Predistortion at Baseband (Digital Domain)

Transcription

1 Predistortion at Baseband (Digital Domain)

2 Schematic Wireless Transmitter I channel Symbol generator Baseband DSP FIR Filter FIR Filter DAC DAC Q channel Reconst ruction filter Reconst ruction filter Quadrature modulator cos LO sin Filter Antenna Duplexer filter or T/R switch PA VGA

3 Gain(dB) Example of Amplifier AM-AM Distortion Pin (dbm) Matlab Representation (table with interpolation) Earlier chart function y=gain2(x) %%% table based amplifier gain function %%% expresses gain in db as function of input in dbm %%% pin=[-1000,-10,-5,0, 5, 10, 12, 14, 16, 18, 20, 50, 100]'; ga=[7, 7,7.2,8,9,10,10.5,11,11.3,10.2,8.5,-21.5,-71.5]'; y=interp1(pin,ga,x); end

4 Phase (degrees) Example of Amplifier AM-PM Distortion Pin (dbm) Matlab Representation (table with interpolation) function y=phase2a(x) %%% table based amplifier phase function %%%expresses phase in degrees as function of input in dbm %%% pin=[-1000,-10,0,5,8,10,12,14,16,18,20,50,100]'; ph=[ 0, 0,0,0,1, 3,4.5,8,12,18,20,20,20]'; y=interp1(pin,-ph,x); end Earlier chart

5 envelope How Can You Generate and Analyze Modulation Signals? Matlab Program for CDMA Signal Generation % cdmawaveform % This program creates an IS-95 OQPSK waveform of n symbols(normalized to % 0dBm). % This program reads in one file containing the baseband FIR filter % coeffecients, is95taps. % Written by Kevin Gard 7/20/98 with modifications by Asbeck % %%%% Load FIR filter coefficients load is95taps; %%%% Set the number of I and Q symbols n=2^14; b=200; n=n+b; % Set up the random input I/Q bits bitsi=sign(randn(n,1)); bitsq=sign(randn(n,1)); chipbitsi=zeros(4*n,1); chipbitsq=chipbitsi; chipbitso_q=chipbitsi; lchip=1:n; % Insert zeros for 4x oversampling without interpolation (1 bit 3 zeros) chipbitsi((lchip-1)*4+1)=bitsi(lchip); chipbitso_q((lchip-1)*4+3)=bitsq(lchip); chipbitsq((lchip-1)*4+1)=bitsq(lchip); % Filter the I and Q data with FIR filter Ichan=filter(is95taps,1,chipbitsI); Qchan=filter(is95taps,1,chipbitsQ); O_Qchan=filter(is95taps,1,chipbitsO_Q); % Add I and Q in quadrature and scale final signal to 0dBm power CDMA_O= *(Ichan(b+1:n)+j*O_Qchan(b+1:n)); %% CDMA_O is the complex CDMA signal, sampled at 4x the chip rate env=abs(cdma_o); time Pave=7; xdbm=20*log10(abs(xcdma))+pave; ycdma=10.^(gain2(xdbm)/20).*exp(j*phase2(xdbm)* ).*xcdma; Use gain, phase tables to compute distorted signal

6 envelope How Can You Generate and Analyze Modulation Signals? Matlab Program for CDMA Signal Generation % cdmawaveform % This program creates an IS-95 OQPSK waveform of n symbols(normalized to % 0dBm). % This program reads in one file containing the baseband FIR filter % coeffecients, is95taps. % Written by Kevin Gard 7/20/98 with modifications by Asbeck % %%%% Load FIR filter coefficients load is95taps; %%%% Set the number of I and Q symbols n=2^14; b=200; n=n+b; % Set up the random input I/Q bits bitsi=sign(randn(n,1)); bitsq=sign(randn(n,1)); chipbitsi=zeros(4*n,1); chipbitsq=chipbitsi; chipbitso_q=chipbitsi; lchip=1:n; % Insert zeros for 4x oversampling without interpolation (1 bit 3 zeros) chipbitsi((lchip-1)*4+1)=bitsi(lchip); chipbitso_q((lchip-1)*4+3)=bitsq(lchip); chipbitsq((lchip-1)*4+1)=bitsq(lchip); % Filter the I and Q data with FIR filter Ichan=filter(is95taps,1,chipbitsI); Qchan=filter(is95taps,1,chipbitsQ); O_Qchan=filter(is95taps,1,chipbitsO_Q); % Add I and Q in quadrature and scale final signal to 0dBm power CDMA_O= *(Ichan(b+1:n)+j*O_Qchan(b+1:n)); %% CDMA_O is the complex CDMA signal, sampled at 4x the chip rate env=abs(cdma_o); time Pave=7; xdbm=20*log10(abs(xcdma))+pave; ycdma=10.^(gain2inv(xdbm)/20).*exp(j*phase2inv(xdbm)* ).*xcdma; Use inverse tables to generate predistorted signal

7 Predistortion Calculation Schematic Wireless Transmitter Symbol generator Baseband DSP FIR Filter FIR Filter I channel DAC Recons truction filter Recons DAC truction filter Q channel Quadrature modulator cos LO sin Filter Antenna Duplexer filter or T/R switch PA VGA

8 Predistortion Equations x y z F pd (x) G PA (y) Vout Desired output z x y Vin Choose y instead of x to get z

9 Predistortion Equations x y z F pd (x) G PA (y) Vout z Choose y instead of x to get z y x Vin More realistic! y stays within bounds

10 Predistortion Equations x y z F pd (x) G PA (y) Vout Measure G PA (y) Choose a linear gain Go Determine F pd (x) such that G PA (F pd (x)) = Go F pd (x)=g PA -1 (Go x) Voutmax Vpd z ymax x x y Slope Go ymax Vin Slope 1 y ymax Vin

11 Adaptive Digital Pre-Distortion Adaptation allows tracking of environmental variations An extra receiver is required The benefits of feedback without bandwidth limitations

12 Output Spectrum Before and After Predistortion Before PD After PD

13 Input Spectrum Before and After Predistortion Before PD After PD

14 Normalized Output Envelope Voltage Normalized Output Envelope Voltage Normalized Output Envelope Voltage Voltage (V) Voltage Time Domain Response of Power Amplifiers Vin and Normalized Vout Input and output waveforms vs time (CDMA signal) Vout vs Vin No correction input Normalized PA output Time x 10-4 Time (100usec) Memoryless correction Full correction (with memory effect) Normalized Input Envelope Voltage Normalized Input Envelope Voltage 14 Normalized Input Envelope Voltage

15 Characteristics of Adaptive Digital Predistortion Technique is similar to feedback schemes, except that the feedback is not continuous The input signal is applied to a memoryless nonlinearity complementary to that of the power amplifier Feedback is only used for adaptation of the predistorted nonlinearity Technique is insensitive to loop delay and frequency of operation Technique is insensitive to aging and environmental factors if the feedback path sensitivity to these factors is negligible Predistortion can be used at baseband, IF or RF. The most practical approach is at baseband.

16 PA Linearization Techniques: Comparison Linearization Technique Linearization Performance Modulation Bandwidth Complexity Comments Feedforward Best Widest High Best Performance Not suitable for handsets Polar / Cartesian Feedback Analog Pre-distortion Adaptive Digital Pre-distortion Good Narrow Moderate Low Wide Low Good Wide Moderate Tracks Environment Variations Loop Stability vs. Bandwidth Simple Difficult to Adapt Tracks Environment Variations Wideband Linearization Depends on DSP Requires a Receiver Adaptive DPD: the ideal approach to achieve wide-band, accurate linearization, in the era of affordable DSP Widely accepted in base-station transmitters DPD for handsets is becoming really attractive!

17 How To Calculate Predistorted Input in Real System? Vpd~xpredistorted as function of Vin~ xin could be computed by evaluating polynomial Generally this is too expensive in time and power Typical approach: LUT Compute once xpredistorted for appropriate values of xin and then store them in lookup table --- which stores dg and df Then for each input xin(n) compute dg *xin(n) *exp(jdf)

18 Gain-Based (Cavers) Predistorter Compute xpred for appropriate values of xin and then store them in lookup table --- which stores dg and df vs xin Then for each input xin(n) compute dg *xin(n) *exp(jdf) Adaptation algorithm

19 Power spectral density (dbc) LUT Organization Issues Number of entries Equal spacing or nonuniform spacing of bins defining inputs / addresses F(xm) Representative results for 16QAM signal [Cavers, 1990] D g 0-20 A: PA, no PD, PB0=0.22 db B: PA with 32 pt PD, PB0=0.22 db C: PA with 64 pt PD, PB0=0.22 db D: PA, no PD, PB0=30 db Xm k-1 Xm k Xm k+1-40 F i = F(xm i ) Where Xm i =D g (i+1/2) D g is bin spacing Typical practice: Frequency F/Fs for handsets: LUT size 16 to 64 entries for basestatons: LUT size 64 to 256 entries

20 Filling in LUT Entries How to find the right values? 1) Precalibrate: Simplest approach is to precompute the LUT for a given amplifier design, or to calibrate it at manufacture => Not generally accurate enough; need to correct in real time due to changes in T, power level, supply voltage, antenna impedance 2) One-Shot Calculation : Can collect output data over an extended "record", down- convert to base-band, and compute a new LUT as a "one-shot" computation 3) Iterative Loop: Can collect output data continuously, and update LUT by small increments continuously in background (as an iterative loop)

21 Voltage How to Determine Coefficients (1) Computation using Block of Data Send envelope x(t) to upconverter and PA Measure output, downconvert and sample to find y(t) Normalize and time align x(t) and y(t) Vin and Normalized Vout vo vs vin input Normalized PA output Time (unit~100usec) Scaling: compute average Vin, Vout and normalize Time alignment: compute correlation function C, time offset is value to get peak of C D phase vs vin

22 Envelope Domain Power Series Approaches Typically used to fit the data and then compute LUT Memory-less nonlinearity in envelope domain can be expressed as complex power series y(n) = a1 x(n) + a2 x(n) x(n) + a3 x(n) 2 x(n) + a4 x(n) 3 x(n) + n is index of time step (sampled time on envelope scale) a1, a2, etc are unknown complex coefficients Determine coefficients by using data set x(n) <=> y(n)

23 N equations How to Determine Coefficients (1 continued) Computation using Block of Data Experimental data set: x(t) => ym(t) (measured result, contains noise, errors, etc) Model: Use for simplicity all real coefficients, real inputs, outputs n is index of time step (sampled time on envelope scale) y(n) = a1 x(n) + a2 x(n) 2 + a3 x(n) 3 + a4 x(n) 4 + y(1) x(1) x 2 (1) x 3 (1) a1 y(2) x(2) x 2 (2) x 3 (2) a2 y(3) = x(3) x 2 (3) x 3 (3) a3 y(4) x(4) x 2 (4) x 3 (4) y(5) x(5) x 2 (5) x 3 (5) M unknowns (3 in this example) y=m a Solve for ai => Can't do this exactly equations are overdetermined Find "best guess" coefficients a1, a2, a3, by minimizing error Define Error= sum( ym(n)-y(n) 2 ) ym: measured values y(n)=calculated with sum

24 M coefficients Calculation of Coefficients Error= sum( ym(n)-y(n) 2 ) N data points M T y = M T M a a = (M T M) -1 M T y

25 Simple operation in matlab! a=m \ y Polynomial Fitting in Matlab Matrix left divide If M is square, M \ y multiplies y by inverse of M Here M is not square : m x n with m>>n Equations are overdetermined Now \ computes the pseudoinverse--- gives best value for result a in the least squares sense The pseudoinverse can be found by a simple heuristic If M is not square, cannot find M -1 But M T M is square! y= M a M T y= M T M a (M T M) -1 M T y = a

26 Least Squares Fitting - Formal Theory Linear Case Unknown coefficients Basis functions

27 x= vector of input data y= vector of output data Polynomial Fitting Example in Matlab M=[x' x.^2' x.^3' x.^4' x.^5' x.^6' x.^7' x.^8' x.^9' x.^10' x.^11' x.^12' ]; a=m \ y '; xtest=(0:100)*0.01; Mtest=[xtest' xtest.^2' xtest.^3' xtest.^4' xtest.^5' xtest.^6' xtest.^7' xtest.^8' xtest.^9' xtest.^10' xtest.^11' xtest.^12']; ycomp=mtest*a; y ycomp x

28 xpred How to Invert Predistortion Equations? PA provides Wish to have Go x= F(xpred) xpred=f -1 (Go x) y=f(x) Yd= Go x Yd= F(xpred) Need to decide what is Go!! F -1 can be expressed as polynomial fit Using same data set x(n), y(n) Only need to plot x (= x pred) vs y (=Go x) %x=[0 xnorm]; %used for modeling %y=[0 ynorm]; %used for modeling y=[0 xnorm]; %use for predistortion x =[0 ynorm]; % use for predistortion y=go x

29 How to Determine Coefficients (2) Successive Approximation Solution to Coefficient Determination For each time sample n, measure ym(n) and compare with desired output y(n)=go x(n) Use difference ym(n)-y(n) to adjust the coefficients by a small amount Follows approach of LMS algorithm used widely for adaptive linear filters Instead of a block of data with error(n) known for a large set of x(n) and y(n) Now we have only one sample: Error(n)= ym(n) -M(x(n)) a Determine updates da to the various components of a By using gradient descent strategy error Change ai by a little bit, in proportion to your estimate of Gradient (error) in a space ai

30 Memory-Less DPD Using Successive Approximation S is a small coefficient chosen to tradeoff convergence time and accuracy C. Presti

31 Time Dependence of ACPR After LUT Reset Standard algorithm Refined algorithm

32 Voltage Waveform Predistortion and Memory Effect Correction Vin and Normalized Vout Input and output waveforms vs time (CDMA signal) 0.01 Vout vs Vin No correction input Normalized PA output Time x 10-4 Memoryless correction Full correction (with memory effect)

33 Frequency Dependent - Memory Effects Gain and phase at time t don t just depend on input at time t But also on inputs at earlier times (on baseband time scale)! Inherent to the active device itself Thermal Effects and Trapping Imposed by external circuitry Bias Networks and Matching Networks May not have proper bandwidth for baseband signal

34 Including Memory in Power Series 1) Memory-less nonlinearity in envelope domain can be expressed as complex power series y(n) = a1 x(n) + a2 x(n) x(n) + a3 x(n) 2 x(n) + a4 x(n) 3 x(n) + n is index of time step (sampled time on envelope scale) 2) "Memory" in envelope time scale is expressed as linear filter y(n)= b0 x(n) + b1 x(n-1) + b2 x(n-2) + b3 x(n-3) + 3) Nonlinearity with memory: Volterra series y(n)= c10 x(n) + c20 x(n) x(n) + c30 x(n) 2 x(n) + c40 x(n) 3 x(n) + c11 x(n-1) + c210 x(n) x(n-1) + c310 x(n) 2 x(n-1) + c410 x(n) 3 x(n-1) + + c211 x(n-1) x(n) + c311 x(n)x(n-1) 2 x(n-1) + c41 x(n) 2 x(n-1) x(n-1) c12 x(n-2) + c220 x(n) x(n-2) + c320 x(n) 2 x(n-2) + c420 x(n) 3 x(n-2) + + c221 x(n-2) x(n) + c321 x(n)x(n-1) 2 x(n-2) + c421 x(n) 2 x(n-1) x(n-2) + Very many terms!!!

35 FIR Filter With Adapted Tapweights Describes memory at baseband (but not nonlinearity)

36 Approximations to Power Series with Memory Pruned Volterra series Hammerstein Model Memory-less nonlinearity Linear filter y(n)~ b0a1 x(n) + b0a2 x(n) x(n) + b0a3 x(n) 2 x(n) + b0a4 x(n) 3 x(n) + b1a1 x(n-1) + b1a2 x(n-1) x(n-1) + b1a3 x(n-1) 2 x(n-1) + b1a4 x(n-1) 3 x(n-1) + b2a1 x(n-2) + b2a2 x(n-2) x(n-2) + b2a3 x(n-2) 2 x(n-2) + b2a4 x(n-2) 3 x(n-2) + b3a1 x(n-3) + b3a2 x(n-3) x(n-3) + b3a3 x(n-3) 2 x(n-3) + b3a4 x(n-3) 3 x(n-3) + (Ex: 8 coefficients) Wiener Model Linear filter Memory-less nonlinearity Memory Polynomial (parallel Wiener model) y(n)~ c10 x(n) + c20 x(n) x(n) + c30 x(n) 2 x(n) + c40 x(n) 3 x(n) + c11 x(n-1) + c21 x(n-1) x(n-1) + c31 x(n-1) 2 x(n-1) + c41 x(n-1) 3 x(n-1) + c12 x(n-2) + c22 x(n-2) x(n-2) + c32 x(n-2) 2 x(n-2) + c42 x(n-2) 3 x(n-2) + c13 x(n-3) + c23 x(n-3) x(n-3) + c33 x(n-3) 2 x(n-3) + c43 x(n-3) 3 x(n-3) + Dynamic Deviation Reduction Model (Anding Zhu) Z -1 Z -1 Nonlinear F0 F1 F2 + (Ex: 16 coefficients) y(n)~ g10 x(n) + g30 x(n) 2 x(n) + g50 x(n) 4 x(n) + g11 x(n-1) + g31 x(n ) 2 x(n-1) +g51 x(n) 4 x(n-1) + g12 x(n-2) + g32 x(n) 2 x(n-2) + g52 x(n) 4 x(n-2) + g13 x(n-3) + g33 x(n) 2 x(n-3) + g53 x(n) 4 x(n-3) + (odd orders only)

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38 Spectrum of Input & Output Signals With & Without Predistortion Spectrum of Input Signal Without Predistortion Spectrum of Output Signal Without Predistortion Spectrum of Input Signal With Predistortion Spectrum of Output Signal With Predistortion

39 I-Q constellation diagrams 1024 QAM Modulation 98 Msymbols/s (0.98 Gb/s) Memory Mitigation Algorithm EVM: 0.7% BER<1e-6 expected Memory Polynomial Memory length: 8 Nonlinearity order: 9 Minicircuits PA At 2 GHz

40 Future Power Amplifiers Multiband and multimode power amplifiers Broadband power amplifiers Tunable and adaptive power amplifiers Digital microwave signals and switching power amplifiers Integrated RF front-ends PAs for mm-wave wireless systems Free-space power combining

41 Proliferation of Operating Bands Operating Band Uplink Downlink I IMT II PCS III DCS IV AWS V CLR VI VII IMT-E VIII GSM IX X XI XII SMH XIII SMH XIV SMH Carrier Aggregation Single Golden PA

42 Applications of DSP in Power Amplifiers Generate input signals at baseband Generate reference signals (eg: envelope) Generate control signals for PA (eg: Vgg control) Predistort input signal (at baseband) Generate waveforms for PWM converter Generate rf waveforms Instead of High Efficiency and Linear Power Amplifier ===> Focus Becomes High Efficiency and Linear Transmitter Need to integrate PA design into overall transmitter design

43 Application of Switching Mode Amplifier with Non-Constant Envelope Class S Amplifier: Class D Amplifier Fed with PWM Signal To Get Linear Operation

44 Application of Delta-Sigma Modulation to RF Bandpass Signals

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46 Digitally Controlled Pre-Power Amplifier Bogdan Staszewski (Texas Instruments)

47 Pout/Pdc [%] Digitally-Modulated CMOS PA Power controlled by number of "on" transistors Amplitude Control Word Bin.-to-Therm. Decoder Vdd Decoder 1 x Tunable Matching Circuit Modulated Signal Input DPA core Output 1 x Decoder 80 Phase-modulated Signal 1 x 127 Unit Cells Vdd = 2.1 V, through Vdd = 1.5 V, through Vdd = 1.0 V, through Vdd = 0.5 V, through Vdd = 2.1 V, input attenuation Vdd = 1.5 V, input attenuation Vdd = 1.0 V, input attenuation Vdd = 0.5 V, input attenuation 1/2 x /8 x 3 Binary Cells Output Power [dbm]

48 Further Challenges for Digital PA Digital techniques can provide flexible / programmable operation high efficiency from switching mode operation architectures that scale with technology node integration into Systems-on-a-chip Difficult areas: Reduction of spurious outputs 2) Signals introduced into RX band Uplink Downlink RX band noise allowed from TX: -174dBm/Hz-6dB=-180 dbm/hz PCS Band Band II 60MHz 80MHz 1960MHz 20MHz Duplexer filter: Suppression by 45 db today (handset) => PA spurious in RX band should be reduced to -135 dbm/hz

49 Power Combining Techniques Spatial power combining

50 Spatial Power Combining -- Products by Wavestream

51 Psat (dbm), DE, PAE (%) S - parameters (db) 90 GHz Stacked FET PAs CMOS SOI 45 nm First demonstration of FET stacking at W-band Highest reported Pout at 90 GHz from CMOS dBm dB % Freq (GHz) Freq (GHz)

52 Mm-wave System Features Small and directional antennas For f = 94GHz lo = 3.2 mm Major difficulties in packaging and interconnects Bond wire inductance=0.3nh => j 177 ohms at 94 GHz

53 Spatial Power Combining for Integrated Power Arrays + Minimize interconnect losses + Phased array possibility + Simple connection to Si ICs

54 94 GHz Antenna & PA Chip Design 8 Antenna Array 8 push-pull PAs Ant X axis Pitch = 1400 um = λ DC PADS RFIN G S S G Balun + Phase Shifter Ant Y axis Pitch = 1800 um =0.56 λ Y axis height = 3.6 mm Driver 1 1 to 2 Wilkinson Divider Driver 2 1 to 4 Wilkinson Divider Driver 2 1 to 4 Wilkinson Divider DC PADS

55 x higher capacity more connected elements 10x quality of experience Gbps data rates everywhere Latency of the order of 1 ms 10x longer battery life 300MHz 3GHz 30GHz 300GHz 55

56 Few antennas Massive MIMO Few transceivers many transceivers TRX integration very important Output power / PA decreases PA cost must decrease Bandwidth must increase to>100mhz Power per transceiver must decrease Microwaves Mm-waves Tolerable Massive computation computation Hybrid beamforming TRX chip TRX chip TRX chip 56 TRX chip

57 Summary / Outlook PA s are crucial elements in modern wireless communications To be efficient, PA is necessarily nonlinear - but the nonlinearity can degrade transmission of spectrally band-limited signals Classical architectures have tradeoff of efficiency and linearity efficiency drops off as power level decreases. But: Advanced architectures can provide better efficiency!! Advanced architectures can provide better linearity!! Future developments will provide better devices, and more complex algorithms Overall system optimization requires considering PA along with signal and air interface design => integrated transmitter => There are lots of exciting possibilities for better PAs and better systems!!!