Look up Table Calibration Aperture ES Antenna Arrays

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