Nonlinear distortion cancellation using LINC transmitters in OFDM systems

Abstract

The LInear amplification using Nonlinear Components (LINC) technique is a well-known power amplifier linearization method to reduce out-of-band interferences in a nonconstant envelope modulation system, such as Digital Video Broadcasting (DVB) system, which is based on a very sensitive to nonlinear distortions OFDM modulation scheme. The major drawback of LINC transmitters is the inherited sensitivity to gain and phase imbalances between the two amplifier branches. In this paper, a novel full-digital base band method, which corrects any gain and phase imbalances in LINC transmitters mainly due to the un-matching of the two amplifier paths, is described. Amplifiers are characterized by a level-dependent complex gain using a memoryless model. The method uses adaptive signal processing techniques to obtain the optimal complex coefficients to correct gain and phase imbalances. Its main advantage is the ability to track the input signal variations and adapt to the changes of amplifier nonlinear characteristics. Other effects are included in the analysis such as quadrature modulator and demodulator impairments. A computer simulation has been carried out to verify method functionality.

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84IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005
Nonlinear Distortion Cancellation Using LINC
Transmitters in OFDM Systems
Paloma García, Alfonso Ortega, Jesús de Mingo, Member, IEEE, and Antonio Valdovinos, Member, IEEE
Abstract—The
Components (LINC) technique is a well-known power amplifier
linearization method to reduce out-of-band interferences in a
nonconstant envelope modulation system, such as Digital Video
Broadcasting (DVB) system, which is based on a very sensitive
to nonlinear distortions OFDM modulation scheme. The major
drawback of LINC transmitters is the inherited sensitivity to gain
and phase imbalances between the two amplifier branches. In
this paper, a novel full-digital base band method, which corrects
any gain and phase imbalances in LINC transmitters mainly
due to the un-matching of the two amplifier paths, is described.
Amplifiers are characterized by a level-dependent complex gain
using a memoryless model. The method uses adaptive signal
processing techniques to obtain the optimal complex coefficients
to correct gain and phase imbalances. Its main advantage is
the ability to track the input signal variations and adapt to the
changes of amplifier nonlinear characteristics. Other effects
are included in the analysis such as quadrature modulator and
demodulator impairments. A computer simulation has been
carried out to verify method functionality.
Index Terms—Adaptive system, amplifier linearization, non-
lineardistortion,ortogonalfrequency-division
(OFDM).
LInearamplification using
Nonlinear
multiplexing
I. INTRODUCTION
T
telecommunication systems that are based on a multicarrier
modulation as the OFDM schemes (Orthogonal Frequency
Division Multiplexing). An OFDM signal consists of a sum
of subcarriers that are modulated by using phase shift keying
(PSK) or quadrature amplitude modulation (QAM) [1]. The
OFDM transmission is an efficient way to deal with multipath
and its implementation is less complex than an equalizer. It
is also robust against narrowband interferences, because such
interferences affect only a small percentage of the subcarriers.
Another advantage of the OFDM system is that the digital
transmitter and receiver can be efficiently implemented using
the Fast Fourier Transform (FFT) algorithm. However, one of
its drawbacks is its sensitivity to nonlinear distortions due to
its greatly variable envelope and high peak to mean envelope
power ratio values [2]–[4]. As a result of nonlinearity effects
HE NEW digital audio broadcasting (DAB) and digital
video broadcasting-terrestrial (DVB-T) are emergent
Manuscript received December 10, 2003; revised May 10, 2004. This
work was supported by the CICYT (Spain) under grant TIC2001-2481 and
TEC2004–04529.
P. García and A. Valdovinos are with Centro Politécnico Superior, University
of Zaragoza, Spain.
A. Ortega is with the Communications Technologies Group (UZ) and the
Aragon Institute of Engineering Research (I3A).
J. de Mingo is with the Departamento de Ingeniería Electrónica y Comunica-
ciones, Universidad de Zaragoza.
Digital Object Identifier 10.1109/TBC.2004.842527
(mainly from power amplifier), the transmission spectrum
is expanded into adjacent channels, an effect known as ACI
(Adjacent Channel Interference). One way to achieve linear
amplification is by using a class A power amplifier working
with a high backoff, which corresponds to moving the operating
point of the amplifier to the linear region. However, it implies
low power efficiency. High power efficiency can be obtained
with class AB power amplifiers, but they show more nonlinear
characteristics. In order to achieve both spectrum and power
efficiency, several classical linearizing techniques for power
amplifiers have been proposed in the technical literature. These
techniques are usually categorized as Feed-forward, Feedback,
Predistortion and LINC transmitter. According to the recent
literature [5]–[8], [17], the predistortion technique has been the
more useful scheme in order to reduce the effects of nonlinear
distortion on the performance of OFDM systems. In this paper
the authors have proposed and analyzed an adaptive digital
LINC transmitter structure. LINC is an acronym for linear
amplification with nonlinear components. A schematic diagram
of a LINC transmitter is depicted in Fig. 1. Its major draw-
back is the inherited sensitivity to gain and phase imbalances
between the two amplifier branches [9], [10]. Several authors
have considered different methods to correct the imbalances in
LINC transmitters [11]–[14], but the novel method presented
here uses adaptive signal processing techniques. It is carried
out in base-band and is full-digital.
II. LINC TRANSMITTER
One of the reasons that the LINC transmitter has not been
widely used, is the difficulty to achieve the accurate gain and
phase matching required between the two paths. Errors in gain
and/orphasematchingwillcauseincompletecancellationofun-
wanted elements in wideband phase modulated signals. As a re-
sult,alargenumberofunwantedspuriousproductsappearinthe
output spectrum, as observed previously [9], [10], [12], [15].
The effect of gain and phase imbalances between the two
paths may be analyzed as follows. The source signal may be
written in complex general format as [15], [20]
(1)
The source signal is separated into two constant-envelope sig-
nalsbyaSignalComponentSeparator(SCS)asshowninFig.1.
These signals are calculated as
(2)
0018-9316/$20.00 © 2005 IEEE

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GARCÍA et al.: NONLINEAR DISTORTION CANCELLATION USING LINC TRANSMITTERS IN OFDM SYSTEMS 85
Fig. 1.Schematic diagram of the LINC transmitter.
Whereis a signal that is in quadrature to the source signal
.
(3)
Thus
(4)
The amplifier of each path is characterized by a level-dependent
complex gain, with an output signal in each path given by
(5)
Where
instantaneous complex envelope amplifier input signal in each
path.
Therefore, if the D-to-A converters and quadrature modu-
lators are supposed to be ideal, that is,
, and both signals
erly added in phase, the output signal in complex format then
becomes
andare the baseband representation of the
and
andare prop-
(6)
Thesecondtermin(6)impliesthatthereisanunwantedresidual
signal due to imperfect cancellation (it tends to zero as the gain
and phase matching are perfected). The term introduces inter-
fering power in the adjacent channel limiting the spectrum effi-
ciency of the system.
The aim of this method is to reduce the factor
as much as possible. The method is based on adap-
tive signal processing techniques and its main advantage is to
track input signal variations and possible changes due to tem-
perature variations, amplifier bias and component aging, among
others.
III. CORRECTION METHOD MODEL
A schematic diagram of the simulation model is depicted in
Fig. 2. The source signal is separated into the two constant-en-
velope signals, given in (2), by an SCS. These signals are multi-
pliedbydifferentcomplexcoefficients,oneforeachbranch(
and). These coefficients are computed and continuously up-
dated to reduce the Adjacent Channel Interference by means of
an adaptive algorithm. This algorithm needs a reference of the
output signal to update the complex coefficients. A feedback
signal,
is obtained by means of a downconversion process
of the output power amplifier signal
downconversion gain, including the output coupler gain. This
downconversiongainallowsadjustingtherangeofsignalvalues
tothequadraturedemodulatorinputanditisdefinedasthemean
of the amplifying branches gain.
The adaptation criterion of the algorithm is to minimize the
mean-squared-error.Theerrorsignaldefinedby(7)isthediffer-
ence between the source signal,
.
, where is the
, and the feedback signal,
(7)
The feedback signal can be written as
(8)
Substituting (4) and (8) into (7), the error signal can be written
as the addition of two error signals,
and.
(9)
(10)
(11)
Where ideal D-to-A, A-to-D converters, quadrature modula-
tors/demodulator and a null loop delay, , are assumed.
The cost function to minimize is defined as
(12)
Where
Forsimplernotation,infollowingformulae,
will be denoted as
The gradient of the cost function is calculated as
denotes the statistical expectation operator.
and
and.
(13)
Where
denotes the real part andthe imaginary part of
.
For the cost function
terms of the gradient must be simultaneously equal to zero.
Computing the cost function (12) gives
to attain its minimum value, all the
(14)
The partial derivatives with respect to
lated to obtain the gradient of the cost function defined by (13).
Approximating the terms with derivation variable
zero in the work region of the amplifier, finally we obtain
andare calcu-
toward
(15)
The cost function depends on two signals, the error signal,
available in the digital processing block and the signal defined

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86IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005
Fig. 2.Simulation model.
by
proposed model, but according to the downconversion gain def-
inition, we can use the approximation
expression (15) can be written as
. This last signal is not available in the
, and thus the
(16)
Therefore, using the instantaneous estimate of the gradient, the
updated value of the adaptive coefficient at time
puted by using the simple recursive relation
is com-
(17)
Where the positive real-valued constant
the speed of convergence and the misadjustment (final excess
error) of the algorithm.
(step-size), controls
IV. SIMULATIONS
A. OFDM Modulation
The source signal for simulations was an OFDM signal, sim-
ilar to the OFDM signal defined in the DVB-T standard [16],
with the following parameters:
•
2 K mode:1705 active subcarriers
•
Subcarrier Spacing: 4.464 KHz
•
Useful Symbol Duration: 224
•
Constellation: 16 QAM
The modulated OFDM signal during a symbol can be expressed
as follows
(18)
is the inverse of the carrier spacing,
guard interval,
denotes the carrier number,
frequency of the RF signal and
carrier .
ThereisaclearresemblancebetweenthisandtheinverseDis-
crete Fourier Transform (DFT)
is the duration of the
is the central
is a complex symbol for
(19)
Since various efficient Fast Fourier Transform algorithms exist
to perform the DFT and its inverse, it is a convenient form of
implementation to use the inverse FFT (IFFT) in a DVB-T
modulator to generate
samples
useful part,
long, of each symbol. The guard interval is
added by taking copies of the last
and appending them in front. This process is then repeated for
each symbol in turn, producing a continuous stream of samples,
which constitutes a complex baseband representation of the
DVB-T signal. A subsequent up-conversion process then gives
the real signal
centred on the frequency,
corresponding to the
of these samples
.
B. Amplifier Model
The amplifier is characterized by a complex gain using a
memoryless model, which depends on the input signal level.
A common method to model power amplifiers taking into
account nonlinearities with memory is to use a Volterra se-
ries representation. For most amplifiers, where the modulation
bandwidth is much less than the carrier frequency, the memory
in the nonlinearity is small enough to be neglected, and the
Volterra series can be simplified into a simple power series with
complex coefficients [18]. The complex gain of the amplifier
is extracted from AM-AM and AM-PM characteristics of a
class AB amplifier. The Class AB power amplifier design is
simulated using the model of the LX802 LDMOS transistor
from Polyfet [27] (with a driver) at 600 MHz (50
polynomic regression is used to model the amplifier complex
gain of each path.
system). A
(20)
(21)
(22)

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GARCÍA et al.: NONLINEAR DISTORTION CANCELLATION USING LINC TRANSMITTERS IN OFDM SYSTEMS 87
(a)(b)
Fig. 3. (a) AM/AM and (b) AM/PM characteristics of the designed class AB amplifier and the corresponding polynomic regression model.
The amplifier in path 1 is characterized with the parameters
equal to 1. The amplifier in path 2 is modeled mod-
ifying appropriately factors
sion of gain and phase imbalances between both amplifying
branches.
Fig. 3 shows the AM/AM and AM/PM characteristics (nor-
malizedtothe1dBcompressionpoint)ofthedesignedclassAB
poweramplifierandthecorrespondingcalculatedpolynomicre-
gressionmodel,whichisusedtosimulatetheamplifierofpath1.
The downconversion gain was simulated as an estimation of
the inverse of the total equivalent linear gain of the amplifier
stage (mean of the equivalent linear gain of the amplifier in path
1 and the one in path 2).
andto simulate the inclu-
C. Transmit Signal Power Spectrum Performance
Due to the coexistence of many digital and analog broadcast
signals in the whole service bandwidth, the requirements re-
spect to the spectrum level outside the channel bandwidth are
determinated in the standard DVB-T through spectrum emis-
sion templates. For example, the spectrum level at frequency
offset of 4.2 MHz from the center frequency is at least 36 dB
lower than the center spectrum level. Fig. 4 shows the normal-
ized power spectral density (PSD) of the output power ampli-
fier signal,
for different values of Output Power Back-off
(OBO) with a single amplifying branch, that is, without a trans-
mitter LINC structure and for a 16-QAM modulated OFDM
input signal operating at a sampling frequency of 29.25 MHz.
According to Fig. 4, the requirement of an attenuation of
36 dB in 4.2 MHz is obtained for OBOs larger than 10 dB,
which implies low power efficiency. The proposed power am-
plifier (with a driver) is designed to optimize the 1 dB compres-
sion output power (
Added Efficiency (PAE),
), resulting its Power
, where
(23)
With a single amplifying branch the total efficiency is [28], [29]
(24)
where
is the modulation scheme efficiency.
Fig.4.
for different values of OBO (with a single amplifying branch).
Normalizedpowerspectraldensityofsimulatedamplifieroutputsignal
The proposed amplifier has a PAE value equal to 17% at
10 dB OBO related to the 1 dB compression point, which sup-
poses a great efficiency reduction to achieve the required Adja-
cent Channel Protection (ACP).
To realize the full power efficiency potential of LINC tech-
nique, not only the PAs but also the recombination process must
be highly efficient. Typically, a hybrid combiner, with the loss
on power efficiency due to the wasted at heat in the load match,
is used. The possibility of reducing this drawback effect by
recycling otherwise wasted energy using a RF-DC converter
to partially recover the wasted energy has been studied [30].
Other combiners proposals are based on the Wilkinson com-
biner without isolation resistor [31]. Some studies about the ap-
propriate susceptance presented to the power amplifier in this
scheme, are described in [32], [33]. This susceptance value can
be automatically adjusted as proposed in [34]. Taking into ac-
count the combiner efficiency, the total system efficiency can be
written as
(25)

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88 IEEE TRANSACTIONS ON BROADCASTING, VOL. 51, NO. 1, MARCH 2005
Fig. 5.
? ??? with several gain imbalances (? ? ?
imbalance in the second branch of a LINC transmitter (without a correction
method).
Normalized power spectral density ofsimulated input ???? and output
? ? dB) and without phase
Fig. 6.
? ??? with several phase imbalances (?
imbalance in the second branch of a LINC transmitter (without a correction
method).
Normalized power spectral density ofsimulated input ???? and output
? ?
? ?? ) and without gain
andare not the objective of this paper, since they have
been widely treated in above referenced works.
As mentioned before, in order to increase the power effi-
ciency, an adaptive LINC transmitter scheme is proposed. If
an ideal transmitter LINC structure is applied, that is, the two
amplifyingbranchesareequal,thenonlineardistortioncancella-
tion is almost perfect, but in a realistic situation, where there are
gain and phase imbalances between both amplifying branches,
the power spectral density of the output power amplifier signal
is degraded as Figs. 5 and 6 show.
Inallthefollowingpresentedresultsa5dBOBOattheoutput
combiner is applied.
Figs.5and6illustratetheeffectofgainandphaseimbalances
andtheneedforamethodtoachievegainandphasematchingas
presented in this paper. It can be seen that a slight gain or phase
imbalancebetweenbothamplifyingbranchesworsenstheLINC
transmitter performance.
Fig. 7 compares the normalized input and output power spec-
tral density with and without the presented adaptive correction
Fig. 7.
? ??? with and without correction( with 1.5 dB gain and 5 phase imbalances
between both amplifying branches).
Normalized powerspectral density of simulatedinput ???? and output
(a)(b)
Fig. 8.
imbalances correction method (b) with the proposed correction method.
Received signal constellation diagram (normalized) (a) without
method and using a 1.5 dB gain imbalance and a 5 phase im-
balance between both amplifying branches.
As it can be seen in Fig. 7, the Adjacent Channel Interference
is reduced after applying the correction method with accurate
gain and phase matching between the two paths.
The Error Vector Magnitude (EVM) is another important
transmission requirement in digital communication systems.
The effects of the gain and phase imbalances on the vector error
may be analyzed as follows
(26)
where
tude of the measured vector, and
them. The measured vector magnitude,
‘ideal’ magnitude,
error present in the system,
as
is the magnitude of the ‘ideal’ vector,is the magni-
is the phase error between
, is composed of the
, plus a component resulting from the gain
. Therefore, (26) can be written
(27)
The 16-QAM received signal constellation without and with
the correction method for a LINC transmitter are depicted in
Fig.8(a)and(b),respectively.TheEVMimprovesafterthepro-
posed correction method is applied. (
correction method,
without the
with the correction method)