A Synchronization Technique to Model Output Behavior of Wide Bandwidth

Signals

Efrain Zenteno & Magnus Isaksson

Center for RF measurement Technology, University of Gävle, Sweden

Signal Processing Lab, The Royal Institute of Technology, KTH, Stockholm, Sweden

RFMTC 2011, Gävle, October, 2011

Agenda

• Introduction (Why is synchronization needed it?)

• Challenges when modeling large bandwidth signals

• Approach

• Results

• Conclusions

Introduction

1. Larger bandwidths are required for newer communication systems.

2. Weakly non-linear devices cause spectrum widening ……( larger for larger bandwidths)

3. Larger bandwidths poses challenges into the measurement systems, modeling and validation.

Set up Description

Synchronization ?

0 0.5 1 1.5 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Time (us)

Am

plitu

de (V

)

• Adquisition in different time.

(periodic signals)

• Sub-sample.

Defining ..

( )F y n Y Fourier Transform:

Measured output ( )MEASY

Error :

2

2( ) ( )j

MEAS MODE Y e Y

that produces the lowest modelling error.

Model

( ) iif x x Gp’s are FIR systems

y H

Approach

“Including the estimation of the delay () into the identification procedure ”

Problems:

• Nonlinear.• High dimensionality.

2

2, argmin( ( ) ( ) )j

MEAS MODY e Y

( )MODY F H

The problem:Linear model parameters Nonlinear delay estimation. (separable least squares)

† 1 ( ) jMEASH F Y e

2

2( ) j

MEASE Y e F H

Now use this solution

The error function depends of only one variable ().

Effect of

-5 -4 -3 -2 -1 0 1 2-35

-30

-25

-20

-15

-10

-5

(Samples)

NM

SE

(d

B)

Minimun at 0 -31.2 dB

Minimun at -1.001-32.6dB

Newton Search

1. Initial Cross-correlation search (integer D)

2. Newton search on D + k, k = -5, -4, -3,…, 3, 4, 5

1 2 3 4 50

0.02

0.04

0.06

0.08

Iteration number

Ste

p S

ize

Results

-1 -0.5 0 0.5 1-100

-50

0

50

Norm. freq ()

PS

D (

dB)

-6 -4 -2 0 2 4 6-40

-30

-20

-10

0

Jc (

dB)

-1 -0.5 0 0.5 1

-100

-50

0

50

Norm. freq ()

PS

D (

dB)

-6 -4 -2 0 2 4 6-40

-30

-20

-10

0

Jc (

dB)

OutputInput

Output

Input

Results

2 4 6 8 10-34

-33

-32

-31

-30N

MS

E (

dB

)

P = 5

OriginalOptimized

2 4 6 8 100

1

2

Memory depthImp

rove

me

nt (

dB

)

Results

2 4 6 8 10-33

-32.5

-32

-31.5

-31N

MS

E (

dB

)

M = 3

OriginalOptimized

2 4 6 8 101.3

1.4

1.5

Polynomial OrderImp

rove

me

nt (

dB

)

Conclussions

• A synchronization technique to model output behavior of parallell Hammerstein system is presented.

• With the same model complexity, the search method, performs better (in NMSE) than similar methods to find the synchronization.

Thanks

Questions ?