Blind-Spectrum Non-uniform Sampling and its Application in Wideband Spectrum Sensing

1. Blind-Spectrum Non-uniform Sampling
and its Application in Wideband
Spectrum Sensing
By.
M. R. Avendi

2. Agenda
• Blind Spectrum Signal Model
• Parameters L, p, q, C
• Spectral Recovery
– Subspace Method
– NLLS Method
• Simulation
• Application for Spectrum Sensing• Application for Spectrum Sensing
– Cognitive Overview
– Spectrum sensing
– Current methods
– Proposed model
– Simulation
• Summary and conclusion
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3. Blind spectrum signal model
• Number of bands N
• Each band no wider than B
• Maximum frequency fmax
• Locations unknown
• Landau lower bound λ(F)=NB
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4. Sampling Parameters
• Number of active slots : qmin < q < qmax
q=3
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Minimum and Maximum number of active slots
q=6

5. Sampling Parameters
• L
• p > qmax
q = N(d+1)
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qmax= N(d+1)
• Sampling Rate

6. Sampling Parameters
• Sample pattern C
- Exhaustive Search- Exhaustive Search
- Random Selection
- Sequential Search
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7. Spectral Recovery
• Ideal model
y(f)=AC(k) z(f)
• Non-ideal model
y(f)= A (k) z(f)+ n(f)y(f)= AC(k) z(f)+ n(f)
y is known, k and z are unknown
n(f) additive white noise
spectral index set k ?
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8. Spectral Recovery
• Subspace method
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9. Number of active slots q
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Ordered Eigenvalues

10. Number of active slots
• Information theoretic criteria approaches
AIC : Akaike Information criterion
MDL: Minimum Description length
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11. Number of active slots
• Exponential fitting test (EFT)
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Ordered Eigenvalues of signal and noise

12. Location of active slots
• MUSIC algorithm
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The k-th column of modulation
matrix

13. MUSIC-Algorithm
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Signal spectrum and MUSIC- Results

14. Spectral Recovery : NLLS method
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Solution:
-Exhaustive search
- Sequential search

15. NLLS method
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Least square error criteria

16. Simulation
• N=3, fmax=20, B=0.9
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Time and frequency domain of multi-band signal

17. simulation
• L=floor(fmax/B)=22
• qmax= N*2=6 => p=q+1=7
• C= {0 5 6 8 11 16 17}
• Sampling rate D= f *p/L= 6.3 !! In compare• Sampling rate D= fmax*p/L= 6.3 !! In compare
20!!
• Compute matrix R7*7
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18. simulation
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simulation result

19. Simulation
Sampling ratio=6.36
p=7
L=22
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Reconstructed signal in time and frequency domain
RMSE=2.7%

20. spectrum sensing
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21. Spectrum sensing
• Narrowbands
• Wideband
• Challenge: High sample rate
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22. Spectrum Sensing: Proposed Model
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23. Model parameters
• Given channel B, Ω , fmax
• L= fmax/B , p= L Ω
• Compression Ratio: CR=p/L > Ω
– Sampling Parameters
Ω
– Sampling Parameters
• Detection Probability:
– Depend on SNR and CR
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24. Spectrum sensing: simulation
• Ω =0.1 , fmax=2 GHz
• Resolution Channel : B=10 MHz
• L=2GHz/10MHz= 200
• p= L Ω= 200 * 0.1= 20• p= L Ω= 200 * 0.1= 20
• fs= fmax * p/L= 200 MHz !!
• CR= 0.1
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25. Simulation
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26. simulation:
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Detection probability vs. SNR for various Compression Ratio

27. Summary & Conclusion
• Periodic non-uniform Sampling & Reconstruction
• Sampling parameters: L, p ,sample pattern C
• Spectral recovery : Subspace, NLLS
• Wideband spectrum sensing
Future works:
• Implementation aspects of non-uniform ADC
• General sample pattern for blind spectrum signal
• Reduce the sample rate for extreme case of blind signals
• Formulation of detection probability vs. SNR and CR
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28. Thank you for attention
• Question ?
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