HPEC_NDP-1MAH 04/19/23

MIT Lincoln Laboratory

Efficient Multidimensional Polynomial Filtering for Nonlinear

Digital Predistortion

Matthew Herman, Benjamin Miller, Joel Goodman

HPEC Workshop 2008

23 September 2008

This work is sponsored by the Defense Advanced Research Projects Agency under Air Force Contract FA8721-05-C-0002. Opinions, interpretations, conclusions, and recommendations are those of the author and are not necessarily endorsed by the United States Government.

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Motivation

• The objective of Nonlinear Digital Predistortion (NDP) is to digitally alter the input to the PA to compensate for the distortions imparted by the device.

– NDP is capable improving power efficiency while reducing ACI and BER.

• Computationally efficient memoryless NDP techniques are not sufficient for linearizing wideband PAs that impart significant memory effects.

• Not feasible to use a computationally complex polynomial predistorter to model/invert state dependent nonlinearities.

– Most previous polynomial approaches consider 1D subkernels as building blocks for the full PD.– Multidimensional filters more easily address asymmetric and aliasing NL.

Distorted Output Constellation

12-4 QAM Constellation

Frequency

Po

wer

Ch

ann

el N

-1

Ch

ann

el N

+1

Po

wer C

h. N

-1

Ch

. N+

1

Frequency

PADAC ×Standard Transmitter:

Spectral regrowth from PA nonlinearities causes

adjacent channel interference (ACI).

Spectral regrowth from PA nonlinearities causes

adjacent channel interference (ACI).

PA nonlinearities also increase Error Vector

Magnitude (EVM) and Bit Error Rate (BER).

PA nonlinearities also increase Error Vector

Magnitude (EVM) and Bit Error Rate (BER).

Full Volterra (polynomial) filter

Full Volterra (polynomial) filter

y(n)

X

x(n)

Z-N+1

Z-N+1

Z-1 X

X

Xh2(0,1)

X

h9(N-1,N-1,…,N-1)

X

+

x2(n)

x(n)x(n-1)

x9(n-N+1)

Z-N+1The full Volterra kernel has

prohibitively high computational complexity.

The full Volterra kernel hasprohibitively high

computational complexity.

h2(0,0)

OBJECTIVE: Use small multidimensional filters to build a computationally efficient nonlinear digital predistorter.

OBJECTIVE: Use small multidimensional filters to build a computationally efficient nonlinear digital predistorter.

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Methods

m1

Full 3rd Order Coefficient Space(Time Domain Representation)

m2

m3

M3-1

M2-1

M1-1

• Divide the full coefficient space into cube coefficient subspaces (CCS),

– i.e., small hypercubes/parallelepipeds (“diagonal” CCS-D) of arbitrary dimension.

• Model the inverse NL by greedily selecting only the CCS components that have the greatest impact on performance.

• CCS allows efficient adaptation in multiple dimensions starting with the first nonlinear component selected.

• CCS has an efficient hardware implementation.

CCS Nonlinear Digital Predistorter:

x(n) FIR

CCS Component 1

+

CCS Component L

+… … …

v(n)v0(n)

v1(n)

vL(n)

2 Tap FIR

z-α

×

+ ×

z-α

z-α

2

3

4

z-α5

z-α1

conj.

2 Tap FIR

z-α

×2

z-α1

conj.z-1

conj.

Full Kernel

CCS ComponentsCCS-D Components

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Results

250 270 290 310 330 350-50

-40

-30

-20

-10

0

Frequency (MHz)

Po

wer

(d

Bc)

No PD

GMP PDCCS PD

Measured Results using Q-Band Solid State PA:

CCS reduces ACI by ~7 dB more than the state-of-the-art GMP with less than half as

many operations per second.

CCS reduces ACI by ~7 dB more than the state-of-the-art GMP with less than half as

many operations per second.

CCS NDP improves ACI by ~20 dB.

CCS NDP improves ACI by ~20 dB.

ArchitectureComplexMult. Per Sample

ComplexAdd. Per Sample

Op’nsPer

Second(GOPS)

Generalized Memory Polynomial

156 144 147

2-D CCS/CCS-D 76 32 62

Computational Complexity: No NDP GMP NDP CCS NDP