Advances in Signal Processing Technology

for Electronic Warfare

b!f
James P. Stephens

Wright Laboratory
Avionics Directorate
Electronic Warfare Division

Abstract possible for manual operators to identify threat signals

efficienlly and effectively because of the proliferation of
complex waveforms used for voice, data, radar, navigation,
The denial of effective communications by enemy and image transmission.
forces during hostile military operations has been a
primary concern for military commanders since the Modern electronic intercept systems must perfom
inception of radio communications on the battlefield before the tasks of detection, classification, identification. and
World War 11. Since then, the electromagnetic exploitation in a complex environment of high noise,
environment has been in a constant state of evolution interference, and multiple signals. Some waveforms are
toward more sophisticatedjam-resistant and convert for" inteiitioiiially designed to make the detection process nearly
of modulation. For example, exotic modulation techniques impossilble. Such signals are referred to LIT or LPD
employing spread spectrum (SS) signaling are routinely waveforms, meaning they offer a low probability-of-
used by our adversaries to provide their communication intercept or low probability-of-detection. After the signals
links an advantage over US and Allied jammers. More are detected, the task of classification requires sorting into
rcccntly, these sane spread spectrum modulation groups having sirnilax characteristics. Parameters such as
techniques are being refined to provide convert, low carrier frequency, moduliation type, data rate, amd time or
probabiIity-of--intercept (LPI) features to the unintended angle-of-arnival are just of few of the fundamental features
interceptor. The thrust of this paper focuses on that disitinguish one signal from another. Data bases are
developments in the theory and algorithms for detection. used to configure these signal parameters into mays that
characterization, and exploitation of advanced waveforms are compared Eo existing kmwledge or to establish new
using new mathematical signal processing tools introduced records. The sorting and cataloging of signals lieads to the
within the past decade. Specifically, quadratic time- process of identification, a critical step when effective
frequency signal representations, wavelet transforms, and electronic countermeasures are to be initiated and the
cyclostationary signal processing are introduced. This
jamming of {onesown resources is to be avoided. Finally,
overview demonstrates the importance of these advanced
the prolblem of effectively and efficiently jamming the
techniques in a clear and concise manner. Applications
signal is met. The electronic attacker must select a
and future research activities are described in this
strategy that requires the least amount of resourlues,but yet
significant area that is gaining much attention in a variety
offer the most effectiveness. Getting feedback: regarding
of technical fields. the success (of your jamming is extremely he1pl:ul. but not
always possible. A technique called "look-thru" allows the
Introduction jammer to observe his effectiveness on the target. This
may be accomplished by stopping to listen periodically or
In the early days of electronic warfare, an operator listening through the jamming by using special filters.
would tune his radio across the band listening for threat Overall, electronic attack; can be thought of as a game and
signals, likely in the form of voice modulation spoken in a many of the strategies of game theory can be aplplied to the
foreign language. Upon detection, he would simply place overall probllem. Each of these initial processes: detection,
his noise jammer at the same carrier frequency with as classification, identification, and exploitation require
much power as possible. The operator, using his ears and advanced signal processing techniques. Many of the
brain, comprised the signal processor. Today, it is not theoretical signal detection concepts in use today were
advanced in the 1920's and 30's during the early

123 U.S. Gowsrnment work not protected by U S . copyright

development of radar technology. But, in the last 20 years whole signal, the process is called taking the short-time
the development of exotic modulation schemes Fourier transform. In implementing the STFT, researchers
implemented through advances ic digital signal processing began to experiment with the window. How large should
gave rise to signals supporting higher information rates, the time interval be? What if we shape the window to give
greater channei capacity, and improved noise immunity. more weight to the central points and less weight to tle
These same techniques are now being used to exploit these end points’? Different windows will produce different
modem waveforms. short-time distributions. Unfortunately, the estimates of
the properties of the signal are window dependent making
interpretation of the results difficult.

A good understanding of the advances in signal

processing technology requires a discussion of the
fundamentals of Fourier Analysis. From this basic tool.
more complex processes have evolved. Some of the more
significant techniques currently being researched for
Electronic Warfare applications are described below.

The Fourier Transform

Traditional signal analysis deals with the

examination of time and frequency separately through the
use of the Fourier Transform. The Fourier Transform and
it digital implementation, the FFT (Fast Fourier
Transform), allow the decomposition of a signal into
individual frequency components and their amplitudes. (a) Stationary
However, the major drawback of these tools is that time
and frequency information cannot be combined to tell how
frequency content is changing in time. For example, if you
look at the light coming from the sun above the earth’s
atmosphere, it is steady state and its frequency content is
the same over millions of years. If we look at the sun’s
light at the surface of the earth, the frequency content
changes dramatically during sunrise and sunset. We refer
to the first case as a stationary event and the second a non-
stationary event. A stationary signal is independent of
time, whereas, a non-stationary signal changes over time.
Figure 1 illustrates stationary and non-stationary signals
through the use of the Short-Time Fourier Transform
(STFT). The S” is also known by the names
“windowed Fourier transform” and “spectrogram.” Almost
all digital signal processing systems use the STFT since the (b) Non-Stationary
environment is typically sampled over some time-interval,
processed (i.e. FFT), and then output to its intended
funcuon. This process is continually repeated. But what is
important to realize is that a only a portion of the RF Figure 1 - Stationary and Non-Stationary Signal
environment is analyzed during a small time segment.

The STFT was the first tool devised for analyzing Time-Frequency Distributions
a signal in both time and frequency simultaneously. The
basic idea i s to Fourier analyze a small part of the signal The motivation for the study of time-frequency-
around the time of interest to determine the frequencies at distributions is to improve upon the STFT. The basic
that time. Since the time interval is short compared to the concept is to devise a joint function of time and frequency

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that will describe the energy of the signal accurately in STFT this condition is inot satisfied. Tal do so would
both time and frequency. The word “distribution” maybe require an arbitrarily small window in both time and
puzzling to some. One should think of it as a 3D surface frequency. This is contradictory. A small vvindow in time
plot of how the energy is “distributed” in the time- results in a wide frequency window. The concept known
frequency cells. For example, in Figure 2, the time- as tihe IJncertainty Principle states that good time and
frequency distribution for several signals is shown. Present frequency resolution cannot be simultaneously achieved.
in this plot is a linear chirp moving down in frequency, a One must be sacrificed at the expense of the other.
frequency hopping signal increasing in frequency, and a
frequency varying signal having non-linear properties. A To satisfy the marginal conditions, other
time-plot of the sum of these three waveforms is toward the distributions such as the Wigner Distribution (WD) have
left running up the page. The power spectral density is been developed. The WD is a quadratic (non-linear)
shown below the main figure. The nature of these signals distribution that will produce interference terms, also
is not obvious from either the time-plot or the power called cross-terms, when multiple signals are analyzed.
spectral density, The time-frequency distribution clearly Although the WD provides improved time and frequency
provides a clearer representation of the characteristics of resollution, the presence of the cross-terms is a
these signals. The time-frequency distribution tells not disadvantage. A variant of the WD, calleld the Wigner-
only what frequencies exist, but at what time each existed Villt: Distribution (WVlD) incorporates smoothing to
making multiple signals much easier to separate and decrease the effect of cross-terms by using independent
identify. In other words, the power spectrum density tells windlows in time and frequency. The WVD is also a
us the frequencies that existed for the whole duration of the quadlratic distribution but through the choice of the length
signal. The time-frequency distribution allows us to of the time and frequency windows, reduced cross-term
determine the frequencies at a particular time. suppression is obtainable. Figure 3 illustrates the
generation of cross-terms from two chirp signals through
the use of the WVD. Other distributions have been
developed both to minimize the effects of cross-terms and
500
because they are simpler to implement in software. The
450
main stumbling block in attempting to use the wide variety
400
of time-frequency analysis methods available is the fact
- 355 that their behavior is dramatically differlent from one
$ 5,o problem to the next and each has peculiar properties. It is
8
n 250
impc~rtantto recognize that even though a distribution may
: 200
not behave properly In all respects or intcxpretations, it
150
may still be useful if a particular property is to be
100 exploitedl. This point is emphasized in Figure 4 using top-
50 down plots of the Wigner-Ville, Choi-Williams, and the
005 01 095 02 025 03 035 04 C45 05 Rihaczek:-Margenau distributions on identically the same
signal environment. Although, each distribution is
different in appearance, they are equivalent in the sense
that each can be obtained from the other and they each
contain the same amount of information. They are very
Figure 2 - Time-frequency distribution for different, bot nonetheless each has been used successfully
multiple signals for particular applications. These are just three
es out of a. large number of choices, all with
different behavior. There has been considerable
What exactly is wrong with the STFT you might controversy in the past few years regarding the choice of a
ask’? The STFT is easily understandable and it gives a quadratic: time-frequency distribution for the analysis of
good time-frequency representation for many signals. nonstatioinary signals. The numerous distributions which
However, it can be shown mathematically that the STFT have been proposed may be interpreted as smoothed
does not satisfy what are called “marginal energies.” versions of the WD, with the type of smoothing
Hence, something is being added or subtracted from the detexmining the amount of attenuation of interference
representation. If the joint density of the time-frequency termis, loss of time-frequency resolution, and mathematical
distribution satisfies the individual intensities in time and properties. Here again, h e choice of the best distribution
frequency, “marginal energies” are satisfied. But, for the depends on the nature of tlhe signals to be analyzed and on
additionail issues such as the mathematilcal properties

131
required and limitations in computation and storage. A Wavelets
successful application of time-frequency distributions
presupposes some degree of expertise on the part of the The Wavelet Transform (WT) is of interest for the
user. It is seldom possible to view time-frequency analysis analysis of non-stationary signals, because it provides still
as a “black box” where the signal is input and some clear another altemative to the STFT and many of the quadratic
and meaningful result is automatically obtained as the time-frequency distributions. The basic difference is in
output. Some prior knowledge about the signal must contrast to the STFT, which uses a fixed signal analysis
generally be known in order to select the most suitable window. The WT uses short windows at high frequencies
distribution and adapt the parameters to the signal. and long windows at low frequencies. This helps to diffuse
Keferences 1 and 2 are outstanding sources for a the effect of the Uncertainty Principle by providing good
description of many of the more common time-frequency time resolution at high frequencies and good frequency
dlseributions. resolution at low frequencies. Unlike many of the
quadratic functions such as the Wigner-Ville and Choi-
Williams distributions, the WT is a linear transformation
n
therefore extraneous cross-terms are not generated. There
is one other major difference between the STFT and the
WT. The STFT uses sines and cosines as an orthogonal
basis set to which the signal of interest is effectively
600 correlated against. The WT uses special “wavelets” which
usually comprise an orthogonal basis set. The WT then
400
computes coefficients, which represents a measure of the
200 similarities, or correlation, of the signal with respecr to the
120
set of wavelets. In other words, the WT of a signal
0 corresponds to its decomposition with respect to a family of
functions obtained by dilations (or contractions) and
-zoo
0 translations (moving window) of an analyzing wavelet. A
filter bank concept is often used to describe the WT. The
WT can be interpreted as the result of filtering the signal
trequency with a set of bandpass filters each with a different center
(a) STFT frequency f. In the STFT case, the bandpass filter’s
bandwidth is independent of the center frequency. In
contrast. the bandwidth of the WT is proportional to f or,
equivalently, the filter’s quality factor Q ( Q = f /
n
bandwidth) is independent off. In other words, the WT
can be viewed as a “constant Q ’ analysis.

Another interpretation of the WT is associated

with multiresolution analysis, where the decomposition,
with respect to an orthonormal basis set, is performed by
an iterative scheme based on high pass and low pass
filtering followed by downsampling. The signal is then
decomposed into a discrete set of orthogonal details from
which the signal can be exactly reconstructed. This offers
the potential for signal and data compression. Still
another interpretation suggests that the bank of filters
represents a set of “matched” filters whose outputs
frequency
represent the degree of correlation to a signal feature of
(b) Wigner-Ville interest. It is important to note that, within certain
technical constraints, the “mother wavelet” may be chosen
Figure 3 - Cross-terms produced from Wigner- arbitrarily. This means that an analyzing wavelet with
Ville distribution properties especially suited to the analysis of some
particular class of signals, such as spread spectrum
waveforms, may be chosen to support a given application.

? 32
Figure 5 illustrates the use of a Fast Wavelet Transform
(FWT) on a BPSK modulated signal. More signal derail is
visible at the lower end of the vertical axis. The actual
BPSK keying can be clearly extracted at the 1/64 scale and
the carrier can be extracted U128 scale.

0 5 IO 15 20 25 30 35 40 45 50
lime

(c) Rihaczek-Margenau

Figure 4 - ]Differences in various quadratilc

distributions

time

(a) Wigner-Ville

Figure 5 - Signal analysis with a Haar wavelet on

a BPSK signal

"0 5 10 15 20 25 30 35 40 45 50
time
Cyclostationarity

Cyclostationarity is a statistical propert:y exhibited

(b) Choi-Williams by essentially all digital signals and some naturally
occumng waveforms. As before, a stationary signal is one
whose statistics do not vary with time. Therefore, a
stationary signal can be sampled at periodic intervals
without being concerned that the signal may be changing exp(-jmt)
over time. A cyclostationary signal is periodically I

stationary. That is by delaying the signal by some amount, M A -

BPF h
the statistics do not vary with respect to the signal before
the delay. By processing signals as cyclostationary, we can
take advantage of the periodic features of a waveform.
These periodicities arise from modulating, sampling,
keying, scanning, coding, multiplexing, and other similar
operations, or from naturally occurring periodic events or
the motion in rotating machinery.

In the same way that the power spectral density Figure 6(b) - Frequency Domain Implementation
(PSD) function fully characterized the second-order of 2nd Order Cyclostationary Process
statistical behavior in the frequency domain of a stationary
random signal, the spectral correlation density (SCD)
funclion fully characterizes the second-order sratistical
behavior in the frequency domain of a cyclostationary Applications
signal. That is, unlike stationary signals, such as thermal
noise, some spectral components in cyclostationary signals Much work is underway to develop new advanced
will correlate with each other. There are two intuitive signal processing techniques which will more effectively
ways to view the concept of cyclostationary signal and efficiently exploit modem digital communication and
processing: in the time domain and in the frequency radar signals. These techniques are directed at improving
domain. In the time domain, consider a simple delay-and- the tasks of detection, classification, and identification.
multipy operation as shown in Figure 6(a). If the signal The traditional STFT has been applied to signal processing
contains a periodic component, and if the delay is chosen problems in many different areas including electronic
properly, a strong sinusoid will be present at the output. warfare. Some of the major applications for the STFT
The computation of the SCD consists of performing this include time-varying signal anaIysis, system identification
operation over a wide range of delays. Taking the Fourier and spectral estimation, signal detection and parameter
Transform of each of these outputs will produce the SCD. estimation, speaker identification, speech coding,
In the frequency domain, Figure 6(b), consider up-shifting estimation of the group delay or the instantaneous
the frequency spectrum of interest by some small amount frequency of a signal, and complex demodulation. Besides
then down-shifting the spectrum by the same amount and processing received signals, these same STFT algorithms
then compute the correlation of the two spectrums. If there are used to synthesize signals using inverse transform.
is correlation between shifted spectral components, spectral techniques. Some applications of STFT synthesis
lines will be generated, Repeating this process over a techniques are time-varying filtering, non-linear noise
range of frequency shifts will also produce the SCD. removal, room dereverberation, time-scale modification,
Figure 7 illustrates a typical SCD for a BPSK signal dynamic range and bandwidth compression, and waveform.
showing both the carrier frequency (16 Hz) and data rate design.
(0.5 Hz). The end view plot helps read these rates. The
cycle frequency equates to the mount of frequency shift in While many conventional statistical signal
the frequency domain interpretation of the SCA. processing methods treat random signals as stationary,
cyclostationary techniques take advantage of periodicities
associated with signals. Cyclostationary signal processing
has been shown to very useful for signal processing tasks
such as the separahon of spectrally overlapping signals and
reliable extraction of information from spectrally
LA Delay I overlapping signals. For example, information such as
emitter location, modulation type, and carrier and clock
frequencies can more easily be removed in congested RF
environments through cyclostationary signal processing.
The presence of signals buried in noise and/or severely
Figure 6(a) - Time Domain Implementation masked by interference can also be more easily detected by
of 2nd Order Cyclostationary Process
exploiting the spectral redundancy associated with recognition. Synthesis techniques have been used to
cyclostationarity. Estimating parameters such as the time- perform time-varying filtering, multi-component signal
difference-of-arrival at two reception platforms or the separation, and window and filter design. A quadratic
direction of arrival at a reception array on a single platform time-frequency representation known as ihe ambiguity
is improved over conventional systems that ignore surface has been used extensively in radar and
cyclostationarity. communications. In the radar case, an estimation of the
distance and velocity of a moving target is made, where the
distance and velocity correspond to the “range” and
“Doppler shift” parameters. The cross-ambiguity surface
provides pertinent information about the performance of
the maxiimum-likelihood estimator, thus aiding in the
design of the transmitted signal. Synthesis techniques can
also be used for isolating a desired component of a
multicomponent signal, provided the signal term of interest
does not coverlap significantly with other signal terms.

Wavelet theory provides a unified framework for a

variety of signal processing applications. For example,
wide use is found in multiresolution signal processing and
speech and image compression and enhancement. While
-20
conceptu;illy, the WT is a classical constant-Q analysis
concept, applied mathematicians have recently recognized
the many different views and applications stem from a
single theory. Still another alternative to the STFT, the
(a) 3-D View main application of the WT in signal processing will be in
non-stationary signal analysis. The zooming property of
,CY (Hz)
x IO’
SPECTRAL CORRELATION DENSITY 19Jul-95 wavelet analysis allows a very good representation of
discontinuities in the signal. For example, as applied to
image processing, the WT is very good at detecting and
enhancing edges. This property is useful foir pulsed radar
signals, detecting the frequency transitions of frequency
hopping radios, OH any abrupt transitions characteristic of
the signal-of-interest. Perhaps the biggest potential use
for wavelet analysis is in signal compression, thus allowing
increased bandwidth efficiency.

Future Research Activities

As military communication, radar, and navigation

systems become more complex, frequently employing
-20 -16 -16 -14 -12 -10 -6
Cycle frequency (Hz)
-6 -4 -2 0
sophisticated anti-jam (AJ) or LPI signaling schemes to
(b) End View provide robustness or covertness, the performance
limitations of the traditional radiometric energy detector
becomes significant. Feature extraction techriiques become
Figure 7 - Spectral correlation density increasingly more difficult as the covert communicator
attempts to suppress and conceal his features. Electronic
countermeasures become more difficult and less effective
Time-frequency representations are powerful tools as A.J techniques are implemented. Classical radiometric
for the analysis and processing of nonstationary signals for methods for energy detection are highly !susceptible to
which separate time-domain and frequency-domain unknown and changing noise level and interference
analysis are not adequate. Researchers have applied the activity. For example, spread spectrum modulation
Wigner Distribution for signal detection, spectrum and techniques make it difficult for the radiometer detectors to
instantaneous frequency estimation, and pattern function because the signal is spread in bandwidth to

135
obtain some processing gain in the presence of offers. For example, new signal processing techniques are
interference. Spread spectrum may also employ spectral currently being developed which exploit the periodic
overlapping techniques such as code-division multiple nature of naturally occumng signals. Periodic, cyclic, or
access (CDMA) which will confuse the radiometer since rhythmic phenomena arise naturally in many areas of
multiple, similar looking signals, share a common disciplines. Some of the fields where periodic, time-series,
bandwidth. New signal detection and feature extraction data are analyzed include medicine, biology, meteorology,
systems are needed to effectively exploit these new climatology, hydrology, oceanology, and economics. The
waveforms in today’s complex signal environment. techniques that are being researched for the detection,
Developing new signal countermeasure techniques and characterization. and identification of LPI waveforms show
assessing the performance of these techniques against great promise in these other scientific and commercial
candidate AJ/LPI waveform designs requires new fields. Quadratic time-frequency distributions have served
theoretical based approaches and computational tools and as useful andysis tools in fields as diverse as quantum
techniques. mechanics. optics, acoustics, bioengineering, image
processing. and oceanography. These techniques have
Time-series data analysis is presently performed been used to analyze speech, seismic data, and mechanical
either with costly and complex instrumentation or through 1,ibrations. An excellent example is use of these techniques
computer analysis. Computer algorithms have been for recognizing cxdiac patterns in the fields of medicine
developed which analyze and graphically display the and biology. Wavelets and time-frequency distributions
results of the data for user interpretation. However, new are being used for the detection of e l ~ c t r o e n c e p h a ~ ( ~ g ~ ~ n
transforms are currently being develope that provide (EEC-) spikes. ventricular fibrillation in
improved graphical representations of time varying data electrncardiographic (ECG) patterns, and a variety of other
beyond that of conventional FFT’s. Pattern recognition biomedical related waveform. Research efforts have been
techniques will k merged with artificial intelligence made and continue to make imponant groundwork
technology and neural networks to develop automated contribution to EW programs. but also continue to provide
analysis and interpretation of signal data in real-time. Ey research benefits to other applications.
establishing a database of signatures, signals will.
ultimately be automatically recognized and an optimal
.jamming strategy generated. References

Spectral correlation analysis instruments or 1. Cohen, Leon, “Time-Frequency Distributions - A

cyclostationary algorithms will become standard equipment Review”, Proceedings of the IEEE, Vol. 77, No. 7, July
in communications laboratories and production facilities 1989.
with either commercial or educationa! missions. Analysis
systems could be designed for quality control monitoring, 2. Hlawatsch, F. and Boudreaux-Barleis, G.F., “Linear
testing, system design, perforrnance evaluation, teaching . and Quadratic Time-Frequency Signal Representations”,
and research and development. Fault testing and IEEE Signal Processing Magazine, April 1992.
prediction are possible through the analysis of time-series
vibration data of rotating mechanical systems such as 3. Rioul, Olivier and Vetterli, Martin, “Wavelets and
engines. Migher-order cyclostationary moments and Signal Processing”, IEEE Signal Processing Maga~ine,
cumulanrs are being researched to find new techniques and October 1991.
algorithms for signal detection. characterization. and
exploitation against LPI waveforms or against signals in 4. Gardner. William A,, “Exploitation of Spectral
difficult environments. Redundancy in C yclostationary Signals”, IEEE Signal
Processing Magazine, April 1991.
Considerable theoretical development as taken
place regarding advanced signal processing techniques in
the last 15 years. Computer models and simulations have
&own the advantages of these techniques. Recently,
algorithms have been developed which speed the data
processing of these potential techniques to realizable goals.
Hardware is being developed and integrated into current
mililary systems using many of these, or related,
techniques. Industry needs to be made aware of the
possibilities that advanced signal processing techniques

136