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Waveform Design For Active Sensing Systems – A Computational Approach

Waveform Design For Active Sensing Systems – A Computational Approach. Outline. Introduction Waveform design – Correlation Single sequence Sequence set Correlation lower bound Waveform design – Correlation & Doppler Concluding remarks. Outline. Introduction

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Waveform Design For Active Sensing Systems – A Computational Approach

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  1. Waveform Design For Active Sensing Systems – A Computational Approach

  2. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  3. Outline • Introduction • Waveform design – Correlation constraint • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  4. Active Sensing System • Radar, Sonar, Medical imaging, Wireless Channel Estimation The goal is to determine properties of targets or propagation medium by transmitting waveforms and analyzing returned ones

  5. Christian Hülsmeyer Telemobiloscope designed in 1904 Reginald Fessenden First acoustic communication and echo ranging experiment in 1914

  6. plain pulse Two targets Pulse compression chirp Pulse compression Why Waveform Design • Better target detection Correct detection

  7. Data bits PN code Transmit bits CDMA system Why Waveform Design • Interference reduction Low correlations of PN codes => low inter-user interference

  8. A ‘bad’ beampattern Why Waveform Design • More flexible beampattern Ultrasound hyperthermia treatment for breast cancer Focal point of the acoustic power needs to match the tumor region

  9. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  10. We want to estimate Waveform Model • Received waveform

  11. correlation sidelobes Design Criterion • Matched filter estimate Auto-correlation of {x(n)} We aim to minimize correlation sidelobes to reduce interference Unit-modulus constraint

  12. Auto-correlation of Barker-7 Existing Waveforms • Binary • Barker code Best binary code in terms of low correlation. But lengths <= 13

  13. Binary • M sequence, aka., PN (pseudo noise) code Easy to generate. Low correlation sidelobes • Polyphase • Golomb sequence Closed-form formula. Low correlation sidelobes.

  14. Wanted: Lower Correlation Sidelobe Can we get lower correlation sidelobes?

  15. Q I Unit-modulus Constraint • Arbitrary phases in [0,2π] An AWG (arbitrary waveform generator), B&K Precision More degrees of freedom => better control of correlation sidelobes We aim to develop computational algorithms, which generate unit-modular sequences with lower correlation sidelobes

  16. CAN (Cyclic Algorithm New) • Minimize the ISL (integrated sidelobe level) metric From time to frequency domain From quartic to quadratic auxiliary phases

  17. CAN • Phase retrieval in optics • Gerchberg & Saxton, 1972 Dr. W. Owen Saxton Computationally efficient. Local convergence. Dependent on Initializations.

  18. Example – Merit Factor • Random-phase sequence, M-sequence, Golomb vs. CAN(G) Merit Factor CAN gives the largest Merit Factor, i.e., the smallest correlation sidelobes

  19. Example – Correlation Level M-seq & Golomb Random-phase & CAN CAN gives the lowest correlation sidelobes

  20. e.g., make small WeCAN (Weighted CAN) • Extend CAN to WeCAN

  21. Example – Channel Estimation The significant channel taps can occur up to a certain max delay P (P < N) Matched filter estimate r(1), …, r(P-1) can be minimized by WeCAN

  22. Example – Channel Estimation • Comparison of Golomb and WeCAN WeCAN provides a lower estimation error than Golomb

  23. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  24. A Set of Sequences Auto- & cross-correlation CDMA System MIMO Radar

  25. Multi-CAN & Multi-WeCAN • Multi-CAN minimizes ISL (auto-correlation sidelobes and all cross-correlations) From time to frequency domain • Multi-WeCAN minimizes weighted ISL

  26. Example – MIMO Radar Imaging Sequence length N=256, M=4 antennas, Targets in P=30 range bins Use a “plain” waveform Use Multi-WeCAN waveform

  27. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  28. Correlation Lower Bound ISL lower bound, 1999 Dr. Dilip Sarwate Multi-CAN sequence sets approach the lower bound closely

  29. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  30. Correlation + Doppler Doppler effect • Ambiguity function (AF) Time delay & Doppler shifts AF is a two-dimensional extension of the auto-correlation function

  31. where AF of a chirp signal(T=10 s, B=5 Hz) 2D 3D Properties of Ambiguity Function (AF) • Maximum value at (0,0) • Symmetry • Constant volume

  32. Dr. Philip Woodward Ambiguity Function (AF) • Desired AF shape • Doppler-tolerant (a high ridge) • Doppler-sensitive (thumbtack) “Probability and Information Theory, with Applications to Radar”, 1953 A heartfelt statement… “The reader may feel some disappointment, not unshared by the writer, that the basic question of what to transmit remains substantially unanswered.” But we can still analyze…

  33. AF of Golomb and CAN(G) Golomb Doppler-tolerant CAN(G)

  34. AF of Random-phase and CAN(R) Random-phase Doppler-sensitive CAN(R)

  35. All values of are contained in Minimize AF Sidelobes in a Region • Minimization of discrete-AF sidelobes in a region Minimizing AF sidelobes  minimizing correlation sidelobes Previous CAN-type algorithms can be used

  36. Example – Minimize AF Sidelobes • Design a unit-modulus sequence of N=100. K=10, P=3 Low sidelobes in the central rectangular region

  37. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • (Waveform design – other constraints) • Concluding remarks

  38. track jam Waveform for Spectrum constraints Avoid reserved frequency bands Avoid the jamming frequency band

  39. Waveform for Wideband Beampattern Phased array Waveform diversity leads to more flexible beampattern

  40. Outline • Introduction • Waveform design – Correlation • Single sequence • Sequence set • Correlation lower bound • Waveform design – Correlation & Doppler • Concluding remarks

  41. Concluding Remarks • Importance of waveform design for active sensing • Range compression, CDMA, channel estimation, beampattern • New computational algorithms of waveform design • Correlation, correlation + Doppler, correlation + spectrum • Unit-modulus (arbitrary phases => more degrees of freedom) • Better performance than existing waveforms

  42. Thanks much

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