Connecting Theory and Practice – Part A

1. Technion Israel Institute of Technology Connecting Theory and Practice – Part A Spring 2013 Final Part A Presentation

2. Contents • Project Definition and Goals • Work Plan Review • Project Main Activities: • Matlab Algorithm + Integration • AWR Activities • Simulations • Gantt

3. Main Challenges • Understanding, fixing and improving the Matlab code • Learning AWR tool and Modeling MWC • Deeper understanding of the main issues the system suffers from • Integrating Co-Projects into one Matlab code

4. Project Main Stages • Matlab Reconstruction • AWR Activities – Part A • AWR Activities – Part B • A-Matrix Calibration • MWC Development Support Systems

5. Work Plan Review – Matlab • Matlab reconstruction algorithm • The current algorithm • What is there, what is missing • Tuning detection SBR4 (SBR2 ?) SBR Special • How do we want to display results of reconstruction • Modulate back up to show the original signal • Combine slices, find signal and demodulate to baseband • Enter first draft of MWC schematic Completed

6. Work Plan Review – AWR activities • Starting AWR activities • Understand current schematics of analog part of new MWC • Get understanding of AWR tool • Define method for in- and output files • Matlab , CSV etc. • Enter first draft of MWC schematic Completed

7. Additional Tasks Completed • Matlab • Calculating recovery success % with correlation technique • Complete rewrite of Sample and Expander algorithms • Implementing support recovery with thresholds • Complete rewrite and debug of MWC System code • Full consistency check with article

8. Additional Tasks Completed • Integration from co-projects • Integrating & comparing different Mixing Series • Integrating Filter Banks Expander • Finally - Achieving great recovery results without noticeable redundant harmonics

9. More tasks completed • AWR • Precise modelling of most linear components using S Parameters – Waiting for new card schematics to complete • Mixing Series full integration into AWR • Almost complete modelling of old MWC card • More details in last meeting’s summary

10. Matlab Code Debug • Main issues solved: • Redundant Harmonics have been (almost) eliminated • Reconstruction (-1) factor has been removed. Entire Reconstruction method has been rebuilt • Parameters names are now consistent throughout the code - mostly L, L0, m, M, etc. • Fixing “minor” things – for example: • exp(jωt) vs. exp(-jωt) • A.’ (transpose) vs. A’ (conj-transpose) • A=SFD vs. A=conj(SFD)

11. Matlab Code Improvements • Features Added • Constructing matlab libraries by subjects • Consistency Check • Error check – Original vs. Recovery signal • Improving signal generation (qpsk, sinc and it’s powers) • Integrating different mixing series

12. Consistency Check • Full article-code consistency check has been implemented • Conditions must be met or user must authorize manual override

13. Error check – Original vs. Recovery • Comparison Method: Correlation between Original & Recovery Signal: • Where : • c = xcorr(x,y) returns the Cross-Correlation sequence in a length 2N-1 vector, where x and y are length N vectors (if x and y are not the same length, the shorter vector is padded to the length of the longer vector).By default, xcorr computes raw correlation with no normalization. • In the denominator, 2-norm of x and y – for normalization • Matlab code (function handle): CorrXY =@(x,y)max(abs(xcorr(x,y)))/(norm(x,2)*norm(y,2));

14. Error check – Original vs. Recovery

15. Frequency Domain Zoom-In

16. Time Domain Zoom-In

17. Console Output

18. MWC Analog Schematics

19. AWR – Top System View

20. AWR – Hierarchy

21. Signal Generator • Analog generated input from AWR • Digital input from Matlab is partially implemented

22. Pre Processing • In this block all of the components are accurately modeled with S-Parameters

23. Mixer • AWR unable to model mixer in the way we intended. • Fallback option – Mathematical Multiplier • Mixing series are generated in Matlab

24. Post Processing • LPF-105 was found inadequate for signal properties • Missing properties for buffers and output driver

25. Sampling + A/D • Quantization doesn’t work perfectly yet - WIP

26. Output to Matlab Server • 4 digital channels are multiplexed into 1 channel • That channel is demuxed in Matlab environment • Timing AWR and Matlab with triggers – WIP • Full DSP of AWR output and A matrix calibration – Main open Task

27. Understanding AWR Signal Types • Signals in AWR can be modeled with 4 different types: • Real Signal – Signals are modeled using real numbers as a very dense function of time(5*Fnyquist) • Complex – Signals are modeled using complex numbers as a dense function of time • Complex Envelope – Signal data contains carrier wave and modulated information separately • Digital Signal – I/O to/from Matlab

28. Complex Envelope Type • AWR utilizes the CE representation of signals whenever possible to gain the tremendous advantage in simulation: • This representation, that is utilized in all mixer components to shorten simulations by order-of-magnitude, annihilates the wide spectrum of the signals that are mixed with the series

29. S-Parameters - Background • S-Parameter files contain the behavior of linear components for different frequencies • They represent the following LTI system: • Usually our components will have b1 and a2 connected to GND • Information for adding components using S-Parameters will be documented in the project book

30. S-Parameters - Example • LFCN-105_Plus25degC.S2P

31. Mix Series Modeling • Frequency, M and tRise were all taken into account:

32. Sine Signal as MWC Input • Sine wave was used as MWC input • Fp = Fnyq/M = 6.144GHz/261 ≈ 23.5Mhz • Sine wave frequency - 400Mhz ≈ 17 Fp • At the MWC output, we expect to see evenly spaced deltas, by 23.5Mhz between them • Different hardware channels should differ only by amplitude • Results comply with theory Reminder: the mixer is implemented as a Mathematical Multiplier!

33. Sine Signal MWC Output – Zoom Out dB

34. Sine Signal MWC Output dB

35. Simulations – Results & Conclusions • Different kind of simulations had been made, with Constant/variable SNR. For example: • Demonstrate fp ≥ B condition • Comparing Different mixing series • Collapsed vs. non collapsed channels – • m = const { m ≡ q*HardwareChannels } • Demonstrate m ≥ 2N Condition • Demonstrate M ≥ L condition

36. Comparison Method (Reminder) • Comparison Method: Correlation between Original & Recovery Signal: • Where : • c = xcorr(x,y) returns the Cross-Correlation sequence in a length 2N-1 vector, where x and y are length N vectors (if x and y are not the same length, the shorter vector is padded to the length of the longer vector).By default, xcorr computes raw correlation with no normalization. • In the denominator, 2-norm of x and y – for normalization • Matlab code (function handle): CorrXY =@(x,y)max(abs(xcorr(x,y)))/(norm(x,2)*norm(y,2));

37. Different fp comparison • For constant B, sampling with different fp rate • fp= [0.8,1,1.2,1.4]*B were taken • fp ≥ B is necessary for blind recovery

38. Different fp comparison SimulationParameters: Signal – 'sinc‘ Mix Series Type - 'GoldSeries' N = 6 HardwareChannels= 4 q = 5 B = 20Mhz Fp = 16,20,24,28 Mhz M = 499 Fnyq = 6.144Ghz Number of simulations = 10

39. Comparison Between Different Mixing Series - WIP • Series Types: • Random Sequences (Using Matlab Function ‘rndsrc’) • One Random Sequence and it’s shift • Gold Sequence • One Gold Sequence and it’s shift • Lu M Sequences • Lu Lagendre Sequences • SNR = 30

40. Comparison Between Different Mixing Series – Ch=4, q=5 Simulation Parameters: Signal – 'sinc' N = 6 HardwareChannels= 4 q = 5 B = 20Mhz Fp = 24Mhz M = 263 Fnyq = 6.144Ghz SNR = 30dB Number of simulations = 300

41. Comparison Between Different Mixing Series – Ch=20, q=1 Simulation Parameters: Signal – 'sinc' N = 6 HardwareChannels = 20 q = 1 B = 20Mhz Fp = 24Mhz M = 263 Fnyq = 6.144Ghz SNR = 30dB Number of simulations = 120

42. Comparison Between Different Mixing Series • Interim conclusions: • For HardwareChannels=4, q=5: • ‘rndsrc’ – Most of the times gives good results • Lu M and shifted Sequences - Mediocre results • Gold Sequence – best results. • Lu Lagendre – bad results! (most of the timeSupport recovery doesn’t succeed)

43. Comparison Between Different Mixing Series • Interim conclusions: • For HardwareChannels=20, q=1: • ‘rndsrc’ – Best results. • Gold Sequence – Mediocre results. • Lu LagendreSequence – Mediocre results

44. Different M comparison • M ≥ L and M ≥ Mmin is necessary for blind recovery • For constant parameters, sampling with different series length • M = [155, 191, 263, 299] were taken • fp = 24Mhz, q=5, fnyq =6.144*109 • L0 = = 130 • L = 2L0+1 = 261 • M = = 257

45. Different M comparison SimulationParameters: Signal – 'sinc‘ Mix Series Type - 'GoldSeries' N = 6 HardwareChannels= 4 q = 5 B = 20Mhz Fp = 24 Mhz M = [155, 191, 263, 299] Fnyq = 6.144Ghz Number of Simulations = 30

46. Collapsed vs. non collapsed – Sim1 • m≥2N is necessary for blind recovery • For constant parameters, and constant SNR sampling with different number of q & hardware channels • HardwareChannels = [1,2,3,4,6,10,20] were taken • q = [1,3,5,9,15,21] were taken • m ≡ q*HardwareChannels

47. Collapsed vs. non collapsed – Sim1 SimulationParameters: Signal – 'sinc‘ Mix Series Type - 'GoldSeries' N = 6 HardwareChannels= [1:4,6,10,20] q = [1,3,5,9,15,21] B = 20Mhz Fp = 16,20,24,28 Mhz M = 263 Fnyq = 6.144Ghz SNR = 30dB Number of simulations = 30

48. Collapsed vs. non collapsed – Sim2 • Let m ≡ q*HardwareChannels • Setting m = constant, Comparing results for variable SNR • m = 105 was taken • HardwareChannels = [105,35,21,15,1] and respectively q = [1,3,5,7,105] were taken • N = 42 was taken

49. Collapsed vs. non collapsed – Sim2 SimulationParameters: Signal – 'sinc‘ Mix Series Type - 'Gold' N = 42 HardwareChannels = [105,35,21,15,1] q = [1,3,5,7,105] B = 12Mhz Fp = 24 Mhz M = 399 Fnyq = 6.144Ghz Num of simulations = 30

50. Future Challenges • Deeper theory understanding, improving and integrating new technologies into the Matlab code • Solving AWR issues • Combining AWR and Matlab into one seamless system • Implementing the solutions on the actual system • Writing comprehensive literature, covering main methodologies used in AWR