ANALYSIS OF PERFORMANCE FOR MEMORYLESS PREDISTORTION LINEARIZERS CONSIDERING POWER AMPLIFIER MEMORY EFFECTS

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1 ANALYI OF PERFORMANE FOR MEMORYLE PREDIORION LINEARIZER ONIDERING POWER AMPLIFIER MEMORY EFFE IEEE opical Workshop on PA for Wireless ommunications eptember, 003 an Diego, A Hyunchul Ku and J. tevenson Kenney chool of Electrical and omputer Engineering Georgia Institute of echnology, Atlanta, GA

2 Acknowledgements his work is supported in part by Danam UA, an Jose, A.

3 Outline Introduction New nonlinear PA model Model verification for real PA Pre-D D improvement vs. Memory Effects onclusions 3

4 Memory Effects in PA Memory Effects: he output depends on the past and current input signal RF frequency response in main signal path Non-constant impedance in D bias circuits elf heating effects at the device level Input & Output domain: Dynamic AM/AM and AM/PM Frequency domain: he asymmetric IMD and spectral regrowth Reasons Phenomena 4

5 Memory Effects in Pre-D Memoryless PA (irenza 0.5W LPA) PA with Memory (Ericsson 45W HPA) With Pre-D Without Pre-D * Result from J.. Kenney, W. Woo, L. Ding, R. Raich, H. Ku, and G.. Zhou, he impact of memory effects on predistortion linearization of RF power amplifiers, Proc. of the 8 th Int. ymp. on Microwave and Optical echn., Montreal, anada, June , pp

6 Research Issues How can we model a PA with memory effects accurately and efficiently? How can we quantify the memory effects in PA? What is the relationship between degradation of Pre-D D and PA memory effects? 6

7 Outline Introduction New nonlinear PA model Model verification for real PA Pre-D D improvement vs. Memory Effects onclusions 7

8 PA Behavioral Modeling start Model tructure Identification PA Model structure depending on memory effects Memoryless ystem PA characterist ic AM/AM Modeling Method aylor series (real polynomial) omment No phase distortion Parameter Estimation ompare model With Physical system No uccess? Yes Final Model Measurement Data For various signals Quasimemoryless system ystems with memory AM/AM, AM/PM Dynamic AM/AM, AM/PM / Asymmetric IMD omplex polynomial or Quadrature AM/AM model for each I & Q Volterra /Wiener Approach ircuit time constant are much smaller than the 1/f m Including Long-term memory effect 8

9 PA with Memory Effects Model I - Volterra Model y( t) = h0 + h τ τ τ + τ τ τ τ τ τ 1( 1) x( t 1) d 1 h ( 1, ) x( t 1) x( t ) d 1d h ( τ, τ,, τ ) x( t τ ) x( t τ ) x( t τ ) dτ dτ dτ + p 1 p 1 p 1 p - Volterra Model Drawback omplexity: he complexity of the model increases immensely with the length of the system memory and the order of the nonlinearity Difficulty in measuring the Volterra kernels: Volterra kernels is not orthogonal, thus each kernels distributions cannot be separated from the total system response Example: Kernel complexity 9

10 PA with Memory Effects Model II wo Box Models: One Filter + Memoryless Nonlinear (Wiener Model) hree Box Models: One Filter + Memoryless Nonlinear + One Filter hese models have been usually used to capture memory effects in PA modeling (H. B. Poza, A. A. aleh,. Vuong, M.. Muha, and et al.) Drawbacks* hese models cannot describe the change of shape in AM/AM and AM/PM function depending on tone spacing. hese models cannot describe the interaction between the instantaneous tone. J. lark, et al., Power Amplifier haracterization Using a wo-one Measurement echnique, IEEE rans. Microwave heory ech., vol. 50, no. 6, pp , June, 00 10

11 PA with Memory Effects Model III Parallel Wiener model Memory polynomial Model (MPM) y( k) = n i= 0 F [ x( k i i)] hese models are simple compared to general Volterra series and complex compared to two or three box model. hese models compensate the drawbacks for Volterra models and two or three box models hese models can quantify the memory effects in power amplifier and can apply to linearizer design 11

12 MPM with parse Delay ap (MPMD) y m n ( m) ( k 1) ( m) [] l = a x[ l d ] x[ l d ] q= 0k = 1 k 1, q q q A unit delay tap delay in MPM is replaced with m n ( k 1) ( m) ( m) sparse k 1, q delay q taps q q = 0 k = 1 y = l = a x l d x l d Longer time constant memory effects may be modeled in parallel with short time constant effects using fewer parameters MPMD can improve convergence rate of error compared to MPM * H. Ku and J.. Kenney, Behavioral modeling of power amplifiers considering IMD and spectral regrowth asymmetries, in IM 003, Philadelphia, PA,

13 Application to PA Modeling Easy implementation using linear matrix equation Adaptive modeling by sliding window Iterative modeling by adding the branch using output data and error 13

14 oefficients Extraction for MPMD oefficients Extraction: Input complex envelope x ( ) ( ) ˆ m m 1 a = H Y Output complex envelope y - H (m) : A matrix from PA input time data ( m) ( m) ( m) ( m) H = H0 Hq Hm Y - Y: Vector from PA output time data [ y [ l] y[ l + 1] y[ l + N 1] ] = M+1: he number of branches Nx(m+1) matrix N: length of sliding window Y Nx1 vector 14

15 Delay ap Extraction for MPMD Objective: o acquire delay tap set which minimize rms error where { ( ) { }} min, d 0 d m ( m) ( m) ( m) ( m) ( m) ( m) opt = = ( m) d d d E d E * { ( m ) ( m Y H a ) } ( m) * ( m ) * ( m ) * ( m ˆ ) ˆ ( m = Y Y + a H H a ) Re ˆ It is difficult to derive optimal sparse delay taps analytically In this case, sequential identification can give simple method to derive delay tap function 15

16 New Memory Effect Figures of Merit Memory effect ratio (MER) MER = E E (0) (0) Y Y Quantify the magnitude of memory effects he value is 0 if memoryless case, and increases with increasing memory effects Memory effect modeling ratio (MEMR) MEMR m = 1 E ( m) E (0) Quantify the improvement in modeling memory effects in the suggested model. his value is 0 when no memory effects are included, and is 1 when all of the memory effects are included. 16

17 Outline Introduction New nonlinear PA model Model verification for real PA Pre-D D improvement vs. Memory Effects onclusions 17

18 Power Amplifier Measurement Agilent VA was used to capture time domain data Measured DMA I-95B timedomain input and output envelope signals for in-phase and quadrature DU: One LDMO PA (MRF9180) section of an Danam 880 MHz 50W HPA system est signal: DMA I-95B ignal 18

19 Measurement Result AM/AM response AM/PM response I-95B Eight-tone 19

20 Extracted Parameters & Results Memoryless Model MPMD Model With 4-additional branches 0

21 ime Domain Results ML Model MPMD Model RM Error

22 Outline Introduction New nonlinear PA model Model verification for real PA Pre-D D improvement vs. Memory Effects onclusions

23 Pre-D est Procedure 1. Design memoryless Pre-D based on memoryless model Design Memoryless Pre-D Function Memoryless PA Model. Apply the extracted memoryless Pre-D to PA model with memory Memoryless Pre-D Function MPMD PA Model 3. he Performance of Pre-D is analyzed by sweeping MER in the MPMD model 3

24 Pre-D Design I (p-th order inverse) p k = 1 k 1 ( k 1) g( x) = b x x f ( x) = n a k = 1 k 1 x ( k 1) x Output: c 1 ( l+ m 1) ( d 1) n p p p * y = f( z) = ac 1 bd 1 bl 1 bm 1 x x x c= 1 d= 1 l= 1 m= 1 Expected output: y = x + e = x + k = p+ 1 a ~ k 1 x ( k 1) x ompare & Extract coefficients of Pre-D Using Pre-D based on Polynomial Equation (p-th order inverse) P ( x ) = ( i ) x+ ( i ) x x 3 P( x) = ( i) x+ ( i) x x 5 + ( i) x x 4 4

25 Pre-D design II (LU) G Φ PA Using Pre-D based on LU [ ] P ( x) = Gain ( P ) exp( j( Phase ( P )) x L L in L in. Look Up able (Gain & Phase) Gain LU Phase LU 5

26 Response for PA with Pre-D AM/AM Response AM/PM Response Linear Response Output with LU PreD & Linear Response Output with LU PreD Output with 5th order PreD Output with 5th order PreD Output with 3rd order PreD Output with 3rd order PreD Output without PreD Output without PreD 6

27 APR Improvement For p-th order predistorter, the performance increase as order increases. But stability decrease as order increases tability Decreases Performance Increases PreD using LU gives best performance: 0dB improvement in APR (IBO=5 db) 7

28 APR Improvement Degradation MER =0% MER =3% MER =6% MER =9% MER =1% By changing MER value 5dB IBO) in model (increasing weighting factor for the additional branches), compare the APR improvements 8

29 Analysis in Frequency Domain he range that memoryless pre-d can improve ase ase MER increases ase1 ase 1 * H. Ku, M. McKinley, and J.. Kenney, Quantifying Memory Effects in Power Amplifiers, IEEE rans. on Microwave heory and ech. vol. 50, no. 1, Dec, 00. 9

30 MER vs. Pre-D Improvement 4 branch MPMD Model By adding more branches As MER increases, the improvement decrease : MER= 0%, 14dB@ MER = 9% MER=1%) : Accurate Prediction for Pre- D improvement Measured MER=8.89% Discrepancy between measured result and simulated result from MPMD Model=> Because 64% of memory effects are captured in the model (36% are not captured) 30

31 onclusions Memory polynomial model with sparsely delayed taps (MPMD) is suggested to model PAs with memory effects such as asymmetric IMD and spectral regrowth: imple method to implement Figure of merits introduced to quantify the amount of memory effects (MER) and quantify the modeling improvement of the suggested model (MEMR). Model was extracted for high power LDMO PA and verified against measurements PreD degradation vs. MER is analyzed and simulated 31