Practical Implementation of Adaptation in a Digital Predistorter for RF Power Amplifiers A. Cesari, D.Dragomirescu, P. Lacroix, J.M. Dilhac LAAS-CNRS Toulouse, France IEEE Topical Workshop on Power Amplifiers for Wireless Communications September 9 and 10, 2002 San Diego, CA

PA 16-QAM signal LNA INTRODUCTION Non Linearity of the Power Amplifier LPF I Q 3 - Compression and warping 4 - Increased BER 3 - Compression and warping 4 - Increased BER 1 - Out of band emission 2 - Energy loss 1 - Out of band emission 2 - Energy loss NEED FOR LINEARITY!

POWER AMPLIFIE R LINEARISATION MECHANISM Analog/Digital Adaptative or not Baseband/RFBand INTRODUCTION Non Linearity of the Power Amplifier

LINEARISATION STRATEGIES Digital & Adaptative Digital: use of DSP chips » Low cost » Low power consumption » Small size » NEWER APPROACH Digital: use of DSP chips » Low cost » Low power consumption » Small size » NEWER APPROACH Adaptative: a feedback path exists » Generic approach » Intended for low development time » Ability for self training » Ability to account for changes in the system and consequent adaptation Adaptative: a feedback path exists » Generic approach » Intended for low development time » Ability for self training » Ability to account for changes in the system and consequent adaptation  DEALING WITH FEEDBACK BETTER PERFORMANCES

LINEARISATION STRATEGIES General Predistortion Strategy g PA (y) x z * O PA In PA Out g PA (.) Desired, linear characteristic x wrong z Forward signal Output signal y x  c y  c f PD z  c g PA + ** + * y Good z f PD (x)

f PD   xIxI yIyI xQxQ yQyQ |x| |y| Complex plane * + x = (x I, x Q ) = |x|e j  y = (y I, y Q ) = |y|e j  * + x  C y  C f PD ? x +  = y x  = y C 1 ·x + C 2 ·x 2 + C 3 ·x 3 … = y Look-Up Table: Polynomial: |x|Ge j  +  = y MAPPING COMPLEX GAIN POLAR LINEARISATION STRATEGIES General Predistortion Strategy Well known techniques or

LINEARISATION STRATEGIES Adaptive Digital predistortion Aging, temperature drifts Changes in work frequency Part to part variation, load mismatch Aging, temperature drifts Changes in work frequency Part to part variation, load mismatch Need for perfect synchronisation Tradeoffs: Bandwidth, f sample, complexity Need for perfect synchronisation Tradeoffs: Bandwidth, f sample, complexity f PD (x) g PA (y) zx y * + O adaptation comparison adaptation comparison Feedback signal

COMPARISON & ADAPTATION Sample-by-Sample basis adaptation comparison +- x z Calculate f PD (x,z,e) error signal FORWARD signal FEEDBACK signal

COMPARISON & ADAPTATION Overview of Delays PD f sx DAC f sx f sz delay = kT sz +  k = 0,1,2,…  < T sz /2 After digital delay estimation Residual delay =  x i,x q adaptation comparison y i,y q z i,z q Nyquist filter Mod PA ADC DeMo d Delay estimate delay FIFO

COMPARISON & ADAPTATION Example error Worst case delay,  = T sz /2 FORWARD signal FEEDBACK signal

COMPARISON & ADAPTATION Parameters of Interest 1. F sx : sampling rate at FWD path, digital stage As high as possible, BW of PreDistortion 2. F sz : sampling rate at feedback path, digital stage As high as possible, accuracy of delay error 3. SS x : samples/symbol at Tx, digital stage As high as possible; accuracy of delay error But if SS x ’s up, F sx needs to be incremented by the same amount in order to maintain BW! 1. F sx : sampling rate at FWD path, digital stage As high as possible, BW of PreDistortion 2. F sz : sampling rate at feedback path, digital stage As high as possible, accuracy of delay error 3. SS x : samples/symbol at Tx, digital stage As high as possible; accuracy of delay error But if SS x ’s up, F sx needs to be incremented by the same amount in order to maintain BW!

COMPARISON & ADAPTATION Our proposal: Multirate DSP Keep F sx as high as possible Keep SS x as low as possible (i.e. IS-95, SS x = 4) Increment F sz : oversampling Keep F sx as high as possible Keep SS x as low as possible (i.e. IS-95, SS x = 4) Increment F sz : oversampling f sz = 2f sx FWD signal Feedback signal samples amplitude

COMPARISON & ADAPTATION Multirate DSP Objective: Study the impact of oversampling & multirate DSP over the delay error magnitude Objective: Study the impact of oversampling & multirate DSP over the delay error magnitude Experience 1: measure of the (worst case) delay error along the Dynamic Range of a QAM signal Experience 2: improvements after oversampling Experience 1: measure of the (worst case) delay error along the Dynamic Range of a QAM signal Experience 2: improvements after oversampling

COMPARISON & ADAPTATION Experience 1 Measure of the (worst case) delay error along the Dynamic Range of a 16-QAM signal Measure of the (worst case) delay error along the Dynamic Range of a 16-QAM signal comparison +- x z FORWARD signal FEEDBACK signal Worst Case sampling Worst Case sampling rms f sx = f sz Digital Delay adjust Digital Delay f sz Delay =  = T sz /2 Delay = kT sz +  Px - Pz Px analogic digital ? Px Pz

COMPARISON & ADAPTATION Experience 1 Px Px - Pz f sx = f sz = 4 SS x f sx = f sz = 16 SS x 0,15

COMPARISON & ADAPTATION Experience 2 Oversampling & Multirate: Keep the samples/symbol ratio at minimum f sz > f sx at ADC & DAC stages Oversampling & Multirate: Keep the samples/symbol ratio at minimum f sz > f sx at ADC & DAC stages Technique 2A: drop samples from the higher rate source (Z) to match the samples of X Technique 2B: true multirate, smoothing through average calculation in the domain of Z Technique 2A: drop samples from the higher rate source (Z) to match the samples of X Technique 2B: true multirate, smoothing through average calculation in the domain of Z

COMPARISON & ADAPTATION Experience 2 Technique 2A: drop samples from the higher rate source (Z-feedback signal) to match the samples of X-forward signal Technique 2A: drop samples from the higher rate source (Z-feedback signal) to match the samples of X-forward signal It results in exactly the same (poor) improvement obtained by increasing both f sx and f sz. Why? f sz sets the limit  = T sz /2 in spite of T sx It results in exactly the same (poor) improvement obtained by increasing both f sx and f sz. Why? f sz sets the limit  = T sz /2 in spite of T sx

COMPARISON & ADAPTATION Experience 1 comparison +- x z FORWARD signal FEEDBACK signal Worst Case sampling Worst Case sampling rms f sx < f sz Digital Delay Adjust & DROP Digital Delay Adjust & f sz Delay =  = T sz /2 Delay = kT sz +  Px - Pz Px analogic digital ? Px Pz Technique 2B: average filtering (by convolution) in the domain of the oversampled signal, then matching with the signal X-FWD signal Technique 2B: average filtering (by convolution) in the domain of the oversampled signal, then matching with the signal X-FWD signal Avg. filter Avg. filter

COMPARISON & ADAPTATION Experience 2 Px Px - Pz Px Px - Pz Oversampling x 2, 4 SS x f sx = f sz = 16 SS x Oversampling x 2, 4 SS x f sx = f sz = 16 SS x Oversampling x 2, 4 SS x

CONCLUSIONS & FUTURE WORK Adaptive digital predistortion Feedback synchronisation problem  Analog delay Traditional solution : high rate samples/symbol Drawbacks :  decreased transmission bandwidth  incompatibility with 3rd generation wireless telecommunication standards Adaptive digital predistortion Feedback synchronisation problem  Analog delay Traditional solution : high rate samples/symbol Drawbacks :  decreased transmission bandwidth  incompatibility with 3rd generation wireless telecommunication standards Our proposal : oversampling, multirate, + average filter Future work : physical implementation on a DSP system