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 Large

Bandwidth

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 (d

Bm

)

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

SF2

SF2

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

SF2

SF2

Sk F S2k F S3k F

f (MHz)f (GHz)

A A

SF2

SF2

f (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:

SF2 Sk F f (GHz)

A

S(k-1)F2

S(k+1)F2

Key: how to find a proper sampling frequency fs

ress

res

fff

kfresf

kkfu

uff f ss

ff

u

f

f

s

res

spectrum frequenciesf sampling frequency

undersampled frequenciesf resolution frequency

Measuring wideband modulated signals- Analytical solution

11

)(f)(f uu jiji

resj

jresi

i fk

kfkk

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 resf fs resfres 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

( ) ( ) ( ) 0u 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 ?