A Synchronization Technique to Model Output Behavior of Wide Bandwidth Signals
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Transcript of A Synchronization Technique to Model Output Behavior of Wide Bandwidth Signals
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.
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.