LOW PROBABILITY OF INTERCEPT (LPI) RADAR SIGNAL IDENTIFICATION TECHNIQUES Contents: Abstract 2 1. Introduction 3 2. Signal processing techniques 4 a. Filter Bank and Higher Order Statistics 4 b. Wigner Distribution 5 c. Quadrature mirror filter bank 7 d. Cyclo-stationary spectral analysis 8 3. LPI Signal data analysis 10 4. Results 19 a. Barker 5 19 b. Polyphase code 25 c. No modulation signal 30 d. Frank signal 32 5. Conclusions 35 6. References 36 1
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LOW PROBABILITY OF INTERCEPT (LPI) RADAR SIGNAL
IDENTIFICATION TECHNIQUES
Contents:
Abstract 2
1. Introduction 3
2. Signal processing techniques 4
a. Filter Bank and Higher Order Statistics 4
b. Wigner Distribution 5
c. Quadrature mirror filter bank 7
d. Cyclo-stationary spectral analysis 8
3. LPI Signal data analysis 10
4. Results 19
a. Barker 5 19
b. Polyphase code 25
c. No modulation signal 30
d. Frank signal 32
5. Conclusions 35
6. References 36
1
Abstract:
Low Probability of Intercept (LPI) radar is a system that represents a confluence between Radar
and Electronic Support (ES) technology. The objective of LPI radar is clear, that is, to escape
detection by the ES receiver. Low probability of intercept (LPI) is that property of an emitter that
because of its low power, wide bandwidth, frequency variability, or other design attributes,
makes it difficult to be detected or identified by means of passive intercept devices such as radar
warning, electronic support and electronic intelligence receivers, In order to detect LPI radar
waveforms new signal processing techniques are required. Higher Order Spectral Analysis
algorithms are used to extract useful information from the input signal. This includes the use of
Bispectrum, Bicoherence and Trispectrum techniques. The images (2D plots) produced by the
above algorithms are unique for each LPI signal and serves as a signature.
2
Introduction:
Many users of radar today are specifying a Low Probability of Intercept (LPI) as an
important tactical requirement.
The term LPI is that property of a radar that because of its low power, wide bandwidth,
frequency variability, or other design attributes, makes it difficult to be detected by means of
passive intercept receiver devices such as electronic support (ES), radar warning receivers
(RWRs), or electronics intelligence (ELINT) receivers. It follows that the LPI radar attempts to
provide detection of targets at longer ranges than intercept receivers can accomplish detection of
the radar. The success of LPI radar is measured by how hard it is for the receiver to detect the
radar emission parameters.
The LPI requirement is in response to the increase in capability of modern intercept
receivers to detect and locate a radar emitter. In applications such as altimeters, tactical airborne
targeting, surveillance and navigation, the interception of the radar transmission can quickly lead
to electronic attack (or jamming). The LPI requirement is also in response to the pervasive threat
of being destroyed by precision guided munitions and Anti-Radiation Missiles (ARMs). The
denial of signal intercept protects these types of emitters from most known threats and is the
objective of having a low probability of intercept. Since LPI radars typically use wideband CW
signals that are difficult to intercept and/or identify, intercept receivers have a difficult time
using only power spectral analysis and must resort to more sophisticated signal processing
systems to extract the waveform parameters necessary to create the proper coherent jamming
response.
This paper compares four intercept receiver signal processing techniques to detect the
LPI radar waveform parameters. To test the four techniques, a variety of LPI CW waveforms
were generated with signal-to-noise ratios of 0 and -6 dB.
LPI waveforms generated include: FMCW, P1 through P4, Frank code, Costas hopping and
combined PSK/FSK. Signal processing techniques compared include (a) filter bank processing
with higher order statistics, (b) Wigner distribution, (c) Quadrature mirror filter banks and (d)
Cyclostationary processing.
3
The need to detect transient signals arises in various applications, such as in communications,
underwater acoustics, and seismic surveillance. When the waveshape and the arrival time of the
signal is known, the optimal detector consists of a matched filter followed by a threshold circuit,
the threshold level of which is chosen to optimize a performance criterion. A number of
suboptimal methods for detection have appeared. Methods based on the short-time Fourier
transform, the Gabor transform, the wavelet transform, and nonlinear methods (such as the
Wigner—Ville distribution) perform well only for a given class of signals and high signal-to-
noise ratio (SNR) assumptions.
The matched filter method requires that both the waveshape and the arrival time be
known, but in practice this is not always possible. In some applications neither the waveshape
nor the arrival time of the transient signal is known; in such cases no matched filter can be
designed. An example of this would be a transient sound, such as a knocking sound or a hydro
acoustic sound pulse, that does not have a well-defined waveshape. Furthermore, the waveshape
from the same source may vary from event to event. It is difficult, therefore, to design a matched
filter for such transient sound signals.
1. Signal Processing Techniques
The signal processing techniques used to extract the LPI radar parameters are described
briefly below.
2.1 Filter Bank and Higher Order Statistics:
The filter bank and higher order statistic technique (shown in Figure 1 is based on the use
of a parallel array of filters and higher order statistics (cumulants). The objective of the filter
bank is to separate the input signal in small frequency bands, providing a complete time-
frequency description of the unknown signal. Then, each sub-band signal is treated individually
and is followed by a third-order estimator that helps suppress the noise. The parameters extracted
can then be used to create the proper jamming waveform to attack the radar [1].
4
Figure 1
The main objective of this method is the detection of a transient signal s(n) from a single
recorded noisy signal x(n). We consider the signal plus noise model for the received signal, i.e.,
x(n) = s(n)+v(n)
The signal s(n) is a transient signal of unknown waveshape and arrival time, v(n) is an
additive zero-mean colored noise of unknown symmetric probability distribution.
We consider the following hypothesis test,
H0 : x(n) = v(n)
H1 : x(n) = s(n)+v(n)
The hypothesis H1 shows the presence of signal plus noise against the null hypothesis
H0, noise alone.
2.2 Wigner Distribution:
The Wigner distribution (WD) has been noted as one of the more useful time-frequency
analysis techniques for LPI waveform parameter extraction. The Wigner distribution W, ( t , w )
is defined as
where t is a time variable, w is a frequency variable, and * denotes the complex conjugate.
5
The Wigner distribution is a two-dimensional function describing the frequency content
of a signal as a function of time, and possesses many interesting properties, such as:
1) It is always real
2) It possesses marginal distributions:
And
where X ( U ) is the Fourier transform of x( t ) ;
3) Its firstorder moments with respect to t and w give two important functions, the instantaneous
frequency and the group delay and
4) It does not suffer from interaction between time and frequency resolutions. It can be shown
that the windowed Wigner distribution can be represented as
where W ( t , w ) is called the pseudo-Wigner distribution, and W,(t, w ) and W,,.(t, w ) are the
Wigner distributions of the signal x ( t ) and the window w ( t ) , respectively.
The last equation indicates that W ( t , U ) is a convolution of two Wigner distributions in
the frequency domain. Therefore, only frequency resolution is affected by the windowing,
whereas the time resolution remains unchanged.
6
The Wigner distribution (with cross-terms included) can reliably extract the waveform
parameters with only a moderate amount of processing needed to derive the kernel function.
2.3 Quadrature mirror filter bank
In many applications, a discrete-time signal x[n] is split into a number of subband signals
by means of an analysis filter bank. The subband signals are then processed. Finally, the
processed subband signals are combined by a synthesis filter bank resulting in an output
signal y[n].
If the subband signals are bandlimited to frequency ranges much smaller than that of the
original input signal x[n], they can be down-sampled before processing. Because of the lower
sampling rate, the processing of the down-sampled signals can be carried out more
efficiently.
After processing, these signals are then up-sampled before being combined by the
synthesis filter bank into a higher-rate signal. The combined structure is called a quadrature-
mirror filter (QMF) bank.
If the down-sampling and up-sampling factors are equal to or greater than the number of
bands of the filter bank, then the output y[n] can be made to retain some or all of the
characteristics of the input signal x[n] by choosing appropriately the filters in the structure. If
the up-sampling and down-sampling factors are equal to the number of bands, then the
structure is called a critically sampled filter bank. The most common application of this
scheme is in the efficient coding of a signal x[n].