# Digital Modulation Identification Model Using  Wavelet Transform and Statistical Parameters

Authors: P. Prakasam; M. Madheswaran
Journal: Journal of Computer Systems, Networks, and Communications
 (2008)

---

## Abstract

A generalized modulation identification scheme is developed and presented. With the help of this scheme, the automatic modulation classification and recognition of wireless communication signals with a priori unknown parameters are possible effectively. The special features of the procedure are the possibility to adapt it dynamically to nearly all modulation types, and the capability to identify. The developed scheme based on wavelet transform and statistical parameters has been used to identify M-ary PSK, M-ary QAM, GMSK, and M-ary FSK modulations. The simulated results show that the correct modulation identification is possible to a lower bound of 5 dB. The identification percentage has been analyzed based on the confusion matrix. When SNR is above 5 dB, the probability of detection of the proposed system is more than 0.968. The performance of the proposed scheme has been compared with existing methods and found it will identify all digital modulation schemes with low SNR.


---

## Body

## 1. Introduction

The rapid growth in the field of mobile communication in general, software defined radio (SDR) in particular, has motivated the
researchers to develop various digital modulation identification algorithms
[1]. As the adaptive receiver in SDR can
communicate with different communication standards like TDMA, CDMA, and GSM,
the identification of digital modulation type of a signal is to be optimized. The
signal identification process is an intermediate step between signal
interception and demodulation. In recent past, several research groups
have developed various modulation identification methods. An extensive survey
of automatic modulation scheme classification was presented in Dobre et al. [2]. The simulation for various methodologies was done and compared. Modulation
scheme recognition using the signal envelope method was described by Druckmann
et al. [3]. This method achieves better recognition
rates at short data records and if the data records are longer, then this
method fails to recognize to recognize. Lopatka and Pedzisa [4] adopted the approach incorporating fuzzy classification for 4DPSK,
16QAM, and FSK schemes. Callaghan et al. [5] proposed a signal envelop and zero-crossing-based
modulation recognizer, but the accuracy of the recognizer was highly dependent
on determining the exact intercepted signal center frequency. This recognizer was
capable of recognizing carrier wave (CW) and frequency shift keying (FSK) but
requires SNR ≥ 20 dB for correct modulation scheme recognition. A pattern
recognition approach for both digital and analog modulation scheme was proposed
by Jondral [6], which can classify AM, ASK2, SSB, PSK2, FSK2, and FSK4
modulation scheme types. The classifier based on pattern recognitions technique
to discriminate between M-ary PSK and QAM signal developed and presented by Beran [7] used the binary image word spotting problems. Aiello et al. [8] proposed an
artificial neural network-(ANN-) based classifier which incorporates pattern
recognition techniques. This classifier had an ability only to identify GMSK
modulation scheme. Software radio technique for automatic digital modulation
scheme recognition was reported in [9] to classify BPSK and QPSK schemes at lower
bound SNR of 9 dB. The 8th-order statistical moment was used to identify the
modulation as either BPSK or QPSK. The classification of BPSK, QPSK, 8PSK, 8QAM,
and 16QAM was done using a DFT of the phase histogram method, and the analysis
was carried out using the maximum likelihood approach in [10]. This method
failed to identify the frequency variable digital modulation schemes. These
methods are either computationally intensive or require a high signal-to-noise
ratio (SNR). The classification of MFSK, MPSK, and QAM was carried out using
number of amplitude levels and phase in the carrier of DFT simulation [11], without
considering the channel noise.Ketterer et al. [12] have
utilized the time-frequency analysis, that is, wavelet transform (WT), when nonstationary
signals were considered. It is reported that the wavelet approach approximates
both the signal envelop and frequency content. This has motivated the
researchers to effectively utilize the WT approach for estimating the pattern [12–15].
Lin and Kuo [13] applied Morlet wavelet to detect the phase changes, and
used the likelihood function based on the total number of detected phase
changes as a feature to classify MPSK signal. Hong and Ho [14] used the Haar WT and statistical
decision theory for identifying identification MPSK, MFSK, and MQAM signals
contaminated by additive white Gaussian noise (AWGN). Binary PSK/CPFSK and MSK
identification was investigated by Pavlík [15]. The complex Shannon wavelet was applied to identify binary modulation
signals under constant envelope scheme and it failed to identify the
nonconstant envelop modulation schemes. Automatic modulation identification
(AMI) algorithm reported by Prakasam and Madheswaran [16] has been developed to
classify QPSK and GMSK signals with additive white Gaussian noise (AWGN) channel.
This algorithm failed to identify when SNR is less than 12 dB.The reported schemes are
capable of identifying few modulation schemes with higher SNR. Therefore, an
attempt is made to propose a generalized modulation identification model to
identify BPSK, QPSK, 8PSK, 16PSK, 2QAM, 4QAM, 8QAM, 16QAM, GMSK, and MFSK
modulation schemes under noisy environment with low SNR considering both
wavelet transform approach as well as statistical moments.


## 2. Mathematical Model

Let the received waveformr(t),0≤t≤T  be described as
(1)r(t)=s(t)+n(t),
where s(t) is transmitted signal and n(t) is an additive white Gaussian
channel noise. The signal s(t) can be represented in complex form as
(2)s(t)=s(t)ej*f(wct+θc),
where ωc is the carrier frequency and θc is the carrier phase. Generally, the complex
envelope of s(t) in (1) may be expressed for all modulation types as
(3)s(t)=s(t)exp⁡(jϕ(t;a)),
where ϕ(t;a) represents the time-varying phase of the
carrier, a represents all possible
values of the information sequence {ak}, in the case of binary symbols ak=±1.The analysis technique is
required for nonstationary signal, which will analyze the signal frequency with
time instants of occurring. The Fourier transform approach gives either the
frequency components or time components. The wavelet transform has the special
feature of multiresolution analysis (MRA), which provides the necessary parameters
to extract the feature of the modulated signals. The wavelet transform of (3)
is given by
(4)C(a,τ)=s(t)e(ϕ(⋅)+θc)jafcEi(n,y),
where  Ei(n,y)=∫1∞exp(−yu/un)du is the exponential integral, y=−jt(2πf−2πfc),
and expression (4) does not reduce to a simple form and must be evaluated
numerically by taking its absolute value |C(a,τ)|.


### 2.1. Classification of Subsystem

The normalized histogram generation of wavelet  transformed coefficient is used to classify the Subsystem1 (M-ary PSK and M-ary QAM) with Subsystem2 (GMSK and
M-ary FSK). Ifni is the
number of occurrence in a particular value then the normalized histogram
(probability of occurrence) of a process is given by
(5)p(xi)=nin,
where n is
total number of samples in the particular process. Subsystem1 signal has
constant transient characteristics; they have a single peak in its normalized
histogram. But the Subsystem2 signals have multifrequency component, they have
multiple peaks in its normalized histogram.The classification of
various modulation schemes may be formulated using the statistical parameters
such as moments and median. The moment plays the major contribution in
nonstationary signal, thus it has been considered for the classification. Thenth-order
moment for p(xi), where i=0,1,2,…,N−1 is given by
(6)μn(x)=∑i=0N−1(xi−μ1)np(xi),
where μ1=∑i=0N−1xip(xi) is the mean of the statistical process. The
second-order moment (variance) of discretized WT can be computed using
(7)μ2=E(|C(a,τ)|2)−[E(|C(a,τ)|)]2=1N∑i=0N−1|Ci(a,τ)|2−[1N∑i=0N−1(|Ci(a,τ)|)]2,
where N is the length of discretized analyzed
signal. Then the classification problem can be formulated as a binary tree hypothesis-testing
problem.LetHi be the ith
modulation format assigned to the received signal, where i is associated with {M-aryPSK,j} and j is
with M-ary QAM. The statistical decision needs the probability density function
(pdf) of the test statistics conditioned on the assigned digitally modulated
signal. Assuming the noise in (1) is AWGN, the wavelet transform coefficient C(a,τ)
has a characteristic of random variables generated from linear combinations of
sinusoidal signal and a Gaussian noise. The two conditional Gaussian pdfs allow
a threshold setting to decide the M-ary PSK and M-ary QAM, when a certain
probability of false identification of both signals is given. The conditional
pdf is
(8)p(xHi)=12πμ2,iexp⁡(−(x−μ1,i)2μ2,i2).Under the hypothesisHM-aryPSK is true, the
probability of M-ary PSK misclassification is simply the probability that μ1,M-aryPSK−x>μ1,M-aryPSK−T1,
that is, μ1<T1. The probability of misclassification error for
M-ary PSK is given by
(9)P(eHM-aryPSK)=12(1+ercf(x−μ1,M-aryPSK2μ2,M-aryPSK)),
where ercf() is
defined as ercf(x)=(2/π)∫0xexp(−t2)dt.
Similarly, if it is assumed that the hypothesis HM-aryQAM is true,
the probability of M-ary QAM signal misclassification is simply the probability
that x−μ1,M-aryPSK>T1−μ2,M-aryPSK, that is, μ1>T1. The probability of misclassification error for M-ary QAM is given by
(10)P(eHM-aryQAM)=12(1+ercf(x−μ1,M-aryQAM2μ2,M-aryQAM)),
where ercf() is
defined as ercf(x)=(2/π)∫0xexp(−t2)dt.
It is obvious that when the Gaussian noise increases, the mean value of M-ary
PSK and M-ary QAM decreases until the point when both the probabilities of
misclassification are equal. Thus, P(e/HM-aryPSK)=P(e/HM-aryQAM)=.01 and the condition for setting the optimal
threshold value T1 can be obtained by equating Gaussian distribution
is zero. Then the related threshold value is obtained as
(11)T1=μ1,M-aryPSKμ2,M-aryQAM+μ1,M-aryQAMμ2,M-aryPSKμ2,M-aryPSK+μ2,M-aryQAM.
Based on the mean value the classification of M-ary
PSK with M-ary QAM can be done.


### 2.2. Classification of M-ary PSK Signals

The
method described in earlier has been used for setting the thresholdTPr (where r is varying from 1,2,3,… to
represent 2-ary, 4-ary, 8-ary, etc.) and the further classification of
substsem1 can be classified based on second- or higher-order statistical
moment. Decision making between BPSK, QPSK, 8PSK, 16PSK, and so on can be
carried out based on the comparison of variance value with computed threshold
value and for 2PSK and 4PSK is given by
(12)TP1=μ1,2PSKμ2,4PSK+μ1,4PSKμ2,2PSKμ2,2PSK+μ2,4PSK.
Similarly, the threshold value TP2,TP3,TP4,… can be defined using the same procedure.


### 2.3. Classification of M-ary QAM Signals

The classification of M-ary QAM
has been classified using the same method prescribed in the last section and
the comparison of variance value with the threshold is used to classify the
subclassification. The threshold value for decision making of 2QAM with 4QAM is
given by(13)TQ1=μ1,2QAMμ2,4QAM+μ1,4QAMμ2,2QAMμ2,2QAM+μ2,4QAM.
Similarly, the threshold value TQ2,TQ3,TQ4,… can be
defined using the same procedure.Decision making between GMSK and
M-ary FSK can be done based on the comparison of variance value with thresholdT2 and is given by
(14)T2=μ1,GMSKμ2,M-aryFSK+μ1,M-aryFSKμ2,GMSKμ2,GMSK+μ2,M-aryFSK.
Based on the mean and variance (or higher-order
moment), the classification of M-ary FSK can be performed.


## 2.1. Classification of Subsystem

The normalized histogram generation of wavelet  transformed coefficient is used to classify the Subsystem1 (M-ary PSK and M-ary QAM) with Subsystem2 (GMSK and
M-ary FSK). Ifni is the
number of occurrence in a particular value then the normalized histogram
(probability of occurrence) of a process is given by
(5)p(xi)=nin,
where n is
total number of samples in the particular process. Subsystem1 signal has
constant transient characteristics; they have a single peak in its normalized
histogram. But the Subsystem2 signals have multifrequency component, they have
multiple peaks in its normalized histogram.The classification of
various modulation schemes may be formulated using the statistical parameters
such as moments and median. The moment plays the major contribution in
nonstationary signal, thus it has been considered for the classification. Thenth-order
moment for p(xi), where i=0,1,2,…,N−1 is given by
(6)μn(x)=∑i=0N−1(xi−μ1)np(xi),
where μ1=∑i=0N−1xip(xi) is the mean of the statistical process. The
second-order moment (variance) of discretized WT can be computed using
(7)μ2=E(|C(a,τ)|2)−[E(|C(a,τ)|)]2=1N∑i=0N−1|Ci(a,τ)|2−[1N∑i=0N−1(|Ci(a,τ)|)]2,
where N is the length of discretized analyzed
signal. Then the classification problem can be formulated as a binary tree hypothesis-testing
problem.LetHi be the ith
modulation format assigned to the received signal, where i is associated with {M-aryPSK,j} and j is
with M-ary QAM. The statistical decision needs the probability density function
(pdf) of the test statistics conditioned on the assigned digitally modulated
signal. Assuming the noise in (1) is AWGN, the wavelet transform coefficient C(a,τ)
has a characteristic of random variables generated from linear combinations of
sinusoidal signal and a Gaussian noise. The two conditional Gaussian pdfs allow
a threshold setting to decide the M-ary PSK and M-ary QAM, when a certain
probability of false identification of both signals is given. The conditional
pdf is
(8)p(xHi)=12πμ2,iexp⁡(−(x−μ1,i)2μ2,i2).Under the hypothesisHM-aryPSK is true, the
probability of M-ary PSK misclassification is simply the probability that μ1,M-aryPSK−x>μ1,M-aryPSK−T1,
that is, μ1<T1. The probability of misclassification error for
M-ary PSK is given by
(9)P(eHM-aryPSK)=12(1+ercf(x−μ1,M-aryPSK2μ2,M-aryPSK)),
where ercf() is
defined as ercf(x)=(2/π)∫0xexp(−t2)dt.
Similarly, if it is assumed that the hypothesis HM-aryQAM is true,
the probability of M-ary QAM signal misclassification is simply the probability
that x−μ1,M-aryPSK>T1−μ2,M-aryPSK, that is, μ1>T1. The probability of misclassification error for M-ary QAM is given by
(10)P(eHM-aryQAM)=12(1+ercf(x−μ1,M-aryQAM2μ2,M-aryQAM)),
where ercf() is
defined as ercf(x)=(2/π)∫0xexp(−t2)dt.
It is obvious that when the Gaussian noise increases, the mean value of M-ary
PSK and M-ary QAM decreases until the point when both the probabilities of
misclassification are equal. Thus, P(e/HM-aryPSK)=P(e/HM-aryQAM)=.01 and the condition for setting the optimal
threshold value T1 can be obtained by equating Gaussian distribution
is zero. Then the related threshold value is obtained as
(11)T1=μ1,M-aryPSKμ2,M-aryQAM+μ1,M-aryQAMμ2,M-aryPSKμ2,M-aryPSK+μ2,M-aryQAM.
Based on the mean value the classification of M-ary
PSK with M-ary QAM can be done.


## 2.2. Classification of M-ary PSK Signals

The
method described in earlier has been used for setting the thresholdTPr (where r is varying from 1,2,3,… to
represent 2-ary, 4-ary, 8-ary, etc.) and the further classification of
substsem1 can be classified based on second- or higher-order statistical
moment. Decision making between BPSK, QPSK, 8PSK, 16PSK, and so on can be
carried out based on the comparison of variance value with computed threshold
value and for 2PSK and 4PSK is given by
(12)TP1=μ1,2PSKμ2,4PSK+μ1,4PSKμ2,2PSKμ2,2PSK+μ2,4PSK.
Similarly, the threshold value TP2,TP3,TP4,… can be defined using the same procedure.


## 2.3. Classification of M-ary QAM Signals

The classification of M-ary QAM
has been classified using the same method prescribed in the last section and
the comparison of variance value with the threshold is used to classify the
subclassification. The threshold value for decision making of 2QAM with 4QAM is
given by(13)TQ1=μ1,2QAMμ2,4QAM+μ1,4QAMμ2,2QAMμ2,2QAM+μ2,4QAM.
Similarly, the threshold value TQ2,TQ3,TQ4,… can be
defined using the same procedure.Decision making between GMSK and
M-ary FSK can be done based on the comparison of variance value with thresholdT2 and is given by
(14)T2=μ1,GMSKμ2,M-aryFSK+μ1,M-aryFSKμ2,GMSKμ2,GMSK+μ2,M-aryFSK.
Based on the mean and variance (or higher-order
moment), the classification of M-ary FSK can be performed.


## 3. Description of Identification Algorithm

The proposed modulation identification scheme is shown in Figure1. The
identification of digital modulation schemes has been done by using a common feature. The
feature extraction has been done by extracting the coefficients of the
modulated signals using wavelet transform. Wavelets are to be selected such a
way that it looks similar to the patterns to be localized in the signal. The
wavelet transform has been computed and the extracted coefficients are used to
generate the histogram peak. Based on the number of peaks, the identifier
identifies that the received signal is either Subsystem1 or Subsystem2 signals.Figure 1
Proposed modulation identification system.The further classification of Subsystem1 and 2 is shown in Figures2 and 3, respectively.Figure 2
Classification of Subsystem1.Figure 3
Classification of Subsystem2.The
classification of subsystem is done based on the decision rules as shown in
Table1.Table 1
Subsystem classification—decision rule.
Classification systemDecision rulesSubsystem1Ifμ1<T1→  M-ary PSK signalIf μ2>TP1→ BPSK signalelse if μ2>TP2→ QPSK signalelse if μ2>TP3→ 8PSK signalelse if μ2>TP4→ 16PSK signalelse  → 32PSK signal and aboveendendendendelse→ M-ary QAM signalIf μ2<TQ1→ 2QAM signalelse if μ2<TQ2→ 4QAM signalelse if μ2<TQ3→ 8QAM signalelse if μ2<TQ4→ 16QAM signalelse  → 32QAM signal and aboveendendendendendSubsystem2Ifμ2>T2→  GMSK signalelse →  M-ary FSK signalend


## 4. Results and Discussion

The entire system including
signal generation, noise addition, reception, feature extraction, and
modulation scheme recognition was developed and tested with the software tools
of MATLAB. Successful tests were carried out with signals used in the mobile radio
systems GSM, CDMA, and UMTS. The
developed algorithm is verified for BPSK, QPSK, 8PSK, 16PSK, 2QAM, 4QAM, 8QAM,
16QAM, GMSK, and MFSK modulation schemes. The above specified modulation
schemes were simulated using MATLAB with 200 symbols input message and AWGN
noise was simulated and added with a transmitting signal as a channel noise.
The wavelet transform has been applied to extract the transient characteristics
of the received signal. Because the wavelet transform has a flexible scaling
factor, depending upon the SNR of the incoming signal, it will choose the
length of the window function. This proposed model has been tested for 1000
individual trials. The effect of sample size plays a major role during the modulation
identification process. It is seen from the observation that wavelet transform
requires minimum of 6 symbols for better identification. The magnitude of Haar
wavelet transform for MQAM and MPSK is a constant, but MFSK and GMSK has a
multistep function since the frequency is variable. This common feature made to
be considering the Haar wavelet as the mother wavelet and it is given by(15)ψ(t)={1,0≤t<12,−1,12≤t<1.After
extracting the transient characteristics, the coefficients were extracted to
generate the histogram peak. The histogram of M-ary QAM and M-ary PSK, M-ary
FSK and GMSK is shown in Figures4 and 5, respectively. These figures
show as the M-ary QAM and M-ary PSK signal has constant transient
characteristics, it has a single peak in its histogram. But the M-ary FSK and GMSK
have more than single peak because these signals have multistep frequency
component.Figure 4
Histogram peak of Subsystem1.Figure 5
Histogram peak of Subsystem2.Then, each subsystem is
further classified based on decision rules shown in Table1. The next step is the
computation of the unknown threshold values. Their computation is derived for
the two binary hypotheses test with 0.01 probability of misclassification of
each the modulated signal. Based on the misclassification rate condition, the
related optimum threshold T1 has been computed from (11) to classify
M-ary PSK and M-ary QAM. Similarly, other related optimum threshold values have
been computed using (12), (13), and (14) and tabulated in Table 2. After
identification of the scheme demodulation is performed by conventional methods.Table 2
Threshold value.
SystemModulation schemesThreshold valueSubsystem1M-ary QAM/M-ary PSKT1=1.09BPSK/Higher MPSKTP1=0.0104QPSK/Higher MPSKTP2=0.00968PSK/Higher MPSKTP3=0.009116PSK/Higher MPSKTP4=0.00892QAM/Higher QAMTQ1=0.01034QAM/Higher QAMTQ2=0.01098QAM/Higher QAMTQ3=0.011516QAM/Higher QAMTQ4=0.0123Subsystem2M-ary FSK/GMSKT2=1.686The performance of the proposed
algorithm was examined based on the confusion matrix receiver operating
characteristics (ROCs) and bit error rate. For the analysis purpose, the
identifier has been tested for 1000 experiments with 200 symbols per
experiments. The results obtained from experiments are represented in the form
of so-called confusion matrix as shown in Table3. The left column
depicts the modulation schemes fed into the proposed identifier and output
modulation schemes indicated in the uppermost row. For an ideal identifier all
results, each 100%, are contained in the diagonal matrix elements. The testing
was carried out for different SNR starting from 20 dB and the confusion matrix
were tabulated at 5 dB for the proposed identifier.Table 3
Confusion matrix for SNR = 5 dB.
Input modulation schemeOutput modulation schemeBPSKQPSK8PSK16PSK2QAM4QAM8QAM16QAMGMSKMFSKREJBPSK98.61.4QPSK97.82.28PSK97.51.21.316PSK97.22.82QAM1004QAM98.41.68QAM97.61.41.016QAM96.83.2GMSK99.10.9MFSK0.998.20.9The spread of identification
results is caused by the similarity of the waveforms. Most of the
nonsuccessfully identified signals were assigned to the reject class REJ. The
identification of 8PSK (1.2%) as 16PSK, 8QAM (1.4%) as 16QAM, and GMSK (0.9%)
as MFSK is because of the lower SNR, these waveforms are similar in some
nature. The numbers of false identification are still moderate for the proposed
system.The second criterion to
evaluate the performance of the proposed modulation identification system is by
computing the receiver operating characteristics (ROCs) curves. The
probabilities of 200 symbols are calculated, tabulated as shown in Table4, and
generated curves according to the results.Table 4
Receiver operating characteristics (ROCs).
SNR = 15 dBSNR = 10 dBSNR = 5 dBPf1Pd1Pf2Pd2Pf3Pd30100.9100.30.0510.050.940.050.50.110.10.960.10.80.210.210.20.850.310.310.30.90.410.410.410.510.510.510.610.610.610.710.710.710.810.810.810.910.910.91111111Figure6 shows the ROC curves for the identifier when SNR is equal to 15 dB, 10 dB, and 5 dB. The performance of the identifier
is better if the curve rises faster. When SNR is 15 dB, Pd1 is 100% independent of Pf1. When SNR is
10 dB and the Pf2 is 0.1, the capability of detection (Pd2)
is 0.96. When SNR is 5 dB and the Pf3 is smaller than 0.3 the Pd3 drops rapidly. This is because the hypothesis of moderate SNR used to obtain
the optimum threshold in the decision device will no longer be valid.Figure 6
Receiver operating characteristics (ROCs) for the proposed system.The
third criterion to evaluate the performance of the proposed modulation
identification system is the computation of bit error rate. The bit error rate of the proposed model has been
computed for various SNR and shown in Figure7. From the figure, it is found
that when SNR increases, the bit error rate decreases. It is also clear that
the bit error rate becomes significant for lower SNR values.Figure 7
Bit error rate versus SNR.


### 4.1. Comparison of Various Methods

Performance of several methods reported for classifying
various digital modulation schemes is presented in Table5.Table 5
Comparison of proposed system with existing methods.
FeaturesModelsModulation schemesLower bound SNR (dB)% of identificationVariance of HWT magnitude and
normalized HWT magnitudeHong and Ho [14]QPSK,
4FSK, 16QAM597%Mean and Variance of complex Shannon WT magnitudePavlík [15]BPSK, CPFSK, MSK893.1%Mean, variance, and correlation coefficient of the received
signalLe Guen and Mansour [17]ASK2, ASK4, PSK2, PSK4, FSK2, FSK412Not mentionedDFT of phase PDFSapiano et al. [18]BPSK,
QPSK, 8PSK1092%Variance of WT magnitudeHo et al. [19]BPSK,
QPSK, 8PSK, 2FSK, 4FSK, 8FSK, MSK696%Fourth- and second-order moments of the received signalMartret and Boiteau [20]QPSK,
16QAM595%Eighth-order cyclic cumulants of
the received signalDobre et al. [21]BPSK, QPSK, 8PSK, 4ASK, 8ASK, 16QAM, 64QAM, 256QAM995%Histogram peaks in WT
magnitude and mean & variance of normalized histogramProposed systemBPSK, QPSK, 8PSK, 16PSK, 2QAM, 4QAM, 8QAM, 16QAM, GMSK, MFSK596.8%The ideal scenario, that is, no prior information is required
about the incoming signal is considered for performance evaluation. Comparison
table shows that, model proposed by Hong and Ho [14], Ho et al. [19] and
proposed system are capable of  identifying
modulation schemes with low SNR of 5 dB. Though the % of identification is same
for Hong and Ho [14] and proposed model, the present model can identify more
number of modulation schemes.


## 4.1. Comparison of Various Methods

Performance of several methods reported for classifying
various digital modulation schemes is presented in Table5.Table 5
Comparison of proposed system with existing methods.
FeaturesModelsModulation schemesLower bound SNR (dB)% of identificationVariance of HWT magnitude and
normalized HWT magnitudeHong and Ho [14]QPSK,
4FSK, 16QAM597%Mean and Variance of complex Shannon WT magnitudePavlík [15]BPSK, CPFSK, MSK893.1%Mean, variance, and correlation coefficient of the received
signalLe Guen and Mansour [17]ASK2, ASK4, PSK2, PSK4, FSK2, FSK412Not mentionedDFT of phase PDFSapiano et al. [18]BPSK,
QPSK, 8PSK1092%Variance of WT magnitudeHo et al. [19]BPSK,
QPSK, 8PSK, 2FSK, 4FSK, 8FSK, MSK696%Fourth- and second-order moments of the received signalMartret and Boiteau [20]QPSK,
16QAM595%Eighth-order cyclic cumulants of
the received signalDobre et al. [21]BPSK, QPSK, 8PSK, 4ASK, 8ASK, 16QAM, 64QAM, 256QAM995%Histogram peaks in WT
magnitude and mean & variance of normalized histogramProposed systemBPSK, QPSK, 8PSK, 16PSK, 2QAM, 4QAM, 8QAM, 16QAM, GMSK, MFSK596.8%The ideal scenario, that is, no prior information is required
about the incoming signal is considered for performance evaluation. Comparison
table shows that, model proposed by Hong and Ho [14], Ho et al. [19] and
proposed system are capable of  identifying
modulation schemes with low SNR of 5 dB. Though the % of identification is same
for Hong and Ho [14] and proposed model, the present model can identify more
number of modulation schemes.


## 5. Conclusion

A generalized modulation identification
algorithm is described which is suited for many digital modulation schemes used
in SDR. The system was tested with 10 modulation schemes with different SNR.
The simulated results using wavelet transform technique and statistical moments
measurement show that the correct modulation scheme identification is possible
even at low channel SNR of 5 dB. The ROC analysis shows that the percentage of
correct modulation identification is higher than 96.8% for 1000 experiments
with 200 symbols when SNR is not lower than 5 dB. The comparison with existing
methods shows that the proposed system is capable of identifying the entire
digital modulation scheme with low SNR.



---

*Source: 175236-2008-05-11.xml*