1. 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 Björsell 1, Peter Händel 2, Zhiyang Zhao 1 1 Center for RF Measurement Technology, University of Gävle, Sweden 2 Signal Processing Lab, Royal Institute of Technology, Stockholm, Sweden 3 Department ELEC, Vrije Universiteit brussel, Belgium 1

2. Outline  Background  Harmonic sampling  Measuring wideband modulated signals Problem formulation Analytical solution Practical considerations Wideband spectrum reconstruction  Validation example Simulation Measurement  Conclusion 2

3. 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

4. Background Wireless Signals Large Bandwidth High Crest factor 4

5. Background +30dB Power Amplifier Nonlinear Input-Output Behavior 5

6. Background +30dB Power Amplifier 6 Nonlinear Input-Output Behavior

7. Background +30dB Power Amplifier Nonlinear Input-Output Behavior Sampling frequency Resolution ADC Violate Nyquist sampling theory Harmonic sampling 7

8. In the normal case, if the spectrum has large distance and narrow bandwidth 8

9. But, if the spectrum has wide band and small distance, what will happen ? Overlap Measuring wideband modulated signals- Problem formulation Full Overlap 9

10. Amplitude and phase ambiguities in aliased frequency components standing on multiples of Nyquist frequency (k*f s /2) Measuring wideband modulated signals- Problem formulation Evolved harmonic sampling 10 Another challenge:

11. Key: how to find a proper sampling frequency fs Measuring wideband modulated signals- Analytical solution 11

12. Irrational satisfies the condition Measuring wideband modulated signals- Analytical solution 12

13. 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

14. It also need consider sampling frequency coherent Furthermore 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

15. Knowing the down-conversion relationship Bins location of down-converted tones Spectrum reconstruction is straight-forward by descrambling Measuring wideband modulated signals- Reconstruction 15

16. Descrambling Measuring wideband modulated signals- Reconstruction Step 1: obtain spectrum of undersampled data Step 2: Find the spectrum of undersampled data corresponds frequency Step 3: reference undersampled tones 16

17. Descrambling Measuring wideband modulated signals- Reconstruction Step 4: find out minimum difference with Step 5: Reconstruct wide band spectrum 17

18. Validation Example- Simulation 18 noise ADC IAI f x+x 3

19. Validation Example- Simulation ADC Original 8192 samplesMeasured 8232 samples Fs (MHz) 69.302263 Reconstructed Error 19

20. Validation Example- Measurement one Reference Measured with 200 MHzMeasured with 79.231771 MHz 20

21. Validation Example- Measurement two Reference: Nyquist sample Sampling frequency:400 MHz Blue one: Sampling frequency:168. 2150223 MHz Red one is the difference between undersampled one and reference one after synchronization 21

22. 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

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24. Questions ? 24