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Radar Power Spectral Density
Analysis and Anti-Jam Filtering
Dr. Haroon Rashid
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Motivation Enhance fidelity of Radar system performance
analysis
Signal power spectral density (PSD) analysis PSD Examples
Signal power transfer ratio computation
Radar transmit signal spectrum filters Radar receive front end filters
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Motivation
Jammer filtering
Adaptive nulling phased array antenna modeling
Radar development direction
All analysis and graphs have been produced with
STKv8.1
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Review of STK/Radar Developments Dynamic Radar Jamming Analysis
Dynamic geometric analysis
Object attitude dynamics Frequency, Doppler shift and Bandwidth overlap
analysis
Jamming power computation as seen by the Radar
Radar performance analysis under jamming
Uniform power distribution model used
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Current STK/Radar Developments Protection of radar from jammers
Review jammer signal types
Interaction of jammer signals with the radar signalsreflected from targets
Compute true jammer power as seen by the radar
How to reduce the jammer power into the radar
receiver
Spectrum Filters
Adaptive nulling phased array antennas
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Power Spectral Density (PSD) Relationship between the signal power and the
bandwidth (viewed in frequency domain)
The basic units are Watts/Hz The power of a waveform can be precisely defined
The bandwidth usually extends to infinity and hasto be defined (-3 dB or Null-to-Null bandwidth) or
limited by filters The PSD is symmetric, i.e. PSD (f) = PSD (-f)
Non-symmetric PSD can be engineered
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RAdio Detection And Ranging
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Radar Equation
43
2
)4( R
LLLLGLGP
r
TxLprrtttP
=
p
sl
G is Gain, L is Loss, R = Range
Radar bandwidth is wide enough to receive all the power
spread over the band.
Targets Radar Cross Section (RCS) may impact parts of
the spectrum differently
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Radar Cross Section (RCS) Each object has a RCS signature
Measure of the fractional power reflected from a target
= GCS x reflectivity x directivity GCS is the Geometric cross-sectional area of the target
Reflectivity is the ratio of the scattered power to the incident power
Directivity is the ratio of the backscatter power to the total isotropic
power
Reflectivity and the directivity are functions of the frequency
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Jammer Types Wideband, white noise
Wideband, colored noise
Narrowband
Single frequency, Continuous wave (CW)
Pulsed
Transponders with delay
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Continuous Wave Radar signal Ideal carrier
Pure sine wave
Bandwidth 1Hz
Real CW signal
Jitter
Drift
Significant bandwidth
Frequency (Hz)
Power
Frequency (Hz)
Power
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CW Radar Signal Model PSD is modeled as a normalized Gaussian curve
User specified RF bandwidth is used as a
reference The power density is spread over the RF
bandwidth as a 6 sigma Gaussian curve
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Gaussian PSD Model
2
2{ }2
6
2
( )
Limit
Limit
f
x
Bwx
PSD f e
s
s
-
=
=
=
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CW Radar PSD
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Pulsed Carrier Radar Signal
tau is the pulse width
T is the pulse period NT is total signal duration
T
tau
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Pulsed Carrier Radar Signal Radar signal is transmitted as series of pulses
Pulse width tau determines the spread of the
spectrum Pulse repetition period T
Pulse repetition Frequency (PRF) = 1 / T
Total signal duration is NT
N is the number of pulses
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Pulsed Radar Signal PSD Model
0
1
0 0
(( ) ) ( )2 2
[ ( ) ( ) ]
2 2
c
n
c c
NTSinc Sinc n
NT NTSinc n Sinc n
t
w w w
w w w w w w
=- +
- + + - -
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Pulsed Radar Signal Model contd
02
2
2
r
c c
fT
f
T pulseperiod
pulsewidthNT SignalDuration
pw p
w p
t
= =
=
=
==
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Pulsed Radar Signal PSD
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Pulsed Radar Signal Model
0
1
0 0
(( ) ) ( )2 2
[ ( ) ( ) ]
2 2
c
n
c c
NTSinc Sinc n
NT NTSinc n Sinc n
t
w w w
w w w w w w
=- +
- + + - -
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Pulsed Radar Signal PSD
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Radar Pulsed Signal Expanded PSD
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Spectrum Filters Filters change the shape of the power spectrum
density (PSD) curves
Allow transmitted signal to conform to theregulation (or the allocated spectrum)
Bandwidth
Total power
PSD
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Filtered Spectrum
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Radar Receiver Matched Filters Match the receiver filter transfer function to the
received signal characteristics
Produce maximum instantaneous S/N ratio (SNR)in the presence of white noise
Referred to as optimum filters in the SNR sense
Perfect matching is difficult to achieve. Some
degree of degradation in real system occurs
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Matching Signal/Receiver Bandwidths Radar signal spectrum is adaptively sampled 6
Sigma or from -15 Nulls to +15 Nulls of thespectrum band
The received spectrum is dynamically adjusted forthe Doppler shift due to the relative velocity of theRadar and the target
Adaptive sampling matches the step size to the
Radars transmit side bandwidth
All signal power within the Radar LNAs bandwidthis captured
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Bandwidth Overlap Ratio Signal spectrum is convolved with the Radars
front end bandwidth
Radar bandwidth to signal PSD ratio is computedon a (0-1) normalized scale
0 represents no bandwidth overlap between the
reflected signal and the receiver
1 represents the 100% of the signal power
received by the receiver
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Signal PSD and Matched Filtering
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Radar PDet no filtering
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PDet with wideband Filter
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Radar PDet with Narrowband Filter
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Phased Array Antennas Hundreds to thousands of
radiating elements are
combined to form the
desired antenna gainpattern
The phase, power, and
frequency of the signal to
each element is computed
and controlled Patriot Phased Array Antenna
(courtesy Wikipedia)
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Phased Array Adaptive Nulling Antenna
Add a spatial dimension to the signal processing to
improve S/N ratio
Adapts the gain pattern by steering the main beamin the direction of the desired signal
Create antenna gain null patterns towards
jammers
STK models the Least Mean Squared (LMS)steepest decent adaptive nulling algorithm
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Adaptive Nulling Algorithms
LMS steepest descent
Howells-Applebaum
Sample Covariance Matrix Inversion
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S
Array Output
Adaptive Antenna Schematic
W
W
W
S
Reference Signal
Error Signal
-
+
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Forming a Pattern Null
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Un-Adapted Pattern
18.77
-1
-2
-3
-5
-10
-20
-20
-20
-20 -20
-20
-20
-30
-30-30
-30
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Adapted Pattern
16.85
-1
-2
-3
-5
-10
-10
-20
-20
-20
-20-2
-20
-30
Jammer
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Adaptive Nulling Phased Array
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Radar Development Direction Radar SAR plug-in constraint
National Imagery Interpretability Rating Scale (NIIRS)
Radar Search/Track plug-in constraint Probability of object detection
Radar system polarizations
Transmit signal polarization
Radar receive antenna polarization
Target RCS polarization
Pulse compression
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Thank you very much for your time and interest
Questions ?