Note: Descriptions are shown in the official language in which they were submitted.
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TITLE OF THE INVENTION
Method and system for detecting and classifying the modulation of unknown
analog and digital telecommunications signals.
FIELD OF THE INVENTION
The invention relates in general to telecommunications and in particular to
the
classification of modulation schemes embedded in unknown telecommunications
signals,
typically: CW, FM, PSK, AM, DSB-SC, BPSK, QPSK, ir/4 - QPSK, MPSK, NOISE,
OTHERS.
BACKGROUND OF THE INVENTION
Automatic recognition of the modulation scheme embedded in an unknown
received signal is an important requirement for civilian, military, and
government
intelligence bodies when monitoring the radio communication spectrum. Although
the
subject has been extensively researched for several years and different
approaches have
been implemented or delineated in theoretical papers, the prior art has
traditionally
assumed that (a) the carrier frequency of the unknown received signal is given
and has
zero error, that (b) the input Signal-to-Noise Ratio (SNR) is sufficiently
high to classify
the modulation correctly, and that (c) the symbol transition of digitally-
modulated signals
is known. Furthermore, the more recent prior art approaches are limited to off
line
operation on stored signals. Some of the recent methods employ probabilistic
models to
minimize misclassification errors, which can achieve good results at SNRs that
are as low
as 0 dB. As shown in reference [ 1], however, they assume a priori knowledge
of the
carrier phase and frequency, the SNR, and the symbol rate of the modulation,
and are
often limited to digital phase modulation schemes.
Other approaches to automatic classification use statistical pattern
recognition
techniques, such as Artificial Neural Networks (ANN), to discern
discriminating features.
As shown in references [2], [3], and [4], ANN classifiers produce reasonably
good results
under simulated conditions, but their practical behaviour is highly dependent
on the
training set chosen. Since they can perform learning vector quantization,
neural networks
are capable of achieving an efficient class definition over a large multi-
dimensional
feature space. The inherent problem however, is that ANN classifiers have
difficulty
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indentifying the set of meaningful features and to train the network
accordingly.
Furthermore, the designer does not have much manipulative control over the
classification
algorithm and may have difficulty applying a priori knowledge of the taxonomy
of the
modulation schemes. A neural network operates like a black box that requires a
new
training phase when new features (or signals) to be identified are added.
Examples of
ANN techniques are described in [4].
Other, more recent, prior art approaches to modulation recognition base their
classification decisions on a number of successive serial tests, each yielding
a binary
output. As described in references [2], [3], and [4], such methods give rise
to a decision
tree in which the outcome of the first binary decision forces a second binary
decision
whose outcome determines the next binary decision, etc. This decision tree
technique
represents an improvement over the vector-based methods described above in
that it
refines and clarifies, in successive decision levels, the information
extracted from the
unknown input signal. Its hierarchical structure allocates the computing
resources more
efficiently. As well, the thresholds established at each decision level may be
quickly
modified in order to reflect operational changes. These alterations can
improve
performance accuracy. Notwithstanding these advantages, the decision tree
methods
published to-date have inherent deficiencies, namely their intolerance to
carrier frequency
errors, their erratic performance at low SNRs, and their inability to classify
modulation
schemes reliably under real-time operations.
Other forms of classification techniques are described in the following US
patents:
In reference [5], the classifier of an IF signal takes the outputs of two
separate
demodulators (one AM, the other FM) to compute different signal statistics (or
features)
and make six binary decisions based on those statistics. It then classifies
the modulating
scheme, within a set consisting of CW, DSB, SSB, ASK, FSK, MUX, NOISE, and
OTHERS, by using the whole vector of six binary decisions as an input to a
logic circuit.
The drawback to this method is that it usually performs the computation of the
vector
features in parallel, without any interaction between these features. It also
uses a sub-
optimum classification circuit.
In reference [6], the probability distribution of the input signal amplitude
is
analyzed to estimate the mean, the variance and the amplitude cumulative
distribution.
This information is combined with the outputs of three phase-locked loops -
one tailored
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to AM signals, one to FM signals and one to DSB signals. The combined
information is
compared with a number of thresholds to form an information vector which is
then
compared to a pre-stored series of vectors representing the modulations within
the set CW,
AM, FM, DSB, SSB, PSK. The main difference between this method and the present
invention is the computationally-intensive parallel processing of the feature
vector, as
opposed to serial processing of the vector which is less computer hungry.
In reference [7], several parameters, including the mean amplitude, the signal-
to-
noise ratio, and the standard deviation, are computed for each of the
frequency lines of the
input signal's power spectrum. These parameters are fed in parallel to a
neural network for
the classification of the input modulation. The main drawback of this method
is that it
performs the computation of the vector features in parallel over a limited set
of features.
In reference [8], the normalized variance of the magnitude of the input
baseband
signal is computed and compared to a predetermined threshold in order to
decide in favour
of one of the following modulation types: FSK, FM or QAM. This method is
limited by
the number of modulation schemes it can identify. As well, it uses only a
single feature to
perform the identification.
In reference [9], histograms based on the power spectrum of the input signals
are
computed. Frequency locations and amplitudes are recorded, as well as the
location of the
centre frequency of the overall spectrum. The particular pattelns of each
histogram are
compared to those of typical modulation schemes, such as AM, FSK, PSK or SSB.
The
main drawback of this method is that it uses only the spectral representation
of the signal
to perform its computation.
In reference [10], a method is used to discriminate between an FM signal and a
7r/4-DQPSK signal in analog AMPS and digital DAMPS systems. The variation in
amplitudes of the two different modulation types determines which one is
present. The
main problem with this method is that it is limited to only two modulation
types.
In reference [ 11 ], the method uses a neural network to demodulate the signal
of a
particular digital communication standard. This method differs from the
present invention
in that it identifies the information content of the signal instead of its
format.
In reference [12], a method is used to discriminate between the VSB and QAM
signals that are encountered in High Definition TV. The main deficiency with
this method
is that it is limited to the two modulation schemes it can identify.
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In reference [13], the spectral energy distribution of the input signal is
compared
with the pre-stored energy distributions of FDM/FM signals containing specific
parameters. Recognition of a specific form of signal is declared if the input
distribution
matches one of the pre-stored versions. This method is limited to a single
form of signal
feature and to a very specific modulation format.
In reference [ 14], the demodulated signal of an FM receiver is classified
according
to the voice coding algorithm that processed it. This method differs from the
present
invention because classification is applied on the demodulated signal.
In reference [ 15], a method is used to generate a decision-tree classifier
from a set
of records. It differs from the present invention in that it does not consider
the specific
classification of modulation formats.
Reference [16] describes a method and apparatus for detecting and classifying
signals that are the additive combination of a few constant-amplitude
sinusoidal
components. The main drawback of this scheme is that it cannot be applied to
the
modulations treated under the present invention, except for CW.
In reference [17], a sequence of estimated magnitudes is generated from the
received signal at the symbol rate, and the result is compared to a
predetermined
representation of known voiceband digital data modem signals. This method is
limited to a
single decision level, as opposed to the series of binary decisions performed
under the
present invention.
Prior art References
[1] C.Y. Huang and A. Polydoros, "Likelihood Methods for MPSK Modulation
Classification", IEEE Transactions on Communications, Vol. 43, Nos. 2, 3 and
4,
(1985), 1493 - 1504.
[2] E.E. Azzouz and A.K. Nandi, "Automatic Modulation Recognition of
Communications Signals", Klewer Academic Press, (1996), 217.
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[3] A.K. Nandi and E.E. Azzouz, "Algorithms for Automatic Modulation
Recognition
of Communication Signals", IEEE Transaction On Communications, Vol. 46, No.
4, (April 1998), 431-436.
[4] E.E. Azzouz and A.K.Nandi, "Automatic Modulation Recognition - I & II", J.
Franklin Institute, Vo1334B, No 2, (1997), 241-305.
[5] Robert L. Carrick, William T. Manning and Robert E. Grimes, US Patent No.
4,227,255, October 7, 1980, "Signal Classifier".
[6] Philip E. D. Wakeman, US Patent No. 4,501,020, February 19, 1985,
"Spectrum
Surveillance Receiver System".
[7] Bruno Lobert and Bruno Sourdillat, US Patent No. 5,271,036, December 14,
1993,
"Method and Device for the Recognition of Modulations".
[8] Nevio Benvenuto, US Patent No. 4,815,137, March 21, 1989, "Voiceband
Signal
Classification".
[9] John T. Apostolos and Robert P. Boland, US Patent No. 4,166,980, September
4,
1979, "Method and Apparatus for Signal Recognition".
[10] Christopher Koszarsky, John Northcutt and Michael Nowak, US Patent No.
5,912,922, June 5, 1999, "Method and Apparatus for Modulation
Differentiation".
[11] Alain Chiodini, US Patent No. 5,909,675, June 1, 1999, "Device for
Recognizing
Information Conveyed by a Received Signal".
[12] Carl G. Scarpa, US Patent No. 5,636,250, June 3, 1997, "Automatic VSB/QAM
Modulation Recognition Method and Apparatus".
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[13] Ronald L. Isaacson and Amy L. Moore-McKee, US Patent No. 4,845,707, July
4,
1989, "Frequency Division Multiplex/FM Modulation Recognition System".
[14] Chin-Pan Wong and Richard S. Young, US Patent No. 5,651,030, July 22,
1997,
"Receiver with Signal Classifier".
[15] Rakesh Agrawal and Manish Mehta, John C. Shafer, US Patent No. 5,870,735,
February 9, 1999, "Method and System for Generating a Decision-Tree Classifier
in
Parallel in a Multi-Processor System".
[16] Neil B. Cox and Edwin L. Froese, US Patent No. 5,353,346, October 4,
1994,
"Multi-Frequency Signal Detector and Classifier".
[17] Nevio Benvenuto and Thomas W. Goeddel, US Patent No. 4,979,211, December
18,
1990, "Classifier for High Speed Voiceband Digital Modem Signals".
SUMMARY OF THE INVENTION
It is now an object of the invention to provide a more straightforward and
computationally simpler method of modulation recognition than neural network
based
methods.
It is another object of the invention to provide a modulation recognition
method
which directly exploits the fundamental principles of the decision tree based
methods in
order to automatically and accurately perform recognition of a wide variety of
modulation
formats that are embedded in unknown communications signals. These modulation
formats comprise the following set: CW, AM, FM, FSK, DSB-SC, BPSK, QPSK, TC/4-
QPSK, MPSK, NOISE, and OTHERS.
It is a further object of the present invention to provide a modulation
recognition
method that successfully classifies the signal's embedded modulation amid SNRs
as low
as 5 dB, carrier frequency errors up to +/- 50% of the sampling rate, and
carrier phase
errors up to +/- 180 degrees - all without a priori knowledge of the symbol
transition
timing of the signal.
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It is a further object of the invention to extract the digital complex
baseband of
unknown signals that are measured off-air in real-time, on-line in real-time,
or from
storage, and then accurately classify the signal's embedded modulation through
an orderly
series of decision functions.
It is still a further object of the invention to provide a system for
recognizing the
type of modulation of a modulated signal having a carrier frequency
comprising:
(a) a receiver section for extracting from the modulated signal a complex
baseband
signal;
(b) a pre-classification stage for generating a pre-processed signal from the
baseband signal;
(c) means for examining amplitude variations in the pre-processed signal to
identify the type of envelope thereof as being one of a constant envelope and
one of an irregular envelope;
(d) means for estimating the carrier frequency error in the pre-processed
signal;
(e) means for correcting the pre-processed signal for the carrier frequency
errors to
generate a carrier-corrected signal;
(f) means for classifying the type of modulation in the carrier-corrected
signal,
based on the type of envelope identified in the examining step.
(g) means for classifying the type of modulation embedded in a constant
envelope
signal according to the phase and frequency contents of the pre-processed and
carrier-corrected signals, such modulations being categorized within the set
{CW, FSK and FM}; and
(h) means for classifying the type of modulation embedded in an irregular
envelope signal according to the phase and amplitude contents of the carrier-
corrected signal, such modulations being categorized within the set {AM,
DSB-SC, BPSK, QPSK, 7t/4-QPSK, MPSK, OTHER}.
The method of the invention provides a unique decision tree architecture that
automatically performs recognition of a wide variety of embedded modulation
formats in
unknown communications signals. The principal method of the invention extracts
the
digital complex baseband of the unknown signal and then determines and
classifies,
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through an orderly series of signal processing functions, the signal's
embedded
modulation scheme with a high degree of accuracy. Without knowledge of the
symbol
transition timing, the method of the invention can be used for successfully
performing
modulation recognition of measured signals amid SNR's as low as 5 dB, carrier
frequency
errors of up to +1-50% of the sampling rate, and carrier phase errors of up to
+/-180
degrees. The tolerance to carrier frequency errors is limited only by the
frequency
bandwidth of the unknown signal, since the only requirement is to prevent the
frequency
error from shifting the input signal outside of the sampling bandwidth of
half of the
sampling rate. The preferred method according to the invention is
computationally simple,
making it possible to observe the signal during a time frame of preferably
less than 100
msecs. The modular architecture of the method of the invention allows for
expansion of
new modulation classifiers.
BRIEF DESCRIPTION OF THE DRAWINGS
Exemplary embodiments of the invention will now be described in more detail
with reference to the appended figures, in which the referenced numerals
designate similar
parts throughout the figures thereof, and wherein:
Figure 1 is a top-level block diagram that illustrates an embodiment of the
present
invention for measuring and classifying an off-air unknown signal.
Figure 2 illustrates, in a top-level flow chart, the modulation classification
section
shown in Figure 1.
Figure 3 illustrates a sample of the spectral power density of the signal and
embedded noise that can be measured in the pre-classification stage shown in
Figure 1 and
detailed in Figure 2.
Figure 4 illustrates in a graph the degradation in the classification success
rate of
four specific signal types versus the normalized carrier frequency errors,
without any
provision for correcting the frequency errors in accordance with this
invention.
Figure 5 is a block diagram illustrating the signal processing functions in
the error
correction block 26 of Figure 2 for correcting the residual carrier frequency
error inherent
in a constant envelope signal.
Figure 6 is a flowchart illustrating the signal processing functions in the
classifier
block 30 of Figure 2 for classifying the modulation of constant envelope
signals.
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Figure 7 is a block diagram illustrating the signal processing functions for
generating the instantaneous frequency components of a constant envelope
signal in the
phase processor block 42 of Figure 6.
Figure 8 is a block diagram illustrating the signal processing functions in
the error
correction block 27 of Figure 2 for correcting the residual carrier frequency
error inherent
in some irregular envelope signals.
Figure 9 is a graph illustrating the performance of the signal processing used
in
Figures 5 and 8 for correcting the residual carrier frequency error inherent
in some
selected signals.
Figure 10 is a flowchart illustrating the signal processing functions used for
classifying the modulation of irregular envelope signals in the classifier
block 31 of
Figure 2.
Figure 11 is a summary flowchart depicting the entire modulation
classification
process of the present invention, which entails the combination of figures 2,
6 and 10.
DETAILED DESCRIPTION OF THE INVENTION
Glossary of Acronyms
For convenience, a glossary of acronyms used in the description of the present
invention is given below:
AM Amplitude Modulation
AMPS Advanced Mobile Phone Services
ASK Amplitude Shift Keying
AWGN Additive White Gaussian Noise
BPSK Binary Phase Shift Keying
BT Product of a filter bandwidth B and the symbol period T
BW Bandwidth
CW Continuous Wave
DSB Double Sideband
DSB-SC Double Sideband Suppressed Carrier
FFT Fast Fourier Transform
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FSK Frequency Shift Keying
FM Frequency Modulation
GMSK Gaussian Minimum Shift Keying
GSM Global System for Mobile (Pan European Digital Cellular)
IS-54 Interim Standard #54 of the Telecommunications Industry
Association (also known as US Digital Cellular)
MPSK M-ary PSK
MUX Multi-Channel or Multiplexing
PSD Power Spectral Density
PSK Phase Shift Keying
QAM Quadrature Amplitude Modulation
QPSK Quarternary Phase Shift Keying
n/4-QPSK 7c/4-shifted Quaternary Phase Shift Keying
RMS Root Mean Square
SNR Signal to Noise Ratio
SSB Single Side Band
VCO Voltage Control Oscillator
VSB Vestigial Sideband
Terminology
Throughout the description of the present invention the following terms are
used in
accordance with their respective definitions given below:
Linear vector quantization "Vector quantization" is a process by which a
vector,
defined over a continuous multi-dimensional vector space, is
assigned one of a limited number of pre-determined
representative vectors. Quantization occurs at the vector
level because an infinite number of vector possibilities is
mapped onto an ensemble containing a finite number of
vectors. The mapping is performed by dividing the original
vector space into a number of regions, each of which
corresponding to one of the finite number of pre-determined
representative vectors. "Learning vector quantization" is the
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process that performs the adaptive segmentation of the
infinite vector space in the pre-determined regions during a
training period or during normal operation of the quantizer.
Training set The training set is an ensemble of known vectors, signals, or
other inputs provided to a system that estimates certain
parameters over the inputs. The system's internal state is
thus allowed to adapt to the training set so that it can
thereafter perform parametric estimations on unknown
inputs.
Centroid frequency The centroid frequency of a given power spectral density is
the frequency corresponding to the "centre of mass" of such
power spectral density. It is a purely geometric property of a
given density and is expressed as:
1
f=11
c ciz where the c,s are the Discrete Fourier Transform (DFT)
coefficients of the input signal and the fs are the
corresponding frequencies.
Zero padding In the computation of the Discrete Fourier Transform (DFT)
of a given discrete-time signal vector x(n) of finite length N,
zero padding refers to the appending (the padding) of a
certain number L of samples (all equal to zero) at the end of
the vector x(n). The DFT is then computed on a new
discrete-time signal vector [x(n) 0 0 0...0], of length N+L.
This process has the effect of increasing the frequency
resolution of the original N-point DFT, since it is then
computed for N+L different frequencies over the same
frequency range.
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Unwrapped phase Unwrapping the phase of a complex signal vector refers to
the process of making the corresponding modulo-27t phase
vector continuous over the range from minus infinity to plus
infinity, by adding multiples of + or -27r as needed.
Digital complex baseband The complex baseband representation of signals (also
referred to as "complex envelope representation") serves the
purpose of mathematically expressing a real bandpass signal
in a format which contains the amplitude and phase
information of the signal but not its carrier or reference
frequency. This representation is an extension of the familiar
two-dimensional phasor (vector) representation of sinusoidal
signals.
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Consider a real bandpass signal with a narrow bandwidth
concentrated around a reference or carrier frequency f. This
real signal can be mathematically expressed as:
s(t) = a(t) cos[2nft + 0(t)]
where a(t) is the signal amplitude and 0(t) is the time-
varying phase. The modulation of the signal is contained in
its amplitude and its phase (the frequency modulation is
equal to the time derivative of the phase). The signals a(t)
and 0(t) show all the modulation information carried by s(t),
and must be preserved in the complex baseband
representation. The above equation can also be expressed as:
s(t) = a(t)cos[O(t)]cos[2nf~t] -a(t)sin[O(t)]sin[2)~'ct]
=Re{[x(t)+ jy(t)]e'"',` },
Substituting:
x(t) = a(t)cos[ 0 (t)]
y(t) = a(t)sin[ 0 (t)].
we then have a signal:
u(t) = x(t) + jy(t)
= a(t)e'o(`)
which is the complex baseband equivalent of s(t) and
contains all the amplitude and phase information of the real
bandpass signal.
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Overview of Present Invention
Figure 1 is a top-level block diagram that shows one aspect of the present
invention - the measurement of off-air unknown signals. This figure includes
an antenna
1, a receiver section 2 and a modulation classification section 3. The
receiver section
includes an amplifier and filter 4, a frequency down-converter 5, a signal
sampling
processor 6, and an analog to digital (A/D) converter 7. Each of these
receiver circuits are
generally recognized in the prior art. The unknown signal, which may comprise
a plurality
of channels, is collected off-air at the antenna 1 and then amplified and
filtered by step 4.
This function also serves to isolate the channel containing the desired
carrier frequency
(f ). The filtered signal is then down-converted in frequency in step 5 to the
analog version
of the complex baseband signal. While this process reduces f~ to near zero Hz,
residual
carrier frequency errors still remain within the converted signal and must be
dealt with
prior to the classification process in order to ensure that the modulation
format is
accurately recognized. From the down-converter 5, the analog complex baseband
signal is
sampled by step 6 at regular time intervals of TS = 1/FS seconds, and the
resulting time
samples are quantized by the A/D converter 7 to produce a series of quantized
time
samples known as the digital complex baseband signal. Quantization is
performed within a
finite number of levels corresponding to the number of bits of the A/D
converter. The
digital complex baseband signal 8 is then forwarded to the modulation
classification
section 3, the principal embodiment of this invention, where the digital
signal processing
for classifying the modulation schemes begins.
The modulation classifier 3 of Figure 1 illustrates a simplified view of the
modulation classification process, consisting of a pre-classification stage 9,
a signal
envelope decision test 10, and two separate classification stages - one for
processing
signals with a constant envelope ( 11 and 13) and the other for processing
signals with an
irregular envelope ( 12 and 14). The purpose of the pre-classification stage 9
is to (a)
determine if sufficient signal power is present, (b) estimate the signal's
bandwidth and
centroidfrequency, (c) perform the first level of carrier frequency error
correction, and (d)
filter the out-of-band background noise power. The first classification test
is performed in
decision step 10 where constant envelope signals are discriminated from those
of irregular
shapes. If the signal has a constant envelope, its modulation format is
categorized within
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the set {CW, FSK, FM}. Conversely, if significant envelope variations are
detected, the
signal's modulation format is categorized within the set {AM, DSB-SC, BPSK,
QPSK,
7r/4-QPSK, MPSK, OTHER}. Following this test, the residual carrier frequency
errors
superimposed on either signal are cancelled when required, in the error-
correction steps 11
and 12 respectively, and the processes for examining, recognizing and
classifying the
modulation schemes on the respective constant envelope or irregular envelope
signals are
performed in the classifiers 13 and 14. The phase and frequency content of the
constant
envelope signal is examined in classifier 13 in order to classify one of the
{CW, FSK,
FM} modulation formats. The phase and amplitude content of the irregular
envelope
signal is examined in classifier 14 in order to classify one of the {AM, DSB-
SC, BPSK,
QPSK, 7c/4-QPSK, MPSK, OTHER} modulation formats.
Pre-classification Stage
Figure 2 shows in a flow chart a more detailed view of the Modulation
Classification Section 3. The process begins at input 15 where a block of
digital complex
samples is obtained from the output 8 of the Receiver Section of Figure 1.
These samples
are forwarded to a signal detector 16 where Fast Fourier processing determines
if
sufficient signal power is available to establish the presence of a signal.
This process is
performed with the aid of an external noise power module 17 that establishes a
power
threshold against which the power spectral density of the observed signal is
compared.
The noise power 17 is also used in by the BW and centroid estimation process
20 to set
another threshold for computing the centroid frequency and estimating the
bandwidth of
the signal. As illustrated in Figure 3, the noise power 17 corresponds to the
level PW . A
signal is declared present at decision step 18 if it bears some frequency
components above
a threshold (PW + Z) dB, where Z is a given value relating to the probability
that a noise
frequency component has a power level above the (PW + Z) dB threshold. Thus,
if the
signal energy is not above the noise-related threshold, the SNR is considered
too small to
allow further processing and the signal is classified as NOISE 19. However, if
a signal is
declared present, then the gross estimate of the carrier frequency inherent in
the signal is
determined in the BW and centroid estimation step 20. This operation is done
by
computing the centroid of the portion of the power spectral density that is
above a certain
threshold (P,y + Y) dB, as shown in Figure 3. This threshold is lower than the
one used in
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step 18 to detect the signal presence. Using Fast Fourier processing, the
centroid frequency
is given by:
f. = PSD[i]
PSD[i] ~1)
where PSD[i] is the power spectral density value corresponding to frequency f,
and the
summation is computed for the frequencies corresponding to power spectral
density values
PSD[i] above the threshold (PW + Y) dB. Frequency translation of the signal is
then
performed in the gross error correction process 21 where the carrier frequency
is corrected
by an amount equal to the centroid frequency. The frequency bandwidth is also
estimated
in step 20. This operation is done by selecting the bandwidth corresponding to
a pre-
selected percentage of the sum of the power spectral density values PSD[i]
above the
given threshold (PW + Y) dB. This estimated bandwidth is then used in step 22
to filter the
out-of-band noise power from the frequency-translated signal in step 20. The
filter is
selected from a bank of pre-stored filters.
The process for detecting and classifying the modulation format embedded in
the
signal is performed in steps 23, 30 and 31. Rapid and precise classification
is possible
provided that the residual carrier frequency error inherent on the output
signals 28 and 29
is kept to within 0.00 1% of the sampling frequency FS used in sampling step 6
of Figure 1.
This limitation is illustrated in Figure 4, where the success rate for four
different
modulation types is maintained at the zero-offset levels for frequency errors
up to 10-5 x
F. It should be noted, however, that the presence of amplitude variation on
the complex
baseband signal is insensitive to any phase vector rotation caused by the
inherent carrier
frequency error. The present invention takes advantage of this feature when
discriminating
between constant envelope signals and irregular envelope signals in decision
test 23. This
binary classification test is performed by using the maximum of the squared
Fourier
Transform on the normalized signal amplitude, given by
max IDFT(a)12 (2)
ymax = N
s
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wheref is the frequency, DFT(.) is the Discrete Fourier Transform (computed
from the
Fast Fourier Transform), NS is the number of samples in the input block, and a
is the
amplitude vector centred on zero and normalized by its mean. Mathematically,
vector a is
expressed as
x
a= -1
E[I x 1]
where x is the observed filtered vector, x is the vector of magnitudes for the
elements of
vector x, and E[Ixl] is the average of the magnitude elements over the vector
x. The test
parameter 7 max is totally independent of the phase variation in x and is
therefore
unaffected by residual carrier frequency errors. At the same time, it allows
for the
identification of information in the signal envelope, which, in most cases of
interest,
results in the reliable discrimination between constant envelope and irregular
envelope
signals. The performance obtained in Equation 2 is very good for SNRs as low
as 5 dB,
where the SNR is defined over the sampling bandwidth.
Frequency Error Correction of Constant Amplitude Signals
When test 23 determines that the signal has a constant envelope, the process
moves
to the error-correction step 26 where the residual carrier frequency error is
estimated and
corrected. The purpose of step 26 is to cancel out the carrier frequency error
inherent in
the constant amplitude signa124 in order to determine if the signal is a
continuous wave
(CW or pure tone). Recognition and classification of a CW signal cannot be
performed on
the constant envelope signal unless its inherent carrier frequency error has
been corrected.
The operation is performed in the frequency domain as shown in Figure 5,
consisting of
three signal processing operations: a coarse estimation of the carrier
frequency ( 32, 33, 34
and 35); a refined estimation of the carrier frequency ( 37); and the carrier
frequency error
correction of the constant envelope signal ( 39 and 40). The process begins at
step 32
where the normalized squared signal is computed. The result is then processed
by a Fast
Fourier Transform (FFT) 33 with zero padding, squared in step 34, and
forwarded to a
coarse frequency estimator 35 where a search is done to locate the frequency
line with
17
CA 02298316 2000-02-14
maximum power. Note that both the zero padding and the squaring of the output
of the
FFT improve the frequency resolution of the coarse frequency estimator 35. The
output
36, denoted byfmax, is forwarded to a fine frequency estimator 37 where the
refined
estimation of the carrier frequency is performed. This signal processor (37)
also receives
the constant envelope signal 24 and computes the estimated residual carrier
frequency
error Af at 38, as follows:
_ f, = PSDD[fmax ] - .fmax - PSDD[ f, ]
~f (3)
PSDD[ fmax ] - PSDD[f, ]
where PSDD[f] is the derivative of the power spectral density at frequencyf,
and fi is a
frequency given by
fl = ,f max Fs12N
where FS is the sampling frequency and N the number of samples used in the FFT
(that is,
including zero padding). The plus sign is selected for fl if PSDD[fmax] is
positive, and the
negative sign is selected if PSDD[fTõax] is negative. PSDD[.] is obtained as
PSDD[.f ] = 2Re[S'(.f )S * (.f )]
where Re[.] indicates the real part, S(f) is the Discrete Fourier Transform
(DFT) of the
filtered observed signal at 24, S*(f) is its complex conjugate, and S'(f) is
its first derivative
with respect to frequency, given by
N 2~
SI(.f )=I - Jk xk exp - j F
s
where xk is a sample of the filtered observed signal vector at 24 and N is the
number of
samples in the input vector.
The estimated frequency error Af at 38 is used to set the frequency of a
digital
VCO 39. The output of this VCO is then multiplied by the constant envelope
signa124 in
a multiplier 40 to cancel out the signal's residual carrier frequency error.
18
CA 02298316 2000-02-14
Classification of Constant Envelope Signals
The output 28 of Figure 5 (and Figure 2) is a frequency-translated, constant
envelope signal. This signal is now forwarded to classifier 30 of Figure 2
where its
embedded modulation is further examined to determine if it is CW, FM or FSK.
This
classification process is illustrated in Figure 6 and consists of two steps:
(a) a test for
significant phase variation to determine if the signal is CW or frequency
modulated ( 41),
and (b) a series of tests for determining specific frequency characteristics
to enable
discrimination between FM and FSK formats (42, 43, 44, and 46). The process
begins at
decision step 41 where the frequency-translated, constant envelope signal 28
is examined
to determine if significant phase variations are present within its envelope.
Since CW
signals have a near-zero variance in the unwrapped phase (direct phase) and
frequency-
modulated signals have relatively high variances, a test that determines the
variability of
the unwrapped phase is used. However, this unwrapped phase test requires care
when the
signal vector amplitude is small because phase variations increase as the SNR
decreases.
The difficulty of this problem is mitigated by discarding any data sample
whose amplitude
is below a threshold. Such threshold lowers the probability of residual phase
variance in
the CW signal, while not affecting the phase variance of frequency-modulated
signals. An
amplitude threshold equal to the mean of the amplitudes of the sampled signal
is chosen
under the preferred embodiment of this invention. Discrimination between CW
and
frequency modulated signals is obtained by first retaining the samples of the
signal 28 at
an amplitude above the amplitude threshold, and then comparing the value of
the
unwrapped phase of these samples to a phase threshold whose value is generally
optimized
through computer simulation experiments. If little or no phase variation
exists, decision
test 41 determines that the signal is CW and notifies the phase processor 42
not to proceed
with further classification. Conversely, if significant phase variations occur
in the signal,
step 41 declares the presence of frequency modulation and notifies the phase
processor 42
to proceed with the next stage of classification process for discrimination
between FM or
FSK formats.
To perform the classification between FM and FSK formats, the frequency-
uncorrected, constant envelope signa124 is used instead of the frequency-
translated signal
19
CA 02298316 2000-02-14
28 because the process for computing the latter signal (described in Figure 5)
may create
large frequency errors for non-CW signals, and such large errors would create
problems in
determining the FM and FSK classifications. On the other hand, the residual
carrier
frequency error inherent in signa124 is sufficiently small to allow for
accurate
discrimination between FM and FSK signals. In order to perform such
discrimination
between FM and FSK, the kurtosis coefficient of the instantaneous frequency
content of
the signal is used. This coefficient represents a measure of the flatness of
the signal
frequency distribution, and its value for analog FM is usually different from
that of digital
frequency modulated signals. The kurtosis coefficient also has a good
behaviour at low
SNRs. The coefficient is given by:
f _ E[fi4(t)]
42 - ~'
(E[Ji2(t)])2
where f(t) is the instantaneous frequency (about the mean) at time t, and
E[f(t)] is the time
average off(t) computed over the length of the observed signal.
The process begins at the phase processor 42 where the instantaneous frequency
is
obtained by computing the phase derivative of the constant envelope signa124.
This
computation is further illustrated in Figure 7, consisting of signal
processing steps 49, 50,
51, 52, and 53. The phase of the constant envelope signa124 is computed in
step 49 to
produce the instantaneous phase signa150. The instantaneous phase signal is
then
processed through a low-pass filter (51 and 52) in order to limit the noise
enhancement
effects of the derivative function in step 53. A simple computation in BW
estimation 51
roughly estimates the effective bandwidth of the phase signal which, in turn,
selects from a
library one of a small number of low-pass filters that has a cut-off frequency
slightly
higher than the signal bandwidth. The output of the derivative function 53 is
the estimate
of the instantaneous frequency 54. This estimated value is required in the
computation of
the kurtosis coefficient in step 44 of Figure 6. It is also required to detect
the possible
presence of a low-modulated commercial FM signal in decision step 43. The FM
modulation of such a signal contains the presence of silent periods, and, when
demodulated, it produces a single discrete tone. Other forms of FM signals
also contain
such tones, such as the analog AMPS signals. Thus, the test performed on the
constant
envelope signa124 in step 43 serves the purpose of detecting the presence of
such a tone.
If the tone is present, the signal is declared to be FM (commercial or AMPS).
Conversely,
CA 02298316 2000-02-14
if such tone is not present, the signal is either narrowband FM or FSK.
Following this
process, the kurtosis coefficient is tested. FM signals usually produce a
kurtosis coefficient
that is larger than 2.5. Conversely, the coefficient produced by FSK signals
is smaller
because such signals are more compactly distributed. Thus, if the kurtosis
coefficient is
below the 2.5 threshold, a decision is made in favour of FSK. When the
kurtosis
coefficient is higher than the 2.5 threshold, an initial decision is made at
45 in favour of
FM. However, a further classification test is required at this point because
FSK signals
with highly filtered data (such as GMSK signals) may also have a high kurtosis
coefficient. A frequency-modulated signal whose digital modulation contains a
symbol
rate of f y,,, and a frequency deviation of a multiple of fõn/4, produces
discrete frequency
lines in the power spectral density (FFT) of the squared signal. For example,
MSK and
GMSK signals have a frequency deviation of 2 x fsy,,, /4 = f y,, /2 and a
modulation level
M = 2. The FFT of the square of either signal produces two discrete frequency
lines.
Accordingly, the discrimination process is further refined in decision test 46
where the
FFT of the squared constant envelope signal 24 is computed. (This computation
is the
same as the one done in steps 33 and 34 of Figure 5). Thus, if two or more
discrete
frequency lines are detected, the signal is classified as FSK at 48.
Conversely, if decision
test 46 produces less than two lines, the signal is classified as FM.
This concludes the detailed description for the classification tests performed
on
constant envelope signals.
Frequency Error Correction of Irregular Envelope Signals
The following steps describe the classification processes for signals that
have
irregular envelopes. When decision step 23 of Figure 2 determines that the
measured
signal has an irregular envelope, the process moves to the error-correction
processor 27
where the residual carrier frequency errors are estimated and corrected. This
operation is
performed in the frequency domain as illustrated in Figure 8, and is similar
to the
operation described in Figure 5. Again, the process consists of three signal
processing
steps: a coarse estimation of the carrier frequency (55, 57, 59, and 61); a
refined
estimation of the carrier frequency (62); and the carrier frequency error
correction of the
irregular envelope signal 25 (65 and 66). The process begins at step 55 where
the square of
the irregular envelope signal 25 is performed. The resulting signal is then
processed by
21
CA 02298316 2000-02-14
the FFT 57 with zero padding, squared in step 59, and forwarded to a coarse
frequency
estimator 61 where a search is done to locate the frequency line with maximum
power.
Zero padding and the squaring of the FFT output 58 perform the same resolution
functions
as those described in Figure 5. Depending on the modulation format of the
unknown
signal, a peak in the frequency will appear in path 60. Choosing the frequency
line with
the highest peak, the process moves to a fine frequency estimator 62, where
the carrier
frequency estimation is further refined. This signal processor (62) also
receives the
normalized squared version 56 of the irregular envelope signal 25 and, using
the one-step
of the secant method as described in equation 3, computes the estimated
carrier frequency
error. This value is halved in step 63 according to the squaring non-linearity
in step 55.
The result Af at 64 is used to set the frequency of a digital VCO 65 whose
output {exp(-
j27cOft)} is then multiplied by the irregular envelope signal 25 in a
multiplier 66 to cancel
out the signal's residual carrier frequency error. As illustrated in Figure 9,
the foregoing
frequency error correction process is capable of obtaining a normalized RMS
frequency
estimation error lower than 10-5 for the SNRs of interest (ie., larger than 5
dB). This carrier
recovery method is therefore sufficiently precise to avoid performance
degradation due to
the limitations described in Figure 4. However, it should be noted that the
frequency error
estimation scheme performed in Figure 8 does not produce an adequate
estimation of the
carrier frequency for MPSK signals. This limitation notwithstanding, the
follow-on
process leading to the classification of MPSK uses the irregular envelope
signal with
residual carrier frequency errors at 25 of Figure 2.
Classification of Irregular Envelope Signals
The frequency-translated, irregular envelope signal 29 of Figure 8 (and Figure
2) is now
forwarded to classifier 31 of Figure 2 where it is further examined to
determine if it is amongst the
set {AM, DSB-SC, BPSK, QPSK, MPSK, OTHER}. This classification process is
illustrated in
Figure 10 and comprises the following signal processing steps: discrimination
between one-
dimensional and two-dimensional signals (67); classification of one-
dimensional signals (68 and
70); and classification of two-dimensional signals (73, 75, and 77). The
process begins at decision
test 67 where the frequency-translated, irregular envelope signal 29 is
examined to determine if
any modulation information is carried in the phase of the signal. If such
information is not present,
the signal modulation corresponds to the actual baseband, such as AM
(transmitted carrier), DSB-
22
CA 02298316 2000-02-14
SC, or BPSK, and is recognized as one-dimensional. These signals are
recognized from their
absolute centred unwrapped phase sequence which has a small variance. In
practice, the process
requires phase unwrapping because the initial carrier phase is random.
However, phase
unwrapping is very sensitive to noise, particularly on DSB-SC and BPSK signals
due to their 1800
phase transitions. Moreover, any phase unwrapping error will seriously
increase the variance of the
absolute centred phase. To avoid phase unwrapping of DSB-SC and BPSK signals,
a new quantity
is introduced in step 67 called the "absolute" phase, and is defined as
0" (t) = L( I(t) + j Q(t) )
where I(t) and Q(t) are the inphase and quadrature samples at time t. By
taking the
absolute values of the real and imaginary parts of a signal, a phase sequence
between 0
and 7r/2 radians is produced. The phase sequence allows for a significant
reduction in the
size of the observation space required to make a decision. For DSB-SC signals
the
variance of the phase of the resulting signal is generally small. Small
variance is also true
for BPSK and AM signals. For two-dimensional signals bearing some phase
information
(such as QPSK and MPSK signals), the variance of the absolute phase is high,
tending
towards the variance of a uniformly distributed random variable in the
interval [0, 7d2]
radians. To provide a better separation between one and two-dimensional
baseband
signals, a threshold on the amplitude of the signal is used in step 67, and
the samples
below this threshold are discarded. The use of the amplitude threshold reduces
the
variance of the phase on one-dimensional signals, without significantly
affecting the
variance on two-dimensional signals. Simulations show that the best results
occur when
the said threshold is set equal to the mean of the amplitude of the phase
sequence. If
decision step 67 determines that the signal modulation is one-dimensional, the
process
moves to decision test 68 where the variance of the unwrapped phase (direct
phase) is
computed. Due to the presence of Tc radian jumps in the instantaneous phase of
DSB-SC
and BPSK signals, the said variance is much higher for these signals than for
AM signals.
Phase unwrapping is useful in this case because errors of this quantity are
unlikely for AM
signals, thus providing a good discriminating feature. In order to reduce the
phase variance
for AM signals, a threshold equal to the mean amplitude is set on the
amplitude of the
signal samples in step 68. An indication of low phase variance thus classifies
the signal as
AM at 69. Note also that ASK modulation is a digital form of amplitude
modulation. ASK
23
CA 02298316 2000-02-14
signals are therefore classified as AM signals at 69. If the phase variance is
high, decision
step 68 determines that the signal is not AM and moves to decision step 70
where a further
test is made to determine if the signal is BPSK or DSB-SC. Unlike BPSK
signals, DSB-
SC signals bear an envelope for which the amplitude varies substantially over
time.
Accordingly, step 70 computes the variance of the envelope and uses it to
discriminate
between a DSB-SC signal at 72 and a BPSK signal at 71.
Returning to step 67, if the test determines that the signal is two-
dimensional, the
process moves to decision steps 73, 75 and 77 where PSK signals are separated
from
QAM and other unidentified modulation types. To perform the classification
between
QPSK, 7r/4-QPSK, MPSK and OTHER types of two-dimensional formats, the
frequency-
uncorrected, constant envelope signa125 from decision step 23 is used instead
of the
frequency-translated signal 29 computed in Figure 8, because the residual
carrier
frequency error inherent in signa125 is sufficiently small to allow for
accurate
discrimination between the QPSK, 7r/4-QPSK, MPSK and OTHER signals. To
initiate this
classification in decision step 73, a simple test on the variance of the
signal amplitude is
performed. If the variance of the amplitude is below a given threshold, the
signal is
assumed to be a PSK signal. Even though band-limited PSK signals do exhibit
amplitude
variations, such variations are much less noticeable than those for QAM, SSB
or VSB
signals. This test is therefore sufficient to discriminate PSK signals from
most of the other
two-dimensional signals as OTHER at 74. If the test determines that the signal
is PSK, the
process moves to decision step 75 where the signal is further examined to
determine if its
embedded modulation is QPSK, n/4-QPSK or MPSK. This test is performed by
computing the fourth power of the signa125. QPSK signals produce a single peak
in the
power spectral density of the resulting signal, while 7r/4-QPSK signals
produce two peaks
separated in frequency by twice the baud rate. Therefore, if the test in step
75 results in
one peak, the signal is classified as QPSK at 76. Otherwise the process moves
to decision
test 77 where the combination of two peaks classifies the modulation as n/4-
QPSK at 78
and the absence of any peak classifies the modulation as MPSK at 79.
This concludes the detailed description for the classification tests of
irregular
envelope signals. The description covering the overall decision tree process
as illustrated
in Figure 11, is given below.
24
CA 02298316 2000-02-14
Overall Description of the Preferred Embodiment
Figure 11 illustrates a complete overview of the modulation classification
section 3
of Figure 1 and collects together the signal processing functions illustrated
in Figures 2, 6
and 10. The process begins at input 15 where a block of digital complex
samples is
obtained from the output 8 of the Receiver Section of Figure 1. These samples
are
forwarded to a signal detector 16 where Fast Fourier processing determines if
sufficient
signal power is available to establish the presence of a signal. This process
is performed
with the aid of an external noise power module 17 that establishes a power
threshold
against which the power spectral density of the observed signal is compared.
The noise
power module 17 is also used in step 20 to set another threshold for computing
the
centroid frequency and estimating the signal bandwidth of the signal. If the
signal energy
is not above a noise-related threshold, the SNR is considered too small to
allow further
processing and the signal is classified as NOISE in step 19. However, if a
signal is
declared present, then the gross estimate of the carrier frequency inherent in
the signal is
determined in step 20. This operation is done by computing the centroid of the
portion of
the power spectral density that is above a certain threshold. Frequency
translation of the
signal is then performed in correction step 21 where the carrier frequency is
corrected by
an amount equal to the centroid frequency. The frequency bandwidth is also
estimated in
estimation step 20. This estimated bandwidth is then used in filter step 22 to
filter the out-
of-band noise power from the frequency-translated signal in estimation step
20. The
process for detecting and classifying the modulation format embedded in the
signal starts
in decision test 23 where discrimination between constant envelope signals and
irregular
envelope signals is performed. When decision test 23 determines that the
signal has a
constant envelope, the process moves to the error-correction step 26 where the
residual
carrier frequency error is estimated and corrected. The classification of
constant-envelope
signals starts in decision test 41 and consists of the following steps: (a) a
test for
significant phase variation to determine if the signal is CW or frequency
modulated (41),
and (b) a series of tests for determining specific frequency characteristics
to enable
discrimination between FM and FSK formats (42, 43, 44 and 46). If little or no
phase
variation exists in the frequency-translated signal, decision test 41
determines that the
CA 02298316 2000-02-14
signal is CW and notifies the phase processor 42 not to proceed with further
classification.
Conversely, if significant phase variations occur in the signal, decision test
41 declares the
presence of frequency modulation and notifies the phase processor 42 to
proceed with the
next stage of classification process for discrimination between FM or FSK
formats. To
perform the classification between FM and FSK formats, the frequency-
uncorrected,
constant-envelope signal 24 from decision step 23 is used. The process begins
at
computing step 42 where the instantaneous frequency is obtained by computing
the phase
derivative of the constant envelope signal 24. This estimated value is
required in the
computation of the kurtosis coefficient in decision test 44. It is also
required to detect the
possible presence of a low-modulated commercial FM signal in decision test 43.
The FM
modulation of such a signal contains the presence of silent periods, and, when
demodulated, it produces a single discrete tone. Other forms of FM signals
also contain
such tones, such as the analog AMPS signals. Thus, the test performed on the
constant
envelope signa124 in decision test 43 serves the purpose of detecting the
presence of such
a tone. If the tone is present, the signal is declared to be FM (commercial or
AMPS).
Conversely, if such tone is not present, the signal is either narrowband FM or
FSK.
Following this process, the kurtosis coefficient is tested in decision test
44. FM signals
usually produce a kurtosis coefficient that is larger than 2.5. Conversely,
the coefficient
produced by FSK signals is smaller because such signals are more compactly
distributed.
Thus, if the kurtosis coefficient is below the 2.5 threshold, a decision is
made in favour of
FSK. When the kurtosis coefficient is higher than the 2.5 threshold, an
initial decision is
made in favour of FM. However, a further classification test is required at
this point
because FSK signals with highly filtered data (such as GMSK signals) may also
have a
high kurtosis coefficient. The discrimination process is further refined in
decision step 46
where the FFT of the squared constant envelope signal 24 is computed. If two
or more
discrete frequency lines are detected, the signal is classified as FSK. The
estimate of the
number of symbols M is obtained in counting step 47 by counting the number of
FFT
peaks. Conversely, if decision test 46 produces less than two lines, the
signal is classified
as FM.
When decision step 23 determines that the measured signal has an irregular
envelope, the process moves to the error-correction step 27 where the residual
carrier
26
CA 02298316 2000-02-14
frequency errors are estimated and corrected. The frequency-translated,
irregular envelope
signal output of error correction step 27 is now forwarded to decision test 67
where it is
further examined to determine if it is amongst the set {AM, DSB-SC, BPSK,
QPSK,
MPSK, OTHER}. This classification process comprises of the following signal
processing
steps: discrimination between one-dimensional and two-dimensional signals
(67);
classification of one-dimensional signals (68 and 70); and classification of
two-
dimensional signals (73, 75, and 77). The process begins at decision test 67
where the
frequency-translated, irregular envelope signal is examined to determine if
any modulation
information is carried in the phase of the signal. If such information is not
present, the
signal modulation corresponds to the actual baseband, such as AM (transmitted
carrier),
DSB-SC, or BPSK, and is recognized as one-dimensional. If decision test 67
determines
that the signal modulation is one-dimensional, the process moves to decision
test 68 where
the variance of the unwrapped phase (direct phase) is computed. An indication
of low
phase variance thus classifies the signal as AM. If the phase variance is
high, decision test
68 determines that the signal is not AM and moves to decision step 70 where a
further test
is made to determine if the signal is BPSK or DSB-SC. Unlike BPSK signals, DSB-
SC
signals bear an envelope for which the amplitude varies substantially over
time.
Accordingly, decision test 70 computes the variance of the envelope and uses
it to
discriminate between a DSB-SC signal from a BPSK signal.
Returning to decision step 67, if the test determines that the signal is two-
dimensional, the process moves to decision steps 73, 75 and 77 where PSK
signals are
separated from QAM and other unidentified modulation types. To perform the
classification between QPSK, 7c/4-QPSK, MPSK and OTHER types of two-
dimensional
formats, the frequency-uncorrected, constant envelope signal 25 from decision
test 23 is
used. To initiate this classification in decision step 73, a simple test on
the variance of the
signal amplitude is performed. If the variance of the amplitude is below a
given threshold,
the signal is assumed to be a PSK signal. Otherwise, it is classified as
OTHER. If the test
determines that the signal is PSK, the process moves to decision step 75 where
the signal
is further examined to determine if its embedded modulation is QPSK, 7r/4-QPSK
or
MPSK. This test is performed by computing the fourth power of the signal 25.
QPSK
signals produce a single peak in the power spectral density of the resulting
signal, while
7t/4-QPSK signals produce two peaks separated in frequency by twice the baud
rate.
27
CA 02298316 2000-02-14
Therefore, if the test in step 75 results in one peak, the signal is
classified as QPSK,
otherwise the process moves to decision step 77 where the combination of two
peaks
classifies the modulation as 7r/4-QPSK and the absence of any peak classifies
the
modulation as MPSK.
Different aspects of the embodiment in Figure 1 are possible. For example, the
signal coming to the Receiver Section 2 can be measured from a tapped
wireline, or from
another receiver or pre-amplification section. The signal may also have been
amplified and
filtered by an alternate receiver, and be introduced before the frequency down
conversion
5. Similarly, the down conversion to complex baseband could be performed on an
alternate set of hardware, and the signal could be introduced before the
sampling function
6. Furthermore, the sampled digital complex baseband signal 8 could be
obtained from a
receiver section with a different configuration, or it could be retrieved from
a digital
memory location where it had been previously stored. Note that, for practical
reasons, the
sampling function 6 and the A/D converter 7 are usually implemented in a
single unit, and
that it is not very likely that the signal could be introduced before the
digital conversion
function 7. Such a procedure is nevertheless conceptually also possible.
PERFORMANCE EVALUATION
In order to demonstrate the methods described in the present invention, 500
simulated signals of each of the modulation types have been generated and
processed.
These signals covered a wide variety of parameters as described in the next
section. A
sampling frequency of 48 kHz was used covering a bandwidth slightly larger
than the
occupied bandwidth of most narrowband communications signals. Sequences of
85.3 msec
(representing 4096 samples) were used as inputs to the modulation classifier
(block 3 of
Figure 1). Complex baseband signals were used, whereas the carrier frequency
and phase
errors were simulated. The frequency error was random and uniformly
distributed over a
range [-4.8 kHz to 4.8 kHz], while the initial carrier phase was uniformly
distributed over
[-7r to 7r]. For digitally modulated signals, a random delay uniformly
distributed over [0 to
Ts] was used to simulate symbol timing uncertainties (where TS is the sampling
interval
equal to 1/48000 seconds).
28
CA 02298316 2000-02-14
Simulation of Specific Signals
Analog Modulations
For analog modulation schemes, two types of source signals were simulated. The
first was
a real voice signal, band-limited to [0 to 4 kHz]. The second was a simulated
voice signal
that used a first-order autoregressive process of the form:
y[k] = 0.95 x y[k-1 ]+ n[k]
where n[k] is a white Gaussian noise process. Furthermore, this pseudo-voice
signal was
band-limited from 300 to 4000 Hz.
For AM signals, a constant value was added to the source signal. The
modulation
index was calculated by using the maximum amplitude value over the whole
source signal.
The index was then uniformly distributed in the interval [50% to 100%]. The
total length
of the real source signal was about 120 seconds, while that for the pseudo-
voice was about
40 seconds. From these two source signals, sequences of 85.3 msec in duration
were
randomly extracted. Thus, the observed modulation index for a sequence was
equal to or
less than the chosen modulation index.
For frequency-modulated signals, a cumulative sum was used to approximate the
integral
of the signal source. Generic FM signals were simulated using real or pseudo-
voice signals
with a modulation index uniformly distributed in the interval [1 to 4]. The
bandwidth
occupied by these signals ranged from 16 kHz to 40 kHz, using the
approximation:
BW ` 2(,8 + 1)fmax
where Pis the modulation index and fmax is the maximum source frequency (4 kHz
in this
case). The AMPS FM signals were approximated using a modulation index of 3.
Digital Modulations
Continuous-phase FSK signals were simulated by using filtered M-ary symbols to
provide frequency modulation to a carrier frequency. Pager signal parameters
were based
on observations of real signals, with 2FSK modulation at a bit-rate of 2400
bps, a
29
CA 02298316 2000-02-14
frequency deviation of 4.8 kHz, and almost no filtering. 4FSK signals were
also simulated,
using the same 4.8 kHz frequency deviation and a symbol rate of 1200 baud. The
19.2
kbps, 2FSK signals from the Racal Jaguar radio were simulated, using a
frequency
deviation of 6.5 kHz and a 5`h order Butterworth pre-modulation filter with a
cutoff
frequency of 9.6 kHz. Also included in the simulation were GMSK signals that
were
similar to GSM signals having a BT product of 0.3.
For PSK and QAM signals, the symbols were filtered with either a raised cosine
function or a square root raised cosine function. The selection was randomly
performed
with equal probabilities. The rolloff factors of 20%, 25%, 30%, 35%, 40%, 45%,
and 50%
were uniformly and randomly selected. For all these signals, the symbol rates
were chosen
randomly between 16 and 20 kbaud. Also simulated were 7r/4-QPSK signals that
were
similar to IS-54 signals, with a symbol rate of 24 kbaud and a square-root
raised cosine
pulse-shaping filter with a rolloff factor of 35%.
Additive Noise
The simulated signals were passed through an additive white Gaussian noise
channel before being classified. For the simulation, no filtering was done at
the receiver,
therefore the signal observed by the modulation classifier was corrupted by
the white
noise. The noise power was calculated from the knowledge of the average power
of the
modulated signal and the SNR over the sampling bandwidth. This SNR was defined
as:
SNR samp = S/(No . Fs)
where S is the signal power, No is the white noise power spectral density, and
FS is the
sampling frequency equal to 48 kHz.
For amplitude-modulated signals [AM, DSB-SC, and SSB], the amplitude power
was calculated by using all source signals (real and pseudo-voice). This
condition implies
that, for a given sequence, the observed SNR might be different from the
overall SNR,
which is especially true for DSB-SC and SSB signals where some segments of the
signals,
because of silence segments, may have no power at all.
CA 02298316 2000-02-14
Binary Decision Thresholds
With respect to the decision tree analyses performed under the present
invention,
each decision compares a signal feature with a threshold. For the simulations
undertaken,
the thresholds were set from the results of direct observations of the feature
distributions
in a training set of simulated signals having an SNR of 5 dB. These selected
thresholds are
summarized in Table 1 for the different features.
Feature Threshold
Power level above noise level, for detection of signal presence (Step 16) 10
dB
Power level above noise level, for bandwidth and centroid estimation 5 dB
(Step 20)
Maximum of the normalized squared FFT of the centered normalized 1.44
envelope (^maX) (Step 23)
Variance of the direct phase (rad) (CW vs. FM/FSK in Step 41) 0.25
Variance of the direct phase (rad) (AM vs. DSB-SC/BPSK in Step 68) 4.0
Variance of the "absolute" phase (rad) (one-dimensional vs two- 0.144
dimensional signals in Step 67)
Kurtosis of the instantaneous frequency (FM vs FSK in Step 44) 2.5
Variance of the normalized amplitude in one-dimensional signals (DSB- 0.25
SC vs BPSK in Step 70)
Variance of the normalized amplitude in MPSK signals (OTHER vs 0.15
QPSK/7L/4-QPSK/MPSK in Step 73)
Table 1: Decision thresholds used in the simulations.
Classification Results
An estimate of the performance of the modulation classification method of the
present invention was obtained by applying the simulated signals described
earlier. For
each modulation type, the 500 generated sequences were classified by using the
preferred
decision tree methods illustrated in Figure 11. Eleven outputs from the
modulation
classifier were possible: NOISE, CW, AM, DSB-SC, FM, FSK, BPSK, QPSK, 7c/4-
QPSK,
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CA 02298316 2000-02-14
MPSK, and OTHER. Table 2 shows the classification results for each of the
simulated
modulation types at a SNR of 5 dB. The results of this table were obtained in
the presence
of uniformly distributed frequency errors between - 4.8 kHz and 4.8 kHz (10%
of the
sampling frequency). The initial carrier phase was also uniformly distributed
over the
range of -7c to 7r. For digitally-modulated signals, a random delay uniformly
distributed
over one sample period, was used to simulate symbol timing uncertainties.
NOISE CW AM DSB- FM FSK BPSK QP 7E/4- MPSK OTHER
SC SK QPSK
CW 99.8 0.2
AM (V) 62.6 37.4
AM 14.4 85.6
(SV)
DSB-SC 34.4 53.8 11.8
(V)
DSB-SC 100.0
(SV)
FM (V) 17.6 0.6 69.0 12.0 0.2 0.6
FM 98.4 1.6
(SV)
AMPS 98.6 1.4
Pager 98.4 0.4 1.2
FSK4 98.2 0.2 0.2 1.4
Jaguar 98.0 2.0
GMSK 99.8 0.2
BPSK 100.0
QPSK 2.6 97. 0.4
0
Tc/4- 0.6 99.4
QPSK
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NOISE CW AM DSB- FM FSK BPSK QP iU4- MPSK OTHER
SC SK QPSK
PSK8 3.8 96.2
PSK16 5.6 94.2 0.2
QAM16 100.0
QAM64 100.0
SSB (V) 29.6 6.0 9.6 1.6 0.6 52.6
SSB 100.0
(SV)
Table 2 - Classification results (in %) for a SNR of 5 dB.
In Table 2, it is important to note the difference between the classification
for
analog modulation signals using real voice (denoted by "V") and those using
simulated
voice (denoted by "SV"). For these modulations, the real voice signals
included pause and
silent durations, whereas the simulated voice signals were generated
continuously,
without any silent duration. For analog modulation, the pauses in a real voice
source
produced unmodulated sequences. For DSB-SC and SSB modulated signals, such
pauses
produced no signal at all. In the case where the duration of the 85.3 msec
sequence was
mostly a pause, the signal was classified as noise or as OTHER. In the case
where the
transition between a pause and voice was not clear within the 85.3 msec
observation,
erroneous modulation types appeared (as the row for SSB(V) in table 2
indicates). For AM
and FM signals, the absence of a source signal produced a CW classification.
If the
duration of the silence occupied most of the 85.3 msec observation time, such
quiet
sequences were classified as CW signals. Again, depending on the transition
time between
a pause and a voice, strange results appeared (as the row for FM(V) of Table 2
indicates).
These results are not considered classification errors as such. Rather, they
reflect the fact
that the classification is more difficult to perform for analog-modulated
signals when
using a very short observation time. Such perceived errors would be eliminated
by either
increasing the length of the observation time before the classification is
undertaken, or
33
CA 02298316 2009-05-29
adding a post-processing step that accumulates the results of several
observations and
performs a decision according to the dominant modulation type.
Modular Construction
The modular nature of the classification process illustrated in Figure 11
allows for
different modulation schemes to be classified. Furthermore, although the
disclosed
approach under the present invention assumes an AWGN channel, there are
possibilities of
extending the channel to more complex models by employing additional
processing, such
as the method of blind equalization.
Changes and modifications in the specifically described embodiments can be
carried out without departing from the scope of the invention which is
intended to be
limited only by the scope of the appended claims.
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