Transcript
Application of Look-Up-Table Calibration to Large Aperture ES Antenna Arrays Peter Ly ES Techniques Group Electronic Warfare and Radar Division
Overview
Background
Large Aperture AOA Estimation & Calibration
Small Aperture AOA Estimation & Calibration
Experimental Results
Conclusion
BACKGROUND
Electronic Support Electronic support (ES) receivers intercept radar signals for selfprotection and surveillance purposes. ELECTRONIC SUPPORT Onboard radar transmits a signal
Aircraft Radar receives the return signal and processes it to determine information about the target
Target can intercept the aircraft’s radar signal first
Radar Target
Objective To apply calibration methods to obtain fast and accurate AOA estimation from a large aperture antenna array. ELECTRONIC SUPPORT Onboard radar transmits a signal
Aircraft Radar receives the return signal and processes it to determine information about the target
Target can intercept the aircraft’s radar signal first
Radar Target
Electronic Support (ES) Testbed BPF
Limiter
LNA
2-18GHz
Amplifier
BPF
0dB-30dB
750MHz - 1250MHz
fLO BPF
Limiter
LNA
2-18GHz
Amplifier
BPF
0dB-30dB
750MHz - 1250MHz
10
FPGA
10
fs = 1333 MSPS fLO BPF
Limiter
LNA
2-18GHz
Amplifier
BPF
0dB-30dB
750MHz - 1250MHz
PC
fLO BPF
Limiter
LNA
2-18GHz
Amplifier
BPF
0dB-30dB
750MHz - 1250MHz
fRF = 2 – 18 GHz fLO fREF = 10 MHz
fIF = 1 GHz BW = 500 MHz
10
fs = 1333 MSPS
FPGA
10
Phase Errors Practical systems have phase errors which can arise due to:
Hardware imperfections Imperfect antenna separations Mutual coupling Cross-talk
The phase errors are generally a function of:
Signal power (amplitude) Frequency Temperature AOA
Uncalibrated Signal Model
AOA-dependent phase error is hardware specific and cannot be changed without changing the hardware
Calibration Data Calibration data needs to be collected using “over the air” transmissions in a RF quiet environment
MDRx
Calibration Data The phase errors in each channel can be quantified by measuring the phase delays from signals at known AOA. This needs to be performed at each frequency of interest. Can also be conducted at each amplitude and temperature of interest.
Channel 1 Channel 2 Channel K
Example of a calibration table at a specific amplitude, frequency and temperature of interest.
Simple Calibration Method
Uncalibrated Signal
Calibrated Signal
+
AOA Estimation
Simple Calibration Method A simple calibration method may be as follows:
Uncalibrated Signal
Calibrated Signal
+
Circular dependency on the AOA
AOA Estimation
The phase error is a function of the AOA. The AOA must be known prior to calibration to determine the appropriate compensation. The AOA can only be estimated from the calibrated signal.
Integrated Calibration Method It is possible to perform AOA estimation using the uncalibrated data as follows:
Uncalibrated Signal
AOA Estimation
The AOA estimation algorithm must incorporate the calibration data into the AOA estimation.
Integrated Calibration Method If desired, the estimated AOA can be used to obtain the calibrated signal.
Uncalibrated Signal
AOA Estimation
Uncalibrated Signal
Calibrated Signal
+
AOA Estimation & Calibration
LARGE APERTURE
Interferometry
Short-Baseline Interferometry Short-baseline interferometers have a unique relationship between the measured phase delays and the AOA. Azimuth vs Measured Phase Delays (Short Baseline) 80
Estimated Azimuth (deg)
60 40 20 0
Unique Relationship
-20 -40 -60 -80 -150
-100
-50 0 50 Measured Phase Delay (deg)
100
150
Long-Baseline Interferometry Long-baseline interferometry is ambiguous!
Azimuth vs Measured Phase Delays (Long Baseline) 80
Estimated Azimuth (deg)
60 40 20 0
Non-Unique Relationship
-20 -40 -60 -80 -150
-100
-50 0 50 Measured Phase Delay (deg)
100
150
Long Baseline Interferometry The set of ambiguous phase delays from multiple long baselines will be unique for each AOA if the baselines are relatively prime. 1
2
3
4
…
K
The set of phase delays in each column is unambiguous
Correlative Interferometry Search through a 2D Look-Up-Table 92˚ -139˚
Measured Phase Delays
45˚
132˚ 175˚ -140˚ -94˚ -47˚
0˚
47˚
Pre-Computed, Ideal, Phase Delays
-172˚ -71˚
141˚ -110˚
0˚
110˚ -141˚ -34˚
71˚
172˚
-80˚ 114˚ -46˚ 156˚
0˚
-156˚ 46˚ -114˚ 80˚
-91˚
Corresponding AOA
-25˚ -20˚
91˚
34˚
-15˚
-10˚
-5˚
0˚
5˚
94˚
10˚
140˚ -175˚ -132˚
15˚
Estimated AOA
20˚
25˚
Long Baseline Interferometry with Phase Errors
Long Baseline Interferometry with Phase Errors
Satisfied if relatively prime
Long Baseline Interferometry with Phase Errors
Long Baseline Interferometry with Phase Errors
Unlikely to be satisfied
Correlative Interferometry Correlative interferometry still works on uncalibrated data Replace ideal phase delays with the measured phase delays 92˚
Measured Phase Delays
-139˚ 45˚
Pre-Computed, Ideal, Phase Delays
132˚ 175˚ -140˚ -94˚ -47˚
0˚
47˚
-172˚ -71˚
141˚ -110˚
0˚
110˚ -141˚ -34˚
71˚
172˚
-80˚ 114˚ -46˚ 156˚
0˚
-156˚ 46˚ -114˚ 80˚
-91˚
Corresponding AOA
-25˚ -20˚
91˚
34˚
-15˚
-10˚
-5˚
0˚
5˚
94˚
10˚
140˚ -175˚ -132˚
15˚
Estimated AOA
20˚
25˚
AOA Estimation & Calibration
SMALL APERTURE
SODA Interferometry Virtual Array
Azimuth vs Measured Phase Delays (Virtual Array)
80
80
60
60
40
40
Estimated Azimuth (deg)
Estimated Azimuth (deg)
Azimuth vs Measured Phase Delays (Long Baseline)
20 0 -20 -40
20 0 -20 -40
-60
-60
-80
-80 -150
-100
-50 0 50 Measured Phase Delay (deg)
100
150
-150
-100
-50 0 50 Measured Phase Delay (deg)
100
150
Short-Baseline Interferometry
Azimuth vs Measured Phase Delays (Short Baseline) 80
This unique relationship can be implemented as a 1D Look-Up Table (LUT)
Estimated Azimuth (deg)
60 40 20 0 -20 -40 -60 -80 -150
-100
-50 0 50 Measured Phase Delay (deg)
100
150
Uncalibrated Signal Model
For simplicity, it is assumed that these phase errors are for a specific amplitude, frequency and temperature
Implications for SODA Interferometry
Example 1: Constant Phase Error Example of a Constant Phase Error 200 150
Phase Error (deg)
100 50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Example 1: Constant Phase Error Phase Delays vs Azimuth (Constant Phase Error) 200 Calibrated Uncalibrated
150
Relationship is offset but still unique
Phase Delay (deg)
100
Unambiguous AOA estimation can still be performed
50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Example 2: Monotonic Phase Error Example of a Monotonic Phase Error (Linear - Ramp Down) 200 150
Phase Error (deg)
100 50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Example 2: Constant Phase Error Phase Delays vs Azimuth (Monotonic Phase Error - Linear Ramp Down)
Relationship is scaled but still unique for all angles
200 Calibrated Uncalibrated
150
Phase Delay (deg)
100
Unambiguous AOA estimation can still be performed
50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Effectively a shorter baseline and so the AOA estimation performance in noise is worse
Example 3: Monotonic Phase Error Example of a Monotonic Phase Error (Linear - Ramp Up) 200 150
Phase Error (deg)
100 50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Example 3: Monotonic Phase Error Relationship is scaled and no longer unique for all angles
Phase Delays vs Azimuth (Monotonic Phase Error - Linear Ramp Up) 200 Calibrated Uncalibrated
150
Phase Delay (deg)
100
Unambiguous AOA estimation cannot be performed for all angles without further ambiguity resolution
50 0 -50 Ambiguities -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Effectively a longer baseline and so the AOA estimation performance in noise is better
Example 4: Non-Monotonic Phase Error Example of a Non-Monotonic Phase Error (Sinusoid) 200 150
Phase Error (deg)
100 50 0 -50 -100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Example 4: Non-Monotonic Phase Error Phase Delays vs Azimuth (Non-Monotonic Phase Error - Sinusoidal) 200 Calibrated Uncalibrated
150
Relationship is no longer unique for all angles
Ambiguity
Phase Delay (deg)
100
Ambiguity
50
Unambiguous AOA estimation cannot be performed without further ambiguity resolution
0 -50
Ambiguity
-100 -150 -200 -100
-80
-60
-40
-20 0 20 Azimuth (deg)
40
60
80
100
Implications for SODA Interferometry
EXPERIMENTAL RESULTS
Antenna Positions
Uncalibrated Phase Delays vs AOA Wrapped, uncalibrated and ambiguous! d31 Baseline
200
200
150
150
100
100
Phase Delay (deg)
Phase Delay (deg)
d21 Baseline
50 0 -50
50 0 -50
-100
-100
-150
-150
-200 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
⦁ Uncalibrated (Measured)
-200 -40
-30
-20
-10
0 10 Azimuth (deg)
△ True (Expected)
20
30
40
50
Calibration Data vs AOA How do you apply the AOA-dependent calibration values? d31 Baseline
200
200
150
150
100
100 Calibration Value (deg)
Calibration Value (deg)
d21 Baseline
50 0 -50
50 0 -50
-100
-100
-150
-150
-200 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
-200 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
Correlative Interferometry The pair of uncalibrated and ambiguous phase delays are unique for every AOA Measured Phase Delays vs Azimuth 200 d21 Baseline 150
d31 Baseline
Phase Delay (deg)
100 50 0 -50 -100 -150 -200 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
Practical Correlative Interferometer
Correlative Interferometer (RMS = 0, f = 9440.6MHz) 50 40 30 20 10 0 -10 -20 -30 -40 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
SODA Phase Delay Phase errors have caused the measured SODA phase delays to be offset, scaled and inverted SODA Phase Delay (f = 9440.6 MHz) 150 Measured Fitted Theoretical
Phase Delay (deg)
100
50
0
-50
-100 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
Practical SODA Interferometer
SODA Interferometer (RMS = 1.4477, f = 9440.6 MHz, SODA Calibration) 50 40 30 20 10 0 -10 -20 -30 -40 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
Comparison Correlative Interferometer SODA Interferometer
Correlative Interferometer (RMS = 0, f = 9440.6MHz)
SODA Interferometer (RMS = 1.4477, f = 9440.6 MHz, SODA Calibration)
50
50
40
40
30
30
20
20
10
10
0
0
-10
-10
-20
-20
-30
-30
-40 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
-40 -40
-30
-20
-10
0 10 Azimuth (deg)
20
30
40
50
Conclusions Large aperture direction finding systems suffer from an AOAdependent phase error as well as ambiguities in the phase delay measurements Practical (unambiguous) interferometers can be implemented using LUTs which “map” uncalibrated phase delay measurements to a corresponding, unique AOA estimate Calibration data must be collected and tabulated prior to AOA estimation Correlative interferometers are implemented using a 2D LUT Better AOA estimation performance The SODA interferometer can be implemented using a 1D LUT Faster computational speed
