY 2008
Open-Loop Digital Predistorter for RF
Power Amplifiers Using Dynamic Deviation
Reduction-Based Volterra Series
Anding Zhu, Member, IEEE, Paul J. Draxler, Member, IEEE, Jonmei J. Yan, Student Member, IEEE,
Thomas J. Brazil, Fellow, IEEE, Donald F. Kimball, Member, IEEE, and Peter M. Asbeck, Fellow, IEEE
Abstract—In this paper, we propose an efficient open-loop
digital predistorter (DPD) derived from the dynamic deviation
reduction-based Volterra series that allows compensation for
both nonlinear distortion and memory effects induced by RF
power amplifiers in wireless transmitters. In this approach, the
parameters of the predistorter can be directly extracted from
an offline system identification process. This eliminates the usual
requirement for a closed-loop real-time parameter adaptation,
which dramatically reduces the implementation complexity of the
system. It is shown that a further reduction in system complexity
can be achieved by applying under-sampling theory in the model
extraction and utilizing parameter interpolation in the DPD
implementation. Experimental results show that by utilizing this
technique with only a small number of parameters, nonlinear
distortion induced by the PA can be significantly reduced, as
evaluated by both adjacent channel power ratio reduction and
normalized root mean square error improvement. A comparison
with a memoryless polynomial function based predistorter and an
analysis of the impact of decresting are also presented.
Index Terms—Behavioral modeling, linearization, power amplifier (PA), predistorter, sampling, Volterra series.
I. INTRODUCTION
F
OR MORE efficient use of the limited frequency spectrum,
nonconstant envelope modulation techniques are normally
employed in modern wireless communication systems. These
modulated signals sometimes have a very high peak-to-average
power ratio (PAPR), which requires that RF transmitter power
amplifiers (PAs) operate with a large level of backoff power to
behave linearly, resulting, however, in very low power efficiency.
To obtain high efficiency and avoid severe distortion caused by
PA nonlinearities, digital predistortion techniques have been
Manuscript received January 17, 2008; revised April 14, 2008. First published
June 6, 2008; last published June 9, 2008 (projected). This work was supported
in part by the Science Foundation Ireland under the Principal Investigator Award
at University College Dublin, Dublin, Ireland, and by the Center for Wireless
Communications, University of California at San Diego, La Jolla.
A. Zhu and T. J. Brazil are with the School of Electrical, Electronic and
Mechanical Engineering, University College Dublin, Dublin 4, Ireland (e-mail:
anding.zhu@ucd.ie; tom.brazil@ucd.ie).
P. J. Draxler is with the Department of Electrical and Computer Engineering,
University of California at San Diego, La Jolla, CA 92093 USA, and also with
Qualcomm Inc., San Diego, CA 92121 USA (e-mail: pdraxler@qualcomm.
com).
J. J. Yan, D. F. Kimball, and P. M. Asbeck are with the Department of
Electrical and Computer Engineering, University of California at San Diego,
La Jolla, CA 92093 USA (e-mail: jjyan@ucsd.edu; dfkimball@soe.ucsd.edu;
asbeck@ece.ucsd.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2008.925211
proposed [1], [2]. The principle of a digital predistorter (DPD)
is intrinsically simple: a nonlinear distortion function is built
up within the numerical or digital domain that is the inverse
of the distortion function exhibited by the amplifier. A highly
linear and low distortion system can be achieved when these
two nonlinear functions are serially combined. An attraction
of this approach is that the nonlinear PA can be linearized by a
standalone add-on block, freeing vendors from the burden and
complexity of manufacturing complex analog/RF circuits.
As wireless communication evolves towards high data-rate
and broadband services, we increasingly encounter components,
including RF PAs, that exhibit frequency- or history- dependent
behavior, i.e., memory effects, which can sometimes severely
degrade system performance, especially in high-speed data
transmission [3]. To effectively linearize these systems, one must
compensate for both static nonlinearities as well as memory
effects. Several techniques have been proposed to compensate
memory effects, e.g., memory polynomials [4], Hammerstein
and Wiener models [5], augmented Wiener model [6], nonlinear
auto-regressive moving average (NARMA) model [7], etc. However, it is very difficult to obtain an exact inverse function for a
PA with memory. Most “memory” predistorters proposed to date
use a closed-loop configuration, e.g., an indirect learning structure [8]–[10], or an iterative parameter adaptation mechanism
[6], [7], [11], [12] in which a full loop of up/down conversion
and real-time digital signal processing (DSP) are required. This
significantly increases the implementation cost of the system.
In this paper, we propose an efficient open-loop DPD to compensate for static distortion and memory effects induced by a
PA using the recently proposed dynamic deviation reductionbased Volterra series [13]. By employing this pruned form of
Volterra series, the model structure can be significantly simplified without impact on system performance. More importantly,
based on the th-order post-inverse theory [14], the parameters of this DPD can be directly estimated from the measured
input and output of the PA with a simple offline characterization
process. This eliminates the real-time closed-loop adaptation
requirement, and removes the necessity to implement the parameter-estimation algorithms in real digital circuits, which dramatically reduces system complexity and implementation cost.
Under-sampling theory and a parameter interpolation method
[15] can also be applied in the system characterization process,
which further reduces the complexity of the system.
This paper is organized as follows. In Section II, after introducing the th-order inverse theory, we propose an openloop DPD approach and then present a new model structure
0018-9480/$25.00 © 2008 IEEE
ZHU et al.: OPEN-LOOP DPD FOR RF PAs
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Fig. 1. Predistortion system.
for the DPD. Section III presents details of the procedure used
to characterize the DPD. The experimental results are given in
Section IV, with a conclusion in Section V.
Fig. 2. pth-order inverse. (a) Pre-inverse. (b) Post-inverse.
II. SYSTEM DESCRIPTION
One way to compensate for the nonlinear effects of a PA using
predistortion is to insert a linearization block in the signal path
prior to the PA, as shown in Fig. 1 [1]. If the transfer function of
the predistorter is the inverse of the transfer function of the
PA , a linear amplification, which is represented by , can be
achieved when these two systems are connected in series.
With the rapid development in DSP techniques, most predistorters today are implemented in the digital envelope domain. In
these systems, the original in-phase/quadrature (I/Q) baseband
signals are pre-processed, e.g., adjusted by the inverse characteristics of the PA, to generate the predistorted signals. The
predistorted signals are then passed through digital-to-analog
converters (DACs), modulated and up-converted to the RF frequency, and finally sent to the PA.
A. Open-Loop DPD System Structure
Since it is very difficult to directly obtain an inverse function
for a PA with memory, most “memory” predistortion techniques
use a closed-loop adaptation mechanism for iterative estimation
of the parameters of the DPD. In these systems, because the value
of the parameters or the expected output of the DPD is unknown
before the system starts, a fraction of the output of the PA must be
down-converted and de-modulated back to the baseband in real
time so that it can be compared with the original input of the PA
to estimate the errors and then update the parameters in the DPD.
Although this closed-loop process only needs to be run at system
setup or during a re-calibration stage, this configuration significantly increases system complexity and implementation cost,
sometimes making it not feasible in real applications.
In this paper, we propose an open-loop system characterization approach, which allows us to extract the parameters for the
DPD with memory through a simple offline process. This is derived from the th-order inverse theory, as described below.
1) th-Order Pre-Inverse: According to the th-order inverse
theory [14], in order to linearize the system , we can make the
system be the th-order pre-inverse of the system , as reprein Fig. 2(a). This requires all transfer functions
sented by
up to th-order of the overall system to be zero, except the
first order, which leads to
(1)
represents th-order
where is the expected gain, and
nonlinearity of . Since the nonlinearities beyond th-order are
assumed to be negligible, we can consider that the system
becomes linear after the th-order inverse. Generally, to derive
this pre-inverse, we have to extract the function
in advance
and then do an inversion by applying (1). This normally involves a very complicated procedure, especially for models with
memory [16], and additional fitting errors may be introduced
during the model inversion.
2) th-Order Post-Inverse: The system
also can be linearized by inserting a block following it, e.g.,
in Fig. 2(b),
which is called the post-inverse. Unlike the pre-inverse case, it
is not necessary to characterize the PA in advance and then obtain the inverse. That is because, for example, if we assume the
input of
is
, to make the overall system become
linear, the expected output of
must be a linearly amplified version of the original input, i.e.,
(2)
is again the expected gain. The post-inverse function
can, therefore, be directly extracted from the input and
output data measured from the PA,
and
. However, the
post-inverse block cannot be employed directly in a real transmitter because it is not feasible to insert a linearization block
after the PA.
In [14], however, it was also proved that, in a Volterra system,
the th-order pre-inverse of is identical to the th-order postinverse of
within th-order nonlinearities. For instance, if
is the th-order post-inverse of , as shown in Fig. 2(b), the
system will become linear, and then, if we replace the pre-inverse
in Fig. 2(a) with
, the system also becomes
linear. This means that, in order to obtain the parameters for the
DPD, i.e., the coefficients of the function
, we can extract the
post-inverse function
in the system instead. Since both
the input and the output of
can be available in advance, the
coefficients of
may be extracted with an offline process and,
therefore, the real-time closed-loop adaptation can be eliminated.
This significantly simplifies the parameter-extraction process.
This open-loop post-inverse idea has been used by other researchers [17] for linearizing PAs, but only in simulations: no
further practical development has been made due to the high
where
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 7, JULY 2008
complexity of the model employed. In this study, we employ
a reduced-complexity Volterra model structure for the DPD to
make this idea become practical, as presented below.
B. DPD Model Description
The Volterra series is a combination of a linear convolution
and a nonlinear power series [14]. It may be employed to describe the relationship between the input and output of an amplifier with memory in a very general way. However, direct
use of the general Volterra series is rather impractical because
the number of parameters to be estimated increases exponentially with the degree of nonlinearity and memory length of the
system. To overcome the complexity of the general Volterra series, an effective model-order reduction method, called dynamic
deviation reduction, was proposed in [13]. This is based on a
new Volterra series representation
(3)
where
and
are the input and output, respectively.1
is the order of nonlinearity and
represents memory length.
In this representation, the input elements are reorganized according to the order of dynamics involved in the model with
a new variable introduced to represent the order of the dynamics. Finally,
is the Volterra kernel
with th-order nonlinearity and th-order dynamics. Since the
effects of dynamics tend to fade with increasing order in many
real PAs, the high-order dynamics can be removed by controlling the value of in (3), leading to a significant simplification
in model complexity [13], [18].
In a similar way to PA modeling, digital predistortion only
needs to compensate static nonlinearities and low-order dynamics, which are the dominant distortion induced by the PA.
In this study, we directly adopt the dynamic deviation reduction-based Volterra model to represent the post-inverse function
and, thus, the DPD function
. For example, if only
the first-order dynamics are taken into account, i.e.,
, then
in the discrete complex envelope domain is found from
(4)
where
and
are the complex envelopes of the input
and output, respectively, and
is the complex Volterra
1For modeling a system in the complex baseband, the Volterra model in (3)
must be transformed to the low-pass equivalent format.
kernel of the system.
represents the complex conjugate operation and
returns the magnitude. Note that only odd-order
nonlinearities are included in (4), i.e., is an odd number, since
the effects from even-order kernels can be omitted in a band-limited modulation system.
Since the pre-inverse function of the PA, i.e., the transfer
, is identical to the post-inverse
,
function of the DPD,
can be immediately written as
we find that
(5)
where
and
are the original input and output of the
DPD, respectively.
Compared to the general Volterra series, this dynamic deviation-based model reduction approach gives us an extra degree-of-freedom, through choosing the dynamic order , to effectively prune the model, which makes the application of the
Volterra model more flexible and more efficient. We can see
that only a 1-D convolution is involved in the model of (4)
and (5) after the first-order dynamic reduction. This dramatically simplifies the model structure. If higher order dynamics
affect the distortion significantly, we can increase the value of
to include higher order dynamics to improve the system performance, while, on the other hand, if only static nonlinearities
need to be compensated, we can simply set to zero, and then
the model becomes a memoryless polynomial function.
The decision on how to select the truncation order depends
on the characteristics of the PA employed and the DPD performance required. It must be recognized that increasing the
number of coefficients does not necessarily increase the modeling accuracy or improve the system performance. That is because more uncertainties may be brought into the model when
more coefficients are involved [13]. In a DPD system, redundant
coefficients may result in overcompensation. For example, if we
use longer memory length than that is necessary in the DPD, we
may introduce extra distortion.
III. SYSTEM CHARACTERIZATION
In this section, we present characterization procedures and
implementation details for the proposed DPD system.
A. Data Acquisition With Under-Sampling
The first step for characterizing the predistorter is to gather
input and output data from the PA. Although the PA usually
causes spectral regrowth resulting in an output signal bandwidth
that is wider than that of the input signal, it has been shown in
[19] and [20] that for modeling a nonlinear system excited by
a band-limited signal, it is sufficient to sample the continuoustime input and output signals at twice the maximum input frequency rather than double the output frequency, which is called
the “generalized sampling” or “under-sampling” theorem. For
the complex baseband I/Q signal, we only need to sample it
with a sampling rate equal to its chip rate, which is twice its
maximum baseband input frequency [15]. This under-sampling
can also be applied in identifying the post-inverse function for
ZHU et al.: OPEN-LOOP DPD FOR RF PAs
compensating a nonlinear Volterra system, as shown in [21].
That is because the one-to-one mapping is still valid under the
band-limited condition, even if the bandwidth of the input of
the post-inverse (the output of the PA) is wider than that of its
expected output (the linearly amplified version of the original
input of the PA). In this study, we apply this under-sampling
theorem for extracting the post-inverse function in (4) and, thus,
the DPD parameters in (5).
Sampling with a lower rate substantially eases the requirements on analog-to-digital converters (ADCs) used in
measurement setups [22]. For modeling a PA or building a
DPD with memory in the discrete-time domain, lower rate
sampling also reduces the number of delay taps needed to take
into account the same duration of memory effects and, thus,
reduces the model complexity. However, as pointed out in [21],
reduced-rate sampling may increase the sensitivity to random
noise components such as quantization noise and measurement
noise, which may degrade the overall system performance. In
a real application, we recommend choosing a slightly higher
sampling rate than the minimum required. For example, we
can choose 7.68 or 15.36 MHz for a wideband code division
multiple access (WCDMA) signal, which is two or four times
its chip rate, but still much lower than twice its maximum
output baseband frequency, e.g., 26.88 MHz if seventh-order
nonlinearities are taken into account.
The under-sampled input and output data can be obtained
through general time-domain stimulus–response measurements,
e.g., the Agilent ADS–ESG–VSA connected solution [23], or
other similar data acquisition configurations, as presented in
Section IV. To remove time delay and phase shift, time alignment must be conducted on the measured data before model extraction.
Note that this under-sampling is only applied for the purpose
of model extraction. In the final DPD implementation, the extracted DPD parameters in the discrete-time domain must be interpolated to meet the higher sampling rate requirement for reconstructing the alias-free output signal from the DPD, as discussed in Section III-D. One must also note that sampling at
double the original input frequency can not be applied in the indirect-learning or iterative structures where the bandwidths of
both the input of the PA (after the DPD) and the output of the
PA are wider than that of the original input. A higher sampling
rate is required in that case.
B. Expected Gain Selection and Data Normalization
Since superposition cannot be applied to a nonlinear system,
generally the power level of the data for model extraction must
be normalized to the same power level of the original input so
that the extracted parameters can be directly used in the DPD
after model extraction; otherwise a nonlinear scaling must be
applied to the parameters. However, this normalization process
strongly depends on the selection of the expected gain, although
it has not been well addressed in the literature to date.
Generally, in a lookup table (LUT)-based predistorter, the
maximum gain, which is the linear response of the PA, is chosen
as the expected linearized gain, as shown in Fig. 3(a). By pre-increasing the amplitudes at the higher power level, gain compression can be compensated. However, because the predistorter
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Fig. 3. Expected gain selection. (a) Linearized for the maximum gain. (b) Linearized for the gain at the targeted maximum power level.
can only successfully correct distortion up to the full saturation
level of the amplifier (after which point any increase in the input
power does not produce an increase in output power), the maximum input allowed for the predistorter can only reach the point
where the linear response intersects the saturation limit. Therefore, in this case, the original input and the predistorted input
(the output of the DPD) have different peak values, as shown in
Fig. 3(a). This has the consequence that in parameter extraction,
the input and the output data measured from the PA must be normalized to different power levels by different scaling factors, in
order to correspond to the different peak values in the original
and the predistorted inputs. This requires an extra calibration
effort and also increases the complexity of the input power control in the final system implementation due to different levels of
peak occurring before and after DPD.
However, if we choose the expected gain at the targeted maximum power level, for example, as shown in Fig. 3(b), the gain
of the overall system becomes
(6)
where
and
are the complex envelopes of the input
and output of the PA, respectively. Note that here we assume
that the output power of the PA increases monotonically with
the input power. In other words, the peak power only occurs at
the maximum input. In this case, both the original input and the
predistorted input will reach the same maximum power level.
Therefore, all input and output waveforms can be normalized
to unity. This significantly simplifies the model extraction because we can directly normalize the input and the output data
measured from the PA by their respective peak values, and then
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use this data as the output and input of
for parameter extraction. Selecting the gain at the maximum power level also
makes the final system implementation become easier because
both the original input and predistorted input can be normalized
by the same scaling factor, which facilitates power control.
Although the overall gain has been decreased in this case, the
average and maximum output power after predistortion are still
the same as in the case of linearizing with the maximum gain. In
terms of the overall linearization performance, these two DPD
systems are equivalent.
C. Parameter Extraction
As indicated in [13], a key advantage of the Volterra series
and its pruned model variants is that the output of the model
is linear with respect to its coefficients. Under the assumption
of stationarity, if we solve for the coefficients with respect to a
minimum mean or least square (LS) error criterion, we will have
a single global minimum. Therefore, it is possible to extract the
nonlinear Volterra model in a direct way by using linear system
identification algorithms.
In this study, we use the LS algorithm to extract the parameters for the DPD. From the point-of-view of system identification, we can consider the coefficients appearing in (4) to be
generalized impulse responses so that a single large parameter
vector may be formed containing all of the unknown coeffi, and we can then define a matrix including
cients
, apall of the product terms
pearing in the input of the model for
,
where is the total length of the available data record. The
, where
expected output is
represents the transpose operation, and the un-modeled error is
, where
. Note that
and
should be normalized. The Volterra model
both
can then be written as
(7)
By using the LS method, a solution for can be estimated as the
value that minimizes the model error criterion
(8)
where
represents the Hermitian transpose. A standard result yields
(9)
In this approach, the parameters of the th-order post-inverse
function can be extracted directly from the measured input and
output data and only one estimation is needed. This will lead to
lower estimation errors than the th-order pre-inverse approach
[16], where extra inversion errors may occur.
D. Parameter Interpolation and Over-Sampling
In a real system, the DPD is run in the digital domain while the
PA is operated in the analog domain. The digital transmission
Fig. 4. Sampling requirement for digital predistortion.
signal must be reconstructed before it is modulated and up-converted to the RF frequency band, and then transmitted through
the analog PA.
Since the signal is nonlinearly processed by the DPD, the
bandwidth of the predistorted signal after the DPD is much
wider than the bandwidth of the original input signal. For example, as shown in Fig. 4(b), after a fifth-order predistortion,
the bandwidth of the input signal will be five times that of the
original signal. In order to correctly reconstruct this signal in
the analog domain, we must sample it at a rate five times higher
compared to that of the input. However, during model extraction, in order to reduce complexity, we capture the input and
the output data at a low sampling rate, e.g., minimum of twice
the input frequency. The parameters (Volterra kernels) we extracted, therefore, only correspond to the under-sampled data.
Although these discrete Volterra kernels can completely represent the behavior of the DPD, they can only be used to generate
an output with the same sampling rate as that of the under-sampled extraction data. For example, if sampling at four times the
input frequency is used, the sampling rate of the output of the
DPD will also be four times the input frequency. This will cause
aliasing, as shown in Fig. 4(c). This aliasing cannot be removed
by over-sampling at the output of the DPD, with the result that
the predistorted signal cannot be correctly reconstructed at a
later stage.
This problem can be solved by parameter interpolation: we
over-sample the original signal at the input to increase the sampling rate and pad zeros to the Volterra kernels to interpolate
the parameters in the DPD, and then an alias-free output signal
can be generated, similar to the approach proposed in [15]. For
example, if -times over-sampling is required, where is the
ZHU et al.: OPEN-LOOP DPD FOR RF PAs
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Fig. 7. Experimental test bench.
Fig. 5. Sample of DPD implementation.
Fig. 6. Block diagram of digital predistortion characterization.
ratio of the sampling rate required for DPD output signal reconstruction versus that of the under-sampled model extraction
is the over-sampled input, then the new output of
data, and
will be
the DPD
(10)
Since the coefficients with zero value do not contribute to
the output, the zero padding can be simply implemented by inserting unit delays into the finite impulse response (FIR) filters
in the system, as depicted in Fig. 5. In real circuits, inserting
unit delays does not significantly increase system complexity.
Compared to the full sampling system where parameters are extracted from the data sampled at twice the output frequency, this
parameter interpolation approach is much less resource-intensive while still linearizing PAs with the same memory length.
time-domain stimulus-response measurements at a low sampling rate. After time alignment and normalization, the input
and output data are used to extract the Volterra kernels, i.e.,
the parameters of the DPD, by employing the LSs estimation
in (9). To avoid aliasing effect, zeros are inserted into the
extracted Volterra kernels to interpolate the parameters to
match the higher sampling rate, corresponding to the order of
the nonlinearities to be compensated, before they are loaded
into the DPD. Finally, the system is operated as an open-loop
topology in which the over-sampled original input signal is first
predistorted by the DPD, and then modulated and up-converted
to the RF frequency, and finally transmitted by the PA.
The advantage of this approach is that the value of the parameters in the DPD can be estimated with an offline process,
e.g., in a software environment in MATLAB before the system
starts. It is not necessary to implement a full real-time feedback
loop or any parameter-estimation algorithms (such as LSs) in
real hardware, which significantly reduces the implementation
cost of the DPD. Of course, if the operating conditions of the PA
are changed, e.g., due to aging, or supply voltage variations, the
parameters of the DPD must be updated, but they can be easily
re-characterized by using the same offline process.
In some applications, online parameter updating may be required, where the feedback loop and the parameter estimation
are normally integrated in the system. Even in that case, the
approach proposed in this paper still have several advantages
against the indirect-learning structure, which are: 1) only lowspeed A/D converters are required in the feedback loop for the
data acquisition; 2) only once-off data acquisition and single estimation for parameter extraction are needed while multiple iterations must be conducted in the indirect-learning; 3) no realtime signal processing is required so that low-speed DSP can
be utilized; and 4) the implementation of the DPD block itself
is also simpler. This is seen in Fig. 5, which uses much fewer
multipliers than the case of a full-sampling solution while compensating for the same length of memory.
IV. EXPERIMENTAL RESULTS
In order to validate the proposed DPD technique, we tested
a gallium–nitride (GaN) PA from Nitronex, Durham, NC. The
V and
PA was biased as a class-AB amplifier with
V. It was operated at 1.94 GHz and excited by
a WCDMA signal with a maximum average output power at
40 dBm.
E. Summary of System Characterization Procedures
A. Experimental Test Bench and Parameter Extraction
Finally, the block diagram of this complete characterization
process is shown in Fig. 6. The complex I/Q data streams are
first captured from the input and output of the PA through
The experimental test bench was set up as shown in Fig. 7.
In this test, a WCDMA signal with a chip rate at 3.84 MHz
and with 9.57-dB PAPR was created at baseband as complex
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I/Q data in MATLAB. To eliminate the effect of I/Q imbalance
in the modulator, we modulated the baseband signal in MATLAB
to a digital IF, which was sampled at 107.52 MHz and fed to
the Agilent pattern generator using the instrument control software LabVIEW. The digital IF signal was then converted to the
analog domain, and up-converted to the RF band at 1.94 GHz,
and finally sent to the PA. To capture the output data, the output
of the PA was first down-converted to the IF band, and then converted to the digital domain and captured by the Logic Analyzer,
and finally demodulated to the baseband in MATLAB.
Around 10 000 I/Q samples were recorded with a sampling
rate at 15.36 MHz, i.e., four samples per chip. After time
alignment and normalization, 2000 samples were used for parameter extraction, while the remaining 8000 different samples
were used for system performance evaluation in separated
measurements.
In order to accurately model the nonlinearity up to saturation, the nonlinearity order in the Volterra model was set to
11. Since only moderate memory effects appeared in this PA,
. To find opwe just considered first-order dynamics, i.e.,
from 1
timum memory length, we swept the memory length
, the memory, which appeared in
to 4, and found that with
the envelope I/Q waveform, was almost entirely removed. Further increasing the memory length caused the distortion to increase. This means that in this particular PA, the memory was
within the duration of one-half WCDMA chip. The total number
of model parameters was 28.
To avoid aliasing in the final system, the original input signal
was over-sampled by a factor of seven, i.e., with a sampling
rate at 107.52 MHz, and zeros were inserted into the Volterra
kernels extracted earlier to match the higher sampling speed.
The system was then operated as an open-loop topology, termed
the “memory DPD” in the following text and results.
For comparison, a polynomial function based model with
11th-order nonlinearities, here called the “memoryless DPD,”
was also extracted and implemented in the system.
Fig. 8. CCDF plots for the original input, original output, and predistorted input
of a WCDMA signal.
Fig. 9. System performance indication: with DPD and without (w/o) DPD.
B. DPD Performance Evaluation
Once a real PA is driven into the nonlinear region, the high
peaks of the signal will be compressed. This means that the
PAPR of the output signal will be reduced compared to the original input, as shown in the complementary cumulative distribution function (CCDF) plots in Fig. 8. To compensate for this
compression and restore the original signal, the PAPR of the
input signal must be pre-enhanced. In other words, the PAPR of
the predistorted signal must be higher than that of the original
signal, also shown in Fig. 8.
As mentioned earlier, the maximum output power is limited
by the saturation of the PA. With this limit, for a given maximum
output power, the average output power in the system with DPD
will be lower than for the system without DPD. For instance,
as shown in Fig. 9, if both systems are driven into saturation,
the average output power of the system without DPD will be at
point A, while the average output of the system with DPD only
can reach point B. This is because, after the PAPR enhancement
by the DPD, the actual average power entering the PA is only
at point E, thus producing the average output power at point C,
which is equal to the power at point B.
In order to make a proper comparison, i.e., to evaluate the
DPD performance with the same average output power both before and after predistortion, we operated the system under two
different conditions:
1) Without Decresting: In the first test, we first drove the
system with DPD to saturation so that the average output power
was at point B, as shown in Fig. 9. To match this average output
power, in the second measurement for the system without DPD,
we reduced the average input power from point D to point E to
produce the average output power at point C. The two systems
then had the same average output power, although the system
without DPD had a lower maximum power.
In this case, the average output power was 38.11 dBm. The
AM/AM and AM/PM plots of the system with and without
DPD are shown in Fig. 10, where we can clearly see that both
nonlinear distortion and memory effects have been successfully
compensated. For comparison, the results from the memoryless
DPD are presented in Fig. 11, where we can see that although
the nonlinearities have been mostly compensated, nevertheless
a large proportion of memory effects still remain. The spectrum
ZHU et al.: OPEN-LOOP DPD FOR RF PAs
1531
Fig. 10. AM/AM and AM/PM plots for the system with memory DPD and
without DPD.
Fig. 11. AM/AM and AM/PM plots for the system with memoryless DPD and
without DPD.
plots are shown in Fig. 12 and the ACPR figures are presented
in Table I.
To evaluate the performance in the time domain, the normalized root mean square error (NRMSE) [24] was used as follows:
%
(11)
and
is the root mean square (rms) of the input
where
and the output
, respectively, and is the number of the
samples to be evaluated. The numerical values for the NRMSEs
are presented in Table I.
From these results, we can see that the “memory DPD”
achieved outstanding performance. The ACPR in the first
adjacent channel was reduced by over 27 dB from 33 to
60 dBc and NRMSE was reduced from 17.72% to 1.76%.
This indicates the distortion induced by the PA has been almost
completely removed.
From the comparison, it is clear that even though the “memoryless DPD” performed quite well in removing the static nonlinearities, a “memory DPD” must be employed to compensate
Fig. 12. Spectra plots of the system with memory DPD, with memoryless DPD
and without DPD.
memory effects in order to further improve the performance, especially the NRMSE. This may become even more critical for
wideband PAs with significant memory.
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 56, NO. 7, JULY 2008
TABLE I
PERFORMANCE OF THE SYSTEM WITHOUT DECRESTING
Fig. 14. CCDF plots for the input and output signals while decresting is
conducted.
Fig. 13. System performance indication while decresting conducted: with DPD
and without (w/o) DPD.
2) With Decresting: Since higher output power is always desirable for a PA, in the second test, instead of reducing the average input in the system without DPD, we increase the average
input power in the system with DPD. For example, we can move
from point D to point G, as shown in Fig. 13, to produce a higher
average output power at point F in order to match the maximum
average power in the system without DPD at point A. However,
since the maximum power is limited by PA saturation, we cannot
directly push the input power higher; otherwise the high peaks
in the signal will be sharply clipped causing enormous distortion. To avoid hard clipping, the original input signal must be
pre-processed.
In this study, we employed a decresting algorithm proposed
in [25] in which soft clipping and filtering are used. The steps
for this measurement can be described as follows.
1) Obtain the target PAPR value, which is equal to the PAPR
of the output signal measured from the PA excited by the
original input without DPD.
2) Decrest the original input to reduce its PAPR to the target
value.
3) Send the decrested input to the DPD to generate the predistorted input.
4) The predistorted signal is then transmitted by the PA.
The CCDF plots of those signals are shown in Fig. 14. Since the
PAPR of the decrested output of the system with DPD is close to
the PAPR of the original output, the final average output power
in the two systems become almost identical. In this case, the
average output was 40 dBm.
Fig. 15. AM/AM and AM/PM plots for the system with memory DPD and
without DPD, while decresting is conducted.
The AM/AM and AM/PM plots are shown in Fig. 15 and the
spectrum plots are shown in Fig. 16. The ACPR and NRMSE
ZHU et al.: OPEN-LOOP DPD FOR RF PAs
1533
REFERENCES
Fig. 16. Spectra plots of the system with memory DPD with memoryless DPD
and without DPD, while decresting is conducted.
TABLE II
PERFORMANCE OF THE SYSTEM WITH DECRESTING
results are presented in Table II. It can be seen that, although
the average output power has been increased by approximately
2 dBm, and the statistical characteristics of the signal have been
slightly changed (e.g., the probability at the high power level
of the predistorted signal becomes denser than in the original
signal due to decresting, as shown in Fig. 15), the distortion still
can be successfully compensated. This can also be observed in
Fig. 14, where the CCDF curve of the output after DPD is almost
overlapping with that of the decrested input, which indicates
that the DPD performs very well in restoring the original signal.
Except for memory effects, the memoryless DPD also produced
similar results in this case, as shown in Fig. 16 and Table II.
Note that the distortion introduced by decresting, which should
be compensated separately and is out of scope of this study, is
not included in the results presented here.
V. CONCLUSION
An efficient open-loop DPD has been presented in this paper.
In this approach, the parameters of the predistorter can be
directly obtained from the input and output data measured from
the amplifier by using a simple offline system identification
process in a software environment before system initialization,
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Anding Zhu (S’00–M’04) received the B.E. degree
in telecommunication engineering from North China
Electric Power University, Baoding, China, in 1997,
the M.E. degree in computer applications from Beijing University of Posts and Telecommunications,
Beijing, China, in 2000, and the Ph.D. degree in
electronic engineering from University College
Dublin (UCD), Dublin, Ireland, in 2004.
He is currently a Lecturer with the School of
Electrical, Electronic and Mechanical Engineering,
UCD. His research interests include high-frequency
nonlinear system modeling and device characterization techniques with a
particular emphasis on Volterra-series-based behavioral modeling for RF PAs.
He is also interested in wireless and RF system design, DSP, and nonlinear
system identification algorithms.
Paul J. Draxler (S’81–M’84) received the B.S.E.E.
and M.S.E.E. degrees (with a special focus on
electromagnetics, RF and microwave circuits, antennas, and plasma physics) from the University of
Wisconsin–Madison, in 1984 and 1986, respectively,
and is currently working toward the Ph.D. degree at
the University of California at San Diego (UCSD),
La Jolla.
Following graduation in 1986, he designed hybrid and GaAs monolithic microwave integrated
circuit (MMIC) PA circuits with Hughes Aircraft
Company and Avantek. From 1988 to 1995, he held various positions with
EEsof and HP-EEsof, where he focused on RF and microwave computer-aided
engineering: custom design environments, nonlinear modeling, and electromagnetic simulation. In 1995, he joined Qualcomm Inc., San Diego, CA, to
lead a team focused on RF computer-aided engineering. In this role, he has
provided consulting to many design teams on system and circuit simulation,
electromagnetic modeling, and board- and chip-level design methodologies.
He is currently a Senior Staff Engineer in corporate research and development
with Qualcomm Inc. He has authored or coauthored numerous symposium
and trade journal papers on electromagnetic simulation, circuit simulation, and
system simulation. He coholds two patents with others pending.
Jonmei J. Yan (S’07) received the B.S.E.E degree
from the University of California at San Diego, La
Jolla, in 2005, and is currently working toward the
M.S.E.E degree at the University of California at San
Diego.
From 2004 to 2006, she was an Analog Designer
with ARM Inc., where she was involved in the design and layout of custom high-speed I/Os such as the
SERDES for PCI-Express applications. She also designed, simulated, and tested electrostatic discharge
(ESD) protection circuitry and guided the automation
of the quality-control process. Her research interests include high-efficiency/
high-power RF amplifiers for wireless communications and adaptive digital predistortion. She is currently engaged in research on envelope-tracking PAs and
advanced digital predistortion techniques.
Thomas J. Brazil (M’86–SM’02–F’04) received the
B.E. degree in electrical engineering from University College Dublin (UCD), Dublin, Ireland, in 1973,
and the Ph.D. degree in electronic engineering from
the National University of Ireland, Dublin, Ireland, in
1977.
He then joined Plessey Research, Caswell, U.K.,
where he was involved with microwave subsystem
development prior to returning to UCD in 1980. He
is currently a Professor of electronic engineering and
holds the Chair of Electronic Engineering at UCD.
His research interests are in the fields of nonlinear modeling and characterization techniques at the device, circuit, and system levels. He also has interests
in nonlinear simulation algorithms and several areas of microwave subsystem
design and applications. He has authored or coauthored numerous publications
in the international scientific literature in these fields.
Prof. Brazil is a Fellow of Engineer Ireland and a Member of the Royal Irish
Academy. From 1998 to 2001, he was an IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Worldwide Distinguished Lecturer in high-frequency computer-aided design (CAD) applied to wireless systems. He is currently a member of the IEEE MTT-1 Technical Committee on CAD.
Donald F. Kimball (S’82–M’83) was born in Cleveland, OH, in 1959. He received the B.S.E.E. degree
(suma cum laude) with distinction and M.S.E.E. degree from The Ohio State University, Columbus, in
1982 and 1983, respectively.
From 1983 to 1986, he was a TEMPEST Engineer with the Data General Corporation. From 1986
to 1994, he was an Electromagnetic Compatibility
Engineer/Manager with Data Products New England.
From 1994 to 1999, he was a Regulatory Product Approval Engineer/Manager with Qualcomm Inc. From
1999 to 2002, he was a Research and Technology Engineer/Manager with Ericsson Inc. Since 2003, he has been a Principal Development Engineer with
Cal(IT)2, University of California at San Diego, La Jolla. He holds four U.S.
patents with two patents pending associated with high-power RF amplifiers
(HPAs). His research interests include HPA envelope elimination and restoration
(EER) techniques, switching HPAs, adaptive digital predistortion, memory-effect inversion, mobile and portable wireless device battery management, and
small electric-powered radio-controlled autonomous aircraft.
Peter M. Asbeck (M’75–SM’97–F’00) received the
B.S. and Ph.D. degrees from the Massachusetts Institute of Technology, Cambridge, in 1969 and 1975,
respectively.
His professional experience includes affiliations
with the Sarnoff Research Center, Princeton, NJ,
and Philips Laboratory, Briarcliff Manor, NY, where
he was involved in the areas of quantum electronics
and GaAlAs/GaAs laser physics. In 1978, he joined
the Rockwell International Science Center, where
he was involved in the development of high-speed
devices and circuits using III–V compounds and heterojunctions. He pioneered efforts to develop heterojunction bipolar transistors (HBTs) based on
GaAlAs/GaAs and InAlAs/InGaAs materials. In 1991, he joined the University
of California at San Diego, La Jolla, where he is the Skyworks Chair Professor
with the Department of Electrical and Computer Engineering. He has authored
or coauthored over 300 publications. His research interests are in development
of high-performance transistor technologies and their circuit applications.
Dr. Asbeck is a member of the National Academy of Engineering (NAE). He
has been a Distinguished Lecturer of the IEEE Electron Device Society and of
the IEEE Microwave Theory and Techniques Society (IEEE MTT-S). He was
the recipient of the 2003 IEEE David Sarnoff Award for his work on HBTs.