Digital Pre-Distortion Techniques for RF Power...

TM

Freescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

Digital Pre-Distortion Techniques for RF Power Amplifiers John Wood

27 January, 2010

TMFreescale™ and the Freescale logo are trademarks of Freescale Semiconductor, Inc. All other product or service names are the property of their respective owners. © Freescale Semiconductor, Inc. 2010.

It doesn’t matter what the raw linearity of the PA looks like, the DPD will take care of it!


Outline

• Modern Communication s Signals and RFPAsSignals, Linearity, and Efficiency

• Some Linearizer BasicsWhat’s nonlinearity?What are memory effects?What does a linearizer do?

• Digital Pre-Distortion DPDSystem ArchitectureLinearization Results


Linearity Requirements

• Wireless Communications Standards place stringent requirements on linearity performance of PAs

-5 -4 -3 -2 -1 0 1 2 3 4 5-80

-70

-60

-50

-40

-30

-20

-10

0

10CDMA2000 Signal with MASK

Normalized Frequency (MHz)

Nor

mal

ized

Pow

er (d

B)

-45dBc (30kHz)

-55dBc (30kHz)

ACLR1 – Adjacent Channel Power RatioACLR2 – Alternate Channel Power RatioSpectral Emission Mask –an absolute power limit


Crest Factor and Peak-to-Average Power Ratio

• Crest Factor

• Peak-to-Average Ratio

• PAR usually expressed in dB as

10*log10( PAR )

CF = Peak Magnitude

Sqrt( Average Power )

PAR = CF2 = Peak PowerAverage Power

0 50 100 150 200 250 300 350 400 450 5000

0.5

1

1.5

2

2.5Sample Signal Envelope

Mag

nitu

de

Samples

Average Magnitude

Peak Magnitude

WCDMA Signal


Amplifier PAR Effects• Peaks will be clipped even

with ideal amplifier if input exceeds Pin,max

• With enough clipping it appears as Gaussian noise to the receiver

• Effects of clipping:In-band distortion

– Degradation of BER– Higher EVM

Out of Band Radiation – ACI problems – ACLR degradation

Pout

Pin

OBO

IBO

Pin,max

Pout,max

G


Measuring PAR• Finding absolute max of a data signal is difficult!!• PAR easier to determine if statistically defined.

• Create a probability density function of signal with histogram

-4 -3 -2 -1 0 1 2 30

200

400

600

800

1000

1200

1400

1600

1800Histogram of Real (Inphase ) Data

0 0.5 1 1.5 2 2.5 3 3.50

200

400

600

800

1000

1200

1400Histogram of Magnitude Data

I and Q parts of signal are Gaussian Magnitude considered Rayleigh

WCDMA Signal Test Model 1: 64 DPCH ( SF = 128 ), No CFR


Cumulative Complementary Distribution Function

CCDF• This is a statistical measure for digital signals


CCDF – Statistical Measure of PAR

0 1 2 3 4 5 6 7 8 9 10

0.01

0.1

1

10

100

Peak Power (dB)

CCDF - Normalized to AVG Pwr

Pro

b (%

)

0.01% PAR value means that the 99.99% of the signal has a magnitude lower than this PAR value (9dB in this case)

From histogram of data CCDF can be derived

CCDF shows the probability that a signal will exceed the peak power


What does this mean for the PA?

• We want to operate the PA at highest efficiency

• This point is at peak output power

• We need to ensure the signal peak is no higher than P-1dB

• For high PAR signals the average efficiency is extremely low

Cripps, RFPA, Ch. 8, p. 225, Figure 8.3

P-1dB


High-Efficiency PA Modes

• Circuit architectures to maximize efficiency• Harmonically-loaded PAs

Class E, F,…• Load modulation

Doherty, LINC• Bias modulation

Drain modulation, Envelope Tracking (ET), EER• Switching PAs

Class D, S,…• High efficiency generally means very nonlinear⇒ Need for Linearization


Linearity and Efficiency

• A Design CompromiseHighest efficiency is the most nonlinear regime of operation

• Figure of Merit Highest efficiency at specified OBO, while still meeting ACLR, spectral mask specifications

Linearizer or Pre-Distorter is essential


Outline





Nonlinearity in a PA

( ) 21 2

1

( ) ( ) ( ) ( ) ... ( ) ( )N

N nN n

n

y t f u t a u t a u t a u t a u t=

= = + + =∑PA memoryless nonlinearity, modeled by a polynomial

( )1 0 1( ) cosu t A tω φ= +

Apply a single-tone CW RF Signal

u(t) y(t)

( ) ( ) ( )2 2 2 21 1 0 1 2 1 0 1 1 0 1( ) cos cos ... cosny t a A t a A t a A tω φ ω φ ω φ= + + + + + +

yields


Trigonometric expansion…

( )1 1 0 1( ) cosy t a A tω φ= +

( )

21

2

21

2 0 1

2

cos 2 22

Aa

Aa tω φ

+

− +

Writing out the response y(t)

( )31

3 03 cos4Aa t 1ω φ+ +

( )31

3 0cos 3 34Aa t 1ω φ+ +

Linear gain

DC Offset, or self-bias

2nd Harmonic distortion

3rd Harmonic distortion

AM-AM &AM-PM

… etc.


Measures of Distortion

• Harmonic DistortionClearly the nonlinear polynomial function will give rise to harmonics of a single-tone input

• AM-to-AM ConversionNonlinear changes in the output signal amplitude in response to input amplitude changes

• AM-to-PM ConversionNonlinear changes in the output signal phase in response to input amplitude changes


Envelope Distortion• Envelope distortion can be estimated from a

Two-Tone Power Series Analysis• The input signal is

and

• The 2-tone signal covers the complete dynamic range of the amplifier

The Peak-to-Average Power Ratio is 3 dB

• The amplifier output is a power series expansion

1 2( ) cos( ) cos( )iu t u t u tω ω= +

1 2 1 2,ω ω ω ω ωΔ = −

2 3 4 51 2 3 4 5 ...i i i i iy a u a u a u a u a u= + + + + +


Two-tone output voltage

Degree and Order• Each line is a ‘degree’

power of v(t) in the polynomial expansion

• The ‘order’ of the mixing frequency is the number of components

3rd-order products are3ω1, 3ω2, 2ω1±ω2, 2ω2±ω1

[ ][ ][ ][ ][ ]

1 1 2

222 1 2

333 1 2

444 1 2

555 1 2

( ) cos( ) cos( )

cos( ) cos( )

cos( ) cos( )

cos( ) cos( )

cos( ) cos( )...

y t a u t t

a u t t

a u t t

a u t t

a u t t

ω ω

ω ω

ω ω

ω ω

ω ω

= +

+ +

+ +

+ +

+ +


Two-tone Intermodulation Products

• Odd-order mixing products are in the signal bandwidth

Close to carrierIntermodulation (IM) products

ω2ω12ω1-ω2 2ω2-ω1

3ω1-2ω2 3ω2-2ω1

Frequency

Power dBm

3rd-order IM

5th-order IM

AM/AM Cross-Mod


Additional Distortion Measures

• In addition toHarmonic DistortionAM/AM and AM/PM conversion

• Intermodulation DistortionNonlinear mixing between the various frequency components of the signal, ω1 and ω2, leading to new frequency components in the signal

• Cross Modulation DistortionNonlinear mixing between the various frequency components of the signal, ω1 and ω2, resulting in products at existing frequency components of the signal


Error Vector Measure

Assume a simple cubic model:

Even though the AM-AM compression is the same, a3 is different

31 3o i iv a v a v= +

S. C. Cripps, Advanced Techniques in RFPA Design, Figs 3.4 & 3.5


Modulated AM-AM & AM-PM

AM-to-AM AM-to-PM

Gain and Phase Deviation dependences on input power, as a function of time captured using a modulated signal, showing the variations in instantaneous values. DUT is a 400 W Doherty amplifier; red = measured, blue = modeled


Memory Effects

• The output at time tn is dependent not only on the input at time tn, but also on the input at previous times

• The number of time samples that need to be considered is the memory depth, M

• Practical systems have a finite memory depth:fading memory

PA


Vg Vd

Input Matching Network

OutputMatchingNetwork

Drain BiasGate Bias

RF Source

Sources of memory in RF PAShort Term Memory

Cg, Cd, τ

Long Term Memory

Thermal,Traps


Short Term Memory Effects

• These are memory effects that occur on the timescale of the signal

For RF PAs this can mean at the carrier timescale or the envelope timescale

• RF frequency responseBand-pass or low-pass nature of the matching networks

• AM-PM Phase changes resulting from large-signal drive

• TransistorDevice capacitancesTransit times

( )( )Q V tt

∂∂} (or more strictly, effects)


Long Term Memory Effects

• Take place on a timescale that is much longer than the signal timescale

• Thermal Thermal time constants in semiconductor devices can range from 10s to 100s of microseconds, to ~ 1 second

• Trapping MechanismsTime constants from microseconds to secondsMore prevalent in III-V semiconductors (HCI in MOS?)

• Bias CircuitsRF filters, capacitors, and chokes on bias lines introduce storage timesRelationship to VBW


Nonlinear Memory Mechanisms

f1 f2 f1 f2f1 f2DC

IM3IM2

vgs

Long Term Memory

Filters out DC and IM2


A Simple Pre-distorter

• Let the amplifier Gain be described by a polynomial

• Linear gain requires

• If we can find another function, G, and pass the signal through first so that:

• We get Linear Gain• We do not get more power• We get sharper saturation

( )2 31 2 3( ) ... F ( )o i i i NL iv t a v a v a v v t= + + + =

( )( ) 1( ) F G ( ) ( )o i iv t v t a v t= =

1( ) ( )oL iv t a v t=Power out

Power In

Actual Gain, F


The Pre-distorter Function

The secret is finding the pre-distorter function G• The pre-distorter function is an inverse of the nonlinear

contributions from the amplifier

IM products:distortion

f0f0

PA

IM productsin anti-phase

f0f0

PA

f0

Note increased input signal bandwidth


The Pre-Distorter…

• …increases the peak-to-average power ratio of the signal that is input to the PA

Gain expansion characteristic of the PD

• …increases the bandwidth of the signal that is input to the PA

Distortion components are added to the signal to cancel out the distortion of the PA


Outline





Digital Pre-distortion in BTS Transmitter

• Signal is sampled at PA output• Down-converted to IF or zero-IF• Digitization using fast ADC• ‘Predistorter’ converts to I & Q, compares with input I & Q

signals, and generates output signal which is converted to analog signal, and up-converted to RF

• Signal pre-conditioning in the digital domain

ADC

DAC PADigital Signal

I

QPre-

emphasisPre-

Distorter

To Antenna

Up-Conversion

Down-Conversion

Digital Domain


Typical Digital Pre-Distortion System

Baseband I & Q signals are combined – can be several carriersCrest Factor Reduction to limit Peak-to-Average Power RatioPre-distortion FunctionDSP also accomplishes time alignment, update of DPD parametersFast ADC/DAC, high dynamic range (16 bit, >200 MSPS typical)RF up/down-conversion

Down-Conversion

RF in

RF out0

90

ADC

DAC

Pre-Distorter

Time-align &

De-interleave

Up-Conversion:IQ Modulator

DSP domain RF domain

DAC

Digital Up-

converter

Crest Factor

Reduction

PatternGenerator

I

Q


Digital Up-Converter• The purpose of the DUC is to take the sampled data

signals and up-convert to the sample rate of the digital signal processing system

• In the digital domain, the up-conversion is performed by re-sampling or interpolation:

The digital signal is padded with zeros to reach the correct sample rateThe signal is then interpolated between the zerosA digital filter is applied to retrieve the correct frequency and phase response

• Example: WCDMA native sampling rate is 3.84 MspsIf the digital IF (DSP clock rate) is 61.44 MHzWCDMA signal needs to be oversampled by 16X


Crest Factor Reduction

• The gain expansion characteristic of the pre-distorter means that the signal input to the PA is of high peak-to-average power ratio

• CFR can reduce this PAPR to manageable levels, and can avoid the PA operating in saturation

Power out

Power In

Actual Gain, F

Essential for DPD Applications

Average power

Peak power

PAPR into PA

Peak power required for DPD


CFR Principle

• The signal peaks above a threshold level are detected• The magnitude of the peak is reduced to below some target

value• Filtering is required to re-shape the signal spectrum


Resampling prior to DPD

• The bandwidth of the signal after DPD (b) is much wider than the original input signal (a)

• To reconstruct this DPD signal in the analog domain, it must be sampled at a higher rate than the input

• Under-sampling will lead to aliasing (c)

• This cannot be removed by over-sampling at the output of the DPD

• Over-sample at DPD input

Figure from Zhu et al, IEEE Trans MTT 56(7) pp1524-34 (2008)


DPD Linearizer Action

Pre-distorter (PD) • takes the input signal• Compares with feedback signal sampled at output of PA• Adjusts the PD function to minimize the difference

Gain, phase parameters of AM-AM and AM-PMCoefficients in polynomial series function

• Memory effects require comparison over several time samples

PD PA


1

0 1[ ] [ ] [ ]

Q P pa qp in in

q pV n V n q V n qα −

= == − −∑∑

Regular polynomial, with added dimensions for delays

Pre-Distortion Block

Memory Polynomial Pre-Distorter

z-1

z-1

z-1

Vin

PA

Polynomial degree P

Polynomialdegree P

Polynomialdegree P

1

2

Q

Va


Linearizer Myths & Misunderstandings

Linearizers• do not increase the output power available• do not increase gain• do not improve the noise floor• have a harder saturation characteristic

In saturation this can create more distortion & noise• work best at low signal levels• do not necessarily accommodate memory effects• have a finite linearizing bandwidth• consume additional power, reducing system

efficiency


Two Carrier GSM Performance

A

*3 RMMINH

Ref 55.7 dBm

**

*

*

CLRWR

2 RMMAXH

3DB

RBW 30 kHzVBW 30 kHz

Offset 46.7 dB↑POS 55.721

LVL

1 RM

SWT 5 sAtt 15 dB*

NOR

*

Center 1.8425 GHz Span 5 MHz500 kHz/

-40

-30

-20

-10

0

10

20

30

40

50

Standard: NONE

Tx Channels

Ch1 43.49 dBm(Ref)

Ch2 43.48 dBm

Total 46.50 dBm

Adjacent Channel

Lower -40.71 dB Upper -41.46 dB Alternate Channel

Lower -60.28 dB Upper -71.00 dB 2nd Alternate Channel

Lower -63.49 dB Upper -65.39 dB

1

Marker 1 [T1 ] -2.91 dB 1.842830500 GHz

↑POS 55.721 dBm

A

*3 RMMINH

Ref 56.2 dBm

**

*2 RMMAXH

3DB

RBW 30 kHzVBW 30 kHz

Offset 46.7 dBPOS 56.176 d

LVL

SWT 2 sAtt 15 dB*

NOR

*

Center 1.8425 GHz Span 5 MHz500 kHz/

*1 RMAVG

-40

-30

-20

-10

0

10

20

30

40

50

Standard: NONE

Tx Channels

Ch1 43.91 dBm(Ref)

Ch2 43.96 dBm

Total 46.95 dBm

Adjacent Channel

Lower -70.11 dB Upper -70.65 dB Alternate Channel

Lower -73.40 dB Upper -74.78 dB 2nd Alternate Channel

Lower -74.55 dB Upper -77.04 dB

SWP 20 of 20

1

Marker 1 [T1 ] -2.68 dB 1.842830500 GHz

POS 56.176 dBm

DPD Results are achieved using TI GC5322 Evaluation ModuleIntermodulation products are below -70dBc up to 46.9dBm of output power42% final stage efficiency and 36% two-stage power added efficiency

Before DPD After DPD


*

*

Center 1.84244 GHz Span 15.2 MHz1.52 MHz/

*

-80

-70

-60

-50

-40

-30

-20

-10

0

Standard: NONE

Tx Channels

Ch1 -2.36 dBm(Ref)

Ch2 -2.46 dBm

Total 0.60 dBm

Lower Upper dB dB Adjacent -29.36 -28.28 Alternate -46.96 -47.17 2nd Alt -50.44 -50.44 3rd Alt -56.71 -56.32 4th Alt -61.18 -61.21 5th Alt -70.41 -70.86 6th Alt -80.71 -81.52 7th Alt -81.29 -81.75 8th Alt -80.84 -82.88 9th Alt -81.16 -82.56 10th Alt -82.31 -83.09 11th Alt -83.39 -83.75

SWP 20 of 20

1

RF PA before DPD

240 W Doherty PA2C-GSM Signal at 1800 MHz


RF PA after DPD

*

*

Center 1.84244 GHz Span 15.2 MHz1.52 MHz/

*

-80

-70

-60

-50

-40

-30

-20

-10

0

Standard: NONE

Tx Channels

Ch1 -2.11 dBm(Ref)

Ch2 -2.08 dBm

Total 0.91 dBm

Lower Upper dB dB Adjacent -70.73 -69.91 Alternate -81.18 -81.33 2nd Alt -79.73 -82.81 3rd Alt -76.54 -78.03 4th Alt -73.46 -73.18 5th Alt -75.14 -74.35 6th Alt -80.57 -80.42 7th Alt -80.72 -82.05 8th Alt -81.35 -82.52 9th Alt -81.94 -84.67 10th Alt -83.91 -84.95 11th Alt -85.99 -85.19

SWP 20 of 20

1

240 W Doherty PA2C-GSM Signal at 1800 MHz

Class 1 linearization at Pout = 47 dBm average


RF PA before DPD

3

N

Center 957.44 MHz Span 18 MHz1.8 MHz/

*

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Standard: NONE

Tx Channels

Ch1 -5.44 dBm(Ref)

Ch2 -5.55 dBm

Ch3 -5.63 dBm

Ch4 -5.79 dBm

T t l 0 42 dB

Lower Upper dB dB Adjacent -32.33 -32.21 Alternate -33.63 -35.00 2nd Alt -40.21 -39.68 3rd Alt -45.76 -44.98 4th Alt -51.58 -52.42 5th Alt -61.89 -60.63 6th Alt -59.40 -59.14 7th Alt -59.02 -59.72 8th Alt -62.78 -63.66 9th Alt -66.51 -65.69

SWP 20 of 20

1↑POS 5.843 dBm

Pout = 100 W average

~500 W Doherty PA4C-GSM Signal at 940 MHz


RF PA after DPD

Center 940.44 MHz Span 18 MHz1.8 MHz/

*

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

Standard: NONE

Tx Channels

Ch1 -5.65 dBm(Ref)

Ch2 -5.69 dBm

Ch3 5 70 dB

Lower Upper dB dB Adjacent -61.68 -61.47 Alternate -65.43 -67.18 2nd Alt -70.29 -69.88 3rd Alt -69.79 -68.37 4th Alt -75.97 -75.71

SWP 20 of 20

1POS 6.368 dBm

~500 W Doherty PA4C-GSM Signal at 940 MHz

Class 2 linearization at Pout = 50 dBm average


9260 Doherty + IC9080 Driver 4C-GSM -- DUC Gain modified (1/15/09)

-80

-75

-70

-65

-60

-55

-50

36 38 40 42 44 46 48 50 52 54

Output Power(dBm)

IM P

rodu

cts

(dB

c)

20

25

30

35

40

45

50

Effic

ienc

y (%

)

ADJ_LADJ_UALT1_LALT1_UALT2_LALT2_UALT3_LALT3_UWide_LWide_UEfficiencyPAE

Class 2 spec.

DPD of 500 W Doherty PA under Drive-up

940 MHz, 4C-GSM


Backup


GSM/EDGE Transmit Mask

Sign

al A

mpl

itude

, dB

c

GSM/EDGE has stringent requirements

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