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Single Electron Spin Detection Slides For Uno Interview

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Single Electron Spin Detection Slides For Uno Interview

  1. 1. Detection in Single Electron Spin Microscopy Huimin Chen * Jos é M.F. Moura Department of Electrical and Computer Engineering Carnegie Mellon University * Visiting researcher at CMU Department of Physics and Astronomy University of California, Los Angeles
  2. 2. M olecular O bservation S pectroscopy A nd I maging using C antilevers <ul><li>The aim: To create a non-invasive, position sensitive, single atom resolution, analytical device at UCLA </li></ul><ul><li>First giant step: a prototype of single electron spin microscope (SESM) </li></ul>
  3. 3. M olecular O bservation S pectroscopy A nd I maging using C antilevers (Cont’d) <ul><li>DSP Algorithm Development at CMU: To search for the best weak signal detection algorithm and implement it with a computer cluster for real time signal probe </li></ul>Best hope: Have a very weak sinusoid signal with phase incoherence at the readout, buried by large shot noise
  4. 4. Outline <ul><li>Formulation of the Electron Spin Signal Detection Problem </li></ul><ul><li>Several Detection Schemes Based on Different Assumptions about the Signal Model </li></ul><ul><li>Performance Comparison </li></ul><ul><li>Implementation Issues </li></ul><ul><li>Conclusions and Future Work </li></ul>
  5. 5. Problem Formulation
  6. 6. Detection Schemes <ul><li>1. Energy Detector </li></ul><ul><li>Assumption: we do not know anything about s [ n ] </li></ul>Performance for large N where
  7. 7. Detection Schemes (Cont’d) <ul><li>2. Matched Filter </li></ul><ul><li>Assumption: we know everything about s [ n ] </li></ul>The best performance one can achieve Energy detector and matched filter set two extremes about the knowledge of the signal.
  8. 8. Detection Schemes (Cont’d) <ul><li>3. Power-Law Detector </li></ul><ul><li>Assumption: s [ n ] is a narrowband process </li></ul><ul><li>Segment data x into L blocks, take FFT and get magnitude squared observations (in frequency domain) for each block X j . </li></ul>The power ν = 2.4 is the best compromised value when the signal extent is unknown. X j = [ X 1 j X 2 j … X Kj ], j =1,…, L where
  9. 9. Detection Schemes (Cont’d) <ul><li>4. M -Quadratic Detector ( M -Envelop Detector) </li></ul><ul><li>Assumption: known signal frequency f 0 and the mean phase coherence time </li></ul><ul><li>Segment data into M blocks; calculate the quadratic “envelop” for each block; take the average. </li></ul><ul><li>M depends on the expected number of samples per one phase jump. </li></ul>
  10. 10. Detection Schemes (Cont’d) <ul><li>5. Generalized Likelihood Ratio (GLR) Detector Assumption: known signal frequency, amplitude, initial phase and mean phase coherence time </li></ul><ul><li>Estimate the signal phase (jump or not); plug in the estimates and do the “matched filter”, also known as the estimator-correlator . </li></ul><ul><li>Two approaches are considered for phase estimation. </li></ul>
  11. 11. Two GLR Detection Schemes <ul><li>GLR-DP: Model the phase jump as a two-state Markov chain and find the most likely phase path using dynamic programming (DP). </li></ul><ul><li>GLR-Bayes: Model the phase jump as a two-state Markov chain and find the phase jump probability recursively by applying Bayes formula. </li></ul>
  12. 12. Simulation Settings <ul><li>Sample frequency f s = 10MHz </li></ul><ul><li>Signal frequency f 0 = 2.5MHz </li></ul><ul><li>Random phase jump: Poisson process with mean phase coherence time = 10 μ s </li></ul><ul><li>Use 1000 Monte Carlo runs for each hypothesis (noise only and signal present). </li></ul><ul><li>Fix probability of false alarm P FA =0.05 and find the detection probability P D for each detector under various SNR ( A 2 /2). </li></ul>
  13. 13. P D vs. SNR, 20000 Samples per Sequence , with f 0 =2.5MHz, mean phase coherence time=10 μ s
  14. 14. P D vs. N , SNR is − 27dB, with f 0 =2.5MHz, mean phase coherence time=10 μ s
  15. 15. Summary of the Simulation Results <ul><li>The more we know about the statistics of the signal, the better performance (in terms of the SNR gains) we can achieve. </li></ul><ul><li>However, estimating phase jumps is bad when the phase jump occurs quite often: the GLR detectors perform worse than the M- quadratic detector. </li></ul><ul><li>The power-law detector is preferred over the energy detector due to the narrowband nature of the signal. </li></ul><ul><li>The M- quadratic detector has the best performance but still leaves a large gap compared with the ideal matched filter. </li></ul>
  16. 16. Implementation Issues <ul><li>Computer cluster: 64-node, newly installed at McGowan Center </li></ul><ul><ul><li>Dual CPU per node, Athlon MP CPUs with AMD-760 MPX chipset, as a server mainly for the study of fMRI </li></ul></ul><ul><ul><li>Redhat Linux 7.2 with MPI library installed </li></ul></ul><ul><ul><li>Grand total cost: $322,300 (provided by Microway, Inc.) </li></ul></ul><ul><li>All detectors implemented using C and MPI </li></ul><ul><ul><li>Each slave node processes the data separately and sends the test statistic to the master node. </li></ul></ul><ul><ul><li>Computational time drops almost linearly with the number of nodes (by ignoring the overhead effect). </li></ul></ul><ul><li>For each detector, we estimate the average computation time per sequence (65536 samples). </li></ul>
  17. 17. Comparison of Total Simulation Time: Parallelization by using more computing nodes
  18. 18. Average Computation Time per One Data Sequence (65536 Samples) All detection schemes can be implemented for real time signal probe.
  19. 19. Conclusions and Future Work <ul><li>Several detection schemes are developed (with real time implementations) and compared with the ideal matched filter. </li></ul><ul><li>Detection performance improves with more knowledge about the characteristics of the signal. </li></ul><ul><li>The M -quadratic detector gains 7dB over the energy detector and the computation time is less than twice of the energy detector. There is still a 14dB gap compared with the ideal matched filter. </li></ul><ul><li>Future work: Develop optimal quadratic detection scheme and transfer the MPI code to UCLA to start searching the single electron spin signal. </li></ul>
  20. 20. Other Research Experiences <ul><li>Flow control and traffic management for high speed networks </li></ul><ul><li>Fractal signal analysis </li></ul><ul><li>Neural networks and genetic algorithm </li></ul><ul><li>Game theoretic approach for decentralized pricing and resource allocation </li></ul><ul><li>Target detection and tracking </li></ul><ul><li>Data association and sensor data fusion </li></ul>

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