Predistortion and Postdistortion Linearization of RF Ampli ers
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Predistortion and Postdistortion Linearization of
RF Ampliers
Patrick Roblin
Dominique Chaillot
Sukkuen Myoung
Xian Cui
Mamta Debnath
March 18, 2004
Department of Electrical and Computer Engineering
&
Microwave Laboratory
The Ohio State University
Columbus, OH 43210
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
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Introduction: Design Trends
Pull for more power ecient ampliers
{ Class B,C, D and E ampliers are more ecient than class A but exhibit poorer linearity
{ call for improved linearization performance
Push for lower cost linearization systems
{ Adaptive predistortion linearization replacing feedforward
{ Alternative novel baseband linearization possible
Increasing signal bandwidth (e.g. from 2.5G to 3G)
{ Need to deal with both slow (thermal drift) and fast (elecrical) memory eects
{ Electrical memory eects degrade the ACPR for wide-bandwidth signals
&
Technique
Correction
Analog Predistortion
3-5 dB
Cross Modulation
15-20 dB
Feed Forward
30 dB
Digital Predistortion 15-20 dB
Microwave Laboratory
Bandwidth
15-25 MHz
10-20 MHz
25-60 MHz
15-20 MHz
Eciency
5-8 %
10-12 %
6-10 %
12-14 %
Flexibility
Cost
Low
Low
Medium Medium
Medium
High
High
Medium
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Memory Eects and Volterra Modeling
A memoryless SISO system can be modeled by:
y(t) = gm x(t) + gm3x3(t)
The most rigorous theory for including memory eects is the Volterra formalism.
In that formalism the system is described by Volterra kernels of various orders.
For example a SISO system with a 3rd order kernel is of the form:
ZZZ 1
y(t) =
h(1; 2; 3)x(t ; 1)x(t ; 2)x(t ; 3)d1d2d3
;1
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Memory Eects
A PA system is memoryless if all coecients are real, e.g. (LSB & USB IMD):
A0 = B0 = 34 gm3
A PA system is quasi-memoryless if the coecients are complex and frequency
independent, e.g. (LSB & USB IMD):
A0 = B0 = 34 ym3 = jym3j exp(jm)
A PA system exhibits memory eects if its coecients are frequency dependent,
e.g. (LSB & USB IMD):
A0 6= B0
or
ym3(;) 6= ym3 (+)
&
Microwave Laboratory
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%
ACPR Degradation
Up to 17 dB degradation of ACPR at low and high bandwidth
27
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RF predistortion (quasi-memoryless algorithm)
VDC
RF(I,Q)
RF
IQ Modulator
RF(I’,Q’)
α
Baseband
2
VE
0110
1010
1010
10
RF
PA
β
1
2
1
2
α=1+ α3 VE +α 5 VE
β=1+ β 3VE +β5 VE
Polynomial functions
&
Microwave Laboratory
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Adaptive baseband digital predistortion (quasi-memoryless algorithm)
I
DAC
Q
DAC
α
RF
β
LO
2 2
I +Q
LUT
Adaptation
Algorithm
ADC
RF
ADC
2
The adaptation can only take care of slow memory eects
The linearization algorithm cannot handle fast memory eects
&
Microwave Laboratory
T . H . E
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UNIVERSITY
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RF Predistortion for Quasi-Memory less Systems
For Two-tone Excitations:
Volterra analysis assumption : A4 = B4 = 0 (5th order noise)
3 and 3 are real coecients for Quasi-memoryless systems
"
3 = ;3Re (1 + j ) yym3
m
&
Microwave Laboratory
#
and
"
3 = ;3Im (1 + j ) yym3
m
#
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Two Band Implementation
The I and Q signals need to be phase shifted to account for memory eects:
RF(I,Q)
RF
IQ Modulator
RF(I’,Q’)
RF
PA
α
β
1
2
Baseband
2
&
Microwave Laboratory
VE
1
2
1
2
α=1+ α3 VE +α 5 VE
β=1+ β 3VE +β5 VE
Polynomial functions
T . H . E
OHIO
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UNIVERSITY
The Ohio State University
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Amplitude (dB)
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OHIO
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275T
270
265
255
260
Frequency (MHz)
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Predistortion Using PA Model
PA modeled as multiple 3rd order systems in parallel:
H30
H34
H31
H33
H32
x
H30’
y
H34’
H31’
H33’
H32’
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Microwave Laboratory
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UNIVERSITY
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Iterative Predistortion for 8 tone Multsine
Model is a 3rd order Volterra system
The correction can be applied iteratively to remove higher order terms
generated
Normal PA output
Ouput for QOBM
Output for Predistortion
0
Amplitude (dB)
−50
−100
&
Microwave Laboratory
T . H . E
−150
235
240
245
250
255
260
Frequency (MHz)
265
270
275
280
OHIO
STATE
UNIVERSITY
The Ohio State University
%
'
$
Novel BaseBand Linearization Schemes
Low frequency feedforward linearization (LFFF)
Input and Output baseband modulation (IBM and OBM)
Bilateral and Quadratic baseband modulation (BBM and QOBM)
&
Microwave Laboratory
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UNIVERSITY
The Ohio State University
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Low frequency feedforward linearization
2
2
3
Ids = gm1 vgs + gd1 vds + gm2 vgs
+ gm1d1 vgs vds + gd2 vds
+ gm3 vgs
2
2
3
4
3
+gm2d1 vgs
vds + gm1d2 vgsvds
+ gd3 vds
+ gm4 vgs
+ gm3d1 vgs
vds
2 2
3
4
+gm2d2 vgs
vds + gm1d3 vgsvds
+ gd4 vds
+ ;
(1)
where Ids = drain-source current, vgs = gate-source voltage, vds = drain-source voltage
Port 1
Port 2
PA
fa
fb
RF
IMN
RF
a1
b1
OMN
RFC
c
2
&
Microwave Laboratory
2
A
Baseband
fc = fb − fa
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Input and Output Baseband Modulation Linearization of PAs
New proposed baseband linearization schemes (IBM,OBM and BBM)
Square law operation is performed directly on the baseband
Filter no longer required
Port 1
LO
Port 2
RF
PA
Baseband
RF
RF
IMN
I&Q
RF
a1
b1
OMN
RFC
c
&
Microwave Laboratory
IBM
I 2+ Q 2
A
1
c
2
OBM
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UNIVERSITY
The Ohio State University
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Perfect IM3 and IM5 cancellation using gmd for memoryless systems
If the RF signal is given by
vin (t) = I (t) cos(!t) + Q(t) sin(!t)
the correction for a 5th order system with gm3 and gm5 terms is
3 g
5 gm5 [I 2 (t) + Q2 (t)]2
vLFFF (t) = ; m3 [I 2 (t) + Q2 (t)] ;
4 gmd
8 gmd
0
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Microwave Laboratory
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Input
Output without Feed Forward
Output with Feed Forward
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−450
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Frequency (MHz)
265
270
275
280
OHIO
STATE
UNIVERSITY
The Ohio State University
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Constraints required by Low Frequency Feedforward
jGj
d ; m
m3 j
= 23 jjyymd
j
= (2m + n + 1)
= n
(2)
Phase shift m and d associated with gm3 and gmd respectively (cancellation of
the 3rd order intermodulation at RF frequencies)
ym3 = jym3j exp(jm )
ymd = jymd j exp(jd)
&
(3)
(4)
(5)
New phase constraint d ; m = n required (Yu and Roblin, 2001)
Microwave Laboratory
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IMD plotted versus phase for dierent gains G (S. Myoung)
xxx
−2
−2
−35
−4 −2
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−40
−1
−4
0
−8
−10
−6
−50
−6
IMD (dBc)
−8
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−55
−8
−60
&
Microwave Laboratory
0
50
100
150
200
phase (deg)
250
300
350
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Experimental Setup for Verication (Xian Cui)
LO
PA
0 1 2 cos wt
RF
IMN
LO rejection
mixer
AWG
Baseband
Arbitrary
wave generator
RF
a1
b1
OMN
RFC
IBM
RFC
c
1
c 2 OBM
A
cos (2wt + φ )
012
The LO rejection mixer and AWG are controlled by a PC using Labwindow.
&
Microwave Laboratory
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UNIVERSITY
The Ohio State University
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Experimental Results for IBL
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−35
IMD power
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−70
Microwave Laboratory
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Phase
250
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400
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Experimental Results for OBL
−35
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IMD power
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−65
&
−70
Microwave Laboratory
0
50
100
150
200
Phase
250
300
350
400
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
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Limitations of IBM, OBM (LFFF)
IBM and OBM do not provide enough degrees of freedom to eliminate both
LSB and USB intermodulation in two-tone exitations.
New methods with more degrees of freedom will be investigated next to cancel
both LSB and USB:
{ Bilateral Baseband modulation (BBM)
{ Quadratic Output Baseband modulation (QOBM)
{ Quadratic Output Baseband modulation (QIBM)
&
Microwave Laboratory
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
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Bilateral Baseband Modulation (BBM) for PA with Memory
Port 1
LO
PA
Baseband
RF
IQ
Port 2
IMN
RF
a1
b1
OMN
RFC
RFC
c
1
c2
A1
I2+ Q2
1
A2
BBL
2
&
Microwave Laboratory
T . H . E
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UNIVERSITY
The Ohio State University
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Volterra Analysis of BBM for Systems with Memory
X1
H30
H30
a1 b1
H34
H31
H34
H31
a21 b1*
a1* b12
H33
H32
a21 b1*
a1* b12
H33
H32
X
a1 b1 c1
H20
H20
H22
H21
X2
a1 c*1
b1 c1
H22
H21
c2
a1 c*2
b1 c2
For a two-tone excitation the intermodulation terms of interest are:
iout (2!1 ; !2 ) = A0a1 2 b1 + A1a1 c1 + A2 a1c2 + A3b1 c1 2 + A4b1 c2 2 + A5 b1 c1 c2
iout (2!2 ; !1 ) = B0a1 b1 2 + B1b1 c1 + B2 b1 c2 + B3 a1c1 2 + B4 a1 c22 + B5a1 c1c2
where A0 A5 and B0 B5 are the coecients for the LSB and USB IMD3 respectively.
The two desired tones at the output of the PA are themselves given by:
iout (!1 ) = D0 a1 + D1b1 c1 + D2b1 c2 + D3a1 2 a1 + D4a1 b1 b1 + D5 c1c1 a1
+D6 c1 c2a1 + D7 c1c2 a1 + D8 c2 c2 a1
iout (!2 ) = E0 b1 + E1 a1 c1 + E2 a1 c2 + E3 b1 2 b1 + E4 b1 a1a1 + E5 c1 c1 b1
T . H . E
OHIO
+E6 c1 c2 b1 + E7 c1c2 b1 + E8 c2 c2 b1
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Microwave Laboratory
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UNIVERSITY
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Volterra Analysis of BBM for Systems with Memory
Power Swept Response
Power Swept Response
−50
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Harmonic current (dB)
Harmonic current (dB)
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&
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−5
0
5
Power (dBm)
10
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20
−400
−15
−10
−5
0
5
Power (dBm)
10
15
20
Under certain operating conditions both the upper and lower IMD3s can be
theoretically reduced by 100dB and 200 dB respectively. Note however that,
depending on the Volterra Kernel, the biquadratic system does not always
admit a solution for certain power levels.
Microwave Laboratory
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UNIVERSITY
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Multitone Performance Limitation
Consider a 2 band case (dierent phase for LSB and USB) with 2-tone and
multitone excitations.
Works for 1 tones per frequency band but degrades for multitones
Disadvantage: the number of linearization constraints increases with the
number of frequency bands
Advantage: no PA modeling required
0
0
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Amplitude (dB)
Amplitude (dB)
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Microwave Laboratory
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T . H . E
940
960
980
1000
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1040
Frequency (MHz)
1060
1080
OHIO
STATE
1100
1120
UNIVERSITY
The Ohio State University
%
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$
QOBM Using a PA Model
Model is a 3rd order Volterra system
Higher order term in the baseband output modulation are neglected
Normal PA output
Ouput for QOBM
Output for Predistortion
0
Amplitude (dB)
−50
−100
&
Microwave Laboratory
T . H . E
−150
940
960
980
1000
1020
1040
Frequency (MHz)
1060
1080
1100
1120
OHIO
STATE
UNIVERSITY
The Ohio State University
%
'
$
Testbed for Digital Vectorial Predistortion, BBM and QOBM
PC
Labwindow
PC control
Adjustable
Gain and Offset
I
Programation
12 bits
ADC
I
RFout
Diff. OpAmp
Diff. OpAmp
FPGA
Diff. OpAmp
Q
I
DAC
LO
Q
Adjustable
Gain and Offset
14 bits
I
LO/RF in
Diff. OpAmp
14 bits
12 bits
RFout
Q
Q
DAC
ADC
Adjustable
Gain and Offset
Adjustable
Gain and Offset
Clock
Distribution
80 MHz
Clock
Goals:
Study impact of memory eects for broadband signals
Compare the performance of the various linearization schemes
Study potential combination of linearization techniques
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Microwave Laboratory
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
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Capabilities of the LSNA
70 dBc dynamic range
-80 dBm noise oor
Calibrated in frequency, time and power
Measure amplitude and phase of up to 10,000 tones
Acquire harmonics up to 20 GHz (in OSU system)
4 channels, 10 W damage level
Equipped with a load pull
Modulated source (E4438C-504) 250 kH to 4 GHz (with WCDMA 3GPP)
&
Microwave Laboratory
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
%
'
$
Applications of the LSNA in PA Design and Linearization
PA design:
{ Model verication
{ Design PA using load pull
{ Tune PA (IF and harmonics impedance terminations) by directly inspecting
the load-line
PA Modeling and Linearization:
{ Extract a Volterra Kernels coecients using multitone exitations
{ Acquire the trajectory of I and Q at the PA output directly from the RF
&
signal
Microwave Laboratory
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
%
'
$
LSNA Testbed
DUT
LSNA
RF Source
Coupler
Coupler
RF
b1
10 MHz
Synchronization
a2
b2
step attenuators
SRD
fSRD
a1
comb
FracN
10 MHz
fIF
20 MHz
&
Microwave Laboratory
Clock
ADCs
(Spectrum MI4022)
PC
T . H . E
OHIO
STATE
UNIVERSITY
The Ohio State University
%
