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.

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

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Outline

Background Harmonic sampling Measuring wideband modulated signals

• Problem formulation• Analytical solution• Practical considerations• Wideband spectrum reconstruction

Validation example• Simulation• Measurement

Conclusion

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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

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Background

Wireless

Signals LargeBandwidth

HighCrest factor

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Background

+30dB

Power Amplifier

Nonlinear Input-Output Behavior

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Background

+30dB

Power Amplifier

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Freq (MHz)

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Nonlinear Input-Output Behavior

Background

+30dB

Power Amplifier

Nonlinear Input-Output Behavior

Sampling frequency

Resolution

ADC

Violate Nyquist sampling theory Harmonic sampling

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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

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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

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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

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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

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)(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

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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

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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

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Knowing the down-conversion relationship

Bins location of down-converted tones

Spectrum reconstruction is straight-forward by descrambling

Measuring wideband modulated signals- Reconstruction

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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

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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

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Validation Example- Simulation

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noise

ADC

IAI

fx+x3

Validation Example- Simulation

ADC

Original 8192 samples Measured 8232 samples

Fs (MHz)69.302263

ReconstructedError

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0.5 1 1.5 2 2.5 3

x 107

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Validation Example- Measurement one

Reference Measured with 200 MHz Measured with 79.231771 MHz

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Validation Example- Measurement two

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Frqueny (Hz)

Pow

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(dB

m)

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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

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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

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THANK YOU

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Questions ?