Evolved Harmonic sampling: a tool to reduce the digital bandwidth requirement of RF receivers

1. 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, Sweden 2Signal Processing Lab, Royal Institute of Technology, Stockholm, Sweden 3Department ELEC, Vrije Universiteit brussel, Belgium

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

3. Wireless communication system is widely spreading Background First generation analog system: analog AMPS Second generation digital system: GSM Third generation system: UMTS Forth generation system: LTE

4. Background High Crest factor • Wireless • Signals Large Bandwidth

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

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

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

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

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

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

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

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

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

14. 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 It also need consider sampling frequency coherent Furthermore

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

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

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

18. Validation Example- Simulation IAI noise x+x3 ADC f

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

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

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

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

23. Thank you

24. Questions ?