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What’s New in Digital Pre-Distortion?!!
Dr. John Wood!
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
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
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
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
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
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
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
-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
LTE Carrier Aggregation!
What's New in DPD? 9
Figure courtesy Agilent Technologies LTE Symposium 2012
January 2015
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
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
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
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
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
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
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
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
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
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
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
‘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
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
! 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
∑
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
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
∑
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
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
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?
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?
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?
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?
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
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
Thank You!Any Questions?!
Shameless Self-Promotion!
January 2015 What's New in DPD? 35
Buy this book!
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