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What’s New in Digital Pre-Distortion?!!
Dr. John Wood!
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Outline!
! What’s Old in DPD?!! Bandwidth!! Multi-Protocol Signals!! Multi-Band Signals!
! Bandwidth!! Sample Rate and Memory Effects!
! Bandwidth!! DPD methods for high-speed implementations!! Real-Time Coefficient Adaption!
What's New in DPD? 1 January 2015
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What does a Digital Pre-Distorter do?!
What's New in DPD? 2
PAvin vout
PredistorterG(vin)
vin vPD
The Predistorter G acts on the input so that the signal out of the PA is linear:
vout = fPA(G(vin)) = A.vin
Gain expansion
January 2015
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The DPD System!
What's New in DPD? 3
Down-ConversionIQ Demodulator
Pre-Distorter
DPD Adaption
Up-Conversion:IQ Modulator
DSP domain RF domain
090
DAC
DAC
Digital Up-
converter
Crest Factor
Reduction
Baseband Signal
Processing
I
Q
CIPRI Interface
PA
Attenuator
090
ADC
ADC
January 2015
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Traditional DPD Systems!
! Look-up Tables (LUT) or nonlinear filters implemented in FPGA or ASICs!
! Limited Signal Bandwidth!! 5-10 MHz…!
! Single Modulation, Multi-Carrier!! MC-GSM is a still a challenge!
! Coefficient Adaption is relatively slow!! Dedicated Floating-Point DSP chip!
What's New in DPD? 4 January 2015
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Digital Pre-Distortion: LUT!
! Complex LUT pre-distorter finds the inverse instantaneous gain and phase of the PA for the input signal power
!
! Need multiple LUTs for memory-capable DPD!! One additional LUT per tap is common!
What's New in DPD? 5
PA Gain
x
_x
x2x1
PD Gain
x
_x
x2x1
January 2015
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Outline!
! What’s Old in DPD?!! Bandwidth!! Multi-Protocol Signals!! Multi-Band Signals!
! Bandwidth!! Sample Rate and Memory Effects!
! Bandwidth!! DPD methods for high-speed implementations!! Real-Time Coefficient Adaption!
What's New in DPD? 6 January 2015
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Multi-Protocol Signals!
! LTE + WCDMA (4-8 channels)!! LTE + MC-GSM (up to 8 carriers)!! Wide Bandwidth!! 40-60 MHz occupied BW in 100 MHz total!
! Multi-band operation!!! Contiguous LTE signals across 2 transmit bands!
! High Sample Rates!! 245.76 – 491.52 MS/s demanded: oversampling!
! Crest Factor Reduction can be challenging!! Can be done at a reduced sampling rate!
What's New in DPD? 7 January 2015
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-60 -40 -20 0 20 40 60
-100
-90
-80
-70
-60
-50
-40
-30
MHz
dB
Wideband MP Signal!
! DPD needs to reduce ACP and wideband IMs!! Receive Band Interference problem!
What's New in DPD? 8
LTE 3C-CDMA
65 MHz
January 2015
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LTE Carrier Aggregation!
What's New in DPD? 9
Figure courtesy Agilent Technologies LTE Symposium 2012
January 2015
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Multi-Band Signals!
! …includes multi-protocol !! Downlink!! Examples include:!
! Band 1 + Band 2 or Band 3: LTE + UMTS + MC-GSM/EDGE!
! Bandwidths include DPD bandwidth expansion!
January 2015 What's New in DPD? 10
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Multi-Band Signals!
! Or even:!! Band 1 + Band 3 + Band 7 LTE + UMTS + MC-GSM/EDGE!
! What is the transmitter system architecture?!
January 2015 What's New in DPD? 11
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Software-Defined Radio DPD!
! Ideal up & down conversion and modulation: no IQ imbalance!! Minimal RF sub-system design or integration!! Disruptive!!
January 2015 What's New in DPD? 12
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Outline!
! What’s Old in DPD?!! Bandwidth!! Multi-Protocol Signals!! Multi-Band Signals!
! Bandwidth!! Sample Rate and Memory Effects!
! Bandwidth!! DPD methods for high-speed implementations!! Real-Time Coefficient Adaption!
What's New in DPD? 13 January 2015
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Wide Signal Bandwidth !
! DPD ‘Rule of Thumb’ requires 5x signal bandwidth to accommodate IM/ACP distortion products!
! 100 MHz Signal BW 500 MHz DPD bandwidth!! DAC & ADC bandwidths!
! 1 GS/s DACs at 16 bits; 500 MS/s ADCs at 12-14 bits!! 6 GS/s DACs at 16 bits; 2-3 GS/s ADCs at 12-14 bits !
! Filters and Interpolation!! Large Oversample rates: 64 or 80x for WCDMA!! Image rejection can be a problem!
What's New in DPD? 14 January 2015
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Memory Effects!
What's New in DPD? 15
t0-10D2t
• Output of PA at time t0 depends on input at t0, and at previous times !• History of the input signal, or Memory Effect!
• If the sampling rate of the input signal is doubled, should we expect the Memory time to remain the same, but more samples are needed?!
January 2015
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Memory or Dynamics?!! PA model #1!
! 61.44 MSps, 2C – WCDMA!
! Volterra-DDR, Memory Delays 0,1,2,3.!
! PA model #2!! Same as PA model #1!! Signal: 245.76 MSps,
8C – WCDMA!! PA model #3!
! Same as PA model #1except…Memory Delays 0,4,8,12.!
! Signal: 245.76 MSps, 8C - WCDMA!
January 2015 What's New in DPD? 16
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Bandwidth, Sample Rate, MACs!
! The higher the required bandwidth The higher the sample rate of the signal The higher the digital system clock
! More arithmetic calculations are needed greater DSP processor power required
! More power consumed
! More memory terms are required More RAM needed for waveform capture
and coefficient storage!What's New in DPD? 17 January 2015
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Example Polynomial Calculation!
! Volterra polynomial:!! 11th degree static poly + 3 memory taps!
! 10 MACs + 3 shift-delays + 3 adds!! 20 ‘Cross-terms’ !
! 60-80 MACs, depending on complexity of dynamics, + 20 adds!! Data sample rate ~ 370 MS/s!! Processing required:
!30 complex gigaMACs or about 200 G-ops!! Power consumption
~ 2pJ per add, 5 pJ per MAC, is about 750 mW! (28 nm CMOS)!
What's New in DPD? 18 January 2015
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Reducing the Sample Rate?!
! Unfortunately, this isn’t possible on the forward path!! Need to include all the nonlinear contributions!
! Can we do this on the Observation Path?!! Sub-sampling!! Aliasing allowed!! Eases ADC implementation!
What's New in DPD? 19 January 2015
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Outline!
! What’s Old in DPD?!! Bandwidth!! Multi-Protocol Signals!! Multi-Band Signals!
! Bandwidth!! Sample Rate and Memory Effects!
! Bandwidth!! DPD methods for high-speed implementations!! Real-Time Coefficient Adaption!
What's New in DPD? 20 January 2015
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‘Indirect’ Learning!
What's New in DPD? 21
DPD2
DPD1
PA
update Attenuator
compare
u[k] y(t)
y(t)/G
Digital to RF
RF to Digital
y[k]
Delay
u'[k]
• Compare Pre-Distorted and Post-Distorted signals !!• Requires two copies of pre-distorter!
• The DPD essentially creates an inverse model of the PA!• Forward Path (DPD2) coefficients are updated only after convergence!• Sub-sampling not possible!
FPGA
DSP IC
January 2015
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Adaptive Control - ‘Direct Learning’!
DPD
EstimateCoefficients
PA
Attenuator
u[k] y(t)
y(t)/G
updatecoefficients
Digital to RF
RF to Digital
y[k]
Delay
What's New in DPD? 22
• Compare Input & Output signals !!• After convergence, these (should) contain no distortion!
• Only one DPD calculation!• Coefficient Adaption Cost Function requires some element to enable
adjustment of DPD coefficients !• Forward Path (DPD) coefficients are updated only after convergence!• Sub-sampling possible!
FPGA
DSP IC
January 2015
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! Memory Polynomial DPD!
Digital Pre-Distortion: Polynomial!
What's New in DPD? 23
∑More Memory
More Nonlinearity
1
0 1[ ] [ ] [ ]
Q P pa qp in in
q pV n V n q V n qα
−
= =
= − −∑∑January 2015
τ
τ
τ
apu
p
p=1
P
∑
apu
p
p=1
P
∑
apu
p
p=1
P
∑
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Digital Pre-Distortion: Volterra Series!
! Real-time calculation of Volterra polynomial !
What's New in DPD? 24
y(t) = f poly u(t −1),u(t −2),...,u(t − M )( )
= a1m1=1
M
∑ m1( )u(t −m1)+ a2 m1,m2( )m2=1
M
∑m1=1
M
∑ u(t −m1)u(t −m2 )+
...+ ... an m1,m2 ,...,mn( )mn=1
M
∑m1=1
M
∑ u(t −m1)u(t −m2 )...u(t −mn )
= ... an m1,m2 ,...,mn( )mn=1
M
∑m1=1
M
∑ u(ts −mjj=1
n
∏n=1
N
∑ )
January 2015
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The impact of Volterra ‘Cross-terms’ on DPD correction!
! Volterra Cross-terms add more complexity!! pruning is essential!
! ‘Dynamic Deviation’ Reduction techniques!
What's New in DPD? 25
∑
January 2015
τ
τ
τ
apu
p
p=1
P
∑
apu
p
p=1
P
∑
apu
p
p=1
P
∑
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Memory Polynomial 3M7P DDR with 2nd-order dynamics and even-degree polynomial terms
DPD Linearization of Behavioural Model!
What's New in DPD? 26 January 2015
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DPD Coefficient Adaption!
! Adaptive DPD adjusts the LUT or polynomial coefficients as the signal changes!
! The nonlinear function is linear-in-parameters!
What's New in DPD? 27
!
! Use linear least squares techniques to find the DPD parameters a!
January 2015
y = an fn u( )n=1
N
∑ = U.a
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Simple (Naïve) Model Solution!
! We have an over-determined systemwhere a is the vector of coefficients we want to find!
! Pseudo-Inverse:!
! U is not square!! Ill-conditioning may still be a problem!! the error in the estimate of parameters
can be very large!
! Need another approach (or two…)!
28
y = U.a
U−1y = a
January 2015 What's New in DPD?
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Least Squares!! The Usual Least Squares approach…!
! Matrix inversion – expensive!! Ill-conditioning can still be a problem!
! Regularization!
! Alter the main diagonal entries – modify eigenvalues!
!! Tikhonov Regularization or Ridge Regression!
29
UHU( )−1UHy = a
UHU→ UHU + h2I
UHU + h2I( )−1UHy = a
January 2015 What's New in DPD?
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A Better Solver!
! Linear algorithms more robust to ill-conditioning:!! Singular Value Decomposition SVD
write!where A, B are orthogonal, Σ is a diagonal matrix whose entries are the eigenvalues of UHU
!
! Then the Moore-Penrose pseudoinverse is!
! Can truncate the eigenvalues below a given value, to reduce the number of parameters to solve!
30
U = AΣBT
U+ = BΣ−1AT
January 2015 What's New in DPD?
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And Another!
! QR Factorizationwrite ! ! !U = QR
where Q is m x n orthonormal matrix, and R is n x n upper-triangular and invertible!
! We can estimate the parameters a
! QR is a straightforward algorithm to implement
31
y = Ua =QRaQHy = QHQRa = Raa = R-1QHy
January 2015 What's New in DPD?
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Linear Least-Squares Methods!
! Least Squares Estimation LSE!! Requires Matrix Inversion!! Use SVD, QR factorization for robustness!! Large processor power and memory required!! ‘Off-line’ method!
! Least Mean Squares LMS!! Avoids Matrix Inversion!! Convergence can be slow!
! Recursive Least Squares!! Avoids Matrix Inversion!! Faster convergence than LSE/LMS techniques!! Can be used in ‘Real-Time’ DPD Coefficient adaption!! Still requires large processor power, but memory
requirements are significantly reduced!What's New in DPD? 32 January 2015
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Summary!DPD Challenges!
! Wide bandwidth!! Multi-Band, Multi--Carrier & Multi-Protocol signals!! Much more DSP processing power required!! Higher data sampling rates & clock frequencies!
! ‘Real-time’ DPD coefficient updates!
! Making it all work with low power consumption and at low cost!
What's New in DPD? 33 January 2015
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Thank You!Any Questions?!
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Shameless Self-Promotion!
January 2015 What's New in DPD? 35
Buy this book!