Genetically Optimized Periodic, Pseudo-Noise Waveforms for Multi-Function Coherent Ladar

Transcription

1 Genetically Optimized Periodic, Pseudo-Noise Waveforms for Multi-Function Coherent Ladar Matthew P. Dierking Air Force Research Laboratory, Sensors Directorate, Wright-Patterson AFB, Ohio USA Bradley D. Duncan Electro Optics Program, University of Dayton, Ohio USA

2 Presentation Outline Ladar Imaging Background Periodic Pseudo-Noise (PPN) Waveforms Genetic Algorithm (GA) Predicted IPR Experimental System & Results Multi-Notch PPN waveforms for Multiple Apertures Predicted IPR Experimental System & Results Summary 2 of 58

3 Ladar Imaging Background Imaging Beyond the Diffraction Limit Focus on imaging where all targets are within the diffraction limited beam y λ 1.22 R D Unresolved in conventional imaging 3 point targets within beam each with: σ 1 σ 2 v 2 Spatial Location v 1 σ 3 Translational velocity r 1 (t) r 2 (t) v 3 (t)=µv 3 cos(ω 3 t) Vibration Motion For A high bandwidth Gaussian Pulse r(t) r 3 (t) R Delay due to geometry θ D Phase due the range and relative motion Targets 1&2 are unresolved in range D x 3 of 58

4 Ladar Imaging Background Four Ladar Modes Exploit the Additional Information Range Image Uses a single pulse to localize target distributions by range No phase Requirement Range Doppler Image Uses single pulse, or multiple pulses, to localize target distributions by range and gross target motion Large Linear Phase SAL Image Uses multiple pulses with controlled sensor motion to localize targets in range and cross range Quadratic Phase (Stripmap) Micro-Doppler Uses multiple pulses to localizes micro-motions of target distributions by range Phase complex sum of sinusoids Intensity Range Range Cross-Range Range Amplitude τ f D2 Doppler Shift Frequency f D1 4 of 58

5 Single PN Code Bandwidth: Chip length Doppler Tolerance: Number of Chips Variable integration for long range operation and noise reduction Periodic PN Code Detect/reject gross Doppler Adaptive Doppler Sensitivity (Doppler SAL µ-doppler) Enhanced Compression via Diversity Multiple TDM Codes MIMO CDMA PPN Measure Phase Between Apertures Shorten Aperture Time Cross Track Imaging Gain PPN Waveform PPN & CDMA Taxonomy +1 - Nc A t = ( ) a k n= kn p T ( t nt ), Tx 1 Tx 2 1 t N T c Single PN Code Periodic PN Code Multi-CodeTDM PPN Multiple Aperture CDMA PPN Rx 1 Rx 2 5 of 58

6 PPN Waveform Requirements & IPR High Peak to Side Lobe Ratio Minimize off axis peaks/ghosting High Integrated Side Lobe Ratio Maximize image contrast Doppler Sensitivity/Tolerance Long or Repetitive Waveform High Average Energy Continuous Waveform Efficient Amplifier Operation PPN waveform Random side lobe structure PNN Waveform IPR ISLR ~ 1/N c PLSR ~ 6 db worse Can do better! 6 of 58

7 PNN Waveform Optimizing the Waveform IPR To Do Better, Exploit Ranges Depth it small Energy under the waveform ambiguity function is conserved Find Codes to Squeeze energy from the IPR ROI Allow noise to grow outside the ROI PNN Waveform IPR Range Depth Allow Growth Question is then: How to Find the Codes? Suppress Side Lobes Around Main lobe 7 of 58

8 Genetic Algorithm IPR Optimization Genetic Search Efficiently Search 2 Nc possible codes Make small perturbations Prune: Keep improved results/paths only Genetic Algorithm Break waveform into Genes Equal lengths are used Smaller than structure trying to generate Mutate a Gene with a New Random Code 2 2 Evaluate Cost Function PSL + ISL Force Ghost to be Low (PSLR) Force Contrast to be High (ISLR) Repeat for each gene sequentially 1111 Discard Mutation No Generate Length 2*Nc PNN Code Loop over Genes Random Gene Mutation Calculate PSLR & ISLR RMS Improved Yes Save Modified Gene T. Bucciarelli, A. Marone, M. Minorenti, and R. Parisi, Genetic Algorithms and Radar Code Design,Proceedings of the 8 th International Conference on Signal Processing Applications and Technology 8 of 58

9 Example Search Code Length N c =2 Gene Length =1 Chips N Genes = N c /Gene = 2 Genetic Algorithm IPR &Algorithm Convergence Convergence fast compared to exhaustive search of 2 Nc Possibilities ~1 successful mutations in 1,, trials Most gain found within the first 1, Random Selection ISLR:~ 43 db 1/Nc GA Results: 6 to 1 db improvement GA-PSLR Original ISLR GA-ISLR Significant Improvements based only on code selection ISL [db] Matched Filter Output [db] PSL [db] Lag [ns] 9 of 58

10 Genetic Algorithm Experimental Block Diagram Experimental Demonstrations GA-PPN Code Implementation Optical Transmission/Reception IPR Resolution & side lobe performance Phase Recovery CNR impacts System Characteristics 1.55 µm CW system 1 GHz phase modulator driven by AWG Transmit leg attenuator & power meter used to monitor transmit power for CNR excursions Quadrature detection MO 96/4 Fiber Splitter IQ Demod 1 GHZ V G 1 1 GHz PM AWG PC DSP 12 in OAP collimator Variable Attn Waveform 1 MHz Sync Power Meter 96/4 Fiber Splitter Optical Return Target TR Switch Optical Trigger 4 GHz ADC TEK AWG7 I:CH1 Q:CH2 1 of 58

11 GA-PPN waveform Code Length N c =2 Notch 5 ns Gene Length =1 Chips Genetic Algorithm Theoretical & Measured IPRs High Single waveform CNR (>1) Ideal IPR i.e. PPN waveform convolved with itself Dashed line side lobe ISLR (σ 2 ) Bottom plot shows the measured IPR Results IPR Notch fully realized at high CNR Achieved theoretical resolution Genetic Algorithm IPR [db] Genetic Algorithm IPR [db] Ideal -5 5 Lag [ns] Measured GA PPN Measured PPN -5 5 Lag [ns] 11 of 58

12 -1 Genetic Algorithm Sub-Code Processing Sub Code Processing Adapt Energy & Doppler Sensitivity Single code produces slightly higher peak side lobes Optimization over composite code Follows theory line N codes increases Provides improvement over random code after Notch develops N Codes =1 N Codes =2 PSLR [db] SubCodes Processed [#] -1 Output [db] -2-3 Output [db] Time [ns] Time [ns] 12 of 58

13 Genetic Algorithm CNR Excursions: PSLR/ISLR Performance as a function of CNR PPN waveform with N c =2, and T c =1ns Maximum Single waveform CNR set to provide full notch realization (~unity) Transmit energy varied by adjusting the transmit leg attenuator Receiver operation conditions unchanged Both PSLR & ISLR match very well Improvements maintained over CNRs PSLR [db] ISLR [db] All GA Theory Attenuation [db] All GA Theory Attenuation [db] 13 of 58

14 Multi-Notch GA-PPN Two MIMO Aperture 2 MIMO Apertures via fiber delay Transmit undelayed and delayed copies of PPN waveform from separate apertures Delayed waveforms are orthogonal Transmit 2m Fiber Delay 5/5 Fiber Splitter CN C1 C2 CN-1 D U R D1 R U1 C1 C2 C3 CN D U A Recombined on reception Each aperture collects it own transmission And the signal from the other aperture Single matched filter operation on composite return Produces IPRs from each aperture and with related phase TR Switch Return C1 C2 C3 CN CN C1 C2 CN-1 CN-1 CN C2 CN-2 C1 C2 C3 CN UU UD DD UU DU DD Matched Filter 14 of 58

15 Multi-Notch GA-PPN Multiple TDMA/CDMA signals appear time delayed in a single record Multiple notched IPR required at delay locations GA modified to suppress 2 notches Convergence is slower but comparable 2 notch IPR shown ISL [db] PSL [db] Matched Filter Output [db] Matched Filter Output [db] Delay [chips] x Delay [chips] x of 58

16 Multi-Notch GA-PPN 2-Channel MIMO Experiment Block Diagram Experimental Demonstrations Multiple CDMA transmission/reception Time delay MIMO approach 5/5 Fiber Splitter 2m Fiber Delay 3.4 mm fiber collimator Target Multiple aperture signals in single return Multiple Aperture Phase Recovery MO Power Meter System Two Transmit/Receive Apertures One Sub-Code Delay (fiber) Remainder of the system unchanged 96/4 Fiber Splitter IQ Demod 1 GHZ 1 GHz PM AWG Variable Attn Waveform 1 MHz Sync 96/4 Fiber Splitter Optical Return TR Switch Optical Trigger V G 1 PC DSP 4 GHz ADC TEK AWG7 I:CH1 Q:CH2 16 of 58

17 Two Apertures 3.4 mm apertures, v-block alignment Single Vibrating Target 3 Hz signal insures multiple phase cycles in measurement time Low displacement amplitude Results Low CNR due to poor short range coupling All paths measured UU,DU,DD Near theoretical resolution on each aperture combination Correctly recovers phase from each aperture Maintains correct phase relationships between the apertures Multi-Notch GA-PPN 2-Channel MIMO Experimental IPR Amplitude [db] Phase [waves] Time [ms] CDMA MIMO Output UU DU DD Time [ms] 17 of 58

18 Summary Genetic Algorithms enhance PPN waveform GA converges quickly GA-IPRs improves performance even at low CNR GA-IPRs improves performance for sub-codes GA can be tailored to produce complex IPRs 2 Notch IPR for MIMO Demonstrated Tapers and others possible by cost function definition IPR & Phase recovery demonstrated for MIMO 18 of 58

19 Questions? j e jωt e -jωt 19 of 58

20 PNN Motivation Wide Time-Bandwidth Requirement Satisfies Bandwidth required for Range Resolution Phase only Modulation Provide agile phase sensitivity required for Range-Doppler SAL - Vibrometry Self Diagnostic Complete record coverage allows ID and Mitigation of Artifacts Supports Phase tracking over a wide variety of Conditions High Energy Waveform Detection with matched filtering depends only on Energy Not Shape CW Enables Long Range Operation Adapts Code Integration TIme Waveform Agility Adjust waveform length and Scanning depending on requirements for CNR, Side lobe Performance, and Doppler Sensitivity Multi-Aperture Phase Recovery with Single Receiver Train Hardware Considerations - Low Peak to Average Power Ratio Minimizes Peak Powers Enables use of saturated Amplifiers Simple/Stable modulation architecture 2 of 58

21 Key Ideas: PN & CDMA Generate and Utilize Multiple Simultaneous waveforms Phase Only Phase & Frequency CDMA Doppler Performance Single Access CAF Use CDMA to transmit and adaptively process multiple orthogonal/diverse waveforms Adaptive Wide Time Bandwidth Product Chip Time Governs resolution Waveform Extent Governs Phase Sensitivity Diversity governs CAF Sidelobe/ambiguity suppression Processing Options Pulse-by-Pulse processing (Amplitude) Sub-Pulse Processing By Code Selection f TDMA FDMA CDMA t PAPR=1 A 1 A k f b 1 b 2 b 3 b 4 b k t LPF Σ f PAPR>1 MF b 1 MF b 2 MF b 3 MF b 4 MF b 5 AF 1 t Σ Complex CAF 21 of 58

22 Ladar Imaging Background Phase Requirement Summary Macro Doppler Phase (dot-dash) Macro motion induces greatest Doppler SAL Phase (dashed line) Smoothly varying parabolic phase Micro-Doppler (solid line) Complex sum of sinusoids Common Requirements Detect and exploit phase Phase [waves] Adaptable Doppler Exploitation/Tolerance Detect and Mitigate Gross Doppler Complete phase record Doppler SAL µ-doppler Time [ms] Range [km] Range [km] Range [km] Doppler SAL Slow-Time [us] Slow-Time [ms] µ-doppler Slow-Time [ms] 22 of 58

23 Genetic Algorithm Convergence with Nc For Each N c, 1 Million gene mutations resulting in ~1 successful mutations The convergence varies with the number of chips Notch reduced as the code becomes a significant fraction of the code length If the ISLR is interpreted as the variance the PSLR could be thought of as the 2σ point 5 ILSR Output [db] PSLR Matched Filter Output [db] Waveform Length [Chips] Lag [ns] 23 of 58

24 Multi-Notch GA-PPN 2-Channel MIMO Wrapped Phase Segment Lower CNRs result in noisier phase estimate Imbalance due to poor near field target coupling Vibration amplitude greater than a wavelength Measured phase segment for 3 Hz signal for each path UU, DU, and DD 3 x 15 UU 2 DU DD x 1 5 Phase [waves] UU DU DD Time [ms] 24 of 58

25 Multi-Notch GA-PPN 2-Channel MIMO Un-wrapped Phase Segment Simulated Phase Nominal phase for small vibration signals from 2 aperture systems Constant phase relationships Measured Phase Low pass filtered and unwrapped Demonstrates the correct frequency Low frequency phase excursions real due to non ideal motion driver Maintains correct phase relationships between the apertures Lower CNRs (coupling) results in noisier phase estimate Phase [waves] Phase [waves] Vertical Offset (3.4mm) UU DU DD Time [ms] UU DU DD Time [ms] 25 of 58

26 Multi-Notch GA-PPN 2-Channel MIMO Experimental Phase Recovery Measured IQ Diagrams of 3 Hz Vibrating Target MIMO with 1 Sub-Code Delay UU, DU, DD Asymmetry due to IQ channel imbalance Removed in post process bottom Stake IQ demodulator alignments Radial distance indicates CNR Imbalance due to poor near field target coupling Vibration amplitude greater than a wavelength x 16-1 UU DU DD x x 15 UU 2 1 DU DD x of 58