1 / 35

Sub- Nyquist Sampling of Wideband Signals

Sub- Nyquist Sampling of Wideband Signals. Optimization of the choice of mixing sequences. Final Presentation. Itai Friedman Tal Miller Supervised by: Deborah Cohen Prof. Yonina Eldar Technion – Israel Institute of Technology. Presentation Outline. Brief System Description

Download Presentation

Sub- Nyquist Sampling of Wideband Signals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Sub-Nyquist Sampling of Wideband Signals Optimization of the choice of mixing sequences Final Presentation Itai Friedman Tal Miller Supervised by: Deborah Cohen Prof. YoninaEldar Technion – Israel Institute of Technology

  2. Presentation Outline • Brief System Description • Project Objective • Simulation Method • Common Communication Sequences • Lu Gan’s Sequences • Sequences Comparison • Expander Performance • Conclusions and Insights

  3. Motivation: Spectrum Sparsity • Spectrum is underutilized • In a given place, at a given time, only a small number of PUs transmit concurrently Shared Spectrum Company (SSC) – 16-18 Nov 2005

  4. Model ~ ~ ~ ~ • Input signal in Multiband model: • Signal support is but it is sparse. • N – max number of transmissions • B – max bandwidth of each transmission • Output: • Reconstructed signal • Blind detection of each transmission • Minimal achievable rate: 2NB << fNYQ Mishali & Eldar ‘09

  5. The Modulated Wideband Converter (MWC) ~ ~ ~ ~ Mishali & Eldar ‘10

  6. MWC – Recovery System

  7. MWC – Mixing & Aliasing • System requirement: are periodic functions with period called “Mixing functions” • Examples for : … 1 -1 Frequency domain

  8. Project Objective • Main objective: Finding optimal Mixing sequencesfor effective signal reconstruction • Finding the characteristics of those sequences.

  9. Research Environment • Based on the basic version of the MWC simulation. • Expanded to support: • Various kinds of sequences • Calculating the correlation parameters • The Expander • Designed to calculate the recovery probability under various conditions

  10. Simulation Method • Building a certain sensing matrix A. • Counting successful recoveries for different signals. • Successful Recovery = supp(original signal) supp(reconstructed signal)

  11. Simulation Method • , with random carriers and energies. • White noise is added according to SNR level.

  12. ExRIP: Conditioning of The Modulated Wideband Converter • The article discusses a few common communication sequences: Gold Kasami and Hadamard. • It also introduces the correlation parameters . Mishali & Eldar ‘10

  13. ExRIP: Conditioning of The Modulated Wideband Converter Mishali & Eldar ‘10

  14. ExRIP: MWC Conditioning • A formula for the recovery probability is obtained. • The theoretical results for the sequences are: Mishali & Eldar ‘10

  15. ExRIP: MWC Conditioning • We simulated the sequences for SNR=10,100dB. • are similar to the article. Mishali & Eldar ‘10

  16. Conclusion: the formula for p obtains a general estimation of the sequences performance, but SNR level is not considered. Mishali & Eldar ‘10

  17. Deterministic Sequences for the MWC • This article offers new sequences for the MWC. • The simulation conditions use deterministic energies. This condition is easier: Gan & Wang ‘13

  18. Deterministic Sequences for the MWC • From now on we will use the same conditions. Gan & Wang ‘13

  19. Matrix from Single Sequence • The following matrix structure is offered: • is a circulant matrix. • Sequences proposed for the first row: Maximal and Legendre. • is a random subsampling operator, which chooses m rows out of M. Gan & Wang ‘13

  20. Random Selection of Rows • We tested the necessity of rows random selection by using three different row selection methods: • Choosing first m rows • Choosing every 6th row, total of m rows • Random selection (MATLAB’s randpermfunction) Gan & Wang ‘13

  21. Random Selection of Rows • The deterministic selection methods led to poor results. • Insight: the correlation parameters do not predict system’s performance: same parameters but dramatically different p. Gan & Wang ‘13

  22. Examination of Article’s Conditions • The theorem in the article predicts high recovery probability for if the signal is ZERO in baseband: • We examined this condition for different sequences: Gan & Wang ‘13

  23. gfhgcg • The condition is not necessary, same results (except for Wrong-Legendre). Gan & Wang ‘13

  24. Matrix from Periodic Complementary Pair (PCP) • Another matrix structure is offered: • is a matrix constructed from a PCP. • is a permutation operator. • is defined in the same way as before. Gan & Wang ‘13

  25. Various Sequences Performance • scscdscsdcdsc

  26. Flatness in Freq. Domain • To understand the poor performance of the Wrong-Legendresequence, we observed the sequences in the frequency domain:

  27. Flatness in Freq. Domain • Unlike the other sequences, Hadamardand Wrong-Legendre are not flatin the frequency domain, thus their poor performance. • HOWEVER, this is an FFT of a single row and it lacks information on the entire matrix. • Therefore, frequency flat sequences can still have poor results.

  28. MWC Performance with Expander • We simulated the Expander in our system by adding additional digital processing, and expanding the sensing matrix A to . • The simulations results:

  29. MWC Demo Performance • Simulation Parameters:

  30. Conclusions and Insights • A few sequences have very good and similar performance: Random, Gold, LU-Maximal, LU-Legendre, LU-PCP. • p>0.9 for SNR>10. • The main difference between these sequences is in the level of randomness: from full randomness, through random cyclic shifts of a single row, to a completely deterministic matrix.

  31. Conclusions and Insights • Lack of flatness in the frequency domain indicates poor performance of the sequence. The opposite is not necessarily true. • The correlation parameters do not predict well the performance of the sequences. • Using the Expander with q=3,5 does not effect the system’s performance.

  32. Future Work • Implementation of the sequences for different systems that use sub-nyquist sampling principles. • Optimization of the mixing sequences for the specifications of a certain MWC system.

  33. Future Work • Examination of different periodic mixing functions other than the {+1,-1} sequences. • Optimization of the mixing sequences for sparse wideband signals with known carriers, as suggested by Prof. Eldar (Huawei)

  34. Thank you For listening Thanks to Debby For Everything For a broader review, see project book

More Related