1 waveform design for active sensing systems – a computational approach
TRANSCRIPT
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Waveform Design For Active Sensing Systems – A Computational Approach
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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Outline
• Introduction
• Waveform design – Correlation constraint Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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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
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Christian Hülsmeyer
Reginald Fessenden
Telemobiloscope designed in 1904
First acoustic communication and echo ranging experiment in 1914
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• Better target detection
Why Waveform Design
Pulse compression
Correct detection
plain pulse Two targets
Pulse compression
chirp
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• Interference reduction
Why Waveform Design
CDMA system
Data bits
PN code
Transmit bits
Low correlations of PN codes => low inter-user interference
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Why Waveform Design
• More flexible beampattern
Ultrasound hyperthermia treatment for breast cancer
Focal point of the acoustic power needs to match the tumor region
A ‘bad’ beampattern
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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Waveform Model
• Received waveform
We want to estimate
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Design Criterion
• Matched filter estimateAuto-correlation of {x(n)}
correlation sidelobes
We aim to minimize correlation sidelobes to reduce interference
Unit-modulus constraint
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Existing Waveforms
• Binary Barker code
Auto-correlation of Barker-7
Best binary code in terms of low correlation. But lengths <= 13
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• Binary M sequence, aka., PN (pseudo noise) code
• Polyphase Golomb sequence
Easy to generate. Low correlation sidelobes
Closed-form formula. Low correlation sidelobes.
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Wanted: Lower Correlation Sidelobe
Can we get lower correlation sidelobes?
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• Arbitrary phases in [0,2π]
I
Q
An AWG (arbitrary waveform generator), B&K Precision
Unit-modulus Constraint
We aim to develop computational algorithms, which generate unit-modular sequences with lower correlation sidelobes
More degrees of freedom => better control of correlation sidelobes
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CAN (Cyclic Algorithm New)
• Minimize the ISL (integrated sidelobe level) metric
auxiliary phases
From time to frequency domain
From quartic to quadratic
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CAN
• Phase retrieval in optics Gerchberg & Saxton, 1972
Computationally efficient. Local convergence. Dependent on Initializations.
Dr. W. Owen Saxton
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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
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Example – Correlation Level
M-seq & Golomb Random-phase & CAN
CAN gives the lowest correlation sidelobes
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WeCAN (Weighted CAN)
• Extend CAN to WeCAN
e.g., make small
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Example – Channel Estimation
Matched filter estimate
The significant channel taps can occur up to a certain max delay P (P < N)
r(1), …, r(P-1) can be minimized by WeCAN
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• Comparison of Golomb and WeCAN
Example – Channel Estimation
WeCAN provides a lower estimation error than Golomb
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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A Set of Sequences
Auto- & cross-correlation
MIMO Radar
CDMA System
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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
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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
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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Correlation Lower Bound
ISL lower bound, 1999
Dr. Dilip Sarwate
Multi-CAN sequence sets approach the lower bound closely
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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Correlation + Doppler
Doppler effect
• Ambiguity function (AF)
AF is a two-dimensional extension of the auto-correlation function
Time delay & Doppler shifts
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Maximum value at (0,0) Symmetry Constant volume
Properties of Ambiguity Function (AF)
where
3D 2D
AF of a chirp signal (T=10 s, B=5 Hz)
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Ambiguity Function (AF)
• Desired AF shape Doppler-tolerant (a high ridge) Doppler-sensitive (thumbtack)
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.”
Dr. Philip Woodward
“Probability and Information Theory, with Applications to Radar”, 1953
But we can still analyze…
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AF of Golomb and CAN(G)
Golomb
CAN(G)
Doppler-tolerant
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AF of Random-phase and CAN(R)
Random-phase
CAN(R)
Doppler-sensitive
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Minimize AF Sidelobes in a Region
• Minimization of discrete-AF sidelobes in a region
All values of are contained in
Minimizing AF sidelobes minimizing correlation sidelobes
Previous CAN-type algorithms can be used
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Example – Minimize AF Sidelobes
• Design a unit-modulus sequence of N=100. K=10, P=3
Low sidelobes in the central rectangular region
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• (Waveform design – other constraints)
• Concluding remarks
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Waveform for Spectrum constraints
Avoid reserved frequency bands
Avoid the jamming frequency band
track
jam
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Waveform for Wideband Beampattern
Phased array
Waveform diversity leads to more flexible beampattern
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Outline
• Introduction
• Waveform design – Correlation Single sequence Sequence set Correlation lower bound
• Waveform design – Correlation & Doppler
• Concluding remarks
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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
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Thanks much