Evolved Harmonic sampling: a tool to reduce the digital bandwidth requirement of RF receivers Charles Nader 1,2,3, Wendy Van Moer 3, Kurt Barbé 3, Niclas.
Post on 20-Dec-2015
212 Views
Preview:
Transcript
Evolved Harmonic sampling: a tool to reduce the digital bandwidth requirement of RF
receivers
Charles Nader1,2,3, Wendy Van Moer3, Kurt Barbé3, Niclas Björsell1, Peter Händel2 , Zhiyang Zhao1
1Center for RF Measurement Technology, University of Gävle, Sweden2Signal Processing Lab, Royal Institute of Technology, Stockholm, Sweden
3Department ELEC, Vrije Universiteit brussel, Belgium
1
Outline
Background Harmonic sampling Measuring wideband modulated signals
• Problem formulation• Analytical solution• Practical considerations• Wideband spectrum reconstruction
Validation example• Simulation• Measurement
Conclusion
2
Background
Wireless communication system is widely spreading
First generation analog system: analog AMPS
Second generation digital system: GSM
Third generation system: UMTS
Forth generation system: LTE
3
Background
Wireless
Signals LargeBandwidth
HighCrest factor
4
Background
+30dB
Power Amplifier
Nonlinear Input-Output Behavior
5
Background
+30dB
Power Amplifier
6
0 100 200 300 400 500 600 700-160
-140
-120
-100
-80
-60
-40
-20
Freq (MHz)
Pow
er le
vel (
dBm
)
Nonlinear Input-Output Behavior
Background
+30dB
Power Amplifier
Nonlinear Input-Output Behavior
Sampling frequency
Resolution
ADC
Violate Nyquist sampling theory Harmonic sampling
7
0 100 200 300 400 500 600 700-140
-120
-100
-80
-60
-40
-20
0
Freq (MHz)
Pow
er (
dBm
)
0 100 200 300 400 500 600 700-160
-140
-120
-100
-80
-60
-40
-20
Freq (MHz)
Pow
er le
vel (
dBm
)
Harmonic sampling
SF
2SF
2
Sk F S2k F S3k F
f (MHz)f (GHz)1 2 3 3x
A A
x 2x
x (MHz) 2x (MHz) 3x (MHz)
In the normal case , if the spectrum has large distance and narrow bandwidth
8
But, if the spectrum has wide band and small distance, what will happen ?
Overlap
SF
2SF
2
Sk F S2k F S3k F
f (MHz)f (GHz)
A A
SF
2SF
2f (MHz)f (GHz)
A A
Measuring wideband modulated signals- Problem formulation
Full Overlap
9
Amplitude and phase ambiguities in aliased frequency components standing on multiples of Nyquist frequency (k*fs/2)
Measuring wideband modulated signals- Problem formulation
Evolved harmonic sampling
10
Another challenge:
SF
2 Sk F f (GHz)
A
S(k-1)F
2S(k+1)F
2
Key: how to find a proper sampling frequency fs
ress
res
ff
f
kfresf
k
kfu
u
ff f s
s
ff
u
f
f
s
res
spectrum frequencies
f sampling frequency
undersampled frequencies
f resolution frequency
Measuring wideband modulated signals- Analytical solution
11
)(f)(f uu jiji
resj
jresi
i fk
kfk
k
i j i j
j ji i
k k k kand i j
k kk k
Irrational satisfies the condition
Measuring wideband modulated signals- Analytical solution
12
Measuring wideband modulated signals- practical consideration
At High frequencies (in the order of MHz), cutting the irrationality property down to a sampling frequency accuracy of 1/0.1Hz can be achieved
13
It also need consider sampling frequency coherent
' ,
'
f l f lres res
f fs resf
res N Ns s
sN l
Furthermore
NNs
Measuring wideband modulated signals- practical consideration
At High frequencies (in the order of MHz), cutting the irrationality property down to a sampling frequency accuracy of 1/0.1Hz can be achieved
14
Knowing the down-conversion relationship
Bins location of down-converted tones
Spectrum reconstruction is straight-forward by descrambling
Measuring wideband modulated signals- Reconstruction
15
Descrambling
Measuring wideband modulated signals- Reconstruction
Step 1: obtain spectrum of undersampled data
Step 2: Find the spectrum of undersampled data corresponds frequency 'f
uA
Step 3: reference undersampled tones
u
kk resf f
16
Descrambling
Measuring wideband modulated signals- Reconstruction
Step 4: find out minimum difference with
Step 5: Reconstruct wide band spectrum
' '( )f k u ( )f k
A
'
' *
( ) ( ) ( ) 0
( ) ( ) ( ) 0
u u
u u
A k A k if f k
A k A k if f k
17
Validation Example- Simulation
18
noise
ADC
IAI
fx+x3
Validation Example- Simulation
ADC
Original 8192 samples Measured 8232 samples
Fs (MHz)69.302263
ReconstructedError
19
0 1 2 3 4 5 6 7 8 9 10
x 108
-180
-160
-140
-120
-100
-80
-60
-40
-20
0 1 2 3 4 5 6 7 8 9 10
x 108
-160
-140
-120
-100
-80
-60
-40
-20
0.5 1 1.5 2 2.5 3
x 107
-140
-120
-100
-80
-60
-40
-20
Validation Example- Measurement one
Reference Measured with 200 MHz Measured with 79.231771 MHz
20
Validation Example- Measurement two
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 108
-90
-80
-70
-60
-50
-40
-30
-20
Frqueny (Hz)
Pow
er L
evel
(dB
m)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 108
-100
-90
-80
-70
-60
-50
-40
-30
-20
Reference: Nyquist sampleSampling frequency:400 MHz
Blue one: Sampling frequency:168. 2150223 MHz
Red one is the difference between undersampled one and reference one after synchronization
21
Conclusion
Method to sample and reconstruct wideband signal
A way to choose the right sampling frequency and number of samples
Method is validated by simulation and measurement
A tool to design wide-band receivers/cognitive radios
22
THANK YOU
23
24
Questions ?
top related