Comparison and Simulation of Digital Modulation Recognition Algorithms

###### Wei Su

U.S. Army CECOM RDEC

Intelligence and Information Warfare Directorate

AMSEL-RD-IW-I

Fort Monmouth, NJ 07703

1-732-427-6332

<wei.su@us.army.mil>

####### John Kosinski

U.S. Army CECOM RDEC

Intelligence and Information Warfare Directorate

AMSEL-RD-IW-I

Fort Monmouth, NJ 07703

1-732-427-5605

<john.kosinski@us.army.mil>

## *Abstract* - Modulation recognition has been studied for decades with numerous amounts of papers published. Modulation classifiers are developed under assumptions and may not be robust in some applications. This paper studies and simulates several popular digital modulation recognition methods and discusses the pros and cons of those algorithms based on the robustness of the modulation feature and algorithm fundamentals.

*Index Terms* -- electronic warfare, communication, modulation
recognition, signal classification, algorithm comparison, modulation
feature.

I.  **INTRODUCTION**

Modulation recognition is an important subject not only in commercial
application but also in classifying emitter types for military
electronic support cases \[1-4\]. Modulation recognition is a
non-cooperative communication practice which, in general, starts with
signal processing to remove center frequency, re-sample the signal,
synchronize baud rate and carrier phase, and equalize the channel
distortion. It is followed by modulation feature extraction to obtain
unique information related to amplitude, phase, and frequency. Then,
feature recognition is applied by using logic analysis to match features
to known templates, or using statistical analysis to find a solution
based on probabilities. Therefore, based on the techniques being used, a
successful modulation recognition technique may depend not only on
factors such as: signal bandwidth, available signal length, digitization
method, number of samples per symbol, modulation types, transmission
environment, signal noise ratio, frequency stability, processing power,
processing time, implementation cost, and dimension of confusion matrix,
but also on qualities of baud rate estimation, pulse synchronization,
pulse re-sampling, carrier synchronization, etc. Many publications
assume to have perfect knowledge of center frequency, baud rate, and
pulse shape so that a fair comparison of different algorithms becomes a
challenge. To compare algorithms based solely on signal to noise ratio
(SNR) and probability of success may have little value. Fundamental
similarities and differences between the algorithmic bases should be
explored.

II. **ALGORITHM COMPARISON**

The modulation recognition includes converting the analog RF signal to a
digital IF signal, extracting modulation features, and recognizing
modulation types. Some classifiers can extract modulation features
directly from an IF signal. But, in most cases, a coarse estimation is
needed to convert IF signal to I and Q components, and extract
modulation features with the presence of pass-band signal residuals such
as center frequency offset (CFO) or timing errors. Many classifiers
extracts features by assuming to have perfect base-band symbols since
those features are very sensitive to pass-band disturbances. The
modulation recognition is conducted by searching the best match between
modulation features and given templates. The result of modulation
recognition could be a confusion-matrix, which is a table of statistical
values obtained with a specified signal-to-noise ratio (SNR). This table
provides the values of probability-of-success in respect to a list of
candidate modulation types. The result of modulation recognition could
also be a set of curves representing candidate modulation types. Each
curve gives the probability-of-success versus SNR for a given modulation
type. Since modulation classifiers are developed under various
assumptions and objectives, the algorithm comparison is nontrivial.
Probability-of-success will be a performance measurement only if two
classifiers are developed under the same assumptions.
Probability-of-false-alarm should also be included to measure the
failures that an unknown type is forced to a know template. Therefore,
fundamental differences between the algorithms should be studied.

### 

***A. Phasor Variation Analysis Classifier***

Phasor analysis approach utilizes the phase variation and amplitude
variation as features in modulation recognition. In this approach, the
IF signal is down-converted to base-band and the symbols are extracted
for analysis. Many algorithms assume the unknown signal is transmitted
through an ideal channel so that the white Gaussian AWGN is the only
concern in estimation error, some of the algorithms, such as Azzouz and
Nandi's modulation classifier \[5,6\], also assume a perfect recovery of
signal symbols. Azzouz and Nandi's classifier recognize both analog and
digital modulation types. The digital modulation includes: ASK2, ASK4,
FSK2, FSK4, PSK2, and PSK4, Figure 1. The standard-deviation of
modulation parameters: nonlinear component of the phase, the absolute
value of the nonlinear component of the phase, the absolute value of the
normalized-centered instantaneous amplitude, and the absolute value of
the normalized-centered frequency are used as features. These standard
deviation features are used together with the amplitude power spectrum
density in a logic flowchart to match the predetermined feature
thresholds to determine the modulation type. Reference \[5\] is a good
tutorial for this type of general modulation recognition. However, the
variance of the nonlinear component of the phase and the variance of the
absolute value of the nonlinear component of the phase require the
removal of the center frequency and linear phase components from the
carried signal. Since most communication systems employ some type of
filtering prior to transmission for shaping the signal for bandwidth
efficiency, as shown in Figure 2, the pulse function of a PSK signal
will have a smooth transition and the pulse shape will not be as
rectangular as shown by the dashed-line of Figure 2. The linear
component of the phase will not be removed easily. In this case, the
performance of phase variation and absolute phase variation tests will
be failed.

![](media/image1.png){width="3.8043307086614173in"
height="1.5291338582677165in"}

![](media/image3.png){width="3.499212598425197in"
height="2.0846456692913384in"}

Furthermore, if the center frequency is not removed perfectly, the phase
samples $\varphi(i) = \varphi(i - 1) + 2\pi\frac{f_{r}}{f_{s}}$ will
drift in time as shown in Figures 3 for a BPSK modulation and Figure 8
for a PSK8 modulation, where $f_{s}$ is the sampling frequency and
$f_{r}$ is the center frequency offset. Carrier timing is another issue
in this approach, if one of the PSK phase states is located close to the
constellation point π as shown in Figure 4, the phase plot may wrap
between -π and π, as shown in Figure 5, due to the random noise. This
wrap effect may generate large phase variations to fail the standard
deviation test.

![](media/image4.jpeg){width="3.0653543307086615in"
height="2.6098425196850394in"}

![](media/image5.png){width="3.0625984251968505in"
height="2.0507874015748033in"}

![](media/image6.png){width="2.985433070866142in"
height="2.527952755905512in"}This approach may be extended \[7\] by
adding a frequency estimator, a symbol phase tracker, and a timing
device as shown in Figure 6. The frequency estimator provides the
instantaneous center frequency of the IF signal. The frequency variance
can be used to determine if it is a single tone modulation type. If the
frequency variance is large, the standard deviations of the estimated
frequency and the absolute value of the frequency are sent to
recognition block. Otherwise, the signal will be down modulated to
base-band using the estimated center frequency. A timing-recovery
circuit is applied to extract amplitude, phase, and frequency symbols.
Since the carrier estimated by the frequency estimator may not be
accurate and the center frequency may be unstable, a phase tracking and
correction block has to be used to remove the residual carrier frequency
and prevent phase warp. Figure 7 illustrates that the phase drift of the
PSK2 signal in Figure 3 is corrected by using a blind carrier phase
tracking algorithm \[8\].

![](media/image7.jpeg){width="3.399212598425197in"
height="2.255511811023622in"}

To solve the center frequency offset problem, Liedtke \[9\] adapted
delta-phase (the phase difference between two adjacent phase symbols) as
a feather rather than phase itself. Figure 8 illustrates the
constellation diagram of a PSK8 signal with center frequency offset.

![](media/image8.png){width="2.998425196850394in"
height="2.677165354330709in"}

The PSK8 phase feature cannot be observed due to the phase rotation
caused by center frequency offset. Figure 9 shows the same signal
plotted with delta phase. The clusters of PSK8 are recovered. Liedtke
recognizes modulation types: ASK2, FSK2, PSK2, PSK4, PSK8 and CW, Figure
10, by utilizing the histograms of delta-phase. This algorithm only
assumes to roughly know the center frequency of the signal and symbol
rate. The signal is converted to almost base-band with the residual
center frequency by using a concentric FIR filter bank centered at the
center frequency. A symbol recovery circuit is employed to extract a
sinusoidal waveform with an appropriately tuned narrow band pass filter
centered at the symbol rate. This waveform is used to recover the PSK
and FSK symbols. Then, the symbol amplitudes and the delta-phase are
obtained. The frequency measurement is conducted by taking the phase
difference of two time samples. The amplitude variance and frequency
variance are used as features for separating modulation types among PSK,
ASK, and FSK. The delta-phase histogram is used for probability density
analysis to separate PSK2, PSK4, and PSK8. An addition-only sub-optimal
histogram separation process is used to recognize PSK modulation types
automatically. The advantage of using the delta-phase as a feature is
that the center frequency offset will be eliminated in PSK recognition.
Figures 11 and 12 show the deference between phase sample histogram and
the delta-phase symbol histogram of a DQPSK signal. Furthermore, with
the timing recovery circuit, all feature parameters are observed at the
Nyquist sampling rate, and pulse shaping will no longer significantly
affect the recognition result.

![](media/image9.png){width="3.202755905511811in"
height="2.0133858267716533in"}

![](media/image10.wmf){width="3.6791338582677167in"
height="2.495275590551181in"}

![](media/image11.wmf){width="3.7311023622047244in"
height="2.2881889763779526in"}

This approach may be extended \[10\] by adding a frequency estimator and
an automated timing-recovery device to replace the manual tuning. Since
the delta-phase is used as the phase feature, the residual carrier
frequency will be eliminated and the phase tracking and correction
operation is not needed. If the frequency variance is larger than the
threshold value, FSK modulation recognition will be considered.
Otherwise, the signal will be down modulated and CW/PSK/ASK modulation
recognition will be processed. The modulation feature recognition of the
phasor variation analysis approach could be conducted by comparing the
feature variances to thresholds \[5, 6, 9, 25, 26\]. Since the variance
is quite sensitive to SNR, this method is better being used for
top-level classification. Histograms analysis \[9, 25, 26\] is another
frequently used technique and it is usually use for PSK modulation
types. If the perfect symbol recovery is possible, maximum likelihood
classifiers \[11-21\] will be an optimal approach for MPSK and QAM
modulation recognitions. It may also be possible to treat constellation
plot as image pixels so that many image recognition algorithms \[22-24\]
can be useful in classifying the PSK and QAM modulation types.

B.  ***Zero-Crossing Modulation Classifier***

Hsue and Soliman \[25,26\] introduced a modulation recognizer for PSK2,
PSK4, PSK8, FSK2, FSK4, and FSK8 modulation types based only on the
zero-crossing characteristics of signals as shown in Figure 14. The
modulation classification procedure extracts the zero-crossing interval
sequence for frequency estimation. The estimated frequency is then used
together with the zero-crossing sequence for phase estimation. Similar
to Liedtke's method, variances are used to separate FSK from single tone
signals, and delta-phase histograms are used for parameter variation
estimation of PSK signals. Variance thresholds, histogram templates, and
likelihood ratio tests are employed for making the modulation decision.
Frequency histogram is used for FSK recognition although the
classification of a frequency histogram is not trivial. Unlike Liedtke's
method, Hsue and Soliman use zero-crossing carrier estimation instead of
manual tuning. Although the estimation is not accurate enough to provide
a precise carrier frequency, the delta-phase approach will overcome the
center frequency offset in PSK recognition. However, the accuracy of
zero-crossing frequency estimation is very sensitive to the SNR as shown
in Figures 15 and 16. When SNR is low, the noise may produce additional
zero-crossing points. A good resolution of zero-crossing measurement
requires a very high sampling rate as shown in Figure 15 for a BPSK
signal, where the solid-line is has 80 samples per symbol and the
dashed-line has only 4 samples per symbol. The low sample rate will
reduce recognition performance greatly, but the high sample rate will
pick up thermal noises. Since some data collecting devices requires only
two samples per symbol, zero-crossing modulation classifier has to
up-sample the data before processing. Our simulation also shows that the
rising-edge/falling edge zero-crossing estimation is less noisy than the
either-edge zero-crossing estimation as shown in Figure 16, where the
smooth dashed-line stands for the frequency estimation of a FSK signal
using rising-edge zero-crossing and the noisy solid-line stands for the
frequency estimation using either-edge zero-crossing. Furthermore,
zero-crossing frequency estimation may yield a single frequency result
for an unknown signal with multiple instantaneous frequencies.

![](media/image12.png){width="3.2255905511811025in"
height="3.6834645669291337in"}

![](media/image13.jpeg){width="3.694488188976378in"
height="2.302755905511811in"}

![](media/image14.wmf){width="3.3271653543307087in"
height="2.6145669291338582in"}

C.  ***Power-Law Modulation Classifier***

DeSimio and Glenn \[27\] introduced a technique to classify digital
modulations: ASK2, PSK2, PSK4, and FSK2, as shown in Figure 17. In this
recognizer a power-law classification is conducted to obtain the squared
and the fourth power of a signal. Therefore, the key features are
magnitude and location of the spectrum peaks in the frequency domain.
That is, the magnitude of the spectral component at twice the carrier
frequency of the signal raised to the second power, or the magnitude of
the spectral component at four times the carrier frequency of the signal
raised to the fourth power. For example, Figure 18 is the frequency
spectrum of 100 symbols of a QPSK signal with center frequency *f~c~* at
12 KHz, sampling frequency at 160 KHz, and SNR=10dB. Figure 19 is the
spectrum of the same signal after taking the forth power. A peak of
*4f~c~* is shown at 48 KHz, which indicates the QPSK modulation type.
This peak will not be seen in Figure 18 or in the spectrum of the
squared signal. The mean and variance of the signal envelope are used
for ASK recognition. A decision tree is used to recognize modulation
type based on the values of above features. The concept of power-law
classification is based on the fact that squaring of an MPSK signal is
another PSK with M/2 phase states. The power-law approach has the
convenience of recognizing modulation type without converting the signal
to base-band. Although band pass filtering of the spectrum peak requires
knowledge of the center frequency, the exact carrier frequency and pulse
shape are not necessary. However, this method is limited by the sampling
rate. The signal must be sufficiently over-sampled (for example: 2X for
PSK2 or 4X for PSK4) in order to satisfy the sampling theorem. Figure 20
shows the same signal sampled at a lower rate of 80 KHz. Since the
sampling theorem limit the frequency range to 40 KHz, the peak at 48KHz
will not be displayed at Figure 20. Although the image of *4f~c~* exists
at 32 KHz, it is too noisy to be properly detected. The peak of *4f~c~*
can be detected by correlating the spectrum of the signal with a
*sinc^2^(x)* reference function \[27\], but a high resolution spectrum
may be needed. Our simulation also shows that the detection of spectrum
peak becomes more difficult if the pulse shaping is used. The capability
in FSK modulation recognition is limited in this approach.

![](media/image15.jpeg){width="3.5381889763779526in"
height="2.710236220472441in"}

![](media/image16.jpeg){width="3.6110236220472443in"
height="2.7598425196850394in"}

![](media/image17.jpeg){width="3.4618110236220474in"
height="2.606299212598425in"}

III. **CONCLUSION**

> Some well-known modulation recognition algorithms are studied and
> simulated. The comparison of modulation recognition algorithms is not
> straightforward since algorithms are developed under different
> motivations and they are all good in solving certain problems. Our
> analysis is based on our application requirements, which may not apply
> to other cases. All signal plots used in this paper are simulated by
> MATLAB software and are not associated with any commercial or military
> devices/systems. Modulation classifiers may be sensitive to center
> frequency offset, and pulse shaping, symbol or carrier timing, and
> sampling frequency. The assumptions, limitations, and the fundamental
> similarities and differences between the algorithms should be explored
> in algorithm comparison.

#### REFERENCES

\[1\] W. Su, "Computing and simulation of optimal location for RF
emitters over rough terrain," in *Proc. of the 46^th^ Joint Electronic
Warfare Conference*, May 2000.

\[2\] B. Abbe et al., "Use of unconventional battlefield systems for
IO," in *Proc. of the 45^th^ Annual Joint Electronic Warfare
Conference*, May 1999.

\[3\] W. Su and T. Huyuh, "A novel method in automated map based
intelligence support systems," in *Proc. of 1998 Joint Electronic
Warfare Conference*, April 1998.

> \[4\] T. Huynh and W. Su, "Analysis of a back-propagation approach for
> automated jammer deployment," in *Research and Development Technical
> Report*, CECOM-TR-99-1, April 1999.
>
> \[5\] E. Azzouz and A. Nandi, "Automatic modulation recognition of
> communication signals," *Kluwer Academic Publishers*, 1996.

\[6\] E. Azzouz and A. Nandi, "Automatic Identification of Digital
Modulations," *Signal Processing*, Vol. 47, No. 1, Nov. 1995, pp.55-69.

\[7\] W. Su and J. Kosinski, \"Comparison and modification of automated
communication modulation recognition methods,\" in Proc. of MILCOM'02,
October 2002.

\[8\] Belouchrani and W. Ren, "Blind Carrier Phase Tracking with
Guaranteed Global Convergence," *IEE Trans*. on Signal Processing,
Vol.45, No.7, July 1997.

\[9\] F. Liedtke, "Computer simulation of an automatic classification
procedure for digitally modulated communications signals with unknown
parameters," *Signal Processin*g, Vol 6, No. 4, pp. 311-323, August
1984.

> \[10\] W. Su and J. Kosinski, "Application of COTS algorithms to
> automated modulation recognition and signal classification method,"
> *2001 AOC Intelligence Electronic Warfare Conference*, August 2001.

\[11\] K. Kim and A. Polydoros, "Digital modulation classification: the
BPSK versus QPSK case", in *Proc.* *IEEE Conf.*, 1988, pp. 431-436.

\[12\] C. Y. Huang and A. Polydoros, "Likelihood methods for MPSK
modulation classification", *IEEE Trans. Commun*., vol. 43, No. 2/3/4,
pp. 1493-1504, Feb./March/April 1995

\[13\] C. Long, K. Chugg and A. Polydoros, "Further results in
likelihood classification of QAM signals," in *Proc. MILCOM* '94, Oct.
1994.

\[14\] K. M. Chugg, C. S. Long and A. Polydoros, "Combined likelihood
power estimation and multiple hypothesis modulation classification", in
*Proc 29^th^ Asilomar Conf.*, pp*.* 1137-1141, 1996

\[15\] J.A. Sills, "Maximum-likelihood modulation classification for
PSK/QAM", in *Proc. IEEE MILCOM*, vol.1, Oct. 1994, pp. 57-61.

\[16\] W. Wei and J. M. Mendel, "Maximum-likelihood classification for
digital amplitude-phase modulations", *IEEE Trans. Commun*., vol. 48,
No. 2, pp. 189-193, Feb. 2000.

\[17\] P. C. Sapiano and J. D. Martin, "Maximum likelihood PSK
classifier", in *Proc. IEEE ICASSP*, 1996, pp. 1010-1014.

\[18\] D. Boiteau and C. Le Martret, "A generalized maximum likelihood
framework for modulation classification", in *Proc. IEEE ICASSP*, vol.
4, pp. 2165-2168, May 1998.

\[19\] P. Panagiotou, A. Anastastasoupoulos and A. Polydoros,
"Likelihood ratio tests for modulation classification", in *Proc. IEEE*,
2000, pp. 670- 674.

\[20\] A. Polydoros and K. Kim, " On the detection and classification of
quadrature digital modulations in broad-band Noise", *IEEE Trans.
Commun*., vol. 38, No. 8, pp. 1199-1211, Aug. 1990.

\[21\] M. Moeneclaey and G. D. Jonghe, "ML-Oriented NDA carrier
synchronization for general rotationally symmetric signal
constellations," IEEE Transactions on communications, Vol 42, No.8, pp.
2531-2533, August 1994.

\[22\] Y. Shi et al., "A Shift-Invariant Modified Kohonen Neural
Network," in *Proc. of 2000 International Conference on Signal
Processing Application and Technology*, October 2000.

\[23\] W. Su, "Method and Apparatus to Process Drawing Images," *US
Patent* Number 5,946,415, August 31, 1999.

\[24\] W. Su, "A Simple and Quick Approach in Processing Drawing
Images," in *Proc. of 1995 International Conference on Signal Processing
Applications and Technology,* August 1995.

\[25\] S-Z. Hsue and Samir S. Soliman, "Automatic Modulation Recognition
of Digitally Modulated Signals," in *Proc. of MILCOM'89*, 1989.

\[26\] S-Z. Hsue and Samir S. Soliman, "Automatic modulation
classification using zero-crossing," *IEE Proceedings*, vol.137, Pt. F,
No.6, pp.459-464, December 1990.

\[27\] M. DeSimio, E. Glenn, "Adaptive Generation of Decision Functions
for Classification of Digitally Modulated Signals," in *Proc. Of
NAECON'88*, pp. 1010-1014.