Digital Pre-Distortion Techniques for RF Power Amplifiers

Digital Pre-Distortion Techniques for RF Power Amplifiers John Wood 27 January, 2010

It doesn t matter what the raw linearity of the PA looks like, the DPD will take care of it!

Modern Communication s Signals and RFPAs Signals, Linearity, and Efficiency Some Linearizer Basics What s nonlinearity? What are memory effects? What does a linearizer do? Digital Pre-Distortion DPD System Architecture Linearization Results Outline

Linearity Requirements Wireless Communications Standards place stringent requirements on linearity performance of PAs ACLR1 Adjacent Channel Power Ratio ACLR2 Alternate Channel Power Ratio Spectral Emission Mask an absolute power limit Normalized Power (db) 10 0-10 -20-30 -40-50 -60-70 CDMA2000 Signal with MASK -45dBc (30kHz) -55dBc (30kHz) -80-5 -4-3 -2-1 0 1 2 3 4 5 Normalized Frequency (MHz)

Crest Factor and Peak-to-Average Power Ratio WCDMA Signal Crest Factor CF = Peak Magnitude Sqrt( Average Power ) 2.5 2 Sample Signal Envelope Peak Magnitude Peak-to-Average Ratio PAR = CF 2 = Peak Power Average Power Magnitude 1.5 1 0.5 Average Magnitude PAR usually expressed in db as 10*log10( PAR ) 0 0 50 100 150 200 250 300 350 400 450 500 Samples

Amplifier PAR Effects Pout Pout,max OBO G Peaks will be clipped even with ideal amplifier if input exceeds P in,max With enough clipping it appears as Gaussian noise to the receiver IBO Pin,max Pin Effects of clipping: In-band distortion Degradation of BER Higher EVM Out of Band Radiation ACI problems ACLR degradation

Finding absolute max of a data signal is difficult!! PAR easier to determine if statistically defined. Measuring PAR 1800 Histogram of Real (Inphase ) Data 1400 Histogram of Magnitude Data 1600 1400 1200 1200 1000 WCDMA Signal Test Model 1: 64 DPCH ( SF = 128 ), No CFR 1000 800 800 600 600 400 400 200 200 0-4 -3-2 -1 0 1 2 3 0 0 0.5 1 1.5 2 2.5 3 3.5 I and Q parts of signal are Gaussian Magnitude considered Rayleigh Create a probability density function of signal with histogram

Cumulative Complementary Distribution Function CCDF This is a statistical measure for digital signals

CCDF Statistical Measure of PAR From histogram of data CCDF can be derived 100 10 CCDF - Normalized to AVG Pwr CCDF shows the probability that a signal will exceed the peak power Prob (%) 1 0.1 0.01 0 1 2 3 4 5 6 7 8 9 10 Peak Power (db) 0.01% PAR value means that the 99.99% of the signal has a magnitude lower than this PAR value (9dB in this case)

What does this mean for the PA? P-1dB 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

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 Compromise Highest 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

Nonlinearity in a PA u(t) y(t) PA memoryless nonlinearity, modeled by a polynomial = ( N 2 N ) = 1 + 2 + = N n= 1 n y() t f ut () aut () au() t... au () t au() t Apply a single-tone CW RF Signal yields ( ω φ ) ut () = Acos t+ 1 0 1 2 2 2 2 ( ω φ ) ( ω φ ) ( ω φ ) yt ( ) = aacos t+ + aa cos t+ +... + aa cos t+ 1 1 0 1 2 1 0 1 n 1 0 1 n

Trigonometric expansion Writing out the response y(t) ( ω φ ) yt () = aacos t+ 1 1 0 1 2 A1 + a DC Offset, or self-bias 2 2 2 A1 2 a2 cos( 2ω0t+ 2φ1) nd Harmonic 2 distortion 3 A1 + a3 cos 3 0t+ 3 1 4 ( ω φ ) Linear gain 3 rd Harmonic distortion 3 3A1 + a3 cos 0t+ 1 4 ( ω φ ) AM-AM & AM-PM etc.

Measures of Distortion Harmonic Distortion Clearly the nonlinear polynomial function will give rise to harmonics of a single-tone input AM-to-AM Conversion Nonlinear changes in the output signal amplitude in response to input amplitude changes AM-to-PM Conversion Nonlinear 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 ui () t = ucos( ω1t) + ucos( ω2t) and Δ ω = ω ω ω, ω 1 2 1 2 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 2 3 4 5 y = au + a u + a u + a u + a u + 1 i 2 i 3 i 4 i 5 i...

Two-tone output voltage [ ω ω ] yt () = aucos( t) + cos( t)... 1 1 2 [ cos( ω ) cos( ω )] + au t + t 2 2 1 2 [ cos( ω ) cos( ω )] + au t + t 3 3 1 2 [ cos( ω ) cos( ω )] + au t + t 4 4 1 2 [ cos( ω ) cos( ω )] + au t + t 5 5 1 2 2 3 4 5 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 3 rd -order products are 3ω 1, 3ω 2, 2ω 1 ±ω 2, 2ω 2 ±ω 1

Two-tone Intermodulation Products Power dbm 3 rd -order IM 5 th -order IM AM/AM Cross-Mod Odd-order mixing products are in the signal bandwidth Close to carrier Intermodulation (IM) products ω 1 ω 2 2ω 1 -ω 2 2ω 2 -ω 1 Frequency 3ω 1-2ω 2 3ω 2-2ω 1

In addition to Harmonic Distortion AM/AM and AM/PM conversion Additional Distortion Measures Intermodulation Distortion Nonlinear mixing between the various frequency components of the signal, ω 1 and ω 2, leading to new frequency components in the signal Cross Modulation Distortion Nonlinear mixing between the various frequency components of the signal, ω 1 and ω 2, resulting in products at existing frequency components of the signal

Error Vector Measure Assume a simple cubic model: v = av + a v 3 o 1 i 3 i Even though the AM-AM compression is the same, a 3 is different S. C. Cripps, Advanced Techniques in RFPA Design, Figs 3.4 & 3.5

Modulated AM-AM & AM-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 AM-to-AM AM-to-PM

Memory Effects PA The output at time t n is dependent not only on the input at time t n, 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

Sources of memory in RF PA Input Matching Network Short Term Memory C g, C d, τ Output Matching Network RF Source Gate Bias Vg Thermal, Traps Vd Drain Bias Long Term Memory

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 response Band-pass or low-pass nature of the matching networks AM-PM Phase changes resulting from large-signal drive Transistor Device capacitances Transit times }(or more strictly, QVt ( ()) effects) t

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 Mechanisms Time constants from microseconds to seconds More prevalent in III-V semiconductors (HCI in MOS?) Bias Circuits RF filters, capacitors, and chokes on bias lines introduce storage times Relationship to VBW

Nonlinear Memory Mechanisms IM2 IM3 f 1 f 2 DC f 1 f 2 f 1 f 2 Filters out DC and IM2 v gs Long Term Memory

Power out Actual Gain, F Power In A Simple Pre-distorter Let the amplifier Gain be described by a polynomial 2 3 vo( t) = av 1 i + a2vi + a3vi +... = F NL( vi( t) ) Linear gain requires v () t = av () t ol If we can find another function, G, and pass the signal through first so that: ( ( )) 1 v () t = F G v () t = av () t o i i We get Linear Gain We do not get more power We get sharper saturation 1 i

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 PA IM products: distortion f 0 f 0 IM products in anti-phase PA f 0 f 0 Note increased input signal bandwidth f 0

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

Digital Pre-distortion in BTS Transmitter Up-Conversion I Digital Signal Q Preemphasis Pre- Distorter DAC PA To Antenna ADC Digital Domain 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 Down-Conversion

Typical Digital Pre-Distortion System I DAC Up-Conversion: IQ Modulator RF out Pattern Generator Digital Upconverter Crest Factor Reduction Pre- Distorter 0 90 Q DAC RF in DSP domain Timealign & Deinterleave ADC Down-Conversion RF domain Baseband I & Q signals are combined can be several carriers Crest Factor Reduction to limit Peak-to-Average Power Ratio Pre-distortion Function DSP also accomplishes time alignment, update of DPD parameters Fast ADC/DAC, high dynamic range (16 bit, >200 MSPS typical) RF up/down-conversion

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 rate The signal is then interpolated between the zeros A digital filter is applied to retrieve the correct frequency and phase response Example: WCDMA native sampling rate is 3.84 Msps If the digital IF (DSP clock rate) is 61.44 MHz WCDMA signal needs to be oversampled by 16X

Crest Factor Reduction Essential for DPD Applications Power out PAPR into PA Actual Gain, F Peak power required for DPD The gain expansion characteristic of the predistorter 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 Average power Peak power Power In

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 PD PA 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-PM Coefficients in polynomial series function Memory effects require comparison over several time samples

Memory Polynomial Pre-Distorter Regular polynomial, with added dimensions for delays V in 1 2 z -1 z -1 Polynomial degree P Polynomial degree P PA V a Q z -1 Polynomial degree P Pre-Distortion Block Q P V [ n] = α V [ n q] V [ n q] a qp in in q= 0 p= 1 p 1

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 Before DPD After DPD Ref 55.7 dbm * Att 15 db * RBW 30 khz * VBW 30 khz * SWT 5 s Marker 1 [T1 ] -2.91 db 1.842830500 GHz Ref 56.2 dbm * Att 15 db * RBW 30 khz * VBW 30 khz * SWT 2 s Marker 1 [T1 ] -2.68 db 1.842830500 GHz 50 Offset POS 46.7 55.721 db dbm 1 50 Offset POS 46.7 56.176 db dbm 1 40 A 40 A 30 30 1 RM * CLRWR 20 10 LVL 1 RM * AVG 20 10 LVL 2 RM * MAXH 0-10 NOR 2 RM * MAXH SWP 20 of 20 0-10 NOR 3 RM * MINH -20-30 3DB 3 RM * MINH -20-30 3DB -40-40 Center 1.8425 GHz 500 khz/ Span 5 MHz Center 1.8425 GHz 500 khz/ Span 5 MHz Standard: NONE Adjacent Channel Standard: NONE Adjacent Channel Tx Channels Ch1 (Ref) 43.49 dbm Ch2 43.48 dbm Total 46.50 dbm Lower -40.71 db Upper -41.46 db Alternate Channel Lower -60.28 db Upper -71.00 db 2nd Alternate Channel Tx Channels Ch1 (Ref) 43.91 dbm Ch2 43.96 dbm Total 46.95 dbm Lower -70.11 db Upper -70.65 db Alternate Channel Lower -73.40 db Upper -74.78 db 2nd Alternate Channel Lower -63.49 db Upper -65.39 db Lower -74.55 db Upper -77.04 db DPD Results are achieved using TI GC5322 Evaluation Module Intermodulation products are below -70dBc up to 46.9dBm of output power 42% final stage efficiency and 36% two-stage power added efficiency

RF PA before DPD 240 W Doherty PA 2C-GSM Signal at 1800 MHz 0 1 * * * -10-20 -30-40 -50-60 -70-80 SWP 20 of 20 Center 1.84244 GHz 1.52 MHz/ Span 15.2 MHz Standard: NONE Tx Channels Ch1 (Ref) -2.36 dbm 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

RF PA after DPD 240 W Doherty PA 2C-GSM Signal at 1800 MHz 0 1 * * * -10-20 -30-40 -50-60 -70-80 SWP 20 of 20 Center 1.84244 GHz 1.52 MHz/ Span 15.2 MHz Standard: NONE Tx Channels Class 1 linearization at P out = 47 dbm average Ch1 (Ref) -2.11 dbm 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

RF PA before DPD ~500 W Doherty PA 4C-GSM Signal at 940 MHz 0-10 POS 5.843 dbm 1 * -20-30 -40-50 SWP 20 of 20-60 -70-80 -90 Center 957.44 MHz 1.8 MHz/ Span 18 MHz N 3 Standard: NONE Tx Channels P out = 100 W average (Ref) Ch1-5.44 dbm Ch2-5.55 dbm Ch3-5.63 dbm Ch4-5.79 dbm 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 T t l 0 42 db

RF PA after DPD ~500 W Doherty PA 4C-GSM Signal at 940 MHz 0-10 POS 6.368 dbm 1 * -20-30 -40-50 -60-70 -80-90 SWP 20 of 20 Center 940.44 MHz 1.8 MHz/ Span 18 MHz Standard: NONE Tx Channels Class 2 linearization at (Ref) Ch1-5.65 dbm P out = 50 dbm average 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

DPD of 500 W Doherty PA under Drive-up -50 940 MHz, 4C-GSM 9260 Doherty + IC9080 Driver 4C-GSM -- DUC Gain modified (1/15/09) 50 IM Products (dbc) -55-60 -65-70 -75 Class 2 spec. 45 40 35 30 25 Efficiency (%) ADJ_L ADJ_U ALT1_L ALT1_U ALT2_L ALT2_U ALT3_L ALT3_U Wide_L Wide_U Efficiency PAE -80 20 36 38 40 42 44 46 48 50 52 54 Output Power(dBm)

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GSM/EDGE Transmit Mask GSM/EDGE has stringent requirements Signal Amplitude, dbc